Before doing anything, close Zotero!
In [1]:
import time
import sqlite3
import sys
First, just copy the sqlite file to this directory for manipulation.
In [2]:
%cp /Users/boyle/Library/Application\ Support/Firefox/Profiles/l1i89wc9.default/zotero/zotero.sqlite zotero.sqlite
%cp /Users/boyle/Library/Application\ Support/Firefox/Profiles/l1i89wc9.default/zotero/zotero.sqlite zotero.sqlite.bak
Now, connect to it, and give us a cursor in the file.
In [3]:
con = sqlite3.connect('zotero.sqlite')
cur = con.cursor()
The following gives the list of tables in this database file:
In [4]:
cur.execute("select name from sqlite_master where type = 'table';").fetchall()
Out[4]:
[('version',),
('settings',),
('itemDataValues',),
('itemData',),
('itemNotes',),
('itemAttachments',),
('itemTags',),
('itemSeeAlso',),
('creatorData',),
('itemCreators',),
('collectionItems',),
('savedSearchConditions',),
('fulltextItems',),
('fulltextWords',),
('fulltextItemWords',),
('annotations',),
('highlights',),
('proxies',),
('proxyHosts',),
('zoteroDummyTable',),
('deletedItems',),
('collections',),
('creators',),
('items',),
('savedSearches',),
('tags',),
('libraries',),
('users',),
('groups',),
('groupItems',),
('storageDeleteLog',),
('relations',),
('syncDeleteLog',),
('customItemTypes',),
('customFields',),
('customItemTypeFields',),
('customBaseFieldMappings',),
('itemTypes',),
('itemTypesCombined',),
('fieldFormats',),
('fields',),
('fieldsCombined',),
('itemTypeFields',),
('itemTypeFieldsCombined',),
('baseFieldMappings',),
('baseFieldMappingsCombined',),
('charsets',),
('fileTypes',),
('fileTypeMimeTypes',),
('creatorTypes',),
('itemTypeCreatorTypes',),
('syncObjectTypes',),
('transactionSets',),
('transactions',),
('transactionLog',),
('translatorCache',),
('syncedSettings',)]
Let's take a look at the layout and contents of some of these tables.
In [5]:
print(cur.execute("select sql from sqlite_master where name = 'collections';").fetchall()[0][0])
print(cur.execute("select * from collections;").fetchall())
CREATE TABLE collections (
collectionID INTEGER PRIMARY KEY,
collectionName TEXT NOT NULL,
parentCollectionID INT DEFAULT NULL,
dateAdded TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
dateModified TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
clientDateModified TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,
libraryID INT,
key TEXT NOT NULL,
UNIQUE (libraryID, key),
FOREIGN KEY (parentCollectionID) REFERENCES collections(collectionID)
)
[(1, 'Quantum Foam and Causal Sets', 8, '2009-02-04 22:01:28', '2014-02-18 15:09:48', '2014-02-18 15:09:48', None, '883NBR42'), (2, 'NR/DA', 8, '2009-02-04 22:01:37', '2015-05-27 21:23:45', '2015-05-27 21:23:45', None, '6C6HU2R5'), (3, 'Gravitational Waves', 8, '2009-02-15 20:03:24', '2015-05-27 21:20:23', '2015-05-27 21:20:23', None, '96M57BK6'), (4, 'Black Holes', 8, '2009-02-04 22:01:32', '2014-01-03 16:32:40', '2014-01-03 16:32:40', None, 'I79TN2G5'), (5, 'Phenom', 34, '2010-12-21 16:19:15', '2011-03-19 03:08:58', '2011-03-19 03:08:58', None, 'UUUQQP5E'), (6, 'Numerical Relativity', 8, '2009-02-04 22:01:40', '2015-05-27 21:41:01', '2015-05-27 21:41:01', None, 'Q6ZFDE7R'), (7, 'Recipes', 19, '2009-02-04 22:03:08', '2014-01-04 16:37:36', '2014-01-04 16:37:36', None, '4XR3UQA6'), (8, 'Physics', None, '2009-02-04 22:01:26', '2015-05-27 21:18:47', '2015-05-27 21:18:47', None, 'CTT77ACF'), (9, 'Momentum in Binaries', 8, '2009-02-25 20:44:06', '2015-05-27 21:17:10', '2015-05-27 21:17:10', None, '6288AR7P'), (10, 'PN', 8, '2009-02-27 19:39:22', '2015-05-27 21:20:07', '2015-05-27 21:20:07', None, 'VZUFBB3V'), (11, 'Hybrids', 8, '2009-05-15 16:24:51', '2015-05-27 21:23:17', '2015-05-27 21:23:17', None, '8ZWR6Q73'), (12, 'EOB', 11, '2009-05-15 17:59:32', '2011-03-19 03:08:58', '2011-03-19 03:08:58', None, 'ZC5HKPVK'), (13, 'DA', 11, '2009-05-15 17:59:56', '2011-03-19 03:08:58', '2011-03-19 03:08:58', None, 'IIS7AJQP'), (14, 'Near Field', 64, '2009-06-04 14:42:15', '2015-05-27 21:41:01', '2015-05-27 21:41:01', None, 'KBWRRGPJ'), (15, 'Memory', 8, '2009-06-16 16:24:37', '2015-05-22 13:57:13', '2015-05-22 13:57:13', None, 'RBCGNWTH'), (16, 'Fish', 7, '2009-06-29 19:41:39', '2009-06-29 19:43:58', '2009-06-29 19:43:58', None, 'U2D92FZI'), (17, 'South Beach', 7, '2009-07-01 19:29:14', '2009-09-15 15:56:14', '2009-09-15 15:56:14', None, 'J625HZBP'), (18, 'Astrophysics & Cosmology', 8, '2009-07-13 16:22:34', '2015-05-27 21:31:18', '2015-05-27 21:31:18', None, '9K4RCRS7'), (19, 'Personal', None, '2009-07-21 15:31:48', '2012-11-07 05:24:13', '2012-11-07 05:24:13', None, '9KQR4GGK'), (20, 'Smoothies', 7, '2009-08-05 12:47:48', '2009-08-05 12:48:24', '2009-08-05 12:48:24', None, '7RMFUB7V'), (21, 'black-holes.org', 19, '2009-08-15 01:06:13', '2011-10-10 14:52:17', '2011-10-10 14:52:17', None, 'V24MTPPB'), (22, 'Pancakes', 7, '2011-01-20 18:48:25', '2012-12-01 09:05:19', '2012-12-01 09:05:19', None, 'RPG8NFB8'), (23, 'Amplitudes', 10, '2011-02-03 22:27:47', '2014-09-12 22:03:44', '2014-09-12 22:03:44', None, 'H28M95JN'), (24, 'Data Analysis', 8, '2009-09-18 00:04:55', '2015-05-20 12:31:48', '2015-05-20 12:31:48', None, 'M3FAHT7J'), (25, 'Detectors', 8, '2009-10-06 19:19:10', '2015-05-27 21:24:08', '2015-05-27 21:24:08', None, 'KIUVTQZ3'), (26, 'Dimensional Analysis', 8, '2009-11-25 23:55:38', '2009-11-25 23:55:53', '2009-11-25 23:55:53', None, 'W4TVP8ZT'), (27, 'SPA', 10, '2010-02-07 06:56:45', '2011-10-10 14:52:17', '2011-10-10 14:52:17', None, 'C6AHT2IN'), (28, 'EOB', 10, '2010-02-08 19:57:07', '2015-05-27 21:21:24', '2015-05-27 21:21:24', None, '3PVU2T5M'), (29, 'Black-Hole Sun', 8, '2010-03-16 02:10:57', '2011-06-09 19:26:43', '2011-06-09 19:26:43', None, 'RCTCTX98'), (30, 'Distance determinations', 14, '2010-06-04 21:24:12', '2012-01-25 15:48:33', '2012-01-25 15:48:33', None, 'RIBXCNCR'), (31, 'Spins', 10, '2010-07-14 19:24:12', '2015-05-27 21:20:07', '2015-05-27 21:20:07', None, 'KCRZVJ5G'), (32, 'Ninja-2', 8, '2010-08-09 19:49:22', '2015-05-27 21:18:58', '2015-05-27 21:18:58', None, '4GMXMKB9'), (33, 'PN', 32, '2010-08-09 19:49:31', '2011-09-05 18:56:39', '2011-09-05 18:56:39', None, 'ESEPZWZW'), (34, 'Initial Frequencies', 63, '2010-08-19 13:45:48', '2013-02-26 13:16:57', '2013-02-26 13:16:57', None, 'X99GDVF3'), (35, 'PN', 34, '2010-08-19 13:50:40', '2011-09-05 18:56:39', '2011-09-05 18:56:39', None, 'R7JNWPAN'), (36, 'NR', 34, '2010-08-19 13:51:47', '2011-03-19 03:08:58', '2011-03-19 03:08:58', None, 'JV3NZDQC'), (37, 'DA', 34, '2010-08-19 13:52:25', '2010-08-21 03:14:54', '2010-08-21 03:14:54', None, '9P8U452M'), (38, 'Symplectic Integration', 28, '2011-02-07 17:12:58', '2011-02-07 17:52:00', '2011-02-07 17:52:00', None, 'H4AMUWXR'), (39, 'Improving SPA', 64, '2011-03-15 17:28:18', '2015-05-27 21:20:23', '2015-05-27 21:20:23', None, 'GDKZ3MSD'), (40, 'IMEX', 6, '2011-03-20 19:23:16', '2015-05-27 21:21:49', '2015-05-27 21:21:49', None, 'IQA9MWT5'), (41, 'Aligned-Spin', 6, '2011-03-21 16:04:25', '2015-02-12 19:16:16', '2015-02-12 19:16:16', None, 'CXMKTNK2'), (42, 'Different Mass Ratios', 6, '2011-03-21 16:04:32', '2015-05-27 21:22:03', '2015-05-27 21:22:03', None, 'PJCKQDJ7'), (43, 'Precessing Systems', 6, '2011-03-21 16:06:34', '2015-05-27 21:24:20', '2015-05-27 21:24:20', None, 'UCK9H4FI'), (44, 'Kick', 6, '2011-03-21 16:23:35', '2015-03-27 15:18:02', '2015-03-27 15:18:02', None, 'AHTUG9W4'), (45, 'Talks', None, '2011-03-29 12:59:08', '2011-03-30 03:57:19', '2011-03-30 03:57:19', None, '2FWUUES8'), (46, 'Papers', 8, '2011-03-29 12:59:12', '2015-05-27 19:25:46', '2015-05-27 19:25:46', None, '5TRICRUM'), (47, 'AstroLunch March 2011', 45, '2011-03-29 13:00:40', '2011-10-10 14:52:17', '2011-10-10 14:52:17', None, 'GRZGH9BF'), (48, 'Matter', 6, '2011-04-26 15:23:10', '2011-10-14 14:45:04', '2011-10-14 14:45:04', None, '8IBTQ252'), (49, 'Spins', 28, '2011-05-27 21:19:40', '2014-07-07 15:03:33', '2014-07-07 15:03:33', None, 'MTPBV6ET'), (50, 'Ringdown', 10, '2011-06-07 12:48:23', '2015-05-27 21:31:24', '2015-05-27 21:31:24', None, 'UXZTARXT'), (51, 'Parameter Estimation', 24, '2011-07-14 11:01:06', '2014-10-28 15:53:36', '2014-10-28 15:53:36', None, '3GDQTH3H'), (52, 'CCE', 8, '2011-06-10 16:29:12', '2015-02-12 18:52:09', '2015-02-12 18:52:09', None, 'K7TJ6T7R'), (53, 'Neutron Stars', 18, '2011-07-14 17:58:04', '2015-05-27 21:30:56', '2015-05-27 21:30:56', None, 'C8SJCIBP'), (54, 'Spheroidal', 8, '2011-06-10 21:20:23', '2015-05-21 13:18:42', '2015-05-21 13:18:42', None, 'RNEUXPSG'), (55, 'Rotating SWSHs', 3, '2011-07-26 21:57:58', '2015-05-27 21:30:50', '2015-05-27 21:30:50', None, '3TVRQPZ4'), (56, 'Tendex/Vortex', 8, '2011-08-30 19:56:24', '2011-08-30 19:56:35', '2011-08-30 19:56:35', None, 'UDVRTAF9'), (57, 'SVD/RB', 24, '2011-08-30 19:57:15', '2012-01-20 09:58:44', '2012-01-20 09:58:44', None, 'FU85397G'), (58, 'Demodulating Precession', 63, '2011-09-08 14:50:11', '2015-05-27 21:24:20', '2015-05-27 21:24:20', None, 'E96Z5J6I'), (59, 'NS Tides', 18, '2011-09-14 12:52:28', '2015-05-27 21:30:29', '2015-05-27 21:30:29', None, '92H7TMG5'), (60, 'Teaching', 19, '2011-09-20 13:40:24', '2012-03-26 18:45:29', '2012-03-26 18:45:29', None, 'DURRDKG6'), (61, 'Math', None, '2011-10-18 15:44:42', '2015-05-27 19:32:57', '2015-05-27 19:32:57', None, 'ZID66CTU'), (62, 'Geometric Algebra', 61, '2011-10-18 15:44:48', '2015-05-27 21:19:53', '2015-05-27 21:19:53', None, '9CSTGX47'), (63, 'Old', 46, '2011-10-21 15:08:36', '2011-10-21 15:08:39', '2011-10-21 15:08:39', None, 'VBJS7XRK'), (64, 'Pipeline', 46, '2011-10-21 15:28:50', '2011-10-21 15:28:54', '2011-10-21 15:28:54', None, 'FIVXPR6R'), (65, 'DM/DE', 18, '2011-10-21 15:28:59', '2013-06-25 15:08:38', '2013-06-25 15:08:38', None, '2BBW3CTI'), (66, 'Relativity', 8, '2011-10-24 01:05:53', '2014-10-09 15:27:11', '2014-10-09 15:27:11', None, 'DZJ7FJN2'), (67, 'AstroLunch November 2011', 45, '2011-10-28 20:10:39', '2011-10-31 18:18:25', '2011-10-31 18:18:25', None, '7GE5FN4N'), (68, 'Alternative theories', 10, '2011-11-23 14:37:02', '2015-01-30 14:27:03', '2015-01-30 14:27:03', None, 'CZETTDAP'), (69, 'EMRIs', 10, '2011-12-21 21:57:50', '2014-05-08 14:50:15', '2014-05-08 14:50:15', None, 'TZT7NS2J'), (70, 'GW Cosmology', 8, '2012-01-20 10:35:42', '2014-06-20 17:31:07', '2014-06-20 17:31:07', None, 'TRCQZWDQ'), (71, 'Books', None, '2012-01-24 18:04:10', '2015-03-06 16:23:06', '2015-03-06 16:23:06', None, 'WSDUIWJN'), (72, 'Fourier Continuation', 24, '2012-03-15 22:22:47', '2013-02-26 13:18:10', '2013-02-26 13:18:10', None, 'KISEHNTG'), (73, 'Statistics', 62, '2014-01-12 17:00:48', '2014-01-12 17:00:59', '2014-01-12 17:00:59', None, 'MHJ7AVVA'), (74, 'Precessing hybrids', 63, '2012-04-06 18:59:40', '2015-05-27 21:23:36', '2015-05-27 21:23:36', None, 'MVG7BNNF'), (75, 'Determining parameters', 74, '2012-04-18 13:31:14', '2015-05-27 21:24:13', '2015-05-27 21:24:13', None, '3JTVRADC'), (76, 'Quaternions and SWSHs', 74, '2012-04-18 13:31:35', '2015-05-27 21:17:52', '2015-05-27 21:17:52', None, 'V4ZGJMEI'), (77, 'PN', 74, '2012-04-18 19:13:20', '2015-05-27 21:31:38', '2015-05-27 21:31:38', None, 'K3GP3AVS'), (78, 'Mine', 71, '2012-05-04 21:32:37', '2012-05-04 21:32:45', '2012-05-04 21:32:45', None, 'XGXC4FTB'), (79, 'Not Mine', 71, '2012-05-04 21:32:50', '2015-04-16 14:13:21', '2015-04-16 14:13:21', None, 'HHI2V2HI'), (80, 'Physics', 78, '2012-05-04 21:33:02', '2015-04-22 23:07:05', '2015-04-22 23:07:05', None, 'SJQU8CS3'), (81, 'Other', 78, '2012-05-04 21:33:10', '2012-05-17 20:06:28', '2012-05-17 20:06:28', None, 'H6UZDEKG'), (82, 'Astrophysics', 74, '2012-05-11 13:40:59', '2015-05-27 21:30:04', '2015-05-27 21:30:04', None, 'HJKF5R4C'), (83, 'Transformations of Scri+', 46, '2012-06-13 14:16:50', '2015-05-27 21:24:20', '2015-05-27 21:24:20', None, 'TC7R7D85'), (84, 'Good/Universal Cuts', 83, '2012-07-17 18:35:08', '2012-07-23 21:38:43', '2012-07-23 21:38:43', None, 'GK5SPUNU'), (85, 'Nice sections', 83, '2012-07-17 18:35:18', '2015-05-27 21:30:10', '2015-05-27 21:30:10', None, 'SHNFXANQ'), (86, 'Kinnersley', 83, '2012-07-24 18:44:53', '2012-07-24 18:45:29', '2012-07-24 18:45:29', None, 'BM3VVKCP'), (87, 'Detection', 74, '2012-07-30 14:23:55', '2015-05-27 21:20:54', '2015-05-27 21:20:54', None, '8X2MAR8M'), (88, "Rubik's Cubes", 19, '2012-10-24 01:38:51', '2012-10-29 19:02:12', '2012-10-29 19:02:12', None, '7WWKAC9T'), (89, 'Standards', 46, '2013-01-10 15:50:14', '2014-01-13 22:06:27', '2014-01-13 22:06:27', None, 'HZV4AD9D'), (90, 'Twistors & Spinors', 83, '2013-03-02 22:22:45', '2013-09-18 18:21:08', '2013-09-18 18:21:08', None, 'QP9RSD72'), (91, 'Reading list', 83, '2013-03-06 23:01:22', '2015-05-27 21:22:49', '2015-05-27 21:22:49', None, 'UJAWQDIV'), (92, 'Riemann charge', 83, '2013-03-25 21:50:13', '2015-05-27 21:22:49', '2015-05-27 21:22:49', None, '7BWPPMZF'), (93, 'Proofs', 74, '2013-04-09 13:41:33', '2014-03-23 03:53:38', '2014-03-23 03:53:38', None, 'AQGEM7FS'), (94, 'Kicks', 10, '2013-04-23 13:39:32', '2014-05-12 13:05:04', '2014-05-12 13:05:04', None, '63BD4ZGS'), (95, 'GR', 62, '2013-04-23 18:23:42', '2015-01-18 19:32:14', '2015-01-18 19:32:14', None, '2MKN7Q6R'), (96, 'Spinors/Twistors', 62, '2013-04-23 18:23:48', '2015-05-27 13:19:29', '2015-05-27 13:19:29', None, 'B72E2666'), (97, 'Guide to GA in Practice', 62, '2013-05-17 16:10:55', '2015-05-27 21:21:38', '2015-05-27 21:21:38', None, 'K4UEWTDQ'), (98, 'Lorentz group representations', 83, '2013-09-10 20:15:33', '2015-05-06 16:58:02', '2015-05-06 16:58:02', None, '9SAGUE32'), (99, 'Bursts', 24, '2013-09-25 15:26:35', '2013-10-09 11:43:38', '2013-10-09 11:43:38', None, 'TEV6TMJ3'), (100, 'Algebra', 62, '2013-05-20 15:42:43', '2015-05-27 13:30:14', '2015-05-27 13:30:14', None, 'TU4D7C57'), (101, 'Computing', 62, '2013-05-31 15:44:07', '2014-11-21 16:13:35', '2014-11-21 16:13:35', None, 'CEN2ZMZN'), (102, 'CCE/Extrapolation', 63, '2013-06-13 14:35:13', '2013-08-15 15:40:46', '2013-08-15 15:40:46', None, 'TREDTSAM'), (103, 'Math', 71, '2013-06-13 21:12:57', '2015-04-27 19:11:25', '2015-04-27 19:11:25', None, '6RV5AJK8'), (104, 'New Approach to Diff. Geom.', 62, '2013-06-19 16:47:49', '2013-06-19 16:57:57', '2013-06-19 16:57:57', None, 'ZVX8IRBN'), (105, 'Looking forward', 83, '2013-06-20 19:21:56', '2013-06-20 19:22:55', '2013-06-20 19:22:55', None, 'IBNBC2H7'), (106, 'Conserved quantities', 83, '2013-07-11 17:55:49', '2015-05-27 21:23:50', '2015-05-27 21:23:50', None, '4NRWH59X'), (107, 'Quaternions v. Vectors', 62, '2013-08-23 18:54:18', '2013-08-23 20:13:25', '2013-08-23 20:13:25', None, 'VP25K3ZG'), (108, 'Chaos', 10, '2013-10-09 01:20:45', '2013-12-04 00:55:54', '2013-12-04 00:55:54', None, 'SACFJ3I7'), (109, 'Sky location', 24, '2013-10-09 03:00:52', '2015-05-27 21:21:54', '2015-05-27 21:21:54', None, '34G93VNB'), (110, 'Hobson, Efstathiou, & Lasenby', 66, '2013-12-10 16:16:36', '2014-01-10 01:49:01', '2014-01-10 01:49:01', None, 'WVZE3P2B'), (111, 'Signature', 62, '2014-01-12 17:18:13', '2015-05-27 19:33:19', '2015-05-27 19:33:19', None, '7IGF8UV8'), (112, 'Hopf bundle', 83, '2014-02-15 22:18:44', '2015-04-21 13:25:16', '2015-04-21 13:25:16', None, 'PR7EMZDC'), (113, 'Tessarines', 62, '2014-02-26 03:31:41', '2014-02-26 03:41:42', '2014-02-26 03:41:42', None, '6TMVX68G'), (114, 'Precessing Waveforms', 46, '2014-03-04 13:58:24', '2014-04-15 16:20:53', '2014-04-15 16:20:53', None, 'DAE2B7X9'), (115, 'Finite Differences', 8, '2014-03-07 18:34:20', '2014-03-07 19:19:51', '2014-03-07 19:19:51', None, 'FMHPWXJH'), (116, 'Mode asymmetry and kicks', 46, '2014-03-15 17:03:01', '2014-04-04 21:34:40', '2014-04-04 21:34:40', None, 'Z6Q3Z5TB'), (117, 'Kicks', 116, '2014-03-15 17:03:07', '2015-05-27 21:20:58', '2015-05-27 21:20:58', None, 'NGED3BRX'), (118, 'PN Waveforms', 116, '2014-03-15 17:03:15', '2014-04-28 14:12:01', '2014-04-28 14:12:01', None, 'CRHGPNV8'), (119, 'Clifford transforms', 64, '2014-05-26 15:17:56', '2014-05-27 04:36:58', '2014-05-27 04:36:58', None, 'I4KHWFZ5'), (120, 'Coherent searches', 24, '2014-05-27 04:29:32', '2014-05-27 04:30:16', '2014-05-27 04:30:16', None, 'M4X8JD8T'), (121, 'Eccentricity', 10, '2014-08-19 18:42:07', '2015-01-29 17:52:19', '2015-01-29 17:52:19', None, 'CNJSTMHA'), (122, 'Symplectic CAs', 62, '2014-09-15 12:05:02', '2014-09-15 12:05:09', '2014-09-15 12:05:09', None, 'DJ2NMHQC'), (123, 'Complex Analysis', 62, '2014-09-25 16:28:28', '2015-04-06 17:50:01', '2015-04-06 17:50:01', None, 'Q46P58E2'), (124, 'Geometry of the Cauchy-Riemann Eqs.', 123, '2014-09-25 16:28:42', '2014-09-25 17:10:06', '2014-09-25 17:10:06', None, 'EZDC3G3D'), (125, 'PaperTemplate', 46, '2014-10-01 01:23:18', '2014-10-01 01:24:16', '2014-10-01 01:24:16', None, '8KFDNDXC'), (126, 'Kähler', 62, '2014-10-01 14:15:08', '2014-11-02 01:52:26', '2014-11-02 01:52:26', None, 'B9ACGJ2D'), (127, 'Precession Dynamics', 46, '2014-10-01 21:38:18', '2015-05-27 21:31:38', '2015-05-27 21:31:38', None, 'DH2W2AWF'), (128, 'Spherical functions', 8, '2014-11-22 16:55:13', '2015-05-27 21:31:05', '2015-05-27 21:31:05', None, 'BS2TDJ2B'), (129, 'Topology', 61, '2015-03-05 14:01:36', '2015-05-27 21:19:21', '2015-05-27 21:19:21', None, 'SZVM3AP9'), (130, 'Octonions', 62, '2015-03-12 15:44:51', '2015-03-12 15:45:19', '2015-03-12 15:45:19', None, 'CZBQK5KM'), (131, 'Tails', 6, '2015-04-15 14:10:04', '2015-05-16 12:29:56', '2015-05-16 12:29:56', None, 'KPUVGUA6'), (132, 'Ringdowns', 46, '2015-04-15 14:53:37', '2015-05-27 21:29:51', '2015-05-27 21:29:51', None, 'UXN8U3FD'), (133, 'Tails', 132, '2015-04-16 13:21:00', '2015-05-27 21:29:51', '2015-05-27 21:29:51', None, '9WU996IW'), (134, 'Null cone cuts', 83, '2015-04-16 17:36:37', '2015-04-16 17:42:51', '2015-04-16 17:42:51', None, '235GKVFG'), (135, 'Efficient multiplication', 62, '2015-04-20 17:55:07', '2015-04-20 18:07:23', '2015-04-20 18:07:23', None, 'UC72G93Q'), (136, 'CMB', 83, '2015-05-04 15:04:27', '2015-05-04 18:04:36', '2015-05-04 18:04:36', None, 'NK9JI7CR'), (137, 'Combinatorics', 83, '2015-05-08 03:30:35', '2015-05-08 20:15:26', '2015-05-08 20:15:26', None, 'VXP4KRGJ'), (138, 'Lie Theory', 61, '2015-05-25 22:32:37', '2015-05-27 14:04:18', '2015-05-27 14:04:18', None, 'QUXXG7F7'), (139, 'General', 61, '2015-05-25 22:50:14', '2015-05-25 23:04:13', '2015-05-25 23:04:13', None, '2BIWTUNW')]
So the collections table just gives me all the collections I see in the left-hand section of zotero, as expected.
In [6]:
print(cur.execute("select sql from sqlite_master where name = 'itemData';").fetchall()[0][0])
print(cur.execute("select * from itemData;").fetchall())
CREATE TABLE itemData (
itemID INT,
fieldID INT,
valueID,
PRIMARY KEY (itemID, fieldID),
FOREIGN KEY (itemID) REFERENCES items(itemID),
FOREIGN KEY (fieldID) REFERENCES fields(fieldID),
FOREIGN KEY (valueID) REFERENCES itemDataValues(valueID)
)
[(1, 110, 1), (1, 14, 2), (1, 1, 3), (1, 12, 4), (1, 90, 5), (1, 62, 6), (1, 27, 7), (2, 110, 8), (2, 1, 9), (2, 27, 10), (3, 110, 11), (3, 14, 12), (3, 1, 13), (3, 12, 14), (3, 90, 15), (3, 62, 6), (3, 27, 16), (4, 110, 17), (4, 1, 18), (4, 27, 19), (7, 110, 27), (7, 14, 28), (7, 1, 29), (7, 12, 30), (7, 90, 31), (7, 62, 6), (7, 27, 32), (7, 116, 33), (8, 110, 34), (8, 1, 35), (8, 27, 36), (9, 110, 37), (9, 14, 28), (9, 1, 38), (9, 12, 39), (9, 90, 40), (9, 62, 6), (9, 27, 41), (9, 116, 42), (10, 110, 43), (10, 1, 44), (10, 27, 41), (13, 110, 46), (13, 14, 28), (13, 1, 47), (13, 22, 48), (13, 12, 49), (13, 90, 50), (13, 62, 6), (13, 27, 51), (14, 110, 52), (14, 1, 53), (14, 27, 54), (19, 110, 63), (19, 14, 64), (19, 1, 65), (19, 12, 66), (19, 90, 67), (19, 62, 6), (19, 27, 68), (20, 110, 69), (20, 1, 70), (20, 27, 71), (21, 1, 73), (21, 27, 74), (11, 110, 75), (11, 14, 76), (11, 1, 77), (11, 12, 78), (11, 90, 79), (11, 62, 6), (11, 27, 80), (11, 116, 81), (12, 110, 82), (12, 1, 83), (12, 27, 84), (22, 22, 87), (22, 110, 88), (22, 4, 89), (22, 5, 90), (22, 10, 91), (22, 14, 92), (22, 12, 93), (22, 25, 94), (22, 1, 95), (22, 26, 96), (22, 90, 97), (22, 62, 98), (22, 27, 99), (23, 110, 100), (23, 1, 101), (23, 27, 102), (25, 110, 109), (25, 1, 110), (25, 27, 111), (26, 110, 112), (26, 14, 113), (26, 1, 114), (26, 12, 115), (26, 90, 116), (26, 62, 6), (26, 27, 117), (26, 116, 118), (27, 110, 119), (27, 1, 120), (27, 27, 121), (32, 110, 143), (32, 14, 144), (32, 12, 133), (32, 25, 94), (32, 4, 145), (32, 5, 90), (32, 10, 146), (32, 1, 147), (32, 26, 148), (32, 62, 139), (32, 27, 149), (32, 116, 150), (34, 110, 153), (34, 14, 154), (34, 12, 133), (34, 25, 94), (34, 4, 155), (34, 5, 156), (34, 10, 157), (34, 1, 158), (34, 26, 159), (34, 62, 139), (34, 27, 160), (35, 110, 161), (35, 14, 162), (35, 12, 133), (35, 25, 94), (35, 4, 163), (35, 5, 135), (35, 10, 164), (35, 1, 165), (35, 26, 166), (35, 62, 139), (35, 27, 167), (38, 110, 172), (38, 14, 173), (38, 1, 174), (38, 12, 175), (38, 90, 176), (38, 62, 6), (38, 27, 177), (38, 116, 178), (39, 110, 179), (39, 1, 180), (39, 27, 181), (40, 110, 182), (40, 14, 183), (40, 12, 133), (40, 25, 94), (40, 4, 145), (40, 5, 156), (40, 10, 184), (40, 1, 185), (40, 26, 186), (40, 62, 139), (40, 27, 187), (42, 110, 190), (42, 1, 191), (42, 27, 192), (43, 110, 193), (43, 14, 194), (43, 1, 195), (43, 12, 196), (43, 90, 197), (43, 62, 6), (43, 27, 198), (44, 110, 199), (44, 1, 200), (44, 27, 201), (45, 110, 202), (45, 14, 203), (45, 1, 204), (45, 12, 205), (45, 90, 206), (45, 62, 6), (45, 27, 207), (46, 110, 208), (46, 1, 209), (46, 27, 210), (53, 110, 240), (53, 14, 241), (53, 1, 242), (53, 12, 243), (53, 90, 244), (53, 62, 6), (53, 27, 245), (53, 116, 246), (54, 110, 247), (54, 1, 248), (54, 27, 249), (64, 110, 272), (64, 14, 273), (64, 12, 133), (64, 25, 94), (64, 4, 145), (64, 5, 274), (64, 10, 275), (64, 1, 276), (64, 26, 277), (64, 62, 139), (64, 27, 278), (66, 110, 190), (66, 1, 281), (66, 27, 282), (67, 110, 283), (67, 14, 284), (67, 10, 285), (67, 12, 286), (67, 4, 287), (67, 5, 288), (67, 13, 289), (67, 90, 290), (67, 1, 291), (67, 62, 292), (67, 27, 293), (69, 110, 297), (69, 14, 298), (69, 12, 133), (69, 25, 94), (69, 4, 134), (69, 5, 299), (69, 10, 300), (69, 1, 301), (69, 26, 302), (69, 62, 139), (69, 27, 303), (71, 110, 190), (71, 1, 306), (71, 27, 307), (72, 110, 308), (72, 14, 284), (72, 10, 309), (72, 12, 286), (72, 4, 287), (72, 5, 310), (72, 13, 289), (72, 90, 311), (72, 1, 312), (72, 62, 292), (72, 27, 313), (73, 110, 294), (73, 1, 314), (73, 27, 315), (74, 110, 190), (74, 1, 316), (74, 27, 317), (75, 110, 190), (75, 1, 318), (75, 27, 319), (76, 110, 190), (76, 1, 320), (76, 27, 321), (78, 110, 328), (78, 1, 329), (78, 27, 330), (79, 1, 331), (79, 27, 332), (83, 1, 337), (83, 27, 338), (84, 110, 339), (84, 1, 340), (84, 27, 341), (85, 110, 342), (85, 1, 343), (85, 27, 344), (86, 110, 345), (86, 1, 346), (86, 27, 347), (87, 110, 348), (87, 1, 349), (87, 27, 350), (88, 110, 351), (88, 1, 352), (88, 27, 353), (89, 110, 354), (89, 14, 298), (89, 12, 133), (89, 25, 94), (89, 4, 134), (89, 5, 299), (89, 10, 355), (89, 1, 356), (89, 26, 357), (89, 62, 139), (89, 27, 358), (89, 116, 359), (91, 110, 190), (91, 1, 362), (91, 27, 363), (92, 110, 364), (92, 14, 284), (92, 10, 365), (92, 12, 286), (92, 4, 287), (92, 5, 288), (92, 13, 289), (92, 90, 366), (92, 1, 367), (92, 62, 292), (92, 27, 368), (92, 116, 369), (93, 110, 294), (93, 1, 370), (93, 27, 371), (94, 110, 372), (94, 14, 273), (94, 10, 373), (94, 12, 286), (94, 4, 374), (94, 5, 90), (94, 13, 289), (94, 90, 375), (94, 1, 376), (94, 62, 292), (94, 27, 377), (95, 110, 294), (95, 1, 378), (95, 27, 379), (96, 110, 380), (96, 14, 381), (96, 12, 133), (96, 25, 94), (96, 4, 382), (96, 5, 274), (96, 10, 383), (96, 26, 385), (96, 62, 139), (96, 27, 386), (98, 110, 190), (98, 1, 389), (98, 27, 390), (96, 1, 391), (101, 110, 400), (101, 14, 401), (101, 1, 402), (101, 12, 403), (101, 90, 404), (101, 62, 6), (101, 27, 405), (102, 110, 406), (102, 1, 407), (102, 27, 408), (103, 1, 410), (103, 27, 411), (104, 1, 413), (104, 27, 414), (105, 110, 412), (105, 1, 413), (105, 27, 415), (106, 110, 409), (106, 1, 410), (106, 27, 416), (107, 110, 336), (107, 1, 337), (107, 27, 417), (109, 22, 87), (109, 110, 418), (109, 4, 287), (109, 5, 274), (109, 10, 419), (109, 14, 420), (109, 12, 93), (109, 25, 94), (109, 1, 421), (109, 26, 422), (109, 90, 423), (109, 62, 98), (109, 27, 424), (110, 110, 100), (110, 1, 425), (110, 27, 426), (112, 110, 427), (112, 14, 434), (112, 27, 432), (114, 1, 439), (114, 27, 440), (116, 110, 438), (116, 1, 439), (116, 27, 445), (112, 89, 446), (117, 1, 448), (117, 27, 449), (117, 110, 450), (118, 22, 87), (118, 110, 451), (118, 4, 452), (118, 5, 135), (118, 10, 453), (118, 14, 454), (118, 12, 455), (118, 25, 456), (118, 1, 457), (118, 26, 458), (118, 90, 459), (118, 62, 98), (118, 27, 460), (120, 1, 464), (120, 27, 465), (121, 110, 463), (121, 1, 464), (121, 27, 466), (120, 110, 467), (122, 13, 468), (122, 12, 469), (122, 25, 470), (122, 4, 90), (122, 5, 274), (122, 14, 471), (122, 10, 472), (122, 26, 473), (122, 1, 474), (122, 110, 475), (123, 110, 190), (123, 1, 476), (123, 27, 477), (124, 110, 478), (129, 110, 513), (154, 110, 514), (132, 110, 516), (135, 110, 517), (152, 110, 520), (149, 110, 521), (133, 110, 531), (139, 110, 541), (140, 110, 542), (127, 110, 550), (126, 110, 551), (147, 110, 552), (146, 110, 553), (145, 110, 554), (144, 110, 555), (138, 110, 556), (151, 110, 557), (128, 110, 558), (148, 110, 559), (143, 110, 560), (134, 110, 561), (150, 110, 562), (153, 110, 563), (131, 110, 564), (130, 110, 565), (142, 110, 566), (141, 110, 567), (137, 110, 568), (136, 110, 569), (125, 110, 570), (155, 110, 572), (156, 110, 573), (156, 14, 577), (157, 110, 578), (157, 6, 579), (157, 1, 580), (157, 118, 581), (160, 110, 586), (157, 14, 587), (161, 90, 591), (161, 8, 592), (161, 14, 593), (161, 1, 594), (162, 110, 595), (162, 1, 596), (162, 27, 597), (163, 110, 601), (161, 110, 602), (167, 110, 199), (167, 1, 200), (167, 27, 604), (168, 1, 606), (168, 27, 607), (168, 110, 608), (169, 110, 608), (169, 14, 609), (170, 110, 610), (170, 14, 609), (170, 75, 611), (171, 110, 612), (171, 1, 613), (171, 27, 614), (172, 110, 615), (172, 14, 616), (172, 1, 617), (172, 12, 618), (172, 90, 619), (172, 62, 6), (172, 27, 620), (173, 110, 621), (173, 1, 622), (173, 27, 623), (174, 110, 103), (174, 14, 104), (174, 1, 105), (174, 22, 624), (174, 26, 625), (174, 12, 106), (174, 90, 626), (174, 62, 6), (174, 27, 627), (175, 110, 109), (175, 1, 110), (175, 27, 628), (176, 110, 629), (176, 14, 630), (176, 1, 631), (176, 12, 632), (176, 90, 633), (176, 62, 6), (176, 27, 634), (176, 116, 635), (177, 110, 636), (177, 1, 637), (177, 27, 638), (180, 110, 639), (180, 14, 640), (180, 1, 641), (180, 12, 642), (180, 90, 643), (180, 62, 6), (180, 27, 644), (181, 110, 645), (181, 1, 646), (181, 27, 647), (182, 110, 438), (182, 1, 439), (182, 27, 648), (183, 110, 438), (183, 1, 439), (183, 27, 649), (184, 12, 650), (184, 110, 651), (184, 4, 652), (184, 5, 653), (184, 13, 654), (184, 1, 655), (184, 14, 656), (184, 10, 657), (184, 22, 658), (184, 90, 659), (184, 62, 660), (184, 27, 661), (185, 110, 662), (185, 1, 663), (185, 27, 664), (186, 110, 665), (186, 14, 666), (186, 1, 667), (186, 12, 668), (186, 90, 669), (186, 62, 6), (186, 27, 670), (187, 110, 671), (187, 1, 672), (187, 27, 673), (188, 1, 675), (188, 27, 676), (189, 110, 674), (189, 1, 675), (189, 27, 677), (190, 1, 679), (190, 27, 680), (191, 110, 678), (191, 1, 679), (191, 27, 681), (190, 110, 682), (188, 110, 683), (192, 1, 685), (192, 27, 686), (193, 110, 684), (193, 1, 685), (193, 27, 687), (192, 110, 688), (194, 1, 690), (194, 27, 691), (195, 110, 689), (195, 1, 690), (195, 27, 692), (196, 1, 694), (196, 27, 695), (197, 110, 693), (197, 1, 694), (197, 27, 696), (198, 1, 698), (198, 27, 699), (199, 110, 697), (199, 1, 698), (199, 27, 700), (200, 1, 702), (200, 27, 703), (201, 110, 701), (201, 1, 702), (201, 27, 704), (202, 1, 706), (202, 27, 707), (203, 110, 708), (203, 14, 709), (203, 7, 710), (203, 75, 711), (202, 110, 712), (204, 1, 714), (204, 27, 715), (205, 110, 713), (205, 1, 714), (205, 27, 716), (204, 110, 717), (200, 110, 718), (198, 110, 719), (196, 110, 720), (194, 110, 721), (206, 1, 723), (206, 27, 724), (207, 110, 722), (207, 1, 723), (207, 27, 725), (206, 110, 726), (208, 1, 728), (208, 27, 729), (209, 110, 727), (209, 1, 728), (209, 27, 730), (208, 110, 731), (210, 110, 732), (210, 14, 733), (210, 1, 734), (210, 12, 735), (210, 90, 736), (210, 62, 6), (210, 27, 737), (212, 110, 740), (212, 1, 741), (212, 27, 742), (213, 110, 743), (213, 14, 744), (213, 1, 745), (213, 12, 746), (213, 90, 747), (213, 62, 6), (213, 27, 748), (215, 110, 750), (215, 1, 751), (215, 27, 752), (218, 110, 760), (218, 1, 761), (218, 27, 762), (219, 110, 763), (219, 14, 754), (219, 1, 764), (219, 12, 765), (219, 90, 766), (219, 62, 6), (219, 27, 767), (221, 110, 769), (221, 1, 770), (221, 27, 771), (222, 110, 772), (222, 14, 773), (222, 1, 774), (222, 12, 775), (222, 90, 776), (222, 62, 6), (222, 27, 777), (222, 116, 778), (224, 110, 780), (224, 1, 781), (224, 27, 782), (225, 110, 783), (225, 14, 784), (225, 1, 785), (225, 12, 786), (225, 90, 787), (225, 62, 6), (225, 27, 788), (227, 110, 790), (227, 1, 791), (227, 27, 792), (228, 110, 793), (228, 14, 794), (228, 1, 795), (228, 12, 796), (228, 90, 797), (228, 62, 6), (228, 27, 798), (228, 116, 799), (230, 110, 801), (230, 1, 802), (230, 27, 803), (231, 110, 804), (231, 14, 805), (231, 1, 806), (231, 12, 807), (231, 90, 808), (231, 62, 6), (231, 27, 809), (233, 110, 811), (233, 1, 812), (233, 27, 813), (234, 110, 814), (234, 14, 815), (234, 1, 816), (234, 12, 817), (234, 90, 818), (234, 62, 6), (234, 27, 819), (236, 110, 821), (236, 1, 822), (236, 27, 823), (237, 110, 824), (237, 14, 825), (237, 1, 826), (237, 12, 827), (237, 90, 828), (237, 62, 6), (237, 27, 829), (237, 116, 830), (239, 110, 832), (239, 1, 833), (239, 27, 834), (240, 110, 835), (240, 14, 836), (240, 1, 837), (240, 12, 838), (240, 90, 839), (240, 62, 6), (240, 27, 840), (242, 110, 842), (242, 1, 843), (242, 27, 844), (245, 110, 645), (245, 1, 646), (245, 27, 847), (246, 110, 848), (246, 1, 849), (246, 27, 850), (247, 110, 851), (247, 14, 852), (247, 7, 853), (247, 75, 711), (247, 1, 849), (251, 110, 861), (251, 1, 862), (251, 27, 863), (252, 1, 865), (252, 27, 866), (253, 110, 864), (253, 1, 865), (253, 27, 867), (252, 110, 868), (254, 110, 869), (254, 12, 870), (254, 14, 871), (254, 5, 274), (254, 4, 872), (254, 1, 873), (255, 110, 874), (255, 1, 875), (255, 27, 876), (103, 110, 877), (83, 110, 879), (21, 110, 880), (114, 110, 881), (104, 110, 882), (258, 1, 884), (258, 27, 885), (259, 110, 883), (259, 1, 884), (259, 27, 886), (258, 110, 888), (261, 110, 889), (261, 14, 273), (261, 10, 890), (261, 12, 286), (261, 4, 374), (261, 5, 891), (261, 13, 289), (261, 62, 292), (261, 27, 894), (263, 110, 294), (263, 1, 897), (263, 27, 898), (264, 110, 899), (264, 14, 900), (264, 1, 901), (264, 12, 902), (264, 90, 903), (264, 62, 6), (264, 27, 904), (266, 110, 906), (266, 1, 907), (266, 27, 908), (270, 110, 56), (270, 14, 28), (270, 1, 57), (270, 12, 58), (270, 90, 269), (270, 62, 6), (270, 27, 920), (272, 110, 61), (272, 1, 62), (272, 27, 922), (274, 1, 923), (274, 27, 924), (275, 1, 923), (275, 27, 925), (274, 110, 926), (276, 1, 928), (276, 27, 929), (277, 110, 927), (277, 1, 928), (277, 27, 930), (276, 110, 931), (278, 110, 932), (278, 1, 933), (278, 27, 934), (279, 110, 932), (279, 1, 933), (279, 27, 935), (280, 110, 936), (280, 1, 937), (280, 27, 938), (281, 110, 936), (281, 1, 937), (281, 27, 939), (282, 110, 940), (282, 1, 941), (282, 27, 942), (283, 110, 940), (283, 1, 941), (283, 27, 943), (284, 110, 944), (284, 1, 945), (284, 27, 946), (285, 110, 944), (285, 1, 945), (285, 27, 947), (286, 110, 948), (286, 1, 949), (286, 27, 950), (287, 110, 948), (287, 1, 949), (287, 27, 951), (289, 110, 948), (289, 1, 949), (289, 27, 953), (290, 110, 954), (290, 1, 955), (290, 27, 956), (291, 110, 954), (291, 1, 955), (291, 27, 957), (292, 110, 958), (292, 1, 959), (292, 27, 960), (293, 110, 958), (293, 1, 959), (293, 27, 961), (294, 110, 962), (294, 1, 963), (294, 27, 964), (295, 110, 962), (295, 1, 963), (295, 27, 965), (296, 1, 967), (296, 27, 968), (297, 110, 966), (297, 1, 967), (297, 27, 969), (296, 110, 970), (298, 1, 972), (298, 27, 973), (299, 110, 971), (299, 1, 972), (299, 27, 974), (298, 110, 975), (300, 1, 977), (300, 27, 978), (301, 110, 976), (301, 1, 977), (301, 27, 979), (300, 110, 980), (302, 1, 982), (302, 27, 983), (303, 110, 981), (303, 1, 982), (303, 27, 984), (302, 110, 985), (304, 1, 987), (304, 27, 988), (305, 110, 986), (305, 1, 987), (305, 27, 989), (304, 110, 990), (306, 1, 992), (306, 27, 993), (307, 110, 991), (307, 1, 992), (307, 27, 994), (306, 110, 995), (308, 1, 997), (308, 27, 998), (309, 110, 996), (309, 1, 997), (309, 27, 999), (308, 110, 1000), (310, 1, 1002), (310, 27, 1003), (311, 110, 1001), (311, 1, 1002), (311, 27, 1004), (310, 110, 1005), (312, 1, 1007), (312, 27, 1008), (313, 110, 1006), (313, 1, 1007), (313, 27, 1009), (312, 110, 1010), (314, 1, 1012), (314, 27, 1013), (315, 110, 1011), (315, 1, 1012), (315, 27, 1014), (314, 110, 1015), (316, 1, 55), (316, 27, 1016), (317, 110, 45), (317, 1, 55), (317, 27, 1017), (316, 110, 1018), (318, 1, 1020), (318, 27, 1021), (319, 110, 1019), (319, 1, 1020), (319, 27, 1022), (318, 110, 1023), (320, 1, 1025), (320, 27, 1026), (321, 110, 1024), (321, 1, 1025), (321, 27, 1027), (320, 110, 1028), (322, 1, 1030), (322, 27, 1031), (323, 110, 1029), (323, 1, 1030), (323, 27, 1032), (322, 110, 1033), (324, 1, 1035), (324, 27, 1036), (325, 110, 1034), (325, 1, 1035), (325, 27, 1037), (324, 110, 1038), (326, 1, 1040), (326, 27, 1041), (327, 110, 1039), (327, 1, 1040), (327, 27, 1042), (326, 110, 1043), (328, 1, 1035), (328, 27, 1044), (329, 110, 1034), (329, 1, 1035), (329, 27, 1045), (328, 110, 1046), (330, 1, 1048), (330, 27, 1049), (331, 110, 1047), (331, 1, 1048), (331, 27, 1050), (330, 110, 1051), (332, 1, 1053), (332, 27, 1054), (333, 110, 1052), (333, 1, 1053), (333, 27, 1055), (332, 110, 1056), (334, 1, 1058), (334, 27, 1059), (335, 110, 1057), (335, 1, 1058), (335, 27, 1060), (334, 110, 1061), (336, 1, 1063), (336, 27, 1064), (337, 110, 1062), (337, 1, 1063), (337, 27, 1065), (336, 110, 1066), (338, 1, 1068), (338, 27, 1069), (339, 110, 1067), (339, 1, 1068), (339, 27, 1070), (338, 110, 1071), (340, 110, 1072), (340, 14, 1073), (340, 12, 1074), (340, 25, 1075), (340, 4, 1076), (340, 5, 1077), (340, 10, 1078), (340, 1, 1079), (340, 26, 1080), (340, 62, 139), (340, 27, 1081), (342, 110, 1084), (342, 1, 1085), (342, 27, 1086), (343, 110, 1087), (343, 12, 1088), (343, 4, 1089), (343, 5, 1090), (343, 10, 1091), (343, 14, 1092), (343, 1, 1093), (344, 110, 1094), (345, 110, 1095), (345, 14, 1096), (345, 1, 1097), (345, 12, 1098), (345, 90, 1099), (345, 62, 6), (345, 27, 1100), (347, 110, 1102), (347, 1, 1103), (347, 27, 1104), (348, 110, 1105), (348, 14, 1106), (348, 1, 1107), (348, 12, 1108), (348, 90, 1109), (348, 62, 6), (348, 27, 1110), (350, 110, 1112), (350, 1, 1113), (350, 27, 1114), (351, 110, 1115), (351, 14, 1116), (351, 1, 1117), (351, 12, 1118), (351, 90, 1119), (351, 62, 6), (351, 27, 1120), (353, 110, 1122), (353, 1, 1123), (353, 27, 1124), (357, 110, 1136), (357, 14, 1137), (357, 1, 1138), (357, 12, 1139), (357, 90, 1140), (357, 62, 6), (357, 27, 1141), (359, 110, 1143), (359, 1, 1144), (359, 27, 1145), (360, 110, 1146), (360, 14, 1147), (360, 1, 1148), (360, 12, 1149), (360, 90, 1150), (360, 62, 6), (360, 27, 1151), (361, 110, 1152), (361, 1, 1153), (361, 27, 1154), (362, 110, 1155), (362, 14, 1156), (362, 12, 1157), (362, 10, 1158), (362, 4, 1159), (362, 5, 1160), (362, 1, 1161), (362, 90, 1162), (362, 26, 1163), (362, 62, 1164), (362, 27, 1165), (364, 110, 1169), (365, 110, 1171), (366, 110, 1172), (363, 110, 72), (363, 14, 384), (363, 1, 430), (363, 12, 433), (363, 90, 447), (363, 62, 6), (363, 27, 481), (367, 110, 482), (367, 1, 483), (367, 27, 484), (368, 110, 485), (368, 14, 486), (368, 1, 487), (368, 12, 488), (368, 90, 489), (368, 62, 6), (368, 27, 490), (369, 110, 491), (369, 1, 492), (369, 27, 493), (370, 110, 494), (370, 14, 495), (370, 10, 496), (370, 12, 286), (370, 4, 497), (370, 5, 156), (370, 13, 289), (370, 90, 498), (370, 1, 499), (370, 62, 292), (370, 27, 500), (371, 110, 294), (371, 1, 501), (371, 27, 502), (372, 22, 87), (372, 110, 503), (372, 4, 504), (372, 5, 156), (372, 10, 505), (372, 14, 506), (372, 12, 507), (372, 25, 508), (372, 1, 509), (372, 26, 510), (372, 90, 511), (372, 62, 98), (372, 27, 512), (373, 110, 100), (373, 1, 515), (373, 27, 518), (374, 110, 519), (374, 14, 522), (374, 12, 133), (374, 25, 94), (374, 4, 163), (374, 5, 156), (374, 10, 523), (374, 1, 524), (374, 26, 525), (374, 62, 139), (374, 27, 526), (378, 110, 190), (379, 110, 190), (380, 110, 539), (380, 14, 530), (380, 12, 507), (380, 25, 508), (380, 4, 532), (380, 5, 288), (380, 10, 540), (380, 1, 543), (380, 26, 544), (380, 62, 139), (380, 27, 545), (382, 110, 548), (383, 110, 549), (383, 14, 571), (383, 12, 133), (383, 25, 94), (383, 4, 134), (383, 5, 156), (383, 10, 574), (383, 1, 575), (383, 26, 576), (383, 62, 139), (383, 27, 588), (383, 116, 265), (385, 110, 190), (386, 110, 598), (386, 14, 605), (386, 1, 705), (386, 22, 878), (386, 12, 887), (386, 90, 1166), (386, 62, 6), (386, 27, 1167), (387, 110, 1168), (387, 1, 1173), (387, 27, 1174), (388, 22, 87), (388, 110, 1175), (388, 4, 90), (388, 5, 310), (388, 10, 1176), (388, 14, 1177), (388, 12, 93), (388, 25, 94), (388, 1, 1178), (388, 26, 1179), (388, 90, 1180), (388, 62, 98), (388, 27, 1181), (389, 110, 100), (389, 1, 1182), (389, 27, 1183), (391, 110, 1191), (392, 110, 1192), (392, 14, 1193), (392, 12, 1074), (392, 25, 1075), (392, 4, 287), (392, 5, 1077), (392, 10, 1194), (392, 1, 1195), (392, 26, 1196), (392, 62, 139), (392, 27, 1197), (394, 110, 190), (394, 1, 1200), (394, 27, 1201), (395, 110, 1202), (395, 14, 1203), (395, 12, 1074), (395, 25, 1075), (395, 4, 1204), (395, 5, 1077), (395, 10, 1205), (395, 1, 1206), (395, 26, 1207), (395, 62, 139), (395, 27, 1208), (397, 110, 190), (397, 1, 1211), (397, 27, 1212), (398, 14, 1214), (398, 12, 1074), (398, 25, 1075), (398, 4, 299), (398, 5, 288), (398, 10, 1215), (398, 1, 1216), (398, 26, 1217), (398, 62, 139), (398, 27, 1218), (400, 110, 190), (400, 1, 1221), (400, 27, 1222), (401, 110, 1223), (401, 14, 1224), (401, 12, 1225), (401, 25, 1226), (401, 4, 1227), (401, 5, 135), (401, 10, 1228), (401, 1, 1229), (401, 26, 1230), (401, 62, 139), (401, 27, 1231), (403, 110, 190), (403, 1, 1234), (403, 27, 1235), (404, 12, 1236), (404, 110, 1237), (404, 4, 163), (404, 5, 135), (404, 13, 1238), (404, 1, 1239), (404, 14, 1240), (404, 10, 1241), (404, 22, 1242), (404, 26, 1243), (404, 62, 660), (404, 27, 1244), (404, 116, 1245), (405, 110, 662), (405, 1, 1246), (405, 27, 1247), (406, 22, 87), (406, 110, 1248), (406, 4, 90), (406, 5, 310), (406, 10, 1249), (406, 14, 1177), (406, 12, 93), (406, 25, 94), (406, 1, 1250), (406, 26, 1251), (406, 90, 1252), (406, 62, 98), (406, 27, 1253), (407, 110, 100), (407, 1, 1254), (407, 27, 1255), (408, 110, 1256), (408, 12, 1257), (408, 4, 90), (408, 5, 135), (408, 10, 1258), (408, 14, 1259), (408, 13, 1260), (408, 26, 1261), (408, 1, 1262), (408, 90, 1263), (408, 62, 1264), (408, 27, 1265), (409, 110, 1266), (409, 1, 1267), (409, 27, 1268), (410, 22, 87), (410, 110, 1269), (410, 4, 1270), (410, 5, 891), (410, 10, 1271), (410, 14, 1272), (410, 12, 507), (410, 25, 508), (410, 1, 1273), (410, 26, 1274), (410, 90, 1275), (410, 62, 98), (410, 27, 1276), (410, 116, 1277), (411, 110, 100), (411, 1, 1278), (411, 27, 1279), (412, 110, 1280), (412, 12, 1281), (412, 4, 1282), (412, 14, 1283), (412, 10, 1284), (412, 1, 1285), (412, 90, 1286), (412, 62, 1287), (412, 27, 1288), (414, 1, 1291), (414, 27, 1292), (415, 110, 392), (415, 14, 1293), (415, 12, 133), (415, 25, 94), (415, 4, 1294), (415, 5, 156), (415, 10, 1295), (415, 1, 1296), (415, 26, 1297), (415, 62, 139), (415, 27, 1298), (417, 110, 190), (417, 1, 1301), (417, 27, 1302), (419, 110, 1310), (419, 1, 1311), (419, 27, 1312), (422, 110, 1321), (422, 1, 1322), (422, 27, 1323), (421, 22, 1318), (421, 110, 1319), (421, 4, 1320), (421, 5, 299), (421, 10, 1324), (421, 14, 1325), (421, 12, 93), (421, 25, 94), (421, 1, 1326), (421, 26, 1327), (421, 90, 1328), (421, 62, 1329), (421, 27, 1330), (421, 116, 1331), (424, 110, 1335), (424, 1, 1336), (424, 27, 1337), (426, 110, 1332), (426, 1, 1347), (426, 27, 1348), (429, 12, 1359), (429, 4, 1360), (429, 5, 135), (429, 10, 1361), (429, 1, 1362), (429, 14, 1363), (429, 90, 1364), (429, 110, 1365), (430, 110, 1366), (430, 1, 1367), (430, 27, 1368), (431, 110, 1369), (432, 110, 1370), (433, 110, 1371), (433, 12, 1372), (433, 4, 1373), (433, 14, 1374), (433, 10, 163), (433, 1, 1375), (433, 90, 1376), (433, 62, 1287), (433, 27, 1377), (435, 1, 1379), (435, 27, 1380), (436, 1, 1382), (436, 27, 1383), (436, 110, 1384), (436, 90, 1385), (438, 110, 1388), (438, 12, 1389), (438, 4, 1390), (438, 14, 1391), (438, 10, 1392), (438, 1, 1393), (438, 90, 1394), (438, 62, 1287), (438, 27, 1395), (440, 1, 1397), (440, 27, 1398), (441, 110, 1321), (442, 1, 1400), (442, 27, 1401), (442, 110, 1402), (443, 1, 1403), (443, 27, 1404), (443, 110, 1405), (443, 90, 1406), (444, 110, 1321), (445, 110, 1321), (446, 13, 1407), (446, 12, 1408), (446, 25, 1409), (446, 4, 1410), (446, 14, 1411), (446, 10, 1412), (446, 26, 1413), (446, 1, 1414), (446, 110, 1415), (446, 62, 1416), (446, 27, 1417), (447, 1, 1418), (447, 27, 1419), (448, 110, 1420), (448, 12, 1421), (448, 4, 1422), (448, 5, 1423), (448, 10, 1424), (448, 14, 1425), (448, 13, 1426), (448, 26, 1427), (448, 1, 1428), (448, 90, 1429), (448, 62, 1264), (448, 27, 1430), (450, 1, 1434), (450, 27, 1435), (450, 110, 1436), (451, 110, 1321), (449, 22, 1318), (449, 110, 1170), (449, 14, 1399), (449, 12, 93), (449, 25, 94), (449, 1, 1431), (449, 26, 1432), (449, 90, 1437), (449, 62, 1329), (449, 27, 1438), (452, 110, 1332), (452, 1, 1439), (452, 27, 1440), (453, 22, 1318), (453, 110, 1441), (453, 4, 163), (453, 5, 274), (453, 10, 1442), (453, 14, 1443), (453, 12, 93), (453, 25, 94), (453, 1, 1444), (453, 26, 1445), (453, 62, 1329), (453, 27, 1446), (453, 116, 1447), (454, 110, 1332), (454, 1, 1448), (454, 27, 1449), (455, 14, 420), (455, 110, 1450), (455, 12, 1451), (455, 10, 1452), (455, 4, 1453), (455, 5, 1454), (455, 26, 1455), (455, 90, 1457), (455, 62, 1458), (455, 27, 1459), (455, 1, 1460), (456, 110, 1461), (458, 110, 1468), (458, 1, 1469), (458, 27, 1470), (459, 110, 1471), (459, 14, 1472), (459, 1, 1473), (459, 12, 1474), (459, 90, 1475), (459, 62, 6), (459, 27, 1476), (460, 110, 1477), (460, 1, 1478), (460, 27, 1479), (462, 110, 1486), (462, 1, 1487), (462, 27, 1488), (465, 22, 1318), (465, 110, 1498), (465, 4, 1358), (465, 5, 90), (465, 10, 1499), (465, 14, 1399), (465, 12, 93), (465, 25, 94), (465, 1, 1500), (465, 26, 1501), (465, 90, 1502), (465, 62, 1329), (465, 27, 1503), (466, 110, 1332), (466, 1, 1504), (466, 27, 1505), (470, 110, 861), (470, 1, 862), (470, 27, 1512), (471, 110, 131), (471, 4, 134), (471, 5, 135), (471, 10, 1514), (471, 14, 1515), (471, 12, 93), (471, 25, 94), (471, 1, 252), (471, 26, 138), (471, 90, 1516), (471, 62, 1329), (471, 27, 1517), (472, 110, 1332), (472, 1, 1518), (472, 27, 1519), (473, 110, 1520), (473, 14, 1521), (473, 1, 1522), (473, 12, 1523), (473, 90, 1524), (473, 62, 6), (473, 27, 1525), (474, 110, 1526), (474, 1, 1527), (474, 27, 1528), (475, 110, 1529), (475, 14, 1530), (475, 1, 1531), (475, 12, 1532), (475, 90, 1533), (475, 62, 6), (475, 27, 1534), (476, 110, 1535), (476, 1, 1536), (476, 27, 1537), (477, 110, 1538), (477, 25, 1539), (477, 14, 1540), (477, 4, 1541), (477, 5, 1542), (477, 10, 1543), (477, 1, 1544), (477, 26, 1545), (477, 12, 1539), (477, 62, 1539), (477, 27, 1546), (478, 110, 1547), (478, 1, 1548), (478, 27, 1549), (479, 110, 1550), (479, 4, 1422), (479, 5, 579), (479, 10, 1551), (479, 14, 1552), (479, 12, 507), (479, 25, 508), (479, 1, 1553), (479, 26, 1554), (479, 90, 1555), (479, 62, 1329), (479, 27, 1556), (480, 110, 1332), (480, 1, 1557), (480, 27, 1558), (481, 13, 1407), (481, 12, 1408), (481, 25, 1409), (481, 4, 1559), (481, 5, 1090), (481, 14, 1560), (481, 10, 1561), (481, 26, 1562), (481, 1, 1563), (481, 110, 1564), (481, 62, 1416), (481, 27, 1565), (483, 110, 1569), (484, 110, 1570), (484, 14, 1571), (484, 1, 1572), (484, 12, 1573), (484, 90, 1574), (484, 62, 6), (484, 27, 1575), (485, 110, 1576), (485, 1, 1577), (485, 27, 1578), (486, 110, 1579), (486, 14, 1580), (486, 1, 1581), (486, 12, 1582), (486, 90, 1583), (486, 62, 6), (486, 27, 1584), (486, 116, 1585), (487, 110, 1586), (487, 1, 1587), (487, 27, 1588), (488, 110, 1589), (488, 14, 1590), (488, 1, 1591), (488, 12, 1592), (488, 90, 1593), (488, 62, 6), (488, 27, 1594), (489, 110, 1595), (489, 1, 1596), (489, 27, 1597), (491, 110, 1606), (491, 1, 1607), (491, 27, 1608), (492, 110, 1598), (492, 12, 1372), (492, 10, 1610), (492, 14, 1363), (492, 1, 1611), (492, 90, 1612), (492, 26, 1613), (492, 62, 1614), (492, 27, 1615), (494, 110, 1619), (494, 14, 1620), (494, 1, 1621), (494, 12, 1622), (494, 90, 1623), (494, 62, 6), (494, 27, 1624), (495, 110, 1625), (495, 1, 1626), (495, 27, 1627), (496, 110, 1628), (496, 14, 1629), (496, 1, 1630), (496, 12, 1631), (496, 90, 1632), (496, 62, 6), (496, 27, 1633), (497, 110, 1634), (497, 1, 1635), (497, 27, 1636), (493, 110, 1433), (493, 4, 382), (493, 5, 274), (493, 10, 1456), (493, 14, 1616), (493, 12, 93), (493, 25, 94), (493, 1, 1617), (493, 26, 1618), (493, 90, 1637), (493, 62, 1329), (493, 27, 1638), (498, 110, 1332), (498, 1, 1639), (498, 27, 1640), (499, 110, 1641), (499, 14, 1642), (499, 1, 1643), (499, 12, 1644), (499, 90, 1645), (499, 62, 6), (499, 27, 1646), (500, 110, 1647), (500, 1, 1648), (500, 27, 1649), (501, 110, 1650), (501, 4, 452), (501, 5, 135), (501, 10, 1651), (501, 14, 1652), (501, 12, 93), (501, 25, 94), (501, 1, 1653), (501, 26, 1654), (501, 90, 1655), (501, 62, 1329), (501, 27, 1656), (502, 110, 1332), (502, 1, 1657), (502, 27, 1658), (503, 110, 1659), (503, 4, 1660), (503, 5, 90), (503, 10, 1661), (503, 14, 1662), (503, 12, 93), (503, 25, 94), (503, 1, 1663), (503, 26, 1664), (503, 90, 1665), (503, 62, 1329), (503, 27, 1666), (504, 110, 1332), (504, 1, 1667), (504, 27, 1668), (505, 110, 1669), (505, 4, 1670), (505, 5, 90), (505, 10, 1671), (505, 14, 1672), (505, 12, 93), (505, 25, 94), (505, 1, 1673), (505, 26, 1674), (505, 90, 1675), (505, 62, 1329), (505, 27, 1676), (505, 116, 1677), (506, 110, 1332), (506, 1, 1678), (506, 27, 1679), (507, 110, 1680), (507, 4, 1358), (507, 5, 135), (507, 10, 1681), (507, 14, 1682), (507, 12, 93), (507, 25, 94), (507, 1, 1683), (507, 26, 1684), (507, 62, 1329), (507, 27, 1685), (507, 116, 1447), (508, 110, 1332), (508, 1, 1686), (508, 27, 1687), (509, 110, 1688), (509, 4, 1320), (509, 5, 274), (509, 10, 1689), (509, 14, 1690), (509, 12, 93), (509, 25, 94), (509, 1, 1691), (509, 26, 1692), (509, 90, 1693), (509, 62, 1329), (509, 27, 1694), (510, 110, 1332), (510, 1, 1695), (510, 27, 1696), (511, 110, 1697), (511, 4, 1698), (511, 5, 872), (511, 10, 1699), (511, 14, 480), (511, 12, 507), (511, 25, 508), (511, 1, 1700), (511, 26, 1701), (511, 90, 1702), (511, 62, 1329), (511, 27, 1703), (512, 110, 1332), (512, 1, 1704), (512, 27, 1705), (513, 110, 1706), (513, 4, 1707), (513, 5, 299), (513, 10, 1708), (513, 14, 1709), (513, 12, 93), (513, 25, 94), (513, 1, 1710), (513, 26, 1711), (513, 90, 1712), (513, 62, 1329), (513, 27, 1713), (514, 110, 1332), (514, 1, 1714), (514, 27, 1715), (515, 110, 1716), (515, 4, 163), (515, 5, 310), (515, 10, 1717), (515, 14, 1718), (515, 12, 93), (515, 25, 94), (515, 1, 1719), (515, 26, 1720), (515, 90, 1721), (515, 62, 1329), (515, 27, 1722), (516, 110, 1332), (516, 1, 1723), (516, 27, 1724), (517, 110, 1725), (517, 4, 1358), (517, 5, 90), (517, 10, 1726), (517, 14, 1727), (517, 12, 93), (517, 25, 94), (517, 1, 1728), (517, 26, 1729), (517, 90, 1730), (517, 62, 1329), (517, 27, 1731), (518, 110, 1332), (518, 1, 1732), (518, 27, 1733), (519, 110, 1734), (519, 4, 1707), (519, 5, 299), (519, 10, 1735), (519, 14, 1736), (519, 12, 93), (519, 25, 94), (519, 1, 1737), (519, 26, 1738), (519, 90, 1739), (519, 62, 1329), (519, 27, 1740), (520, 110, 1332), (520, 1, 1741), (520, 27, 1742), (521, 110, 1743), (521, 4, 1744), (521, 5, 274), (521, 10, 1745), (521, 14, 480), (521, 12, 93), (521, 25, 94), (521, 1, 1746), (521, 26, 1747), (521, 90, 1748), (521, 62, 1329), (521, 27, 1749), (522, 110, 1332), (522, 1, 1750), (522, 27, 1751), (523, 110, 1752), (523, 4, 1358), (523, 5, 156), (523, 10, 1753), (523, 14, 1754), (523, 12, 93), (523, 25, 94), (523, 1, 1755), (523, 26, 1756), (523, 90, 1757), (523, 62, 1329), (523, 27, 1758), (523, 116, 1759), (524, 110, 1332), (524, 1, 1760), (524, 27, 1761), (525, 110, 1762), (525, 4, 163), (525, 5, 299), (525, 10, 1763), (525, 14, 1764), (525, 12, 93), (525, 25, 94), (525, 1, 1765), (525, 26, 1766), (525, 62, 1329), (525, 27, 1767), (525, 116, 1447), (526, 110, 1332), (526, 1, 1768), (526, 27, 1769), (529, 110, 1762), (529, 4, 382), (529, 5, 90), (529, 10, 1772), (529, 14, 1773), (529, 12, 93), (529, 25, 94), (529, 1, 1774), (529, 26, 1775), (529, 62, 1329), (529, 27, 1776), (529, 116, 1447), (530, 110, 1332), (530, 1, 1777), (530, 27, 1778), (531, 13, 289), (531, 12, 286), (531, 25, 1779), (531, 4, 497), (531, 5, 1077), (531, 14, 1780), (531, 10, 1781), (531, 26, 1782), (531, 1, 1783), (531, 110, 1784), (531, 62, 1416), (531, 27, 1785), (532, 13, 289), (532, 12, 286), (532, 25, 1779), (532, 4, 497), (532, 5, 1090), (532, 14, 1786), (532, 10, 1787), (532, 26, 1788), (532, 1, 1789), (532, 110, 1790), (532, 62, 1416), (532, 27, 1791), (532, 116, 1792), (533, 110, 1793), (533, 4, 1794), (533, 5, 156), (533, 10, 1795), (533, 14, 1796), (533, 12, 93), (533, 25, 94), (533, 1, 1797), (533, 26, 1798), (533, 90, 1799), (533, 62, 1329), (533, 27, 1800), (534, 110, 1332), (534, 1, 1801), (534, 27, 1802), (535, 110, 529), (535, 14, 1804), (535, 12, 507), (535, 25, 508), (535, 1, 1805), (535, 26, 535), (535, 90, 1806), (535, 62, 1329), (535, 27, 1807), (536, 110, 1332), (536, 1, 1808), (536, 27, 1809), (537, 110, 1810), (537, 14, 1811), (537, 1, 1812), (537, 22, 1813), (537, 26, 1814), (537, 12, 1815), (537, 90, 1816), (537, 62, 6), (537, 27, 1817), (538, 110, 1818), (538, 1, 1819), (538, 27, 1820), (539, 110, 1821), (539, 14, 1642), (539, 1, 1822), (539, 12, 1823), (539, 90, 1824), (539, 62, 6), (539, 27, 1825), (540, 110, 1826), (540, 1, 1827), (540, 27, 1828), (541, 110, 1829), (541, 4, 1830), (541, 5, 135), (541, 10, 1831), (541, 14, 1832), (541, 12, 93), (541, 25, 94), (541, 1, 1833), (541, 26, 1834), (541, 90, 1835), (541, 62, 1329), (541, 27, 1836), (542, 110, 1332), (542, 1, 1837), (542, 27, 1838), (543, 110, 1839), (543, 4, 1840), (543, 5, 135), (543, 10, 1841), (543, 14, 1842), (543, 12, 93), (543, 25, 94), (543, 1, 1843), (543, 26, 1844), (543, 90, 1845), (543, 62, 1329), (543, 27, 1846), (544, 110, 1332), (544, 1, 1847), (544, 27, 1848), (545, 110, 1849), (545, 14, 1850), (545, 1, 1851), (545, 22, 1852), (545, 26, 1853), (545, 12, 1854), (545, 90, 1855), (545, 62, 6), (545, 27, 1856), (545, 116, 1857), (546, 110, 1858), (546, 1, 1859), (546, 27, 1860), (549, 110, 1872), (549, 14, 1873), (549, 1, 1874), (549, 12, 1875), (549, 90, 1876), (549, 62, 6), (549, 27, 1877), (550, 110, 1878), (550, 1, 1879), (550, 27, 1880), (551, 110, 1881), (551, 14, 1882), (551, 1, 1883), (551, 22, 1884), (551, 26, 1885), (551, 12, 1886), (551, 90, 1887), (551, 62, 6), (551, 27, 1888), (552, 110, 1889), (552, 1, 1890), (552, 27, 1891), (553, 110, 1892), (553, 14, 1893), (553, 1, 1894), (553, 22, 1895), (553, 26, 1896), (553, 12, 1897), (553, 90, 1898), (553, 62, 6), (553, 27, 1899), (553, 116, 1900), (554, 110, 1901), (554, 1, 1902), (554, 27, 1903), (555, 110, 1904), (555, 14, 1905), (555, 1, 1906), (555, 22, 1907), (555, 26, 1908), (555, 12, 1909), (555, 90, 1910), (555, 62, 6), (555, 27, 1911), (556, 110, 1912), (556, 1, 1913), (556, 27, 1914), (557, 110, 1915), (557, 14, 1916), (557, 1, 1917), (557, 22, 1918), (557, 26, 1919), (557, 12, 1920), (557, 90, 1921), (557, 62, 6), (557, 27, 1922), (558, 110, 1923), (558, 1, 1924), (558, 27, 1925), (559, 110, 1926), (559, 4, 155), (559, 5, 90), (559, 10, 1726), (559, 14, 1927), (559, 12, 93), (559, 25, 94), (559, 1, 1928), (559, 26, 1929), (559, 90, 1930), (559, 62, 1329), (559, 27, 1931), (559, 116, 1932), (560, 110, 1332), (560, 1, 1933), (560, 27, 1934), (561, 110, 1935), (561, 14, 1936), (561, 1, 1937), (561, 12, 1938), (561, 90, 1939), (561, 62, 6), (561, 27, 1940), (562, 110, 1941), (562, 1, 1942), (562, 27, 1943), (563, 13, 1944), (563, 12, 1074), (563, 25, 1075), (563, 4, 90), (563, 5, 1204), (563, 14, 1945), (563, 10, 1946), (563, 26, 1947), (563, 1, 1948), (563, 110, 1949), (563, 62, 1950), (563, 27, 1951), (564, 110, 190), (567, 13, 1944), (567, 12, 1074), (567, 25, 1075), (567, 4, 1954), (567, 5, 1077), (567, 14, 471), (567, 10, 1955), (567, 26, 1956), (567, 1, 1957), (567, 110, 1958), (567, 62, 1950), (567, 27, 1959), (568, 110, 190), (572, 110, 1976), (572, 14, 1977), (572, 12, 1978), (572, 10, 1979), (572, 4, 1970), (572, 5, 1980), (572, 1, 1974), (572, 90, 1981), (572, 26, 1973), (572, 62, 1164), (572, 27, 1982), (573, 110, 1983), (573, 1, 1984), (573, 27, 1985), (577, 110, 1991), (577, 14, 1992), (577, 1, 1993), (577, 22, 1994), (577, 26, 1995), (577, 12, 1996), (577, 90, 1997), (577, 62, 6), (577, 27, 1998), (578, 110, 1999), (578, 1, 2000), (578, 27, 2001), (581, 110, 2002), (581, 4, 134), (581, 5, 90), (581, 10, 2014), (581, 14, 2015), (581, 12, 93), (581, 25, 94), (581, 1, 2016), (581, 26, 2017), (581, 90, 2018), (581, 62, 1329), (581, 27, 2019), (581, 116, 2010), (582, 110, 1332), (582, 1, 2020), (582, 27, 2021), (583, 110, 1441), (583, 4, 2022), (583, 5, 299), (583, 10, 2023), (583, 14, 2024), (583, 12, 93), (583, 25, 94), (583, 1, 2025), (583, 26, 2026), (583, 62, 1329), (583, 27, 2027), (583, 116, 1447), (584, 110, 1332), (584, 1, 2028), (584, 27, 2029), (587, 110, 2032), (587, 14, 2033), (587, 1, 2034), (587, 22, 2035), (587, 26, 2036), (587, 12, 2037), (587, 90, 2038), (587, 62, 6), (587, 27, 2039), (588, 110, 2040), (588, 1, 2041), (588, 27, 2042), (589, 110, 2043), (590, 13, 1407), (590, 12, 1408), (590, 25, 1409), (590, 4, 2044), (590, 14, 2045), (590, 10, 2046), (590, 26, 2047), (590, 1, 2048), (590, 110, 2049), (590, 62, 1416), (590, 27, 2050), (591, 1, 2051), (591, 27, 2052), (592, 110, 2053), (592, 14, 2054), (592, 1, 2055), (592, 12, 2056), (592, 90, 2057), (592, 62, 6), (592, 27, 2058), (593, 110, 2059), (593, 1, 2060), (593, 27, 2061), (594, 110, 2062), (594, 14, 2063), (594, 1, 2064), (594, 12, 2065), (594, 90, 2066), (594, 62, 6), (594, 27, 2067), (595, 110, 2068), (595, 1, 2069), (595, 27, 2070), (596, 110, 2071), (596, 14, 2054), (596, 1, 2072), (596, 12, 2073), (596, 90, 2074), (596, 62, 6), (596, 27, 2075), (597, 110, 2076), (597, 1, 2077), (597, 27, 2078), (600, 110, 2079), (600, 4, 2090), (600, 5, 310), (600, 10, 2091), (600, 14, 2092), (600, 12, 93), (600, 25, 94), (600, 1, 2093), (600, 26, 2094), (600, 90, 2095), (600, 62, 1329), (600, 27, 2096), (601, 110, 1332), (601, 1, 2097), (601, 27, 2098), (602, 110, 2099), (602, 4, 2100), (602, 5, 274), (602, 10, 2101), (602, 14, 2102), (602, 12, 93), (602, 25, 94), (602, 1, 2103), (602, 26, 2104), (602, 90, 2105), (602, 62, 1329), (602, 27, 2106), (603, 110, 1332), (603, 1, 2107), (603, 27, 2108), (604, 110, 2109), (604, 4, 2110), (604, 5, 299), (604, 10, 2111), (604, 14, 2112), (604, 12, 93), (604, 25, 94), (604, 1, 2113), (604, 26, 2114), (604, 90, 2115), (604, 62, 1329), (604, 27, 2116), (605, 110, 1332), (605, 1, 2117), (605, 27, 2118), (606, 110, 2119), (606, 14, 2120), (606, 1, 2121), (606, 22, 2122), (606, 26, 2123), (606, 12, 2124), (606, 90, 2125), (606, 62, 6), (606, 27, 2126), (607, 110, 2127), (607, 1, 2128), (607, 27, 2129), (609, 110, 1901), (609, 1, 1902), (609, 27, 2131), (610, 110, 2135), (610, 14, 2136), (610, 1, 2133), (610, 27, 2134), (615, 110, 2154), (615, 14, 2155), (615, 1, 2151), (615, 27, 2152), (613, 110, 2148), (613, 14, 2149), (613, 1, 2146), (613, 27, 2147), (617, 110, 2156), (617, 1, 2157), (617, 27, 2159), (618, 110, 2160), (618, 1, 2161), (618, 27, 2162), (616, 110, 2156), (616, 14, 2163), (616, 1, 2157), (616, 27, 2158), (622, 110, 2178), (622, 4, 145), (622, 5, 299), (622, 10, 2179), (622, 14, 2180), (622, 12, 93), (622, 25, 94), (622, 1, 2181), (622, 26, 2182), (622, 90, 2183), (622, 62, 1329), (622, 27, 2184), (623, 110, 1332), (623, 1, 2185), (623, 27, 2186), (622, 22, 2187), (624, 110, 2188), (624, 1, 2189), (624, 27, 2190), (625, 110, 2191), (626, 110, 2188), (626, 1, 2189), (626, 27, 2192), (624, 14, 2194), (624, 31, 2195), (627, 110, 2196), (627, 14, 284), (629, 110, 2200), (630, 110, 2201), (631, 110, 2202), (632, 110, 2203), (633, 110, 2204), (634, 110, 2205), (635, 110, 2206), (636, 110, 2207), (637, 110, 2208), (638, 110, 2209), (639, 110, 2210), (640, 110, 2211), (641, 110, 2212), (642, 110, 2213), (642, 14, 2214), (642, 1, 2215), (642, 12, 2216), (642, 90, 2217), (642, 62, 6), (642, 27, 2218), (643, 110, 2219), (643, 1, 2220), (643, 27, 2221), (644, 110, 2222), (644, 1, 2223), (644, 27, 2224), (648, 110, 2241), (648, 1, 2242), (648, 27, 2243), (649, 110, 2244), (649, 12, 286), (649, 4, 2245), (649, 5, 274), (649, 10, 2246), (649, 1, 2247), (649, 14, 1690), (649, 90, 2248), (650, 110, 2249), (261, 1, 2251), (654, 110, 435), (655, 110, 435), (656, 110, 2260), (656, 14, 2261), (656, 1, 2262), (656, 12, 2263), (656, 90, 2264), (656, 62, 6), (656, 27, 2265), (657, 110, 2266), (657, 1, 2267), (657, 27, 2268), (659, 110, 1486), (659, 1, 1487), (659, 27, 2272), (660, 110, 2273), (660, 14, 2274), (660, 1, 2275), (660, 12, 2276), (660, 90, 2277), (660, 62, 6), (660, 27, 2278), (660, 116, 2279), (661, 110, 2280), (661, 1, 2281), (661, 27, 2282), (662, 110, 2283), (662, 14, 2284), (662, 1, 2285), (662, 12, 2286), (662, 90, 2287), (662, 62, 6), (662, 27, 2288), (663, 110, 2289), (663, 1, 2290), (663, 27, 2291), (664, 110, 2292), (664, 14, 2293), (664, 1, 2294), (664, 22, 2295), (664, 12, 2296), (664, 90, 2297), (664, 62, 6), (664, 27, 2298), (665, 110, 2299), (665, 1, 2300), (665, 27, 2301), (666, 110, 2302), (666, 14, 2303), (666, 1, 2304), (666, 12, 2305), (666, 90, 2306), (666, 62, 6), (666, 27, 2307), (667, 110, 2308), (667, 1, 2309), (667, 27, 2310), (668, 110, 2311), (668, 14, 2312), (668, 1, 2313), (668, 12, 2314), (668, 90, 2315), (668, 62, 6), (668, 27, 2316), (668, 116, 2317), (669, 110, 2318), (669, 1, 2319), (669, 27, 2320), (679, 110, 909), (679, 4, 134), (679, 5, 310), (679, 10, 2321), (679, 14, 2322), (679, 12, 93), (679, 25, 94), (679, 1, 2323), (679, 26, 2324), (679, 90, 2325), (679, 62, 1329), (679, 27, 2338), (680, 110, 1332), (680, 1, 2330), (680, 27, 2339), (681, 13, 2340), (681, 12, 2341), (681, 25, 2342), (681, 4, 2343), (681, 14, 2344), (681, 10, 2345), (681, 26, 2346), (681, 1, 2347), (681, 110, 2348), (681, 62, 1416), (681, 27, 2349), (682, 110, 2350), (682, 1, 2351), (682, 27, 2352), (683, 110, 2353), (683, 14, 1116), (683, 1, 1117), (683, 12, 1118), (683, 90, 2354), (683, 62, 6), (683, 27, 2355), (685, 110, 1122), (685, 1, 1123), (685, 27, 2364), (687, 13, 289), (687, 12, 286), (687, 25, 1779), (687, 4, 497), (687, 5, 2368), (687, 14, 2369), (687, 10, 2370), (687, 26, 2371), (687, 1, 2372), (687, 110, 2373), (687, 62, 1416), (687, 27, 2374), (689, 110, 2378), (690, 110, 2379), (690, 4, 2022), (690, 5, 299), (690, 10, 2380), (690, 14, 2381), (690, 12, 93), (690, 25, 94), (690, 1, 2382), (690, 26, 2383), (690, 90, 2384), (690, 62, 1329), (690, 27, 2385), (690, 116, 265), (691, 110, 1332), (691, 1, 2386), (691, 27, 2387), (692, 110, 2388), (692, 4, 1840), (692, 5, 310), (692, 10, 2389), (692, 14, 2390), (692, 12, 93), (692, 25, 94), (692, 1, 2391), (692, 26, 2392), (692, 90, 2393), (692, 62, 1329), (692, 27, 2394), (693, 110, 2395), (693, 4, 2396), (693, 5, 299), (693, 10, 2397), (693, 14, 2398), (693, 12, 93), (693, 25, 94), (693, 1, 2399), (693, 26, 2400), (693, 90, 2401), (693, 62, 1329), (693, 27, 2402), (694, 110, 1332), (694, 1, 2403), (694, 27, 2404), (695, 110, 1332), (695, 1, 2405), (695, 27, 2406), (688, 110, 1968), (688, 4, 1390), (688, 5, 1969), (688, 10, 2132), (688, 14, 2153), (688, 12, 507), (688, 25, 508), (688, 1, 2193), (688, 26, 2250), (688, 90, 2254), (688, 62, 1329), (688, 27, 2375), (696, 110, 1332), (696, 1, 2376), (696, 27, 2377), (697, 12, 2407), (697, 13, 2408), (697, 1, 2409), (697, 14, 2410), (697, 110, 2411), (697, 15, 2412), (697, 62, 2413), (697, 27, 2414), (697, 116, 2415), (698, 12, 2407), (698, 13, 2408), (698, 1, 2416), (698, 14, 2417), (698, 110, 2418), (698, 15, 2412), (698, 62, 2413), (698, 27, 2419), (698, 116, 2420), (699, 12, 2407), (699, 13, 2408), (699, 1, 2421), (699, 14, 2422), (699, 110, 2423), (699, 15, 2424), (699, 62, 2413), (699, 27, 2425), (700, 12, 2407), (700, 13, 2408), (700, 1, 2426), (700, 14, 2427), (700, 110, 2428), (700, 15, 2424), (700, 62, 2413), (700, 27, 2429), (701, 12, 2407), (701, 13, 2408), (701, 1, 2430), (701, 14, 2410), (701, 110, 2431), (701, 15, 2412), (701, 62, 2413), (701, 27, 2432), (701, 116, 2433), (702, 110, 2434), (702, 14, 2435), (702, 1, 2436), (702, 22, 2437), (702, 12, 2438), (702, 90, 2439), (702, 62, 6), (702, 27, 2440), (702, 116, 2441), (703, 110, 2442), (703, 1, 2443), (703, 27, 2444), (705, 110, 2446), (706, 110, 1338), (706, 14, 1341), (706, 12, 93), (706, 25, 94), (706, 1, 1342), (706, 26, 1343), (706, 90, 1344), (706, 62, 1329), (706, 27, 2447), (706, 116, 1346), (707, 110, 1332), (707, 1, 2448), (707, 27, 2449), (708, 110, 2450), (708, 4, 1660), (708, 5, 310), (708, 10, 2451), (708, 14, 2452), (708, 12, 93), (708, 25, 94), (708, 1, 2453), (708, 26, 2454), (708, 90, 2455), (708, 62, 1329), (708, 27, 2456), (708, 116, 2457), (709, 110, 1332), (709, 1, 2458), (709, 27, 2459), (710, 110, 2460), (710, 4, 2461), (710, 5, 156), (710, 10, 2462), (710, 14, 2463), (710, 12, 93), (710, 25, 94), (710, 1, 2464), (710, 26, 2465), (710, 90, 2466), (710, 62, 1329), (710, 27, 2467), (711, 110, 1332), (711, 1, 2468), (711, 27, 2469), (712, 110, 2470), (712, 14, 2471), (712, 1, 2472), (712, 12, 2473), (712, 90, 2474), (712, 62, 6), (712, 27, 2475), (713, 110, 2476), (713, 1, 2477), (713, 27, 2478), (714, 12, 2407), (714, 13, 2408), (714, 1, 2479), (714, 14, 2480), (714, 110, 2481), (714, 15, 2412), (714, 62, 2413), (714, 27, 2482), (715, 110, 2483), (715, 4, 2090), (715, 5, 274), (715, 10, 2484), (715, 14, 2485), (715, 12, 93), (715, 25, 94), (715, 1, 2486), (715, 26, 2487), (715, 90, 2488), (715, 62, 1329), (715, 27, 2489), (716, 110, 1332), (716, 1, 2490), (716, 27, 2491), (718, 110, 2493), (718, 12, 870), (718, 14, 284), (718, 1, 2494), (720, 110, 2495), (721, 110, 2496), (721, 14, 2497), (721, 1, 2498), (721, 22, 2499), (721, 26, 2500), (721, 12, 2501), (721, 90, 2502), (721, 62, 6), (721, 27, 2503), (722, 110, 2504), (722, 1, 2505), (722, 27, 2506), (725, 110, 2516), (725, 14, 2517), (725, 1, 2518), (725, 12, 2519), (725, 90, 2520), (725, 62, 6), (725, 27, 2521), (726, 110, 2522), (726, 1, 2523), (726, 27, 2524), (727, 110, 2525), (727, 14, 1350), (727, 1, 2526), (727, 22, 2527), (727, 26, 2528), (727, 12, 2529), (727, 90, 2530), (727, 62, 6), (727, 27, 2531), (728, 110, 2532), (728, 1, 2533), (728, 27, 2534), (729, 110, 2535), (729, 14, 2536), (729, 1, 2537), (729, 22, 2538), (729, 26, 2539), (729, 12, 2540), (729, 90, 2541), (729, 62, 6), (729, 27, 2542), (730, 110, 2543), (730, 1, 2544), (730, 27, 2545), (731, 110, 2546), (731, 12, 2547), (731, 4, 2548), (731, 5, 1090), (731, 10, 2549), (731, 14, 2550), (731, 13, 2551), (731, 26, 2552), (731, 1, 2553), (731, 90, 2554), (731, 62, 1264), (731, 27, 2555), (732, 110, 1266), (732, 1, 2556), (732, 27, 2557), (733, 110, 2558), (733, 12, 2559), (733, 4, 2560), (733, 5, 2561), (733, 10, 2562), (733, 14, 2563), (733, 13, 2564), (733, 26, 2565), (733, 1, 2566), (733, 90, 2567), (733, 62, 1264), (733, 27, 2568), (734, 110, 1266), (734, 1, 2569), (734, 27, 2570), (735, 110, 2574), (735, 1, 2572), (735, 27, 2573), (735, 14, 2575), (736, 110, 2576), (736, 1, 2577), (736, 27, 2578), (737, 110, 2579), (737, 4, 2580), (737, 5, 310), (737, 10, 2581), (737, 14, 530), (737, 12, 93), (737, 25, 94), (737, 1, 2582), (737, 26, 2583), (737, 90, 2584), (737, 62, 1329), (737, 27, 2585), (738, 110, 1332), (738, 1, 2586), (738, 27, 2587), (739, 110, 2588), (739, 4, 1840), (739, 5, 156), (739, 10, 2589), (739, 14, 2590), (739, 12, 93), (739, 25, 94), (739, 1, 2591), (739, 26, 2592), (739, 90, 2593), (739, 62, 1329), (739, 27, 2594), (740, 110, 1332), (740, 1, 2595), (740, 27, 2596), (741, 110, 2137), (741, 4, 2597), (741, 5, 156), (741, 10, 2598), (741, 14, 2599), (741, 12, 93), (741, 25, 94), (741, 1, 2600), (741, 26, 2601), (741, 90, 2602), (741, 62, 1329), (741, 27, 2603), (742, 110, 1332), (742, 1, 2604), (742, 27, 2605), (743, 110, 2606), (743, 4, 2607), (743, 5, 135), (743, 10, 2608), (743, 14, 2609), (743, 12, 93), (743, 25, 94), (743, 1, 2610), (743, 26, 2611), (743, 90, 2612), (743, 62, 1329), (743, 27, 2613), (744, 110, 1332), (744, 1, 2614), (744, 27, 2615), (745, 110, 2616), (745, 4, 145), (745, 5, 274), (745, 10, 2617), (745, 14, 273), (745, 12, 93), (745, 25, 94), (745, 1, 2618), (745, 26, 2619), (745, 90, 2620), (745, 62, 1329), (745, 27, 2621), (746, 110, 1332), (746, 1, 2622), (746, 27, 2623), (747, 110, 2624), (747, 4, 1670), (747, 5, 310), (747, 10, 2625), (747, 14, 2626), (747, 12, 93), (747, 25, 94), (747, 1, 2627), (747, 26, 2628), (747, 90, 2629), (747, 62, 1329), (747, 27, 2630), (747, 116, 2631), (748, 110, 1332), (748, 1, 2632), (748, 27, 2633), (749, 13, 2634), (749, 12, 2635), (749, 25, 2636), (749, 4, 1969), (749, 5, 1954), (749, 14, 2637), (749, 10, 2638), (749, 26, 2639), (749, 1, 2640), (749, 110, 2641), (749, 62, 1416), (749, 27, 2642), (750, 110, 1321), (751, 1, 2644), (751, 27, 2645), (751, 110, 2646), (754, 13, 289), (754, 12, 286), (754, 25, 1779), (754, 26, 2651), (754, 1, 2652), (754, 110, 322), (754, 62, 1416), (754, 27, 2653), (755, 110, 2654), (756, 110, 2655), (756, 14, 2656), (756, 1, 2657), (756, 22, 2658), (756, 26, 2659), (756, 12, 2660), (756, 90, 2661), (756, 62, 6), (756, 27, 2662), (757, 110, 2663), (757, 1, 2664), (757, 27, 2665), (758, 110, 2666), (758, 4, 155), (758, 5, 310), (758, 10, 2625), (758, 14, 495), (758, 12, 93), (758, 25, 94), (758, 1, 2667), (758, 26, 2668), (758, 90, 2669), (758, 62, 1329), (758, 27, 2670), (759, 110, 1332), (759, 1, 2671), (759, 27, 2672), (760, 110, 2673), (760, 4, 145), (760, 5, 135), (760, 10, 2674), (760, 14, 2675), (760, 12, 93), (760, 25, 94), (760, 1, 2676), (760, 26, 2677), (760, 90, 2678), (760, 62, 1329), (760, 27, 2679), (761, 110, 1332), (761, 1, 2680), (761, 27, 2681), (762, 110, 2682), (762, 4, 1840), (762, 5, 299), (762, 10, 2683), (762, 14, 2390), (762, 12, 93), (762, 25, 94), (762, 1, 2684), (762, 26, 2685), (762, 90, 2686), (762, 62, 1329), (762, 27, 2687), (763, 110, 1332), (763, 1, 2688), (763, 27, 2689), (764, 110, 2690), (764, 4, 2110), (764, 5, 156), (764, 10, 2691), (764, 14, 2692), (764, 12, 93), (764, 25, 94), (764, 1, 2693), (764, 26, 2694), (764, 90, 2695), (764, 62, 1329), (764, 27, 2696), (764, 116, 2697), (765, 110, 1332), (765, 1, 2698), (765, 27, 2699), (766, 110, 2700), (768, 110, 2707), (768, 1, 2708), (768, 27, 2709), (769, 110, 2710), (769, 4, 155), (769, 5, 90), (769, 10, 2711), (769, 14, 2712), (769, 12, 93), (769, 25, 94), (769, 1, 2713), (769, 26, 2714), (769, 90, 2715), (769, 62, 1329), (769, 27, 2716), (770, 110, 1332), (770, 1, 2717), (770, 27, 2718), (771, 110, 2719), (771, 4, 1670), (771, 5, 135), (771, 10, 2720), (771, 14, 2721), (771, 12, 93), (771, 25, 94), (771, 1, 2722), (771, 26, 2723), (771, 90, 2724), (771, 62, 1329), (771, 27, 2725), (771, 116, 2726), (772, 110, 1332), (772, 1, 2727), (772, 27, 2728), (777, 110, 2745), (777, 14, 2746), (777, 1, 2747), (777, 22, 2748), (777, 26, 2749), (777, 12, 2750), (777, 90, 2751), (777, 62, 6), (777, 27, 2752), (777, 116, 2753), (778, 110, 2754), (778, 1, 2755), (778, 27, 2756), (779, 110, 2757), (779, 4, 2758), (779, 5, 135), (779, 10, 2759), (779, 14, 2760), (779, 12, 93), (779, 25, 94), (779, 1, 2761), (779, 26, 2762), (779, 90, 2763), (779, 62, 1329), (779, 27, 2764), (780, 110, 1332), (780, 1, 2765), (780, 27, 2766), (781, 110, 2767), (781, 14, 2768), (781, 1, 2769), (781, 12, 2770), (781, 90, 2771), (781, 62, 6), (781, 27, 2772), (782, 110, 2773), (782, 1, 2774), (782, 27, 2775), (783, 110, 2776), (783, 14, 2777), (783, 1, 2778), (783, 12, 2779), (783, 90, 2780), (783, 62, 6), (783, 27, 2781), (784, 110, 2782), (784, 1, 2783), (784, 27, 2784), (785, 110, 1489), (785, 14, 1490), (785, 1, 1491), (785, 12, 1492), (785, 90, 2785), (785, 62, 6), (785, 27, 2786), (786, 110, 1495), (786, 1, 1496), (786, 27, 2787), (787, 110, 2788), (787, 4, 2789), (787, 5, 156), (787, 10, 2790), (787, 14, 2791), (787, 12, 93), (787, 25, 94), (787, 1, 2792), (787, 26, 2793), (787, 90, 2794), (787, 62, 1329), (787, 27, 2795), (787, 116, 2796), (788, 110, 1332), (788, 1, 2797), (788, 27, 2798), (789, 13, 289), (789, 12, 286), (789, 25, 1779), (789, 26, 2802), (789, 1, 2803), (789, 110, 2804), (789, 62, 1416), (789, 27, 2805), (790, 110, 2806), (790, 1, 2807), (790, 27, 2808), (791, 13, 1407), (791, 12, 1408), (791, 25, 1409), (791, 4, 2809), (791, 5, 1090), (791, 14, 2810), (791, 10, 2811), (791, 26, 2812), (791, 1, 2813), (791, 110, 2814), (791, 62, 1416), (791, 27, 2815), (791, 116, 2816), (792, 110, 2817), (792, 1, 2818), (792, 27, 2819), (793, 13, 1407), (793, 12, 1408), (793, 25, 1409), (793, 4, 2820), (793, 5, 1090), (793, 14, 2821), (793, 10, 2822), (793, 26, 2823), (793, 1, 2824), (793, 110, 2825), (793, 62, 1416), (793, 27, 2826), (794, 110, 2827), (794, 1, 2828), (794, 27, 2829), (795, 110, 2830), (795, 4, 1707), (795, 5, 90), (795, 10, 2831), (795, 14, 2832), (795, 12, 93), (795, 25, 94), (795, 1, 2833), (795, 26, 2834), (795, 90, 2835), (795, 62, 1329), (795, 27, 2836), (796, 110, 1332), (796, 1, 2837), (796, 27, 2838), (797, 110, 2839), (797, 4, 2758), (797, 5, 299), (797, 10, 2840), (797, 14, 2841), (797, 12, 93), (797, 25, 94), (797, 1, 2842), (797, 26, 2843), (797, 90, 2844), (797, 62, 1329), (797, 27, 2845), (798, 110, 1332), (798, 1, 2846), (798, 27, 2847), (799, 13, 1407), (799, 12, 1408), (799, 25, 1409), (799, 4, 2848), (799, 5, 1090), (799, 14, 2849), (799, 10, 2850), (799, 26, 2851), (799, 1, 2852), (799, 110, 2853), (799, 62, 1416), (799, 27, 2854), (800, 110, 2855), (800, 1, 2856), (800, 27, 2857), (801, 13, 1407), (801, 12, 1408), (801, 25, 1409), (801, 4, 2858), (801, 5, 135), (801, 14, 2859), (801, 10, 2860), (801, 26, 2861), (801, 1, 2862), (801, 110, 2863), (801, 62, 1416), (801, 27, 2864), (802, 110, 2865), (802, 1, 2866), (802, 27, 2867), (804, 110, 2874), (804, 1, 2875), (804, 27, 2876), (805, 13, 1407), (805, 12, 1408), (805, 25, 1409), (805, 10, 2879), (805, 26, 2880), (805, 1, 2881), (805, 62, 1416), (805, 27, 2883), (805, 110, 2884), (806, 110, 2885), (806, 1, 2886), (806, 27, 2887), (807, 110, 2888), (807, 4, 1840), (807, 5, 299), (807, 10, 2889), (807, 14, 2390), (807, 12, 93), (807, 25, 94), (807, 26, 2891), (807, 90, 2892), (807, 62, 1329), (807, 27, 2893), (808, 110, 1332), (808, 1, 2894), (808, 27, 2895), (809, 110, 2896), (809, 14, 2897), (809, 1, 2898), (809, 12, 2899), (809, 90, 2900), (809, 62, 6), (809, 27, 2901), (810, 110, 2902), (810, 1, 2903), (810, 27, 2904), (811, 110, 2905), (811, 4, 2396), (811, 5, 156), (811, 10, 2906), (811, 14, 2907), (811, 12, 93), (811, 25, 94), (811, 26, 2909), (811, 90, 2910), (811, 62, 1329), (811, 27, 2911), (811, 116, 2912), (812, 110, 1332), (812, 1, 2913), (812, 27, 2914), (813, 114, 2915), (813, 110, 2916), (813, 14, 2917), (813, 26, 2919), (814, 110, 2920), (5, 110, 23), (5, 27, 22), (5, 4, 310), (5, 14, 24), (5, 10, 25), (5, 25, 26), (6, 110, 59), (5, 1, 60), (15, 13, 85), (15, 12, 86), (15, 25, 122), (15, 5, 124), (15, 14, 284), (15, 10, 125), (15, 26, 126), (15, 1, 127), (15, 62, 1416), (15, 27, 129), (16, 110, 130), (16, 1, 132), (16, 27, 136), (15, 110, 137), (17, 110, 140), (17, 14, 141), (17, 1, 142), (17, 22, 151), (17, 26, 152), (17, 12, 168), (17, 90, 169), (17, 62, 6), (17, 27, 170), (18, 110, 171), (18, 1, 188), (18, 27, 189), (29, 110, 2234), (29, 14, 2235), (29, 1, 2236), (29, 22, 214), (29, 26, 215), (29, 12, 2237), (29, 90, 216), (29, 62, 6), (29, 27, 217), (29, 116, 2240), (30, 110, 2241), (30, 1, 2242), (30, 27, 218), (31, 110, 219), (31, 14, 220), (31, 1, 221), (31, 22, 222), (31, 26, 223), (31, 12, 224), (31, 90, 225), (31, 62, 6), (31, 27, 226), (33, 110, 227), (33, 1, 228), (33, 27, 229), (36, 110, 230), (36, 14, 231), (36, 1, 232), (36, 12, 233), (36, 90, 234), (36, 62, 6), (36, 27, 235), (37, 110, 236), (37, 1, 237), (37, 27, 238), (41, 110, 239), (41, 14, 250), (41, 1, 251), (41, 22, 253), (41, 26, 254), (41, 12, 255), (41, 90, 256), (41, 62, 6), (41, 27, 257), (47, 110, 258), (47, 1, 259), (47, 27, 260), (48, 110, 753), (48, 14, 754), (48, 1, 755), (48, 22, 261), (48, 26, 262), (48, 12, 756), (48, 90, 263), (48, 62, 6), (48, 27, 264), (49, 110, 760), (49, 1, 761), (49, 27, 266), (50, 13, 267), (50, 12, 1372), (50, 4, 268), (50, 5, 274), (50, 14, 270), (50, 10, 271), (50, 26, 279), (50, 1, 280), (50, 110, 304), (50, 62, 1416), (50, 27, 305), (55, 110, 387), (55, 1, 360), (55, 27, 388), (56, 110, 393), (56, 14, 394), (56, 1, 395), (56, 22, 396), (56, 12, 397), (56, 90, 398), (56, 62, 6), (56, 27, 399), (57, 110, 428), (57, 1, 429), (57, 27, 436), (58, 110, 437), (58, 14, 441), (58, 1, 442), (58, 22, 443), (58, 26, 444), (58, 12, 527), (58, 90, 528), (58, 62, 6), (58, 27, 537), (59, 110, 538), (59, 1, 546), (59, 27, 547), (60, 13, 1407), (60, 12, 1408), (60, 25, 1409), (60, 4, 582), (60, 5, 135), (60, 14, 583), (60, 10, 584), (60, 26, 585), (60, 1, 589), (60, 110, 590), (60, 62, 1416), (60, 27, 599), (61, 110, 600), (61, 1, 738), (61, 27, 739), (62, 13, 1407), (62, 12, 1408), (62, 25, 1409), (62, 4, 749), (62, 5, 135), (62, 14, 759), (62, 10, 768), (62, 26, 779), (62, 1, 789), (62, 110, 800), (62, 62, 1416), (62, 27, 810), (62, 116, 820), (63, 110, 831), (65, 110, 841), (65, 14, 846), (65, 1, 860), (65, 12, 893), (65, 90, 895), (65, 62, 6), (65, 27, 896), (70, 110, 905), (70, 1, 910), (70, 27, 911), (80, 110, 912), (80, 1, 913), (80, 27, 914), (81, 110, 915), (81, 4, 2607), (81, 5, 310), (81, 10, 916), (81, 14, 917), (81, 12, 93), (81, 25, 94), (81, 1, 918), (81, 26, 919), (81, 90, 921), (81, 62, 1329), (81, 27, 1082), (82, 110, 1332), (82, 1, 1083), (82, 27, 1101), (90, 13, 289), (90, 12, 286), (90, 25, 1779), (90, 4, 497), (90, 5, 156), (90, 14, 583), (90, 10, 1111), (90, 26, 1121), (90, 1, 1125), (90, 110, 1126), (90, 62, 1416), (90, 27, 1127), (97, 110, 1128), (97, 1, 1129), (97, 27, 1130), (51, 110, 20), (51, 14, 21), (51, 1, 128), (51, 22, 333), (51, 26, 334), (51, 12, 335), (51, 90, 1131), (51, 62, 6), (51, 27, 1132), (99, 110, 1133), (99, 1, 1134), (99, 27, 1135), (100, 110, 1142), (100, 14, 1198), (100, 1, 1199), (100, 12, 1209), (100, 90, 1210), (100, 62, 6), (100, 27, 1219), (100, 116, 1220), (108, 110, 1232), (108, 1, 1233), (108, 27, 1289), (115, 110, 1290), (113, 14, 1299), (113, 110, 1300), (113, 75, 1333), (158, 13, 289), (158, 12, 286), (158, 25, 1779), (158, 10, 1349), (158, 26, 1351), (158, 1, 1352), (158, 110, 1462), (158, 62, 1416), (158, 27, 1353), (159, 110, 1354), (159, 1, 1355), (159, 27, 1356), (164, 110, 1354), (164, 1, 1355), (164, 27, 1357), (178, 110, 1378), (165, 110, 1396), (813, 1, 1953), (807, 1, 1966), (811, 1, 1967), (211, 110, 1971), (211, 14, 1972), (211, 1, 1975), (211, 12, 1986), (211, 90, 1987), (211, 62, 6), (211, 27, 2003), (214, 110, 2004), (214, 1, 2005), (214, 27, 2006), (217, 110, 2007), (217, 14, 2008), (217, 1, 2009), (217, 22, 2011), (217, 26, 2012), (217, 12, 2013), (217, 90, 2030), (217, 62, 6), (217, 27, 2031), (217, 116, 2080), (220, 110, 2081), (220, 1, 2082), (220, 27, 2083), (223, 110, 2084), (223, 14, 2085), (223, 1, 2086), (223, 12, 2087), (223, 90, 2088), (223, 62, 6), (223, 27, 2089), (226, 110, 2138), (226, 1, 2139), (226, 27, 2140), (229, 110, 2141), (229, 14, 2142), (229, 1, 2143), (229, 12, 2144), (229, 90, 2145), (229, 62, 6), (229, 27, 2150), (232, 110, 2164), (232, 1, 2165), (232, 27, 2166), (235, 110, 2167), (235, 14, 2168), (235, 1, 2169), (235, 12, 2170), (235, 90, 2171), (235, 62, 6), (235, 27, 2172), (238, 110, 2173), (238, 1, 2174), (238, 27, 2175), (241, 110, 2176), (241, 12, 1372), (241, 4, 2177), (241, 14, 2197), (241, 10, 2198), (241, 1, 2199), (241, 90, 2225), (241, 62, 1287), (241, 27, 2226), (250, 110, 2229), (262, 110, 2230), (262, 14, 2231), (262, 1, 2232), (262, 12, 2233), (262, 90, 2252), (262, 62, 6), (262, 27, 2253), (262, 116, 2255), (265, 110, 2256), (265, 1, 2257), (265, 27, 2258), (267, 110, 2259), (267, 14, 2326), (267, 1, 2327), (267, 22, 2328), (267, 26, 2329), (267, 12, 2331), (267, 90, 2332), (267, 62, 6), (267, 27, 2333), (268, 110, 2334), (268, 1, 2335), (268, 27, 2336), (52, 110, 361), (52, 14, 1386), (52, 1, 1387), (52, 12, 1493), (52, 90, 1494), (52, 62, 6), (52, 27, 1497), (248, 110, 1566), (248, 1, 1567), (248, 27, 1568), (269, 13, 1770), (269, 12, 1771), (269, 25, 2337), (269, 4, 90), (269, 5, 288), (269, 14, 2356), (269, 10, 2357), (269, 26, 2358), (269, 1, 2359), (269, 110, 2360), (269, 62, 1416), (269, 27, 2361), (271, 110, 2362), (273, 12, 2407), (273, 13, 2408), (273, 1, 2363), (273, 14, 2365), (273, 110, 2366), (273, 15, 2412), (273, 62, 2413), (273, 27, 2367), (273, 116, 2445), (341, 110, 2492), (341, 14, 2571), (341, 1, 2643), (341, 12, 2730), (341, 90, 2731), (341, 62, 6), (341, 27, 2732), (346, 110, 2733), (346, 1, 2734), (346, 27, 2735), (349, 110, 2736), (349, 14, 2882), (349, 1, 2890), (349, 12, 2908), (349, 90, 2921), (349, 62, 6), (349, 27, 2922), (352, 110, 2923), (352, 1, 2924), (352, 27, 2925), (354, 110, 2926), (354, 14, 2927), (354, 1, 2928), (354, 12, 2929), (354, 90, 2930), (354, 62, 6), (354, 27, 2931), (355, 110, 2932), (355, 1, 2933), (355, 27, 2934), (356, 110, 2935), (356, 14, 2882), (356, 1, 2936), (356, 12, 2937), (356, 90, 2938), (356, 62, 6), (356, 27, 2939), (358, 110, 2940), (358, 1, 2941), (358, 27, 2942), (375, 110, 2943), (375, 14, 2882), (375, 1, 2944), (375, 12, 2945), (375, 90, 2946), (375, 62, 6), (375, 27, 2947), (377, 110, 2948), (377, 1, 2949), (377, 27, 2950), (381, 110, 2951), (381, 14, 2952), (381, 1, 2953), (381, 22, 2954), (381, 26, 2955), (381, 12, 2956), (381, 90, 2957), (381, 62, 6), (381, 27, 2958), (381, 116, 2959), (384, 110, 2960), (384, 1, 2961), (384, 27, 2962), (393, 110, 2963), (393, 14, 2882), (393, 1, 2964), (393, 12, 2965), (393, 90, 2966), (393, 62, 6), (393, 27, 2967), (396, 110, 2968), (396, 1, 2969), (396, 27, 2970), (399, 110, 2971), (399, 14, 2972), (399, 1, 2973), (399, 12, 2974), (399, 90, 2975), (399, 62, 6), (399, 27, 2976), (402, 110, 2977), (402, 1, 2978), (402, 27, 2979), (413, 110, 2980), (413, 4, 2580), (413, 5, 156), (413, 10, 2981), (413, 14, 2982), (413, 12, 93), (413, 25, 94), (413, 1, 2983), (413, 26, 2984), (413, 90, 2985), (413, 62, 1329), (413, 27, 2986), (416, 110, 1332), (416, 1, 2987), (416, 27, 2988), (423, 110, 2989), (423, 14, 2990), (423, 1, 2991), (423, 12, 2992), (423, 90, 2993), (423, 62, 6), (423, 27, 2994), (427, 110, 2995), (427, 1, 2996), (427, 27, 2997), (428, 110, 2998), (428, 4, 382), (428, 5, 135), (428, 10, 2999), (428, 14, 3000), (428, 12, 93), (428, 25, 94), (428, 1, 3001), (428, 26, 3002), (428, 90, 3003), (428, 62, 1329), (428, 27, 3004), (434, 110, 1332), (434, 1, 3005), (434, 27, 3006), (439, 110, 3012), (439, 1, 3009), (439, 27, 3013), (463, 110, 3007), (463, 14, 3014), (463, 1, 3015), (463, 12, 3016), (463, 90, 3010), (463, 62, 6), (463, 27, 3017), (464, 110, 3018), (464, 1, 3019), (464, 27, 3020), (244, 110, 2227), (244, 4, 1089), (244, 5, 135), (244, 10, 1841), (244, 14, 2228), (244, 12, 93), (244, 25, 94), (244, 1, 3021), (244, 26, 3022), (244, 90, 3023), (244, 62, 1329), (244, 27, 3024), (244, 116, 3025), (467, 110, 1332), (467, 1, 3026), (467, 27, 3027), (468, 110, 3028), (468, 4, 1294), (468, 5, 90), (468, 10, 1671), (468, 14, 3029), (468, 12, 93), (468, 25, 94), (468, 1, 3030), (468, 26, 3031), (468, 90, 3032), (468, 62, 1329), (468, 27, 3033), (482, 110, 1332), (482, 1, 3034), (482, 27, 3035), (527, 110, 3036), (527, 14, 3037), (527, 1, 3038), (527, 12, 3039), (527, 90, 3040), (527, 62, 6), (527, 27, 3041), (528, 110, 3042), (528, 1, 3043), (528, 27, 3044), (565, 110, 3045), (565, 14, 3046), (565, 1, 3047), (565, 12, 3048), (565, 90, 3049), (565, 62, 6), (565, 27, 3050), (566, 110, 3051), (566, 1, 3052), (566, 27, 3053), (571, 110, 3054), (571, 14, 3055), (571, 1, 3056), (571, 12, 3057), (571, 90, 3058), (571, 62, 6), (571, 27, 3059), (574, 110, 3060), (574, 1, 3061), (574, 27, 3062), (575, 110, 3063), (575, 14, 3064), (575, 1, 3065), (575, 12, 3066), (575, 90, 3067), (575, 62, 6), (575, 27, 3068), (579, 110, 3069), (579, 1, 3070), (579, 27, 3071), (580, 110, 3072), (580, 14, 3073), (580, 1, 3074), (580, 12, 3075), (580, 90, 3076), (580, 62, 6), (580, 27, 3077), (585, 110, 3078), (585, 1, 3079), (585, 27, 3080), (586, 13, 289), (586, 12, 286), (586, 25, 1779), (586, 4, 287), (586, 5, 1090), (586, 14, 3081), (586, 10, 3082), (586, 26, 3083), (586, 1, 3084), (586, 110, 3085), (586, 62, 1416), (586, 27, 3086), (598, 110, 3087), (599, 110, 3088), (599, 4, 382), (599, 5, 135), (599, 10, 3089), (599, 14, 3090), (599, 12, 93), (599, 25, 94), (599, 1, 3091), (599, 26, 3092), (599, 90, 3093), (599, 62, 1329), (599, 27, 3094), (611, 110, 1332), (611, 1, 3095), (611, 27, 3096), (619, 110, 3109), (619, 4, 163), (619, 5, 156), (619, 10, 3110), (619, 14, 3111), (619, 12, 93), (619, 25, 94), (619, 1, 3112), (619, 26, 3113), (619, 90, 3114), (619, 62, 1329), (619, 27, 3115), (620, 110, 1332), (620, 1, 3116), (620, 27, 3117), (612, 110, 3118), (612, 14, 3119), (612, 1, 3120), (612, 12, 3121), (612, 90, 3122), (612, 62, 6), (612, 27, 3097), (614, 110, 3124), (614, 1, 3125), (614, 27, 3098), (646, 110, 3102), (646, 4, 155), (646, 5, 3103), (646, 10, 3104), (646, 14, 3105), (646, 12, 507), (646, 25, 508), (646, 1, 3106), (646, 26, 3107), (646, 90, 3108), (646, 62, 1329), (646, 27, 3127), (646, 116, 3128), (651, 110, 1332), (651, 1, 3129), (651, 27, 3130), (653, 110, 3131), (653, 12, 870), (653, 14, 506), (653, 5, 90), (653, 4, 299), (653, 1, 3132), (670, 110, 3133), (671, 110, 3134), (671, 4, 3135), (671, 5, 90), (671, 10, 3136), (671, 14, 3137), (671, 12, 93), (671, 25, 94), (671, 1, 3138), (671, 26, 3139), (671, 90, 3140), (671, 62, 1329), (671, 27, 3141), (672, 110, 1332), (672, 1, 3142), (672, 27, 3143), (673, 110, 3144), (673, 14, 3147), (673, 12, 507), (673, 25, 508), (673, 1, 3148), (673, 26, 3149), (673, 90, 3150), (673, 62, 1329), (673, 27, 3151), (674, 110, 1332), (674, 1, 3152), (674, 27, 3153), (675, 13, 289), (675, 12, 286), (675, 25, 1779), (675, 4, 2799), (675, 5, 1204), (675, 14, 3154), (675, 10, 3155), (675, 26, 3156), (675, 1, 3157), (675, 110, 3158), (675, 62, 1416), (675, 27, 3159), (675, 116, 3160), (677, 110, 2308), (677, 1, 2309), (677, 27, 3162), (678, 110, 3163), (678, 1, 3164), (678, 27, 3165), (686, 110, 2543), (686, 1, 2544), (686, 27, 3167), (704, 110, 3168), (704, 14, 3169), (704, 12, 3170), (704, 10, 3171), (704, 4, 3172), (704, 5, 3173), (704, 1, 3174), (704, 90, 3175), (704, 26, 3176), (704, 62, 1164), (704, 27, 3177), (773, 110, 3180), (717, 110, 3178), (717, 14, 3179), (717, 1, 3181), (717, 12, 3182), (717, 90, 3183), (717, 62, 6), (717, 27, 3184), (717, 116, 3185), (774, 110, 3186), (774, 1, 3187), (774, 27, 3188), (815, 13, 1944), (815, 12, 1074), (815, 25, 1075), (815, 4, 1969), (815, 5, 872), (815, 14, 3189), (815, 10, 3190), (815, 26, 3191), (815, 1, 3192), (815, 110, 3193), (815, 62, 1416), (815, 27, 3194), (816, 110, 3195), (816, 14, 3196), (816, 1, 3197), (816, 12, 3198), (816, 90, 3199), (816, 62, 6), (816, 27, 3200), (817, 110, 3201), (817, 1, 3202), (817, 27, 3203), (818, 110, 3204), (818, 4, 155), (818, 5, 90), (818, 10, 3205), (818, 14, 3206), (818, 12, 93), (818, 25, 94), (818, 1, 3207), (818, 26, 3208), (818, 90, 3209), (818, 62, 1329), (818, 27, 3210), (818, 116, 3211), (819, 110, 1332), (819, 1, 3212), (819, 27, 3213), (820, 110, 3214), (820, 14, 3073), (820, 1, 3215), (820, 12, 3216), (820, 90, 3217), (820, 62, 6), (820, 27, 3218), (821, 110, 3219), (821, 1, 3220), (821, 27, 3221), (822, 110, 3222), (822, 4, 2789), (822, 5, 310), (822, 10, 3223), (822, 14, 3224), (822, 12, 93), (822, 25, 94), (822, 1, 3225), (822, 26, 3226), (822, 90, 3227), (822, 62, 1329), (822, 27, 3228), (822, 116, 3229), (823, 110, 1332), (823, 1, 3230), (823, 27, 3231), (825, 110, 3233), (825, 14, 3234), (825, 1, 3235), (825, 12, 3236), (825, 90, 3237), (825, 62, 6), (825, 27, 3238), (826, 110, 3239), (826, 1, 3240), (826, 27, 3241), (827, 110, 3242), (827, 14, 3243), (827, 1, 3244), (827, 22, 3245), (827, 12, 3246), (827, 90, 3247), (827, 62, 6), (827, 27, 3248), (828, 110, 3249), (828, 1, 3250), (828, 27, 3251), (829, 110, 3252), (829, 14, 3253), (829, 1, 3254), (829, 12, 3255), (829, 90, 3256), (829, 62, 6), (829, 27, 3257), (830, 110, 3258), (830, 1, 3259), (830, 27, 3260), (831, 110, 3261), (831, 14, 3262), (831, 1, 3263), (831, 12, 3264), (831, 90, 3265), (831, 62, 6), (831, 27, 3266), (831, 116, 3267), (832, 110, 3268), (832, 1, 3269), (832, 27, 3270), (833, 110, 3271), (833, 14, 3272), (833, 1, 3273), (833, 12, 3274), (833, 90, 3275), (833, 62, 6), (833, 27, 3276), (834, 110, 3277), (834, 1, 3278), (834, 27, 3279), (835, 110, 3280), (835, 14, 3262), (835, 1, 3281), (835, 12, 3282), (835, 90, 3283), (835, 62, 6), (835, 27, 3284), (835, 116, 3285), (836, 110, 3286), (836, 1, 3287), (836, 27, 3288), (28, 110, 211), (28, 14, 212), (28, 1, 213), (28, 12, 3099), (28, 90, 3100), (28, 62, 6), (28, 27, 3101), (621, 110, 3123), (621, 1, 3126), (621, 27, 3289), (628, 110, 3290), (628, 14, 3291), (628, 1, 3292), (628, 22, 3293), (628, 26, 3294), (628, 12, 3295), (628, 90, 3296), (628, 62, 6), (628, 27, 3297), (645, 110, 3298), (645, 1, 3299), (645, 27, 3300), (837, 110, 3301), (837, 14, 3302), (837, 1, 3303), (837, 22, 3304), (837, 26, 3305), (837, 12, 3306), (837, 90, 3307), (837, 62, 6), (837, 27, 3308), (838, 110, 3309), (838, 1, 3310), (838, 27, 3311), (839, 110, 3312), (839, 14, 3313), (839, 1, 3314), (839, 22, 3315), (839, 26, 3316), (839, 12, 3317), (839, 90, 3318), (839, 62, 6), (839, 27, 3319), (840, 110, 3320), (840, 1, 3321), (840, 27, 3322), (841, 110, 3323), (841, 14, 3324), (841, 1, 3325), (841, 12, 3326), (841, 90, 3327), (841, 62, 6), (841, 27, 3328), (842, 110, 3329), (842, 1, 3330), (842, 27, 3331), (843, 110, 3332), (843, 14, 3324), (843, 1, 3333), (843, 12, 3334), (843, 90, 3335), (843, 62, 6), (843, 27, 3336), (844, 110, 3337), (844, 1, 3338), (844, 27, 3339), (846, 110, 2164), (846, 1, 2165), (846, 27, 3341), (824, 110, 3232), (824, 14, 3344), (824, 12, 93), (824, 25, 94), (824, 1, 3345), (824, 26, 3346), (824, 90, 3347), (824, 62, 1329), (824, 27, 3348), (847, 110, 1332), (847, 1, 3349), (847, 27, 3350), (848, 110, 3351), (848, 4, 3352), (848, 5, 299), (848, 10, 3353), (848, 14, 3354), (848, 12, 93), (848, 25, 94), (848, 1, 3355), (848, 26, 3356), (848, 90, 3357), (848, 62, 1329), (848, 27, 3358), (849, 110, 1332), (849, 1, 3359), (849, 27, 3360), (850, 110, 3361), (850, 14, 3362), (850, 1, 3363), (850, 12, 3364), (850, 90, 3365), (850, 62, 6), (850, 27, 3366), (851, 110, 3367), (851, 1, 3368), (851, 27, 3369), (852, 110, 3370), (852, 4, 3371), (852, 5, 90), (852, 10, 3372), (852, 14, 3373), (852, 12, 93), (852, 25, 94), (852, 1, 3374), (852, 26, 3375), (852, 90, 3376), (852, 62, 1329), (852, 27, 3377), (853, 110, 1332), (853, 1, 3378), (853, 27, 3379), (854, 110, 3380), (854, 14, 3362), (854, 1, 3381), (854, 12, 3382), (854, 90, 3383), (854, 62, 6), (854, 27, 3384), (855, 110, 3385), (855, 1, 3386), (855, 27, 3387), (857, 110, 3286), (857, 1, 3287), (857, 27, 3389), (858, 110, 3390), (858, 14, 3253), (858, 1, 3391), (858, 12, 3392), (858, 90, 3393), (858, 62, 6), (858, 27, 3394), (858, 116, 3395), (859, 110, 3396), (859, 1, 3397), (859, 27, 3398), (860, 110, 3399), (860, 14, 3400), (860, 1, 3401), (860, 90, 3402), (860, 62, 1287), (860, 27, 3403), (860, 116, 3404), (861, 110, 3405), (861, 1, 3401), (861, 27, 3406), (862, 110, 3407), (862, 14, 3408), (862, 1, 3409), (862, 12, 3410), (862, 90, 3411), (862, 62, 6), (862, 27, 3412), (862, 116, 3413), (863, 110, 3414), (863, 1, 3415), (863, 27, 3416), (864, 110, 3417), (864, 14, 3418), (864, 1, 3419), (864, 22, 3420), (864, 26, 3421), (864, 12, 3422), (864, 90, 3423), (864, 62, 6), (864, 27, 3424), (865, 110, 3425), (865, 1, 3426), (865, 27, 3427), (866, 110, 3428), (866, 14, 3429), (866, 1, 3430), (866, 12, 3431), (866, 90, 3432), (866, 62, 6), (866, 27, 3433), (867, 110, 3434), (867, 1, 3435), (867, 27, 3436), (868, 12, 3437), (868, 25, 3438), (868, 4, 3439), (868, 5, 3440), (868, 13, 3441), (868, 14, 3442), (868, 10, 3443), (868, 26, 3444), (868, 1, 3445), (868, 110, 3446), (868, 62, 1416), (868, 27, 3447), (869, 110, 3448), (870, 12, 3449), (870, 25, 3450), (870, 4, 1954), (870, 5, 1077), (870, 13, 3451), (870, 14, 3452), (870, 10, 3453), (870, 26, 3454), (870, 1, 3455), (870, 110, 3456), (870, 62, 1416), (870, 27, 3457), (871, 110, 3458), (872, 12, 3459), (872, 25, 3460), (872, 4, 1077), (872, 5, 1954), (872, 13, 3461), (872, 14, 3462), (872, 10, 3463), (872, 26, 3464), (872, 1, 3465), (872, 110, 3466), (872, 62, 1416), (872, 27, 3467), (873, 110, 3468), (874, 110, 3469), (874, 14, 3408), (874, 1, 3470), (874, 12, 3471), (874, 90, 3472), (874, 62, 6), (874, 27, 3473), (875, 110, 3474), (875, 1, 3475), (875, 27, 3476), (876, 110, 3477), (876, 4, 145), (876, 5, 274), (876, 10, 3478), (876, 14, 273), (876, 12, 93), (876, 25, 94), (876, 1, 3479), (876, 26, 3480), (876, 90, 3481), (876, 62, 1329), (876, 27, 3482), (877, 110, 1332), (877, 1, 3483), (877, 27, 3484), (878, 110, 3485), (878, 14, 3486), (878, 1, 3487), (878, 12, 3488), (878, 90, 3489), (878, 62, 6), (878, 27, 3490), (879, 110, 3491), (879, 1, 3492), (879, 27, 3493), (880, 110, 3494), (880, 4, 2607), (880, 5, 299), (880, 10, 3495), (880, 14, 3496), (880, 12, 93), (880, 25, 94), (880, 1, 3497), (880, 26, 3498), (880, 90, 3499), (880, 62, 1329), (880, 27, 3500), (881, 110, 1332), (881, 1, 3501), (881, 27, 3502), (882, 12, 1771), (882, 25, 2337), (882, 4, 872), (882, 5, 310), (882, 13, 1770), (882, 14, 3503), (882, 10, 3504), (882, 26, 3505), (882, 1, 3506), (882, 110, 3507), (882, 62, 1416), (882, 27, 3508), (883, 110, 3509), (884, 110, 3510), (885, 110, 3511), (885, 14, 3512), (886, 12, 1074), (886, 25, 1075), (886, 4, 3513), (886, 5, 872), (886, 13, 1944), (886, 14, 3514), (886, 10, 3515), (886, 26, 3516), (886, 1, 3517), (886, 110, 3518), (886, 62, 1416), (886, 27, 3519), (887, 110, 3520), (888, 110, 3521), (888, 14, 3522), (888, 1, 3523), (888, 12, 3524), (888, 90, 3525), (888, 62, 6), (888, 27, 3526), (888, 116, 3527), (889, 110, 3528), (889, 1, 3529), (889, 27, 3530), (890, 110, 3531), (890, 14, 3532), (890, 1, 3533), (890, 12, 3534), (890, 90, 3535), (890, 62, 6), (890, 27, 3536), (891, 110, 3537), (891, 1, 3538), (891, 27, 3539), (892, 110, 3540), (892, 14, 3522), (892, 1, 3541), (892, 12, 3542), (892, 90, 3543), (892, 62, 6), (892, 27, 3544), (892, 116, 3545), (893, 110, 3546), (893, 1, 3547), (893, 27, 3548), (895, 110, 3549), (894, 110, 3550), (894, 1, 3551), (894, 27, 3553), (896, 110, 3554), (896, 14, 3532), (896, 1, 3555), (896, 12, 3556), (896, 90, 3557), (896, 62, 6), (896, 27, 3558), (897, 110, 3559), (897, 1, 3560), (897, 27, 3561), (898, 110, 3562), (898, 14, 3563), (898, 1, 3564), (898, 12, 3565), (898, 90, 3566), (898, 62, 6), (898, 27, 3567), (898, 116, 3568), (899, 110, 3569), (899, 1, 3570), (899, 27, 3571), (900, 110, 3572), (900, 14, 3573), (900, 1, 3574), (900, 12, 3575), (900, 90, 3576), (900, 62, 6), (900, 27, 3577), (900, 116, 3578), (901, 110, 3579), (901, 1, 3580), (901, 27, 3581), (902, 110, 3582), (902, 14, 3583), (902, 1, 3584), (902, 12, 3585), (902, 90, 3586), (902, 62, 6), (902, 27, 3587), (903, 110, 3588), (903, 1, 3589), (903, 27, 3590), (904, 110, 3591), (904, 14, 3583), (904, 1, 3592), (904, 12, 3593), (904, 90, 3594), (904, 62, 6), (904, 27, 3595), (905, 110, 3596), (905, 1, 3597), (905, 27, 3598), (906, 110, 3599), (906, 4, 3600), (906, 5, 497), (906, 10, 3601), (906, 14, 3602), (906, 12, 507), (906, 25, 508), (906, 1, 3603), (906, 26, 3604), (906, 90, 3605), (906, 62, 1329), (906, 27, 3606), (907, 110, 1332), (907, 1, 3607), (907, 27, 3608), (908, 110, 3609), (908, 4, 2607), (908, 5, 90), (908, 10, 1381), (908, 14, 3610), (908, 12, 93), (908, 25, 94), (908, 1, 3611), (908, 26, 3612), (908, 90, 3613), (908, 62, 1329), (908, 27, 3614), (909, 110, 1332), (909, 1, 3615), (909, 27, 3616), (910, 12, 286), (910, 25, 1779), (910, 4, 3617), (910, 5, 2245), (910, 13, 289), (910, 14, 3618), (910, 10, 3619), (910, 26, 3620), (910, 1, 3621), (910, 110, 2729), (910, 62, 1416), (910, 27, 3622), (911, 110, 3623), (913, 12, 2635), (913, 25, 2636), (913, 4, 288), (913, 5, 135), (913, 13, 2634), (913, 14, 3624), (913, 10, 3625), (913, 26, 3626), (913, 1, 3631), (913, 110, 3628), (913, 62, 1416), (913, 27, 3632), (913, 116, 3630), (914, 110, 1321), (915, 110, 2701), (915, 14, 2702), (915, 1, 2703), (915, 22, 3633), (915, 26, 3634), (915, 12, 2704), (915, 90, 2705), (915, 62, 6), (915, 27, 3635), (916, 110, 2707), (916, 1, 2708), (916, 27, 3636), (917, 110, 3637), (917, 14, 3638), (917, 1, 3639), (917, 12, 3640), (917, 90, 3641), (917, 62, 6), (917, 27, 3642), (917, 116, 3643), (918, 110, 3644), (918, 1, 3645), (918, 27, 3646), (919, 110, 3647), (919, 14, 3648), (919, 1, 3649), (919, 12, 3650), (919, 90, 3651), (919, 62, 6), (919, 27, 3652), (919, 116, 3653), (920, 110, 3654), (920, 1, 3655), (920, 27, 3656), (921, 110, 3657), (921, 14, 3658), (921, 1, 3659), (921, 12, 3660), (921, 90, 3661), (921, 62, 6), (921, 27, 3662), (921, 116, 3663), (922, 110, 3664), (922, 1, 3665), (922, 27, 3666), (923, 12, 286), (923, 25, 1779), (923, 4, 2799), (923, 5, 299), (923, 13, 289), (923, 14, 3154), (923, 10, 3667), (923, 26, 3668), (923, 1, 3669), (923, 110, 3670), (923, 62, 1416), (923, 27, 3671), (924, 110, 3672), (925, 110, 3673), (925, 14, 3674), (925, 1, 3675), (925, 12, 3676), (925, 90, 3677), (925, 62, 6), (925, 27, 3678), (926, 110, 3679), (926, 1, 3680), (926, 27, 3681), (927, 110, 3682), (927, 14, 3683), (927, 1, 3684), (927, 12, 3685), (927, 90, 3686), (927, 62, 6), (927, 27, 3687), (928, 110, 3688), (928, 1, 3689), (928, 27, 3690), (929, 110, 1861), (929, 12, 93), (929, 25, 94), (929, 4, 2110), (929, 5, 90), (929, 10, 3691), (929, 14, 3692), (929, 1, 3693), (929, 26, 3694), (929, 90, 3695), (929, 62, 1329), (929, 27, 3696), (930, 110, 1332), (930, 1, 3697), (930, 27, 3698), (931, 110, 3699), (931, 12, 507), (931, 25, 508), (931, 4, 1422), (931, 5, 3103), (931, 10, 3700), (931, 14, 3701), (931, 1, 3702), (931, 26, 3703), (931, 90, 3704), (931, 62, 1329), (931, 27, 3705), (932, 110, 1332), (932, 1, 3706), (932, 27, 3707), (933, 110, 3708), (933, 12, 507), (933, 25, 508), (933, 4, 374), (933, 5, 579), (933, 10, 3709), (933, 14, 3710), (933, 1, 3711), (933, 26, 3712), (933, 90, 3713), (933, 62, 1329), (933, 27, 3714), (934, 110, 1332), (934, 1, 3715), (934, 27, 3716), (15, 4, 310), (935, 110, 3717), (935, 14, 3718), (935, 1, 3719), (935, 12, 3720), (935, 90, 3721), (935, 62, 6), (935, 27, 3722), (935, 116, 3723), (936, 110, 3724), (936, 1, 3725), (936, 27, 3726), (937, 110, 3727), (937, 12, 93), (937, 25, 94), (937, 14, 3729), (937, 1, 3730), (937, 26, 3731), (937, 90, 3732), (937, 62, 1329), (937, 27, 3733), (938, 110, 1332), (938, 1, 3734), (938, 27, 3735), (939, 110, 3736), (939, 12, 93), (939, 25, 94), (939, 4, 382), (939, 5, 274), (939, 10, 3737), (939, 14, 3738), (939, 1, 3739), (939, 26, 3740), (939, 90, 3741), (939, 62, 1329), (939, 27, 3742), (939, 116, 3743), (940, 110, 1332), (940, 1, 3744), (940, 27, 3745), (941, 1, 3746), (941, 26, 3747), (941, 4, 579), (941, 5, 1090), (941, 12, 3748), (941, 13, 3749), (941, 110, 3750), (941, 87, 3751), (941, 14, 3752), (941, 10, 3753), (941, 90, 3754), (941, 62, 3755), (941, 27, 3756), (943, 110, 3760), (548, 110, 1863), (548, 1, 1864), (548, 27, 1865), (813, 84, 1513), (813, 7, 1507), (813, 62, 1416), (813, 10, 1952), (789, 90, 1484), (789, 4, 2799), (789, 5, 89), (789, 10, 2801), (789, 14, 1866), (365, 12, 1313), (365, 26, 1315), (365, 1, 1314), (365, 62, 1316), (365, 14, 1184), (718, 4, 156), (718, 5, 135), (754, 90, 326), (754, 4, 287), (754, 5, 891), (754, 10, 2650), (754, 14, 1867), (535, 4, 532), (535, 5, 288), (535, 10, 1803), (706, 4, 1339), (706, 5, 310), (706, 10, 1340), (158, 4, 2799), (158, 5, 299), (158, 14, 3154), (805, 4, 2877), (805, 5, 135), (805, 14, 1868), (492, 4, 1609), (492, 5, 1090), (673, 4, 3145), (673, 5, 579), (673, 10, 3146), (652, 110, 3510), (724, 110, 1869), (724, 1, 1870), (724, 27, 1871), (752, 12, 2507), (752, 4, 2799), (752, 13, 2508), (752, 14, 2509), (752, 10, 2510), (752, 26, 2511), (752, 1, 2512), (752, 110, 2513), (752, 62, 1416), (752, 27, 2514), (753, 110, 2515), (775, 110, 2647), (775, 14, 2648), (775, 1, 2737), (775, 12, 2738), (775, 90, 2739), (775, 62, 6), (775, 27, 2740), (776, 110, 2741), (776, 1, 2742), (776, 27, 2743), (912, 110, 2744), (912, 14, 3552), (912, 1, 3627), (912, 12, 3629), (912, 90, 3757), (912, 62, 6), (912, 27, 3758), (942, 110, 3759), (942, 1, 3761), (942, 27, 3762), (945, 110, 3764), (945, 12, 870), (945, 14, 2575), (945, 5, 135), (945, 4, 135), (945, 1, 3765), (946, 110, 3766), (946, 1, 3767), (946, 27, 3768), (949, 110, 3118), (949, 12, 93), (949, 25, 94), (949, 10, 3775), (949, 14, 3776), (949, 1, 3777), (949, 26, 3778), (949, 90, 3779), (949, 62, 1329), (949, 27, 3780), (951, 110, 3783), (952, 110, 3784), (952, 14, 3785), (952, 1, 3786), (952, 12, 3787), (952, 90, 3788), (952, 62, 6), (952, 27, 3789), (953, 110, 3790), (953, 1, 3791), (953, 27, 3792), (954, 110, 3793), (954, 14, 3794), (954, 1, 3795), (954, 12, 3796), (954, 90, 3797), (954, 62, 6), (954, 27, 3798), (955, 110, 3799), (955, 1, 3800), (955, 27, 3801), (956, 110, 3802), (956, 14, 3803), (956, 1, 3804), (956, 12, 3805), (956, 90, 3806), (956, 62, 6), (956, 27, 3807), (957, 110, 3808), (957, 1, 3809), (957, 27, 3810), (958, 110, 3811), (958, 14, 3803), (958, 1, 3812), (958, 12, 3813), (958, 90, 3814), (958, 62, 6), (958, 27, 3815), (959, 110, 3816), (959, 1, 3817), (959, 27, 3818), (960, 12, 93), (960, 4, 3774), (960, 13, 3819), (960, 14, 3820), (960, 26, 3821), (960, 1, 3822), (960, 110, 3823), (960, 62, 1416), (960, 27, 3824), (960, 116, 3825), (962, 110, 3829), (963, 110, 3830), (963, 14, 3831), (963, 1, 3832), (963, 12, 3833), (963, 90, 3834), (963, 62, 6), (963, 27, 3835), (964, 110, 3836), (964, 1, 3837), (964, 27, 3838), (965, 110, 3839), (965, 14, 3840), (965, 1, 3841), (965, 12, 3842), (965, 90, 3843), (965, 62, 6), (965, 27, 3844), (966, 110, 3845), (966, 1, 3846), (966, 27, 3847), (967, 110, 3848), (967, 14, 3849), (967, 1, 3850), (967, 22, 3851), (967, 26, 3852), (967, 12, 3853), (967, 90, 3854), (967, 62, 6), (967, 27, 3855), (968, 110, 3856), (968, 1, 3857), (968, 27, 3858), (969, 110, 3859), (969, 14, 3860), (969, 1, 3861), (969, 12, 3862), (969, 90, 3863), (969, 62, 6), (969, 27, 3864), (970, 110, 3865), (970, 1, 3866), (970, 27, 3867), (971, 110, 3868), (971, 12, 93), (971, 25, 94), (971, 4, 1339), (971, 5, 156), (971, 10, 3869), (971, 14, 3870), (971, 1, 3871), (971, 26, 3872), (971, 90, 3873), (971, 62, 1329), (971, 27, 3874), (972, 110, 1332), (972, 1, 3875), (972, 27, 3876), (973, 110, 1498), (973, 12, 93), (973, 25, 94), (973, 14, 1399), (973, 1, 1500), (973, 26, 1501), (973, 90, 1502), (973, 62, 1329), (973, 27, 3877), (974, 110, 1332), (974, 1, 1504), (974, 27, 3878), (975, 110, 3879), (975, 14, 3880), (975, 1, 3881), (975, 12, 3882), (975, 90, 3883), (975, 62, 6), (975, 27, 3884), (976, 110, 3885), (976, 1, 3886), (976, 27, 3887), (978, 12, 3896), (978, 4, 2368), (978, 13, 3897), (978, 14, 3898), (978, 10, 3891), (978, 26, 3899), (978, 1, 3900), (978, 110, 3894), (978, 62, 1416), (978, 27, 3895), (979, 110, 3901), (980, 1, 3902), (980, 110, 3903), (980, 12, 3904), (980, 14, 3905), (980, 4, 1954), (980, 10, 3906), (981, 12, 286), (981, 13, 3907), (981, 14, 3908), (981, 10, 3909), (981, 26, 3910), (981, 1, 3911), (981, 110, 3912), (981, 62, 3913), (981, 27, 3914), (983, 110, 3917), (984, 110, 3918), (984, 14, 3919), (984, 1, 3920), (984, 12, 3921), (984, 90, 3922), (984, 62, 6), (984, 27, 3923), (985, 110, 3924), (985, 1, 3925), (985, 27, 3926), (986, 110, 3927), (986, 12, 93), (986, 25, 94), (986, 4, 134), (986, 5, 310), (986, 10, 3928), (986, 14, 3929), (986, 1, 3930), (986, 26, 3931), (986, 90, 3932), (986, 62, 1329), (986, 27, 3933), (987, 110, 1332), (987, 1, 3934), (987, 27, 3935), (723, 110, 3511), (723, 14, 3512), (24, 110, 107), (24, 14, 108), (24, 1, 123), (24, 12, 323), (24, 90, 324), (24, 62, 6), (24, 27, 325), (77, 110, 327), (77, 1, 533), (77, 27, 534), (179, 110, 758), (179, 12, 455), (179, 25, 456), (179, 4, 2597), (179, 5, 274), (179, 10, 845), (179, 14, 854), (179, 1, 855), (179, 26, 856), (179, 90, 857), (179, 62, 1329), (179, 27, 858), (216, 110, 1332), (216, 1, 859), (216, 27, 952), (243, 12, 1317), (243, 4, 452), (243, 13, 1334), (243, 14, 2575), (243, 10, 1794), (243, 26, 1345), (243, 1, 1463), (243, 110, 1464), (243, 62, 1416), (243, 27, 1465), (249, 110, 1466), (288, 12, 286), (288, 4, 374), (288, 13, 3907), (288, 14, 1467), (288, 10, 1480), (288, 26, 1481), (288, 1, 1482), (288, 110, 1483), (288, 62, 3913), (288, 27, 1485), (420, 12, 286), (420, 4, 3103), (420, 13, 3907), (420, 14, 1509), (420, 10, 1510), (420, 26, 1511), (420, 1, 1599), (420, 110, 1600), (420, 62, 3913), (420, 27, 1601), (461, 12, 286), (461, 4, 374), (461, 13, 3907), (461, 14, 1965), (461, 10, 2130), (461, 26, 2238), (461, 1, 2239), (461, 110, 2269), (461, 62, 3913), (461, 27, 2270), (608, 110, 2870), (608, 31, 2871), (608, 7, 2872), (608, 14, 3905), (608, 62, 2873), (608, 1, 2878), (647, 12, 286), (647, 4, 287), (647, 13, 3907), (647, 14, 2918), (647, 10, 3008), (647, 26, 3011), (647, 1, 3161), (647, 62, 1416), (647, 27, 3340), (647, 110, 3388), (658, 110, 3915), (658, 1, 3916), (658, 27, 3936), (676, 12, 286), (676, 4, 3617), (676, 13, 3907), (676, 14, 3272), (676, 10, 3937), (676, 26, 3938), (676, 1, 3939), (676, 110, 3940), (676, 62, 3913), (676, 27, 3941), (684, 110, 294), (684, 1, 3942), (684, 27, 3943), (376, 110, 1506), (376, 14, 1508), (376, 1, 1602), (376, 12, 1603), (376, 90, 1605), (376, 62, 6), (376, 27, 1862), (425, 110, 2271), (425, 1, 2649), (425, 27, 2868), (457, 110, 2869), (457, 14, 1508), (457, 1, 3944), (457, 12, 3945), (457, 90, 3946), (457, 62, 6), (457, 27, 3947), (469, 110, 3948), (469, 1, 3949), (469, 27, 3950), (547, 110, 3951), (547, 12, 93), (547, 25, 94), (547, 10, 3952), (547, 14, 3953), (547, 1, 3954), (547, 26, 3955), (547, 90, 3956), (547, 62, 1329), (547, 27, 3957), (719, 110, 1332), (719, 1, 3958), (719, 27, 3959), (767, 110, 3960), (767, 14, 3961), (767, 1, 3962), (767, 12, 3963), (767, 90, 3964), (767, 62, 6), (767, 27, 3965), (803, 110, 3966), (803, 1, 3967), (803, 27, 3968), (845, 12, 286), (845, 4, 2799), (845, 13, 3907), (845, 14, 3969), (845, 10, 3970), (845, 26, 3971), (845, 1, 3972), (845, 110, 3973), (845, 62, 3913), (845, 27, 3974), (845, 116, 3975), (856, 110, 294), (856, 1, 3976), (856, 27, 3977), (989, 110, 3984), (989, 12, 870), (989, 14, 3985), (989, 5, 1954), (989, 4, 310), (989, 1, 3986), (990, 110, 3987), (990, 1, 3988), (990, 27, 3989), (991, 110, 3978), (991, 12, 870), (991, 14, 871), (991, 5, 310), (991, 4, 872), (991, 1, 3990), (992, 110, 3981), (992, 1, 3982), (992, 27, 3991), (993, 110, 3992), (993, 14, 3993), (993, 1, 3994), (993, 12, 3995), (993, 90, 3996), (993, 62, 6), (993, 27, 3997), (994, 110, 3998), (994, 1, 3999), (994, 27, 4000), (944, 110, 3166), (944, 14, 3763), (944, 1, 3769), (944, 12, 3770), (944, 90, 3771), (944, 62, 6), (944, 27, 3772), (947, 110, 3773), (947, 1, 3781), (947, 27, 3782), (948, 110, 3232), (948, 12, 93), (948, 25, 94), (948, 4, 3342), (948, 5, 156), (948, 10, 3343), (948, 14, 3344), (948, 1, 3345), (948, 26, 3346), (948, 90, 3347), (948, 62, 1329), (948, 27, 4001), (950, 110, 1332), (950, 1, 4002), (950, 27, 4003), (995, 12, 2635), (995, 4, 4004), (995, 13, 4005), (995, 14, 4006), (995, 10, 4007), (995, 26, 4008), (995, 1, 4009), (995, 110, 4010), (995, 62, 1416), (995, 27, 4011), (996, 12, 1408), (996, 4, 4012), (996, 13, 4013), (996, 14, 4014), (996, 10, 4015), (996, 26, 4016), (996, 1, 4017), (996, 110, 4018), (996, 62, 1416), (996, 27, 4019), (997, 110, 4020), (998, 110, 1321), (998, 1, 4021), (998, 27, 4022), (999, 110, 4023), (999, 12, 1372), (999, 4, 4024), (999, 14, 4025), (999, 10, 4026), (999, 1, 4027), (999, 90, 4028), (999, 62, 1287), (999, 27, 4029), (1001, 110, 4031), (1002, 110, 4032), (1002, 12, 507), (1002, 25, 508), (1002, 4, 3774), (1002, 5, 891), (1002, 10, 4033), (1002, 14, 4034), (1002, 1, 4035), (1002, 26, 4036), (1002, 90, 4037), (1002, 62, 1329), (1002, 27, 4038), (1003, 110, 1332), (1003, 1, 4039), (1003, 27, 4040), (1004, 110, 2869), (1004, 14, 1508), (1004, 1, 3944), (1004, 12, 3945), (1004, 90, 3946), (1004, 62, 6), (1004, 27, 4041), (1005, 110, 3948), (1005, 1, 3949), (1005, 27, 4042), (1006, 110, 4043), (1006, 14, 3763), (1006, 1, 4044), (1006, 12, 4045), (1006, 90, 4046), (1006, 62, 6), (1006, 27, 4047), (1007, 110, 4048), (1007, 1, 4049), (1007, 27, 4050), (1008, 110, 4051), (1008, 14, 4052), (1008, 1, 4053), (1008, 22, 4054), (1008, 26, 4055), (1008, 12, 4056), (1008, 90, 4057), (1008, 62, 6), (1008, 27, 4058), (1009, 110, 4059), (1009, 1, 4060), (1009, 27, 4061), (1010, 12, 1539), (1010, 4, 4062), (1010, 13, 4063), (1010, 14, 4064), (1010, 10, 4065), (1010, 26, 4066), (1010, 1, 4067), (1010, 110, 4068), (1010, 62, 1416), (1010, 27, 4069), (1010, 116, 4070), (1011, 110, 4071), (1012, 110, 4072), (1012, 115, 4073), (1012, 8, 592), (1012, 7, 4074), (1012, 14, 4075), (1012, 10, 4076), (1013, 110, 4077), (1014, 14, 4079), (1014, 8, 592), (1014, 7, 4080), (1015, 110, 4081), (1014, 110, 4082), (1016, 110, 4083), (1016, 6, 4084), (1016, 8, 592), (1016, 7, 4085), (1016, 14, 4086), (1019, 110, 4088), (1019, 8, 4089), (1019, 14, 3985), (1019, 7, 4090), (1020, 118, 4091), (1020, 11, 4092), (1020, 8, 4093), (1020, 110, 4094), (1020, 87, 3751), (1020, 90, 4095), (1020, 14, 4096), (1020, 62, 4097), (1020, 116, 4098), (1021, 110, 4099), (1021, 1, 4100), (1021, 27, 4101), (1022, 110, 4102), (1022, 12, 93), (1022, 25, 94), (1022, 4, 1830), (1022, 5, 310), (1022, 10, 4103), (1022, 14, 4104), (1022, 1, 4105), (1022, 26, 4106), (1022, 90, 4107), (1022, 62, 1329), (1022, 27, 4108), (1023, 110, 1332), (1023, 1, 4109), (1023, 27, 4110), (1024, 110, 4111), (1024, 115, 4112), (1024, 14, 3985), (1024, 10, 4113), (1024, 8, 4114), (1025, 110, 4115), (1026, 12, 286), (1026, 4, 4116), (1026, 13, 289), (1026, 14, 4117), (1026, 10, 4118), (1026, 26, 4119), (1026, 1, 4120), (1026, 110, 4121), (1026, 62, 3913), (1026, 27, 4122), (1026, 116, 4123), (1028, 110, 4126), (1029, 110, 4127), (1029, 14, 4128), (1029, 12, 4129), (1029, 10, 4130), (1029, 4, 4131), (1029, 5, 4132), (1029, 1, 4133), (1029, 90, 4134), (1029, 26, 4135), (1029, 62, 1164), (1029, 27, 4136), (1031, 110, 4139), (1032, 110, 4140), (1032, 14, 4141), (1032, 75, 4142), (1032, 7, 4143), (1032, 1, 4144), (1033, 110, 4145), (1034, 110, 4146), (1034, 12, 93), (1034, 25, 94), (1034, 4, 1358), (1034, 5, 310), (1034, 10, 4147), (1034, 14, 871), (1034, 1, 4148), (1034, 26, 4149), (1034, 90, 4150), (1034, 62, 1329), (1034, 27, 4151), (1035, 110, 1332), (1035, 1, 4152), (1035, 27, 4153), (1036, 1, 4155), (1036, 27, 4156), (1036, 110, 4157), (1027, 110, 4078), (1027, 14, 4124), (1027, 1, 4125), (1027, 12, 4137), (1027, 90, 4138), (1027, 62, 6), (1027, 27, 4158), (1030, 110, 4159), (1030, 1, 4160), (1030, 27, 4161), (1037, 110, 4162), (1037, 14, 4163), (1037, 1, 4164), (1037, 22, 4165), (1037, 26, 4166), (1037, 12, 4167), (1037, 90, 4168), (1037, 62, 6), (1037, 27, 4169), (1038, 110, 4170), (1038, 1, 4171), (1038, 27, 4172), (1039, 110, 4173), (1039, 14, 4174), (1039, 1, 4175), (1039, 12, 4176), (1039, 90, 4177), (1039, 62, 6), (1039, 27, 4178), (1040, 110, 4179), (1040, 1, 4180), (1040, 27, 4181), (1041, 110, 4182), (1041, 14, 4183), (1041, 1, 4184), (1041, 12, 4185), (1041, 90, 4186), (1041, 62, 6), (1041, 27, 4187), (1042, 110, 4188), (1042, 1, 4189), (1042, 27, 4190), (1043, 110, 4191), (1043, 1, 4192), (1043, 27, 4193), (1046, 12, 1408), (1046, 4, 4205), (1046, 13, 4013), (1046, 14, 4206), (1046, 10, 4207), (1046, 26, 4198), (1046, 1, 4208), (1046, 110, 4209), (1046, 62, 3913), (1046, 27, 4210), (1048, 12, 1408), (1048, 4, 4213), (1048, 13, 4013), (1048, 14, 4214), (1048, 10, 4215), (1048, 26, 4216), (1048, 1, 4217), (1048, 110, 4218), (1048, 62, 1416), (1048, 27, 4219), (1049, 110, 4220), (1050, 110, 4221), (1051, 12, 1408), (1051, 4, 4222), (1051, 13, 4013), (1051, 14, 4223), (1051, 10, 4224), (1051, 26, 4225), (1051, 1, 4226), (1051, 110, 4227), (1051, 62, 1416), (1051, 27, 4228), (1052, 110, 4229), (1053, 110, 4230), (1053, 12, 93), (1053, 25, 94), (1053, 4, 4231), (1053, 5, 299), (1053, 10, 4232), (1053, 14, 4233), (1053, 1, 4234), (1053, 26, 4235), (1053, 90, 4236), (1053, 62, 1329), (1053, 27, 4237), (1054, 110, 1332), (1054, 1, 4238), (1054, 27, 4239), (1055, 110, 4240), (1055, 12, 93), (1055, 25, 94), (1055, 4, 4231), (1055, 5, 135), (1055, 10, 4241), (1055, 14, 4242), (1055, 1, 4243), (1055, 26, 4244), (1055, 90, 4245), (1055, 62, 1329), (1055, 27, 4246), (1056, 110, 1332), (1056, 1, 4247), (1056, 27, 4248), (1057, 110, 4249), (1057, 12, 93), (1057, 25, 94), (1057, 4, 1707), (1057, 5, 90), (1057, 10, 4250), (1057, 14, 4251), (1057, 1, 4252), (1057, 26, 4253), (1057, 90, 4254), (1057, 62, 1329), (1057, 27, 4255), (1058, 110, 1332), (1058, 1, 4256), (1058, 27, 4257), (1059, 110, 4258), (1059, 14, 4259), (1059, 1, 4260), (1059, 12, 4261), (1059, 90, 4262), (1059, 62, 6), (1059, 27, 4263), (1060, 110, 4264), (1060, 1, 4265), (1060, 27, 4266), (961, 110, 3826), (961, 12, 455), (961, 25, 456), (961, 4, 374), (961, 5, 1954), (961, 10, 3827), (961, 14, 3828), (961, 1, 4154), (961, 26, 4211), (961, 62, 1329), (961, 27, 4212), (1047, 110, 1332), (1047, 1, 4267), (1047, 27, 4268), (1061, 110, 4269), (1061, 12, 93), (1061, 25, 94), (1061, 4, 1076), (1061, 5, 299), (1061, 10, 4270), (1061, 14, 4271), (1061, 1, 4272), (1061, 26, 4273), (1061, 90, 4274), (1061, 62, 1329), (1061, 27, 4275), (1061, 116, 4276), (1062, 110, 1332), (1062, 1, 4277), (1062, 27, 4278), (1063, 110, 4279), (1064, 12, 1408), (1064, 4, 4280), (1064, 13, 4013), (1064, 14, 4281), (1064, 10, 4282), (1064, 26, 4283), (1064, 1, 4284), (1064, 62, 1416), (1064, 27, 4286), (1064, 110, 4288), (1065, 110, 4289), (1066, 110, 4290), (1066, 12, 93), (1066, 25, 94), (1066, 4, 2597), (1066, 5, 90), (1066, 10, 4291), (1066, 14, 4292), (1066, 1, 4293), (1066, 26, 4294), (1066, 90, 4295), (1066, 62, 1329), (1066, 27, 4296), (1067, 110, 1332), (1067, 1, 4297), (1067, 27, 4298), (1068, 110, 4299), (1068, 12, 93), (1068, 25, 94), (1068, 4, 4300), (1068, 5, 135), (1068, 10, 4301), (1068, 14, 4302), (1068, 1, 4303), (1068, 26, 4304), (1068, 90, 4305), (1068, 62, 1329), (1068, 27, 4306), (1068, 116, 4307), (1069, 110, 1332), (1069, 1, 4308), (1069, 27, 4309), (1070, 12, 1074), (1070, 4, 156), (1070, 13, 1944), (1070, 14, 1374), (1070, 10, 4310), (1070, 26, 4311), (1070, 1, 4312), (1070, 110, 4313), (1070, 62, 1416), (1070, 27, 4314), (1071, 110, 4315), (1072, 12, 286), (1072, 4, 3617), (1072, 13, 3907), (1072, 14, 4316), (1072, 10, 4317), (1072, 26, 4318), (1072, 1, 4319), (1072, 110, 4320), (1072, 62, 3913), (1072, 27, 4321), (1074, 110, 4324), (1075, 110, 4325), (1075, 12, 93), (1075, 25, 94), (1075, 4, 3774), (1075, 5, 274), (1075, 10, 4326), (1075, 14, 4327), (1075, 1, 4328), (1075, 26, 4329), (1075, 90, 4330), (1075, 62, 1329), (1075, 27, 4331), (1076, 110, 1332), (1076, 1, 4332), (1076, 27, 4333), (1077, 110, 4334), (1077, 14, 871), (1078, 110, 4335), (1079, 1, 4336), (1079, 26, 4337), (1079, 4, 4338), (1079, 5, 1090), (1079, 12, 1372), (1079, 13, 4339), (1079, 110, 4340), (1079, 87, 3751), (1079, 14, 4341), (1079, 10, 4342), (1079, 90, 4343), (1079, 62, 3755), (1079, 27, 4344), (1080, 110, 4345), (1080, 1, 4346), (1080, 27, 4347), (124, 14, 871), (124, 8, 4348), (1081, 110, 4349), (1081, 12, 1257), (1081, 10, 4351), (1081, 14, 4352), (1081, 13, 1260), (1081, 26, 4353), (1081, 1, 4354), (1081, 90, 4355), (1081, 62, 1264), (1081, 27, 4356), (1082, 110, 1266), (1082, 1, 4357), (1082, 27, 4358), (1083, 110, 4359), (1083, 14, 4360), (1083, 1, 4361), (1083, 12, 4362), (1083, 90, 4363), (1083, 62, 6), (1083, 27, 4364), (1084, 110, 4365), (1084, 1, 4366), (1084, 27, 4367), (1085, 110, 4368), (1085, 14, 4369), (1085, 1, 4370), (1085, 12, 4371), (1085, 90, 4372), (1085, 62, 6), (1085, 27, 4373), (1086, 110, 4374), (1086, 1, 4375), (1086, 27, 4376), (1087, 110, 4377), (1087, 14, 4378), (1087, 1, 4379), (1087, 12, 4380), (1087, 90, 4381), (1087, 62, 6), (1087, 27, 4382), (1088, 110, 4383), (1088, 1, 4384), (1088, 27, 4385), (1089, 110, 4386), (1089, 1, 4387), (1089, 27, 4388), (1090, 12, 1225), (1090, 4, 1707), (1090, 13, 4389), (1090, 14, 3985), (1090, 10, 4390), (1090, 26, 4391), (1090, 1, 4392), (1090, 110, 4393), (1090, 62, 1416), (1090, 27, 4394), (1090, 116, 4395), (1091, 110, 4396), (1092, 12, 1225), (1092, 4, 1707), (1092, 13, 4389), (1092, 14, 3985), (1092, 10, 4397), (1092, 26, 4398), (1092, 1, 4399), (1092, 110, 4400), (1092, 62, 1416), (1092, 27, 4401), (1093, 110, 4402), (1094, 12, 4403), (1094, 4, 4404), (1094, 13, 4405), (1094, 14, 4406), (1094, 10, 4407), (1094, 26, 4408), (1094, 1, 4409), (1094, 110, 4410), (1094, 62, 1416), (1094, 27, 4411), (1095, 110, 4412), (1096, 110, 4413), (1096, 12, 1372), (1096, 4, 4414), (1096, 14, 4415), (1096, 10, 4416), (1096, 1, 4417), (1096, 90, 4418), (1096, 62, 1287), (1096, 27, 4419), (1097, 110, 4413), (1097, 1, 4417), (1097, 27, 4420), (1098, 110, 4421), (1099, 110, 4422), (1099, 14, 4423), (1099, 1, 4424), (1099, 12, 4425), (1099, 90, 4426), (1099, 62, 6), (1099, 27, 4427), (1099, 116, 4428), (1100, 110, 4429), (1100, 1, 4430), (1100, 27, 4431), (1101, 110, 4432), (1101, 14, 4433), (1101, 1, 4434), (1101, 22, 4435), (1101, 26, 4436), (1101, 12, 4437), (1101, 90, 4438), (1101, 62, 6), (1101, 27, 4439), (1102, 110, 4440), (1102, 1, 4441), (1102, 27, 4442), (1103, 110, 4443), (1103, 14, 4444), (1103, 1, 4445), (1103, 12, 4446), (1103, 90, 4447), (1103, 62, 6), (1103, 27, 4448), (1104, 110, 4449), (1104, 1, 4450), (1104, 27, 4451), (1105, 110, 4452), (1105, 12, 93), (1105, 25, 94), (1105, 4, 3342), (1105, 5, 156), (1105, 10, 4453), (1105, 14, 4454), (1105, 1, 4455), (1105, 26, 4456), (1105, 90, 4457), (1105, 62, 1329), (1105, 27, 4458), (1106, 110, 1332), (1106, 1, 4459), (1106, 27, 4460), (1107, 110, 4461), (1107, 14, 4462), (1107, 1, 4463), (1107, 22, 4464), (1107, 26, 4465), (1107, 12, 4466), (1107, 90, 4467), (1107, 62, 6), (1107, 27, 4468), (1108, 110, 4469), (1108, 1, 4470), (1108, 27, 4471), (1109, 110, 4472), (1109, 14, 4473), (1109, 1, 4474), (1109, 12, 4475), (1109, 90, 4476), (1109, 62, 6), (1109, 27, 4477), (1110, 110, 4478), (1110, 1, 4479), (1110, 27, 4480), (1111, 110, 4481), (1111, 84, 4482), (1111, 4, 4483), (1111, 14, 4484), (1111, 10, 4485), (1111, 1, 4486), (1111, 90, 4487), (1111, 62, 1287), (1111, 27, 4488), (1111, 116, 4489), (1113, 110, 4491), (1114, 110, 4492), (1114, 14, 4493), (1114, 1, 4494), (1114, 12, 4495), (1114, 90, 4496), (1114, 62, 6), (1114, 27, 4497), (1115, 110, 4498), (1115, 1, 4499), (1115, 27, 4500), (1116, 12, 1317), (1116, 4, 2110), (1116, 13, 1334), (1116, 14, 4327), (1116, 10, 1339), (1116, 26, 4501), (1116, 1, 4502), (1116, 110, 4503), (1116, 62, 1416), (1116, 27, 4504), (1117, 110, 4505), (1118, 110, 4506), (1118, 14, 4507), (1118, 1, 4508), (1118, 12, 4509), (1118, 90, 4510), (1118, 62, 6), (1118, 27, 4511), (1119, 110, 4512), (1119, 1, 4513), (1119, 27, 4514), (1120, 110, 4515), (1120, 14, 4507), (1120, 1, 4516), (1120, 12, 4517), (1120, 90, 4518), (1120, 62, 6), (1120, 27, 4519), (1120, 116, 4520), (1121, 110, 4521), (1121, 1, 4522), (1121, 27, 4523), (1073, 110, 4285), (1073, 14, 4287), (1073, 1, 4322), (1073, 12, 4323), (1073, 90, 4524), (1073, 62, 6), (1073, 27, 4525), (1122, 110, 4526), (1122, 1, 4527), (1122, 27, 4528), (1123, 110, 4529), (1123, 14, 4530), (1123, 1, 4531), (1123, 12, 4532), (1123, 90, 4533), (1123, 62, 6), (1123, 27, 4534), (1124, 110, 4535), (1124, 1, 4536), (1124, 27, 4537), (1125, 12, 286), (1125, 4, 3617), (1125, 13, 3907), (1125, 14, 3272), (1125, 10, 4538), (1125, 26, 4539), (1125, 1, 4540), (1125, 110, 4541), (1125, 62, 3913), (1125, 27, 4542), (1125, 116, 4543), (1126, 110, 294), (1126, 1, 4544), (1126, 27, 4545), (1127, 110, 4547), (1127, 8, 4548), (1127, 7, 4549), (1128, 110, 4550), (1129, 110, 4551), (1130, 110, 4552), (1130, 14, 4553), (1130, 1, 4554), (1130, 12, 4555), (1130, 90, 4556), (1130, 62, 6), (1130, 27, 4557), (1131, 110, 4558), (1131, 1, 4559), (1131, 27, 4560), (1132, 110, 4561), (1132, 14, 4553), (1132, 1, 4562), (1132, 12, 4563), (1132, 90, 4564), (1132, 62, 6), (1132, 27, 4565), (1133, 110, 4566), (1133, 1, 4567), (1133, 27, 4568), (1134, 110, 4569), (1134, 14, 4570), (1134, 1, 4571), (1134, 22, 4572), (1134, 26, 4573), (1134, 12, 4574), (1134, 90, 4575), (1134, 62, 6), (1134, 27, 4576), (1135, 110, 4577), (1135, 1, 4578), (1135, 27, 4579), (1136, 110, 4580), (1136, 12, 4581), (1136, 25, 4582), (1136, 4, 4583), (1136, 5, 274), (1136, 10, 4584), (1136, 14, 4585), (1136, 1, 4586), (1136, 26, 4587), (1136, 90, 4588), (1136, 62, 1329), (1136, 27, 4589), (1137, 110, 1332), (1137, 1, 4590), (1137, 27, 4591), (1138, 110, 4592), (1138, 12, 507), (1138, 25, 508), (1138, 4, 497), (1138, 5, 2245), (1138, 10, 4593), (1138, 14, 4594), (1138, 1, 4595), (1138, 26, 4596), (1138, 90, 4597), (1138, 62, 1329), (1138, 27, 4598), (1140, 110, 4601), (1141, 12, 286), (1141, 4, 287), (1141, 13, 3907), (1141, 14, 4602), (1141, 10, 4603), (1141, 26, 4604), (1141, 1, 4605), (1141, 110, 4606), (1141, 62, 3913), (1141, 27, 4607), (1143, 110, 4610), (977, 110, 3252), (977, 12, 93), (977, 25, 94), (977, 10, 479), (977, 14, 4327), (977, 1, 3888), (977, 26, 3889), (977, 90, 3890), (977, 62, 1329), (977, 27, 3892), (1142, 110, 4599), (1144, 1, 4600), (1144, 26, 4608), (1144, 4, 4609), (1144, 5, 1090), (1144, 12, 1372), (1144, 13, 4339), (1144, 110, 4611), (1144, 87, 3751), (1144, 14, 4612), (1144, 10, 4613), (1144, 90, 4614), (1144, 62, 3755), (1144, 27, 4615), (1145, 110, 4345), (1145, 1, 4616), (1145, 27, 4617), (1146, 110, 4618), (1146, 14, 4619), (1146, 1, 4620), (1146, 12, 4621), (1146, 90, 4622), (1146, 62, 6), (1146, 27, 4623), (1147, 110, 4624), (1147, 1, 4625), (1147, 27, 4626), (1148, 110, 4627), (1148, 14, 4619), (1148, 1, 4628), (1148, 12, 4629), (1148, 90, 4630), (1148, 62, 6), (1148, 27, 4631), (1148, 116, 4632), (1149, 110, 4633), (1149, 1, 4634), (1149, 27, 4635), (1150, 110, 4636), (1150, 14, 4637), (1150, 1, 4638), (1150, 12, 4639), (1150, 90, 4640), (1150, 62, 6), (1150, 27, 4641), (1151, 110, 4642), (1151, 1, 4643), (1151, 27, 4644), (1152, 110, 4645), (1152, 12, 1408), (1152, 4, 4646), (1152, 14, 4647), (1152, 10, 4648), (1152, 1, 4649), (1152, 90, 4650), (1152, 62, 1287), (1152, 27, 4651), (1154, 110, 4653), (1155, 110, 4654), (1155, 12, 1408), (1155, 4, 4655), (1155, 14, 4647), (1155, 10, 4656), (1155, 1, 4657), (1155, 90, 4658), (1155, 62, 1287), (1155, 27, 4659), (1157, 110, 4661), (1158, 110, 4662), (1158, 1, 4663), (1158, 27, 4664), (166, 110, 536), (166, 12, 93), (166, 25, 94), (166, 4, 4231), (166, 5, 299), (166, 10, 603), (166, 14, 757), (166, 1, 1604), (166, 26, 2706), (166, 90, 2800), (166, 62, 1329), (166, 27, 3979), (166, 116, 3980), (490, 110, 4665), (982, 110, 4666), (982, 14, 4667), (982, 1, 4668), (982, 77, 4669), (982, 90, 4670), (982, 62, 4671), (982, 27, 4672), (988, 110, 3992), (988, 14, 3993), (988, 1, 3994), (988, 12, 3995), (988, 90, 4673), (988, 62, 6), (988, 27, 4674), (1000, 110, 3998), (1000, 1, 3999), (1000, 27, 4675), (1159, 110, 4676), (1159, 14, 4677), (1159, 1, 4678), (1159, 22, 4679), (1159, 12, 4680), (1159, 90, 4681), (1159, 62, 6), (1159, 27, 4682), (1160, 110, 4683), (1160, 1, 4684), (1160, 27, 4685), (1161, 110, 4686), (1161, 12, 4687), (1161, 4, 4688), (1161, 5, 4689), (1161, 10, 4690), (1161, 14, 4691), (1161, 13, 4692), (1161, 26, 4693), (1161, 1, 4694), (1161, 62, 1264), (1161, 27, 4695), (1162, 110, 1266), (1162, 1, 4696), (1162, 27, 4697), (1163, 110, 4698), (1163, 14, 4699), (1163, 1, 4700), (1163, 22, 4701), (1163, 26, 4702), (1163, 12, 4703), (1163, 90, 4704), (1163, 62, 6), (1163, 27, 4705), (1164, 110, 4706), (1164, 1, 4707), (1164, 27, 4708), (1165, 110, 4709), (1165, 14, 4710), (1165, 1, 4711), (1165, 12, 4712), (1165, 90, 4713), (1165, 62, 6), (1165, 27, 4714), (1165, 116, 4715), (1166, 110, 4716), (1166, 1, 4717), (1166, 27, 4718), (1167, 110, 4719), (1167, 14, 4720), (1167, 1, 4721), (1167, 12, 4722), (1167, 90, 4723), (1167, 62, 6), (1167, 27, 4724), (1167, 116, 4725), (1168, 110, 4726), (1168, 1, 4727), (1168, 27, 4728), (1169, 110, 4051), (1169, 14, 4052), (1169, 1, 4053), (1169, 22, 4054), (1169, 26, 4055), (1169, 12, 4056), (1169, 90, 4057), (1169, 62, 6), (1169, 27, 4729), (1170, 110, 4059), (1170, 1, 4060), (1170, 27, 4730), (1171, 110, 4731), (1171, 14, 4732), (1171, 1, 4733), (1171, 22, 4734), (1171, 26, 4735), (1171, 12, 4736), (1171, 90, 4737), (1171, 62, 6), (1171, 27, 4738), (1172, 110, 4739), (1172, 1, 4740), (1172, 27, 4741), (1173, 110, 4742), (1173, 14, 4743), (1173, 1, 4744), (1173, 12, 4745), (1173, 90, 4746), (1173, 62, 6), (1173, 27, 4747), (1174, 110, 4748), (1174, 1, 4749), (1174, 27, 4750), (1175, 110, 4751), (1175, 14, 4752), (1175, 1, 4753), (1175, 12, 4754), (1175, 90, 4755), (1175, 62, 6), (1175, 27, 4756), (1175, 116, 4757), (1176, 110, 4758), (1176, 1, 4759), (1176, 27, 4760), (119, 12, 1408), (119, 4, 461), (119, 13, 4013), (119, 14, 462), (119, 10, 4194), (119, 26, 4195), (119, 1, 4196), (119, 110, 4197), (119, 62, 1416), (119, 27, 4199), (1044, 110, 4200), (1178, 110, 4201), (1178, 12, 93), (1178, 25, 94), (1178, 4, 1294), (1178, 5, 299), (1178, 10, 4202), (1178, 14, 4203), (1178, 1, 4204), (1178, 26, 4761), (1178, 90, 4762), (1178, 62, 1329), (1178, 27, 4766), (1179, 110, 1332), (1179, 1, 4764), (1179, 27, 4767), (1180, 110, 4768), (1180, 12, 93), (1180, 25, 94), (1180, 4, 1294), (1180, 5, 299), (1180, 10, 4769), (1180, 14, 4770), (1180, 1, 4771), (1180, 26, 4772), (1180, 90, 4773), (1180, 62, 1329), (1180, 27, 4774), (1181, 110, 1332), (1181, 1, 4775), (1181, 27, 4776), (1112, 110, 4490), (1112, 14, 4777), (1112, 1, 4778), (1112, 12, 4779), (1112, 90, 4780), (1112, 62, 6), (1112, 27, 4781), (1182, 110, 4782), (1182, 1, 4783), (1182, 27, 4784), (1183, 110, 4785), (1183, 14, 4786), (1183, 1, 4787), (1183, 12, 4788), (1183, 90, 4789), (1183, 62, 6), (1183, 27, 4790), (1184, 110, 4791), (1184, 1, 4792), (1184, 27, 4793), (1185, 110, 4794), (1185, 12, 93), (1185, 25, 94), (1185, 10, 4795), (1185, 14, 1363), (1185, 1, 4796), (1185, 26, 4797), (1185, 90, 4798), (1185, 62, 1329), (1185, 27, 4799), (1186, 110, 1332), (1186, 1, 4800), (1186, 27, 4801), (1187, 110, 4794), (1187, 12, 93), (1187, 25, 94), (1187, 4, 2597), (1187, 5, 274), (1187, 10, 4795), (1187, 14, 1363), (1187, 1, 4796), (1187, 26, 4797), (1187, 90, 4798), (1187, 62, 1329), (1187, 27, 4802), (1188, 110, 1332), (1188, 1, 4803), (1188, 27, 4804), (1189, 110, 4805), (1189, 14, 4806), (1189, 1, 4807), (1189, 12, 4808), (1189, 90, 4809), (1189, 62, 6), (1189, 27, 4810), (1190, 110, 4811), (1190, 1, 4812), (1190, 27, 4813), (1139, 110, 3893), (1139, 14, 4806), (1139, 1, 4546), (1139, 12, 4814), (1139, 90, 4815), (1139, 62, 6), (1139, 27, 4816), (1191, 110, 4817), (1191, 1, 4818), (1191, 27, 4819), (1192, 110, 4820), (1192, 14, 4821), (1192, 1, 4822), (1192, 12, 4823), (1192, 90, 4824), (1192, 62, 6), (1192, 27, 4825), (1193, 110, 4826), (1193, 1, 4827), (1193, 27, 4828), (1194, 110, 4829), (1194, 14, 4830), (1194, 1, 4831), (1194, 12, 4832), (1194, 90, 4833), (1194, 62, 6), (1194, 27, 4834), (1195, 110, 4835), (1195, 1, 4836), (1195, 27, 4837), (1196, 110, 4838), (1196, 12, 93), (1196, 25, 94), (1196, 4, 145), (1196, 5, 299), (1196, 10, 2111), (1196, 14, 4839), (1196, 1, 4840), (1196, 26, 4841), (1196, 90, 4842), (1196, 62, 1329), (1196, 27, 4843), (1197, 110, 1332), (1197, 1, 4844), (1197, 27, 4845), (1198, 110, 4846), (1198, 14, 4847), (1198, 1, 4848), (1198, 12, 4849), (1198, 90, 4850), (1198, 62, 6), (1198, 27, 4851), (1199, 110, 4852), (1199, 1, 4853), (1199, 27, 4854), (1200, 110, 4855), (1200, 12, 93), (1200, 25, 94), (1200, 4, 145), (1200, 5, 299), (1200, 10, 4856), (1200, 14, 4857), (1200, 1, 4858), (1200, 26, 4859), (1200, 90, 4860), (1200, 62, 1329), (1200, 27, 4861), (1201, 110, 1332), (1201, 1, 4862), (1201, 27, 4863), (437, 110, 3983), (437, 14, 4030), (437, 1, 4652), (437, 12, 4660), (437, 90, 4864), (437, 62, 6), (437, 27, 4865), (1153, 110, 4866), (1153, 1, 4867), (1153, 27, 4868), (1045, 110, 4763), (1045, 14, 4765), (1045, 1, 4869), (1045, 12, 4870), (1045, 90, 4871), (1045, 62, 6), (1045, 27, 4872), (1156, 110, 4873), (1156, 1, 4874), (1156, 27, 4875), (1177, 110, 4876), (1177, 14, 4877), (1177, 1, 4878), (1177, 12, 4879), (1177, 90, 4880), (1177, 62, 6), (1177, 27, 4881), (1177, 116, 4882), (1202, 110, 4883), (1202, 1, 4884), (1202, 27, 4885), (1203, 110, 4886), (1203, 14, 4887), (1203, 1, 4888), (1203, 12, 4889), (1203, 90, 4890), (1203, 62, 6), (1203, 27, 4891), (1204, 110, 4892), (1204, 1, 4893), (1204, 27, 4894), (1205, 110, 4895), (1205, 14, 4896), (1205, 1, 4897), (1205, 12, 4898), (1205, 90, 4899), (1205, 62, 6), (1205, 27, 4900), (1206, 110, 4901), (1206, 1, 4902), (1206, 27, 4903), (1207, 110, 4904), (1207, 14, 4030), (1207, 1, 4905), (1207, 12, 4906), (1207, 90, 4907), (1207, 62, 6), (1207, 27, 4908), (1208, 110, 4909), (1208, 1, 4910), (1208, 27, 4911), (1209, 110, 4912), (1209, 14, 4913), (1209, 1, 4914), (1209, 12, 4915), (1209, 90, 4916), (1209, 62, 6), (1209, 27, 4917), (1210, 110, 4918), (1210, 1, 4919), (1210, 27, 4920), (1211, 110, 4921), (1211, 14, 4922), (1211, 1, 4923), (1211, 12, 4924), (1211, 90, 4925), (1211, 62, 6), (1211, 27, 4926), (1212, 110, 4927), (1212, 1, 4928), (1212, 27, 4929), (1213, 110, 4930), (1213, 8, 4933), (1213, 62, 4934), (1214, 11, 4936), (1214, 8, 4933), (1214, 14, 480), (1214, 62, 4934), (1214, 116, 4938), (1215, 110, 4939), (1215, 11, 4940), (1215, 8, 4942), (1215, 14, 4943), (1215, 62, 4934), (1216, 11, 4945), (1216, 6, 4946), (1216, 8, 4089), (1216, 14, 871), (1216, 62, 4934), (1216, 116, 4947), (1217, 110, 4948), (1217, 14, 4949), (1217, 1, 4950), (1217, 12, 4951), (1217, 90, 4952), (1217, 62, 6), (1217, 27, 4953), (1218, 110, 4954), (1218, 1, 4955), (1218, 27, 4956), (1219, 110, 4957), (1219, 14, 4958), (1219, 1, 4959), (1219, 12, 4960), (1219, 90, 4961), (1219, 62, 6), (1219, 27, 4962), (1220, 110, 4963), (1220, 1, 4964), (1220, 27, 4965), (1221, 12, 286), (1221, 4, 1270), (1221, 5, 274), (1221, 13, 3907), (1221, 14, 4966), (1221, 10, 4967), (1221, 26, 4968), (1221, 1, 4969), (1221, 110, 4970), (1221, 62, 3913), (1221, 27, 4971), (1222, 110, 294), (1222, 1, 4972), (1222, 27, 4973), (1223, 110, 4974), (1223, 14, 4975), (1223, 1, 4976), (1223, 12, 4977), (1223, 90, 4978), (1223, 62, 6), (1223, 27, 4979), (1224, 110, 4980), (1224, 1, 4981), (1224, 27, 4979), (1225, 110, 4982), (1225, 12, 1372), (1225, 4, 4983), (1225, 14, 4984), (1225, 10, 4985), (1225, 1, 4986), (1225, 90, 4987), (1225, 62, 1287), (1225, 27, 4988), (1227, 110, 4991), (1228, 110, 4992), (1228, 1, 4993), (1228, 27, 4994), (1230, 110, 4992), (1230, 1, 4993), (1230, 27, 4998), (1231, 118, 4999), (1231, 11, 5000), (1231, 8, 5001), (1231, 110, 5002), (1231, 87, 3751), (1231, 90, 5003), (1231, 14, 2390), (1231, 62, 4097), (1232, 110, 4099), (1232, 1, 5004), (1232, 27, 5005), (1233, 110, 5006), (1233, 14, 5007), (1233, 1, 5008), (1233, 12, 5009), (1233, 90, 5010), (1233, 62, 6), (1233, 27, 5011), (1234, 110, 5012), (1234, 1, 5013), (1234, 27, 5011), (1235, 110, 5014), (1235, 12, 93), (1235, 25, 94), (1235, 4, 3774), (1235, 5, 156), (1235, 10, 5015), (1235, 14, 5016), (1235, 1, 5017), (1235, 26, 5018), (1235, 90, 4046), (1235, 62, 1329), (1235, 27, 5019), (1236, 110, 1332), (1236, 1, 5020), (1236, 27, 5019), (1237, 110, 5021), (1237, 12, 5022), (1237, 4, 5023), (1237, 5, 135), (1237, 10, 5024), (1237, 14, 5025), (1237, 13, 5026), (1237, 26, 5027), (1237, 1, 5028), (1237, 90, 5029), (1237, 62, 1264), (1237, 27, 5030), (1238, 110, 1266), (1238, 1, 5031), (1238, 27, 5030), (1239, 110, 5032), (1239, 14, 5033), (1239, 1, 5034), (1239, 12, 5035), (1239, 90, 5036), (1239, 62, 6), (1239, 27, 5037), (1240, 110, 5038), (1240, 1, 5039), (1240, 27, 5037), (1241, 110, 5040), (1241, 14, 5041), (1241, 1, 5042), (1241, 12, 5043), (1241, 90, 5044), (1241, 62, 6), (1241, 27, 5045), (1242, 110, 5046), (1242, 1, 5047), (1242, 27, 5045), (1246, 110, 5061), (1247, 110, 5062), (1247, 12, 5063), (1248, 110, 5064), (1248, 1, 5066), (1249, 110, 5067), (1250, 110, 5068), (1251, 110, 5069), (1253, 110, 5073), (1253, 14, 5074), (1253, 1, 5075), (1253, 12, 5076), (1253, 90, 5077), (1253, 62, 6), (1253, 27, 5078), (1253, 116, 5079), (1254, 110, 5080), (1254, 1, 5081), (1254, 27, 5078), (1255, 110, 5082), (1255, 14, 5083), (1255, 1, 5084), (1255, 12, 5085), (1255, 90, 5086), (1255, 62, 6), (1255, 27, 5087), (1255, 116, 5088), (1256, 110, 5089), (1256, 1, 5090), (1256, 27, 5087), (1229, 110, 4995), (1229, 14, 4996), (1229, 1, 4997), (1229, 12, 5065), (1229, 90, 5091), (1229, 62, 6), (1229, 27, 5092), (1257, 110, 5093), (1257, 1, 5094), (1257, 27, 5092), (1259, 110, 5098), (1258, 1, 5095), (1258, 27, 5096), (1258, 110, 3903), (1258, 12, 5099), (1258, 4, 5100), (1258, 14, 3905), (1260, 110, 5101), (1261, 110, 5102), (1228, 14, 5103), (1262, 110, 3951), (1262, 12, 93), (1262, 25, 94), (1262, 4, 134), (1262, 5, 299), (1262, 10, 3952), (1262, 14, 3953), (1262, 1, 3954), (1262, 26, 3955), (1262, 90, 3956), (1262, 62, 1329), (1262, 27, 5104), (1264, 110, 5106), (1265, 110, 5107), (1265, 1, 5108), (1265, 27, 5109), (1263, 110, 5097), (1263, 14, 5105), (1263, 1, 5110), (1263, 12, 5111), (1263, 90, 5112), (1263, 62, 6), (1263, 27, 5113), (1266, 110, 5114), (1266, 1, 5115), (1266, 27, 5113), (1267, 110, 5116), (1267, 14, 5117), (1267, 1, 5118), (1267, 12, 5119), (1267, 90, 5120), (1267, 62, 6), (1267, 27, 5121), (1268, 110, 5122), (1268, 1, 5123), (1268, 27, 5121), (1269, 12, 5124), (1269, 110, 5125), (1269, 4, 5126), (1269, 5, 1954), (1269, 13, 5127), (1269, 1, 5128), (1269, 14, 5129), (1269, 10, 5130), (1269, 90, 5131), (1269, 22, 5132), (1269, 26, 5133), (1269, 62, 660), (1269, 27, 5134), (1270, 110, 662), (1270, 1, 5135), (1270, 27, 5134), (1271, 12, 5124), (1271, 4, 5126), (1271, 5, 1090), (1271, 13, 5127), (1271, 1, 5137), (1271, 14, 5129), (1271, 10, 5138), (1271, 90, 5139), (1271, 22, 5132), (1271, 26, 5140), (1271, 62, 660), (1271, 27, 5141), (1272, 110, 662), (1272, 1, 5142), (1272, 27, 5141), (1273, 118, 5143), (1273, 11, 5144), (1273, 8, 5145), (1273, 110, 5146), (1273, 87, 3751), (1273, 90, 5147), (1273, 14, 5148), (1273, 62, 4097), (1274, 110, 4099), (1274, 1, 5149), (1274, 27, 5150), (1275, 110, 5151), (1275, 114, 5152), (1275, 3, 5153), (1275, 14, 5154), (1275, 11, 5155), (1275, 10, 5156), (1275, 1, 5157), (1275, 26, 5158), (1275, 8, 5159), (1275, 7, 5160), (1275, 62, 5161), (1275, 27, 5162), (1277, 110, 5151), (1277, 114, 5152), (1277, 3, 5153), (1277, 14, 5154), (1277, 11, 5155), (1277, 10, 5156), (1277, 1, 5157), (1277, 26, 5158), (1277, 8, 5159), (1277, 7, 5160), (1277, 62, 5161), (1277, 27, 5165), (1279, 110, 5168), (1276, 110, 5163), (1276, 12, 5164), (1276, 4, 2368), (1276, 5, 1954), (1276, 10, 5166), (1276, 14, 5167), (1276, 13, 5169), (1276, 26, 5170), (1276, 1, 5171), (1276, 90, 5172), (1276, 62, 1264), (1276, 27, 5173), (1276, 116, 5174), (1278, 110, 1266), (1278, 1, 5175), (1278, 27, 5173), (1280, 110, 5176), (1280, 12, 507), (1280, 25, 508), (1280, 10, 5177), (1280, 14, 3905), (1280, 1, 5178), (1280, 26, 5179), (1280, 90, 5180), (1280, 62, 1329), (1280, 27, 5181), (1280, 116, 5182), (1282, 110, 5176), (1282, 12, 507), (1282, 25, 508), (1282, 4, 2022), (1282, 5, 310), (1282, 10, 5177), (1282, 14, 3905), (1282, 1, 5178), (1282, 26, 5179), (1282, 90, 5180), (1282, 62, 1329), (1282, 27, 5184), (1282, 116, 5182), (1283, 110, 1332), (1283, 1, 5185), (1283, 27, 5184), (1284, 110, 4995), (1284, 14, 4996), (1284, 1, 4997), (1284, 12, 5065), (1284, 90, 5091), (1284, 62, 6), (1284, 27, 5186), (1285, 110, 5093), (1285, 1, 5094), (1285, 27, 5186), (1281, 110, 5183), (1281, 8, 5187), (1281, 14, 5188), (1281, 7, 4090), (1287, 110, 5189), (1288, 110, 5190), (1288, 1, 5191), (1288, 27, 5192), (1289, 1, 5194), (1289, 27, 5195), (1289, 110, 5196), (1290, 110, 5197), (1291, 110, 5198), (1291, 14, 5199), (1291, 1, 5200), (1291, 12, 5201), (1291, 90, 5202), (1291, 62, 6), (1291, 27, 5203), (1292, 110, 5204), (1292, 1, 5205), (1292, 27, 5203), (1293, 12, 1771), (1293, 4, 1270), (1293, 5, 1969), (1293, 13, 5206), (1293, 14, 5207), (1293, 10, 5208), (1293, 26, 5209), (1293, 1, 5210), (1293, 62, 3913), (1293, 27, 5212), (1293, 110, 5214), (1295, 110, 5215), (1296, 110, 5216), (1296, 14, 5217), (1296, 1, 5218), (1296, 12, 5219), (1296, 90, 5220), (1296, 62, 6), (1296, 27, 5221), (1296, 116, 5222), (1297, 110, 5223), (1297, 1, 5224), (1297, 27, 5221), (1294, 110, 5193), (1294, 11, 5213), (1294, 8, 4089), (1294, 14, 480), (1294, 62, 4934), (1298, 110, 5226), (1298, 11, 5227), (1298, 6, 5228), (1298, 8, 4933), (1298, 14, 2575), (1298, 62, 4934), (1299, 110, 5229), (1299, 11, 5230), (1299, 6, 5231), (1299, 8, 4089), (1299, 14, 5232), (1299, 62, 4934), (1300, 110, 5233), (1300, 11, 5234), (1300, 6, 5235), (1300, 8, 5236), (1300, 14, 5237), (1300, 62, 4934), (1301, 110, 5238), (1301, 11, 5239), (1301, 6, 5240), (1301, 8, 5241), (1301, 14, 5242), (1301, 62, 4934), (1303, 110, 5247), (1303, 11, 5248), (1303, 8, 5249), (1303, 14, 2390), (1303, 62, 4934), (1304, 110, 5250), (1304, 11, 5251), (1304, 8, 5253), (1304, 14, 284), (1304, 62, 4934), (1305, 110, 5254), (1305, 11, 5255), (1305, 8, 4089), (1305, 14, 1540), (1305, 62, 4934), (1306, 110, 5257), (1306, 11, 5258), (1306, 6, 5259), (1306, 8, 5260), (1306, 14, 2112), (1306, 62, 4934), (1307, 110, 5261), (1307, 11, 5262), (1307, 8, 5263), (1307, 14, 1177), (1307, 62, 4934), (1308, 110, 5264), (1308, 11, 5265), (1308, 8, 5249), (1308, 14, 2575), (1308, 62, 4934), (1309, 110, 5266), (1309, 11, 5267), (1309, 6, 5268), (1309, 8, 5269), (1309, 14, 4079), (1309, 62, 4934), (1310, 110, 5270), (1310, 11, 5271), (1310, 6, 5272), (1310, 8, 4933), (1310, 14, 495), (1310, 62, 4934), (1311, 110, 5273), (1311, 11, 5274), (1311, 6, 5275), (1311, 8, 5276), (1311, 14, 5277), (1311, 62, 4934), (1312, 110, 5278), (1312, 11, 5279), (1312, 8, 5280), (1312, 14, 4086), (1312, 62, 4934), (1313, 110, 5281), (1313, 11, 5282), (1313, 8, 5241), (1313, 14, 3514), (1313, 62, 4934), (1314, 110, 5284), (1314, 11, 5285), (1314, 6, 5286), (1314, 8, 5236), (1314, 14, 3514), (1314, 62, 4934), (1316, 11, 5291), (1316, 6, 5292), (1316, 8, 5293), (1316, 14, 4075), (1316, 62, 4934), (1316, 116, 5294), (1317, 110, 5295), (1317, 11, 5296), (1317, 6, 5297), (1317, 8, 4933), (1317, 14, 495), (1317, 62, 4934), (1316, 110, 5298), (1216, 110, 5299), (1214, 110, 5300), (1318, 110, 5301), (1318, 11, 5302), (1318, 6, 4937), (1318, 8, 5303), (1318, 14, 495), (1318, 62, 4934), (1319, 110, 5304), (1319, 11, 5305), (1319, 8, 4093), (1319, 14, 2390), (1319, 62, 4934), (1320, 110, 5306), (1320, 12, 507), (1320, 25, 508), (1320, 4, 5307), (1320, 5, 310), (1320, 10, 5308), (1320, 14, 5309), (1320, 1, 5310), (1320, 26, 5311), (1320, 62, 1329), (1320, 27, 5312), (1321, 110, 1332), (1321, 1, 5313), (1321, 27, 5312), (1322, 1, 5314), (1322, 90, 5315), (1322, 14, 5316), (1322, 26, 5317), (1322, 13, 1944), (1322, 5, 310), (1322, 10, 5318), (1322, 12, 1074), (1322, 110, 5319), (1322, 4, 310), (1322, 62, 5320), (1322, 27, 5321), (1324, 110, 5325), (1324, 1, 5326), (1324, 27, 5327), (1325, 110, 5082), (1325, 14, 5083), (1325, 1, 5084), (1325, 12, 5085), (1325, 90, 5086), (1325, 62, 6), (1325, 27, 5328), (1325, 116, 5088), (1326, 110, 5089), (1326, 1, 5090), (1326, 27, 5328), (1327, 8, 4089), (1327, 14, 5329), (1327, 6, 1954), (1327, 11, 5330), (1327, 118, 5331), (1327, 110, 5332), (1327, 62, 5333), (1327, 116, 5334), (1329, 110, 5338), (1327, 7, 4090), (1330, 110, 5339), (1330, 14, 5340), (1330, 1, 5341), (1330, 12, 5342), (1330, 90, 5343), (1330, 62, 6), (1330, 27, 5344), (1330, 116, 5345), (1331, 110, 5346), (1331, 1, 5347), (1331, 27, 5344), (1332, 110, 5348), (1332, 14, 5349), (1332, 1, 5350), (1332, 12, 5351), (1332, 90, 5352), (1332, 62, 6), (1332, 27, 5353), (1332, 116, 5354), (1333, 110, 5355), (1333, 1, 5356), (1333, 27, 5353), (1335, 110, 5358), (1335, 14, 5359), (1335, 1, 5360), (1335, 12, 5361), (1335, 90, 5362), (1335, 62, 6), (1335, 27, 5363), (1336, 110, 5364), (1336, 1, 5365), (1336, 27, 5363), (1337, 110, 5366), (1337, 6, 5368), (1337, 7, 5369), (1337, 8, 5371), (1337, 14, 5277), (1338, 110, 5372), (1339, 8, 5373), (1339, 14, 5374), (1339, 11, 5375), (1339, 118, 5376), (1339, 110, 5377), (1339, 7, 5369), (1339, 6, 5380), (1341, 110, 5381), (1342, 110, 5382), (1342, 11, 5383), (1342, 8, 5384), (1342, 14, 2112), (1342, 62, 4934), (1343, 110, 5385), (1343, 11, 5274), (1343, 8, 5386), (1343, 62, 4934), (1344, 11, 5388), (1344, 8, 5389), (1344, 14, 1177), (1344, 62, 4934), (1345, 11, 5390), (1345, 8, 5389), (1345, 14, 1177), (1345, 62, 4934), (1348, 11, 5391), (1348, 8, 5392), (1348, 14, 1177), (1348, 62, 4934), (1345, 110, 5396), (1345, 4, 135), (1345, 45, 1954), (1344, 110, 5398), (1344, 4, 1954), (1344, 45, 1954), (1348, 22, 5399), (1348, 110, 5400), (1348, 4, 1090), (1348, 45, 1954), (1351, 110, 5401), (1352, 110, 5402), (1353, 110, 5403), (1354, 110, 5404), (1354, 11, 5405), (1354, 6, 5406), (1354, 8, 5407), (1354, 14, 2112), (1354, 62, 4934), (1354, 116, 5408), (1355, 110, 5409), (1355, 11, 5410), (1355, 8, 5411), (1355, 14, 1363), (1355, 62, 4934), (1355, 116, 5412), (1356, 110, 5413), (1356, 11, 5414), (1356, 6, 5415), (1356, 8, 5416), (1356, 14, 1363), (1356, 62, 4934), (1356, 116, 5417), (1357, 110, 5418), (1312, 6, 5419), (1214, 6, 5368), (1304, 6, 5419), (1308, 6, 5368), (1313, 6, 5368), (1303, 6, 5368), (1294, 6, 5420), (1358, 110, 5421), (1358, 14, 5422), (1358, 1, 5423), (1358, 12, 5424), (1358, 90, 5425), (1358, 62, 6), (1358, 27, 5426), (1359, 110, 5427), (1359, 1, 5428), (1359, 27, 5426), (1360, 118, 5429), (1360, 11, 5430), (1360, 8, 5431), (1360, 110, 5432), (1360, 87, 3751), (1360, 90, 5433), (1360, 14, 5434), (1360, 62, 4097), (1360, 116, 5435), (1361, 110, 4099), (1361, 1, 5436), (1361, 27, 5437), (1362, 110, 5438), (1362, 12, 5439), (1362, 4, 1090), (1362, 5, 1954), (1362, 10, 5440), (1362, 14, 5441), (1362, 13, 5442), (1362, 26, 5443), (1362, 1, 5444), (1362, 90, 5445), (1362, 62, 1264), (1362, 27, 5446), (1363, 110, 1266), (1363, 1, 5447), (1363, 27, 5446), (1364, 110, 5448), (1364, 12, 5449), (1364, 4, 1660), (1364, 5, 1090), (1364, 10, 5450), (1364, 14, 284), (1364, 26, 5451), (1364, 1, 5452), (1364, 90, 5453), (1364, 62, 5454), (1364, 27, 5455), (1366, 110, 5457), (1367, 110, 5458), (1367, 14, 3532), (1367, 1, 5459), (1367, 12, 5460), (1367, 90, 5461), (1367, 62, 6), (1367, 27, 5462), (1368, 110, 5463), (1368, 1, 5464), (1368, 27, 5462), (1369, 110, 5465), (1369, 12, 93), (1369, 25, 94), (1369, 4, 1670), (1369, 5, 274), (1369, 10, 5466), (1369, 14, 5467), (1369, 1, 5468), (1369, 26, 5469), (1369, 90, 5470), (1369, 62, 1329), (1369, 27, 5471), (1369, 116, 5472), (1370, 110, 1332), (1370, 1, 5473), (1370, 27, 5471), (1371, 12, 1408), (1371, 13, 4013), (1371, 14, 5474), (1371, 10, 2860), (1371, 26, 2861), (1371, 1, 5475), (1371, 110, 2863), (1371, 62, 3913), (1371, 27, 5476), (1372, 110, 294), (1372, 1, 2866), (1372, 27, 5476), (1373, 110, 5477), (1373, 12, 93), (1373, 25, 94), (1373, 4, 5478), (1373, 5, 90), (1373, 10, 5479), (1373, 14, 5480), (1373, 1, 5481), (1373, 26, 5482), (1373, 90, 5483), (1373, 62, 1329), (1373, 27, 5484), (1373, 116, 5472), (1375, 110, 5486), (1376, 110, 5487), (1376, 12, 93), (1376, 25, 94), (1376, 4, 1670), (1376, 5, 299), (1376, 10, 5488), (1376, 14, 5489), (1376, 1, 5490), (1376, 26, 5491), (1376, 90, 5492), (1376, 62, 1329), (1376, 27, 5493), (1376, 116, 5472), (1377, 110, 1332), (1377, 1, 5494), (1377, 27, 5493), (1378, 110, 5495), (1378, 12, 93), (1378, 25, 94), (1378, 4, 4231), (1378, 5, 299), (1378, 10, 1708), (1378, 14, 5496), (1378, 1, 5497), (1378, 26, 5498), (1378, 90, 5499), (1378, 62, 1329), (1378, 27, 5500), (1379, 110, 1332), (1379, 1, 5501), (1379, 27, 5500), (1380, 110, 5502), (1380, 14, 5503), (1380, 12, 1372), (1380, 4, 5504), (1380, 5, 274), (1380, 26, 5505), (1380, 87, 3751), (1380, 10, 5506), (1380, 13, 4339), (1380, 1, 5507), (1380, 27, 5508), (1380, 62, 5509), (1380, 90, 5510), (1381, 110, 1983), (1381, 1, 5511), (1381, 27, 5508), (1382, 12, 1408), (1382, 4, 5512), (1382, 5, 1090), (1382, 13, 4013), (1382, 14, 5513), (1382, 10, 5514), (1382, 26, 5515), (1382, 1, 5516), (1382, 110, 5517), (1382, 62, 3913), (1382, 27, 5518), (1382, 116, 5519), (1383, 110, 294), (1383, 1, 5520), (1383, 27, 5518), (1384, 110, 5521), (1384, 12, 93), (1384, 25, 94), (1384, 4, 452), (1384, 5, 310), (1384, 10, 5522), (1384, 14, 5154), (1384, 1, 5523), (1384, 26, 5524), (1384, 90, 5525), (1384, 62, 1329), (1384, 27, 5526), (1385, 110, 1332), (1385, 1, 5527), (1385, 27, 5526), (1386, 110, 5528), (1386, 14, 5529), (1386, 12, 1539), (1386, 4, 5530), (1386, 5, 5531), (1386, 26, 5532), (1386, 90, 5533), (1386, 10, 5534), (1386, 1, 5535), (1386, 27, 5536), (1386, 62, 5537), (1387, 110, 1983), (1387, 1, 5538), (1387, 27, 5536), (1388, 12, 286), (1388, 4, 287), (1388, 5, 288), (1388, 13, 3907), (1388, 14, 5539), (1388, 10, 5540), (1388, 26, 5541), (1388, 1, 5542), (1388, 110, 5543), (1388, 62, 3913), (1388, 27, 5544), (1388, 116, 5545), (1390, 110, 5547), (1391, 12, 1408), (1391, 4, 5548), (1391, 5, 135), (1391, 13, 4013), (1391, 14, 5549), (1391, 10, 5550), (1391, 26, 5551), (1391, 1, 5552), (1391, 110, 5553), (1391, 62, 3913), (1391, 27, 5554), (1391, 116, 5555), (1392, 110, 294), (1392, 1, 5556), (1392, 27, 5554), (1393, 12, 1408), (1393, 4, 5557), (1393, 5, 1090), (1393, 13, 4013), (1393, 14, 5558), (1393, 10, 5559), (1393, 26, 5560), (1393, 1, 5561), (1393, 110, 5562), (1393, 62, 3913), (1393, 27, 5563), (1393, 116, 5564), (1394, 110, 294), (1394, 1, 5565), (1394, 27, 5563), (1365, 110, 4935), (1365, 12, 93), (1365, 25, 94), (1365, 4, 5478), (1365, 5, 90), (1365, 10, 4944), (1365, 14, 5211), (1365, 1, 5225), (1365, 26, 5252), (1365, 90, 5283), (1365, 62, 1329), (1365, 27, 5290), (1365, 116, 5367), (1374, 110, 1332), (1374, 1, 5370), (1374, 27, 5290), (1389, 110, 5387), (1389, 12, 93), (1389, 25, 94), (1389, 14, 5456), (1389, 1, 5485), (1389, 26, 5546), (1389, 90, 5566), (1389, 62, 1329), (1389, 27, 5567), (1395, 110, 1332), (1395, 1, 5568), (1395, 27, 5567), (1396, 12, 286), (1396, 4, 1969), (1396, 5, 497), (1396, 13, 3907), (1396, 14, 5569), (1396, 10, 5570), (1396, 26, 5571), (1396, 1, 5572), (1396, 110, 5573), (1396, 62, 3913), (1396, 27, 5574), (1398, 110, 5576), (1399, 110, 5577), (1399, 12, 93), (1399, 25, 94), (1399, 4, 2090), (1399, 5, 90), (1399, 10, 5578), (1399, 14, 5579), (1399, 1, 5580), (1399, 26, 5581), (1399, 90, 5582), (1399, 62, 1329), (1399, 27, 5583), (1399, 116, 5584), (1400, 110, 1332), (1400, 1, 5585), (1400, 27, 5583), (1401, 12, 286), (1401, 4, 5586), (1401, 5, 3103), (1401, 13, 3907), (1401, 14, 5587), (1401, 10, 5588), (1401, 26, 5589), (1401, 1, 5590), (1401, 110, 5591), (1401, 62, 3913), (1401, 27, 5592), (1403, 110, 5594), (1407, 1, 5605), (1407, 90, 5596), (1407, 14, 5597), (1407, 26, 5598), (1407, 13, 1944), (1407, 5, 1204), (1407, 10, 5599), (1407, 12, 1074), (1407, 110, 5600), (1407, 4, 5601), (1407, 62, 5320), (1407, 27, 5607), (1409, 110, 5325), (1409, 1, 5603), (1409, 27, 5609), (1397, 110, 5575), (1397, 11, 5593), (1397, 6, 5610), (1397, 8, 5236), (1397, 14, 5611), (1397, 62, 4934), (1402, 110, 5612), (1402, 11, 5613), (1402, 8, 5615), (1402, 14, 3514), (1402, 62, 4934), (1410, 110, 5616), (1410, 11, 5617), (1410, 8, 5619), (1410, 14, 5620), (1410, 62, 4934), (1410, 6, 5420), (1410, 7, 4090), (1402, 6, 5420), (1402, 7, 4090), (1411, 110, 5621), (1411, 14, 5622), (1411, 26, 5623), (1411, 87, 3751), (1411, 12, 1978), (1411, 25, 5624), (1411, 4, 5625), (1411, 5, 5626), (1411, 1, 5627), (1411, 10, 5628), (1411, 13, 5629), (1411, 27, 5630), (1411, 62, 5631), (1411, 90, 5632), (1415, 110, 5634), (1415, 14, 5635), (1415, 26, 5636), (1415, 87, 3751), (1415, 12, 1978), (1415, 25, 5624), (1415, 4, 4024), (1415, 5, 5637), (1415, 1, 5638), (1415, 10, 5639), (1415, 13, 5629), (1415, 27, 5643), (1415, 62, 5631), (1415, 90, 5641), (1417, 110, 5644), (1418, 110, 5645), (1419, 1, 5646), (1419, 90, 5647), (1419, 14, 5648), (1419, 26, 5649), (1419, 13, 1944), (1419, 10, 5650), (1419, 12, 1074), (1419, 110, 1958), (1419, 62, 5320), (1419, 27, 5651), (1421, 110, 5325), (1421, 1, 5654), (1421, 27, 5655), (1422, 110, 5656), (1422, 12, 4581), (1422, 25, 4582), (1422, 4, 5657), (1422, 5, 310), (1422, 10, 5658), (1422, 14, 5659), (1422, 1, 5660), (1422, 26, 5661), (1422, 90, 5662), (1422, 62, 1329), (1422, 27, 5663), (1423, 110, 1332), (1423, 1, 5664), (1423, 27, 5663), (1424, 110, 5665), (1425, 110, 5666), (1425, 14, 5667), (1425, 1, 5668), (1425, 12, 5669), (1425, 90, 5670), (1425, 62, 6), (1425, 27, 5671), (1426, 110, 5672), (1426, 1, 5673), (1426, 27, 5671), (1427, 110, 5674), (1427, 14, 5675), (1427, 1, 5676), (1427, 12, 5677), (1427, 90, 5678), (1427, 62, 6), (1427, 27, 5679), (1428, 110, 5680), (1428, 1, 5681), (1428, 27, 5679), (1429, 12, 286), (1429, 4, 1270), (1429, 5, 156), (1429, 13, 3907), (1429, 14, 5682), (1429, 10, 5683), (1429, 26, 5684), (1429, 1, 5685), (1429, 110, 4957), (1429, 62, 292), (1429, 27, 5686), (1430, 110, 294), (1430, 1, 5687), (1430, 27, 5686), (1334, 110, 2935), (1334, 12, 93), (1334, 25, 94), (1334, 10, 5323), (1334, 14, 4327), (1334, 1, 5324), (1334, 26, 5336), (1334, 90, 5337), (1334, 62, 1329), (1334, 27, 5357), (1412, 110, 1332), (1412, 1, 5614), (1412, 27, 5357), (1416, 12, 286), (1416, 4, 5586), (1416, 5, 3103), (1416, 13, 3907), (1416, 14, 5587), (1416, 10, 5588), (1416, 26, 5589), (1416, 1, 5590), (1416, 110, 5591), (1416, 62, 292), (1416, 27, 5618), (1432, 12, 286), (1432, 13, 3907), (1432, 14, 5587), (1432, 10, 5588), (1432, 26, 5589), (1432, 1, 5590), (1432, 110, 5591), (1432, 62, 292), (1432, 27, 5688), (1434, 110, 5690), (1435, 12, 286), (1435, 4, 287), (1435, 5, 274), (1435, 13, 3907), (1435, 14, 5691), (1435, 10, 5692), (1435, 26, 5693), (1435, 1, 5694), (1435, 110, 5695), (1435, 62, 292), (1435, 27, 5696), (1437, 110, 5698), (1437, 12, 93), (1437, 25, 94), (1437, 4, 155), (1437, 5, 274), (1437, 10, 5699), (1437, 14, 495), (1437, 1, 5700), (1437, 26, 5701), (1437, 90, 5702), (1437, 62, 1329), (1437, 27, 5703), (1438, 110, 1332), (1438, 1, 5704), (1438, 27, 5703), (1439, 110, 5705), (1440, 12, 286), (1440, 4, 1077), (1440, 5, 1954), (1440, 13, 289), (1440, 14, 5706), (1440, 10, 5707), (1440, 26, 5708), (1440, 1, 5709), (1440, 110, 5710), (1440, 62, 292), (1440, 27, 5711), (1442, 110, 5713), (1443, 110, 5714), (1443, 12, 286), (1443, 4, 1954), (1443, 5, 274), (1443, 10, 5715), (1443, 1, 5716), (1443, 14, 1540), (1443, 90, 5717), (1444, 110, 5718), (1431, 1, 5633), (1431, 90, 5689), (1431, 14, 5697), (1431, 26, 5712), (1431, 13, 1944), (1431, 5, 1204), (1431, 10, 5719), (1431, 12, 1074), (1431, 110, 5720), (1431, 4, 2368), (1431, 62, 5320), (1431, 27, 5721), (1433, 110, 5325), (1433, 1, 5722), (1433, 27, 5723), (1340, 14, 5188), (1340, 110, 5335), (1340, 12, 1451), (1340, 10, 5378), (1340, 4, 5379), (1340, 5, 124), (1340, 26, 5394), (1340, 62, 1458), (1346, 110, 5395), (1346, 1, 5397), (1346, 27, 5726), (1347, 110, 5727), (1347, 14, 3905), (1347, 90, 5728), (1347, 62, 5729), (1349, 110, 5730), (1349, 1, 5731), (1349, 27, 5732), (1350, 110, 5733), (1350, 12, 93), (1350, 25, 94), (1350, 4, 5379), (1350, 5, 274), (1350, 10, 5734), (1350, 14, 5735), (1350, 1, 5736), (1350, 26, 5737), (1350, 90, 5738), (1350, 62, 1329), (1350, 27, 5739), (1441, 110, 1332), (1441, 1, 5740), (1441, 27, 5739), (1445, 12, 1225), (1445, 4, 5601), (1445, 5, 1090), (1445, 13, 4389), (1445, 14, 5741), (1445, 10, 1090), (1445, 26, 5742), (1445, 1, 5743), (1445, 110, 5744), (1445, 62, 1416), (1445, 27, 5745), (1446, 110, 5746), (1446, 14, 5747), (1446, 26, 5748), (1446, 87, 3751), (1446, 12, 3170), (1446, 25, 5624), (1446, 4, 5749), (1446, 5, 5750), (1446, 1, 5751), (1446, 10, 5752), (1446, 13, 5629), (1446, 27, 5753), (1446, 62, 5631), (1446, 90, 5754), (1448, 110, 5756), (1447, 1, 5755), (1447, 90, 5757), (1447, 14, 5758), (1447, 26, 5759), (1447, 13, 1944), (1447, 5, 90), (1447, 10, 5760), (1447, 12, 1074), (1447, 110, 5761), (1447, 4, 5307), (1447, 62, 5320), (1447, 27, 5762), (1451, 110, 5765), (1452, 1, 5766), (1452, 90, 5767), (1452, 14, 5758), (1452, 26, 5768), (1452, 13, 1944), (1452, 5, 90), (1452, 10, 5769), (1452, 12, 1074), (1452, 110, 5770), (1452, 4, 5307), (1452, 62, 5320), (1452, 27, 5771), (1455, 110, 5774), (1456, 110, 5775), (1456, 12, 870), (1456, 14, 284), (1456, 5, 310), (1456, 4, 156), (1456, 1, 5776), (1457, 110, 5777), (1458, 110, 5778), (1458, 12, 5779), (1458, 4, 156), (1458, 14, 284), (1458, 1, 5780), (1458, 27, 5781), (1458, 62, 5782), (1459, 110, 5783), (1460, 12, 286), (1460, 4, 135), (1460, 5, 1090), (1460, 13, 3907), (1460, 14, 5784), (1460, 10, 5785), (1460, 26, 5786), (1460, 1, 5787), (1460, 110, 5788), (1460, 62, 292), (1460, 27, 5789), (1462, 110, 5791), (1463, 1, 5796), (1463, 90, 5797), (1463, 14, 5798), (1463, 26, 5799), (1463, 13, 1944), (1463, 5, 1954), (1463, 10, 5800), (1463, 12, 1074), (1463, 110, 1963), (1463, 4, 1954), (1463, 62, 5320), (1463, 27, 5801), (1466, 110, 5805), (1467, 1, 5806), (1467, 14, 5807), (1467, 26, 5808), (1467, 13, 1944), (1467, 5, 1204), (1467, 10, 5809), (1467, 12, 1074), (1467, 110, 5810), (1467, 4, 274), (1467, 62, 5320), (1467, 27, 5811), (1467, 116, 5812), (1470, 110, 5815), (1471, 1, 5816), (1471, 90, 5817), (1471, 14, 5818), (1471, 26, 5819), (1471, 13, 1944), (1471, 5, 1954), (1471, 10, 5820), (1471, 12, 1074), (1471, 110, 5821), (1471, 4, 135), (1471, 62, 5320), (1471, 27, 5822), (1474, 110, 5826), (1475, 1, 5827), (1475, 90, 5828), (1475, 14, 5829), (1475, 26, 5830), (1475, 13, 1944), (1475, 5, 299), (1475, 10, 5831), (1475, 12, 1074), (1475, 110, 5832), (1475, 4, 5586), (1475, 62, 5320), (1475, 27, 5833), (1478, 12, 286), (1478, 4, 2799), (1478, 5, 497), (1478, 13, 3907), (1478, 14, 5837), (1478, 10, 5838), (1478, 26, 5839), (1478, 1, 5840), (1478, 110, 5841), (1478, 62, 292), (1478, 27, 5842), (1480, 110, 5844), (1481, 110, 5845), (1323, 110, 5640), (1323, 14, 5642), (1323, 1, 5652), (1323, 12, 5653), (1323, 90, 5724), (1323, 62, 6), (1323, 27, 5725), (1323, 116, 5843), (1413, 110, 5846), (1413, 1, 5847), (1413, 27, 5725), (1414, 1, 5848), (1414, 90, 5849), (1414, 14, 5850), (1414, 26, 5851), (1414, 13, 1944), (1414, 5, 1077), (1414, 10, 5852), (1414, 12, 1074), (1414, 110, 5853), (1414, 4, 2799), (1414, 62, 5854), (1414, 27, 5855), (1436, 110, 5858), (1479, 110, 5859), (1482, 110, 5860), (1482, 14, 5861), (1482, 1, 5862), (1482, 22, 5863), (1482, 26, 5864), (1482, 12, 5865), (1482, 90, 5866), (1482, 62, 6), (1482, 27, 5867), (1482, 116, 5868), (1483, 110, 5869), (1483, 1, 5870), (1483, 27, 5867), (1484, 110, 5871), (1484, 14, 5872), (1484, 1, 5873), (1484, 12, 5874), (1484, 90, 5875), (1484, 62, 6), (1484, 27, 5876), (1485, 110, 5877), (1485, 1, 5878), (1485, 27, 5876), (1488, 110, 5881), (1488, 12, 93), (1488, 25, 94), (1488, 4, 2607), (1488, 5, 274), (1488, 10, 2484), (1488, 14, 5882), (1488, 1, 5883), (1488, 26, 5884), (1488, 90, 5885), (1488, 62, 1329), (1488, 27, 5886), (1488, 116, 5887), (1489, 110, 1332), (1489, 1, 5888), (1489, 27, 5886), (1490, 12, 286), (1490, 4, 2799), (1490, 5, 1204), (1490, 13, 3907), (1490, 14, 5889), (1490, 10, 4603), (1490, 26, 5890), (1490, 1, 5891), (1490, 110, 5892), (1490, 62, 292), (1490, 27, 5893), (1492, 110, 5895), (1493, 110, 5896), (1494, 110, 5897), (1495, 1, 5898), (1495, 90, 5899), (1495, 14, 5900), (1495, 26, 5901), (1495, 13, 1944), (1495, 5, 156), (1495, 10, 5902), (1495, 12, 1074), (1495, 110, 5903), (1495, 4, 5904), (1495, 62, 5854), (1495, 27, 5905), (1497, 110, 5908), (1498, 1, 5909), (1498, 90, 5910), (1498, 14, 5911), (1498, 26, 5912), (1498, 13, 1944), (1498, 5, 288), (1498, 10, 5913), (1498, 12, 1074), (1498, 110, 5914), (1498, 4, 3439), (1498, 62, 5854), (1498, 27, 5915), (1498, 116, 1447), (1499, 110, 5325), (1499, 1, 5916), (1499, 27, 5917), (1501, 12, 286), (1501, 4, 89), (1501, 5, 1969), (1501, 13, 3907), (1501, 14, 5920), (1501, 10, 5921), (1501, 26, 5922), (1501, 1, 5923), (1501, 110, 5924), (1501, 62, 292), (1501, 27, 5925), (1503, 110, 5927), (1504, 12, 286), (1504, 4, 274), (1504, 5, 1077), (1504, 13, 3907), (1504, 14, 5928), (1504, 10, 5929), (1504, 26, 5930), (1504, 1, 5931), (1504, 110, 5932), (1504, 62, 292), (1504, 27, 5933), (1506, 110, 5935), (1487, 110, 5880), (1487, 14, 5894), (1487, 1, 5926), (1487, 12, 5934), (1487, 90, 5936), (1487, 62, 6), (1487, 27, 5937), (1487, 116, 5938), (1491, 110, 5939), (1491, 1, 5940), (1491, 27, 5937), (1502, 1, 5941), (1502, 90, 5942), (1502, 14, 5943), (1502, 26, 5944), (1502, 13, 1944), (1502, 5, 274), (1502, 10, 5945), (1502, 12, 1074), (1502, 110, 5946), (1502, 4, 579), (1502, 62, 5854), (1502, 27, 5947), (1505, 110, 5325), (1505, 1, 5948), (1505, 27, 5949), (1508, 110, 5952), (1508, 12, 507), (1508, 25, 508), (1508, 4, 1294), (1508, 5, 3103), (1508, 10, 5953), (1508, 14, 5954), (1508, 1, 5955), (1508, 26, 5956), (1508, 90, 5957), (1508, 62, 1329), (1508, 27, 5958), (1509, 110, 1332), (1509, 1, 5959), (1509, 27, 5958), (1510, 110, 5960), (1510, 12, 93), (1510, 25, 94), (1510, 4, 3342), (1510, 5, 299), (1510, 10, 5961), (1510, 14, 3905), (1510, 1, 5962), (1510, 26, 5963), (1510, 90, 5964), (1510, 62, 1329), (1510, 27, 5965), (1511, 110, 1332), (1511, 1, 5966), (1511, 27, 5965), (1512, 12, 1771), (1512, 4, 5904), (1512, 5, 274), (1512, 13, 5206), (1512, 14, 1147), (1512, 10, 5967), (1512, 26, 5968), (1512, 1, 5969), (1512, 110, 5970), (1512, 62, 292), (1512, 27, 5971), (1514, 110, 5973), (1515, 11, 5975), (1515, 110, 5976), (1515, 87, 3751), (1515, 6, 5368), (1515, 8, 5236), (1515, 14, 284), (1515, 118, 5981), (1517, 110, 5982), (1513, 12, 286), (1513, 4, 374), (1513, 5, 5601), (1513, 13, 3907), (1513, 14, 5972), (1513, 10, 5983), (1513, 26, 5984), (1513, 1, 5985), (1513, 110, 5986), (1513, 62, 292), (1513, 27, 5987), (1519, 110, 5989), (1520, 110, 5990), (1520, 12, 2559), (1520, 4, 5991), (1520, 5, 5992), (1520, 10, 5993), (1520, 14, 5994), (1520, 13, 2564), (1520, 26, 5995), (1520, 1, 5996), (1520, 90, 5997), (1520, 62, 1264), (1520, 27, 5998), (1521, 110, 1266), (1521, 1, 5999), (1521, 27, 5998), (1522, 110, 6000), (1522, 12, 93), (1522, 25, 94), (1522, 4, 145), (1522, 5, 299), (1522, 10, 1708), (1522, 14, 6001), (1522, 1, 6002), (1522, 26, 6003), (1522, 90, 6004), (1522, 62, 1329), (1522, 27, 6005), (1523, 110, 1332), (1523, 1, 6006), (1523, 27, 6005), (1524, 110, 6007), (1524, 14, 6008), (1524, 1, 6009), (1524, 12, 6010), (1524, 90, 6011), (1524, 62, 6), (1524, 27, 6012), (1525, 110, 6013), (1525, 1, 6014), (1525, 27, 6012), (1526, 12, 2341), (1526, 4, 6015), (1526, 13, 2340), (1526, 14, 6016), (1526, 10, 6017), (1526, 26, 6018), (1526, 1, 6019), (1526, 110, 6020), (1526, 62, 292), (1526, 27, 6021), (1527, 110, 294), (1527, 1, 6022), (1527, 27, 6021), (1528, 110, 6023), (1528, 12, 93), (1528, 25, 94), (1528, 10, 6024), (1528, 14, 6025), (1528, 1, 6026), (1528, 26, 6027), (1528, 90, 6028), (1528, 62, 1329), (1528, 27, 6029), (1529, 110, 1332), (1529, 1, 6030), (1529, 27, 6029), (1530, 110, 6031), (1530, 12, 93), (1530, 25, 94), (1530, 4, 155), (1530, 5, 156), (1530, 10, 6032), (1530, 14, 6033), (1530, 1, 6034), (1530, 26, 6035), (1530, 90, 6036), (1530, 62, 1329), (1530, 27, 6037), (1531, 110, 1332), (1531, 1, 6038), (1531, 27, 6037), (1449, 110, 5763), (1449, 14, 5764), (1449, 1, 5772), (1449, 12, 5773), (1449, 90, 5974), (1449, 62, 6), (1449, 27, 5977), (1450, 110, 5978), (1450, 1, 5988), (1450, 27, 5977), (1453, 110, 5082), (1453, 14, 5083), (1453, 1, 5084), (1453, 12, 5085), (1453, 90, 5086), (1453, 62, 6), (1453, 27, 6039), (1453, 116, 5088), (1454, 110, 5089), (1454, 1, 5090), (1454, 27, 6039), (1213, 11, 6041), (1213, 6, 6042), (1213, 14, 1363), (1532, 110, 6043), (1532, 12, 4403), (1532, 13, 6044), (1532, 10, 6045), (1532, 4, 3103), (1532, 5, 872), (1532, 1, 6046), (1532, 14, 4075), (1532, 26, 6047), (1532, 62, 1316), (1532, 27, 6048), (1533, 110, 6049), (1533, 1, 6050), (1533, 27, 6048), (1534, 110, 6051), (1534, 12, 93), (1534, 25, 94), (1534, 4, 6052), (1534, 5, 135), (1534, 10, 6053), (1534, 14, 6054), (1534, 1, 6055), (1534, 26, 6056), (1534, 90, 6057), (1534, 62, 1329), (1534, 27, 6058), (1535, 110, 1332), (1535, 1, 6059), (1535, 27, 6058), (1420, 110, 4931), (1420, 12, 5022), (1420, 4, 4932), (1420, 5, 135), (1420, 10, 5790), (1420, 14, 5792), (1420, 13, 5026), (1420, 26, 5793), (1420, 1, 5794), (1461, 110, 5795), (1464, 110, 5802), (1464, 14, 5803), (1464, 1, 5804), (1464, 22, 5813), (1464, 26, 5814), (1464, 12, 5823), (1464, 90, 5824), (1464, 62, 6), (1464, 27, 5825), (1465, 110, 5834), (1465, 1, 5835), (1465, 27, 5825), (1468, 110, 5836), (1468, 14, 5856), (1468, 1, 5857), (1468, 12, 5879), (1468, 90, 5906), (1468, 62, 6), (1468, 27, 5907), (1468, 116, 5918), (1469, 110, 5919), (1469, 1, 5950), (1469, 27, 5907), (1472, 110, 5951), (1472, 25, 5979), (1472, 4, 3439), (1472, 14, 4079), (1472, 10, 5980), (1472, 1, 6040), (1472, 90, 6060), (1472, 12, 5979), (1472, 62, 1287), (1472, 27, 6061), (1473, 110, 6062), (1473, 1, 6063), (1473, 27, 6061), (1476, 110, 6064), (1476, 14, 6065), (1476, 1, 6066), (1476, 12, 6067), (1476, 90, 6068), (1476, 62, 6), (1476, 27, 6069), (1486, 110, 6072), (1496, 110, 6073), (1496, 14, 6074), (1496, 1, 6075), (1496, 12, 6076), (1496, 90, 6077), (1496, 62, 6), (1496, 27, 6078), (1500, 110, 6079), (1500, 1, 6080), (1500, 27, 6078), (1507, 110, 6081), (1507, 12, 2635), (1507, 13, 2634), (1507, 10, 6082), (1507, 4, 3439), (1507, 5, 872), (1507, 1, 6083), (1507, 90, 6084), (1507, 14, 273), (1507, 26, 6085), (1507, 62, 1316), (1507, 27, 6086), (1507, 116, 6087), (1516, 110, 6049), (1516, 1, 6088), (1516, 27, 6086), (1536, 110, 6089), (1536, 14, 6090), (1536, 1, 6091), (1536, 12, 6092), (1536, 90, 6093), (1536, 62, 6), (1536, 27, 6094), (1537, 110, 6095), (1537, 1, 6096), (1537, 27, 6094), (1538, 26, 6097), (1538, 110, 6098), (1538, 12, 93), (1538, 25, 94), (1538, 1, 6100), (1538, 14, 6101), (1538, 90, 6102), (1538, 62, 1329), (1538, 27, 6103), (1538, 116, 2240), (1540, 110, 6105), (1541, 110, 6106), (1541, 25, 1539), (1541, 4, 6107), (1541, 5, 6108), (1541, 10, 6109), (1541, 1, 6110), (1541, 26, 6111), (1541, 14, 6112), (1541, 12, 1539), (1543, 110, 6113), (1544, 110, 6114), (1544, 14, 6074), (1544, 1, 6115), (1544, 12, 6116), (1544, 90, 6117), (1544, 62, 6), (1544, 27, 6118), (1544, 116, 6119), (1545, 110, 6120), (1545, 1, 6121), (1545, 27, 6118), (1539, 110, 3131), (1539, 12, 5779), (1539, 4, 5307), (1539, 14, 5792), (1539, 1, 6104), (1539, 27, 6122), (1539, 62, 5782), (1546, 110, 6123), (1547, 110, 6124), (1547, 14, 6125), (1547, 1, 6126), (1547, 12, 6127), (1547, 90, 6128), (1547, 62, 6), (1547, 27, 6129), (1548, 110, 6130), (1548, 1, 6131), (1548, 27, 6129), (1549, 26, 6132), (1549, 110, 3280), (1549, 12, 93), (1549, 25, 94), (1549, 10, 6133), (1549, 1, 6134), (1549, 14, 6135), (1549, 90, 6136), (1549, 62, 1329), (1549, 27, 6137), (1549, 116, 3285), (1551, 110, 6139), (1552, 26, 6140), (1552, 110, 6141), (1552, 12, 93), (1552, 25, 94), (1552, 4, 145), (1552, 5, 274), (1552, 10, 6142), (1552, 1, 6143), (1552, 14, 6144), (1552, 90, 6145), (1552, 62, 1329), (1552, 27, 6146), (1553, 110, 1332), (1553, 1, 6147), (1553, 27, 6146), (1554, 110, 6148), (1554, 14, 6149), (1554, 1, 6150), (1554, 12, 6151), (1554, 90, 6152), (1554, 62, 6), (1554, 27, 6153), (1554, 116, 6154), (1555, 110, 6155), (1555, 1, 6156), (1555, 27, 6153), (1556, 110, 6157), (1556, 14, 6158), (1556, 1, 6159), (1556, 12, 6160), (1556, 90, 6161), (1556, 62, 6), (1556, 27, 6162), (1557, 110, 6163), (1557, 1, 6164), (1557, 27, 6162), (1550, 26, 6138), (1550, 110, 6165), (1550, 12, 455), (1550, 25, 456), (1550, 4, 1270), (1550, 5, 274), (1550, 10, 6166), (1550, 1, 6167), (1550, 14, 6168), (1550, 62, 1329), (1550, 27, 6169), (1558, 110, 1332), (1558, 1, 6170), (1558, 27, 6169), (1559, 26, 6171), (1559, 110, 5763), (1559, 12, 93), (1559, 25, 94), (1559, 10, 2179), (1559, 1, 6172), (1559, 14, 6173), (1559, 90, 6174), (1559, 62, 1329), (1559, 27, 6175), (1560, 110, 1332), (1560, 1, 6176), (1560, 27, 6175), (1561, 110, 6177), (1561, 14, 6178), (1563, 110, 6177), (1563, 1, 6182), (1563, 27, 6183), (1564, 110, 6184), (1565, 110, 6185), (1566, 110, 6186), (1567, 110, 6187), (261, 90, 6188), (1568, 110, 6189), (261, 22, 6190), (1569, 110, 6191), (1570, 110, 6192), (1573, 12, 2407), (1573, 13, 2408), (1573, 1, 6193), (1573, 14, 6194), (1573, 110, 6195), (1573, 15, 6196), (1573, 62, 2413), (1573, 27, 6200), (1575, 1, 6203), (1575, 27, 6204), (1575, 110, 6205), (1576, 110, 6202), (1576, 1, 6203), (1576, 27, 6206), (1477, 1, 6070), (1477, 27, 6071), (1577, 110, 892), (1577, 1, 6070), (1577, 27, 6207), (1578, 110, 6208), (1578, 1, 6209), (1578, 27, 6210), (1477, 110, 6211), (576, 110, 1988), (576, 14, 1989), (576, 1, 1990), (576, 12, 6179), (576, 90, 6180), (576, 62, 6), (576, 27, 6181), (1562, 110, 6197), (1562, 1, 6199), (1562, 27, 6181), (1579, 110, 6219), (1579, 14, 6220), (1579, 1, 6221), (1579, 12, 6222), (1579, 90, 6223), (1579, 62, 6), (1579, 27, 6224), (1580, 110, 6225), (1580, 1, 6226), (1580, 27, 6224), (1271, 110, 6227), (1581, 12, 286), (1581, 13, 3907), (1581, 14, 5682), (1581, 26, 5684), (1581, 1, 5685), (1581, 110, 4957), (1581, 62, 292), (1581, 27, 6228), (1583, 110, 6230), (1584, 110, 6231), (1584, 1, 6232), (1584, 27, 6233), (1585, 110, 6234), (1586, 110, 6231), (1586, 1, 6232), (1586, 27, 6235), (1587, 110, 6236), (1587, 1, 6237), (1587, 27, 6238), (1588, 110, 6241), (1591, 110, 6246), (1592, 110, 6248), (1590, 110, 6249), (1589, 110, 6250), (1593, 110, 6254), (1594, 110, 6255), (1595, 110, 6258), (1596, 110, 6261), (1597, 110, 6263), (1598, 110, 6264), (1599, 110, 6266), (1601, 110, 6270), (1602, 110, 6271), (1600, 110, 6273), (1582, 110, 5136), (1582, 14, 6229), (1582, 1, 6274), (1582, 12, 6275), (1582, 90, 6276), (1582, 62, 6), (1582, 27, 6277), (1582, 116, 6278), (1603, 110, 6279), (1603, 1, 6280), (1603, 27, 6277), (1604, 110, 2002), (1604, 14, 6281), (1604, 1, 6282), (1604, 22, 6283), (1604, 26, 6284), (1604, 12, 6285), (1604, 90, 6286), (1604, 62, 6), (1604, 27, 6287), (1604, 116, 2010), (1605, 110, 6288), (1605, 1, 6289), (1605, 27, 6287), (1606, 26, 6290), (1606, 110, 6291), (1606, 12, 93), (1606, 25, 94), (1606, 4, 6052), (1606, 5, 90), (1606, 10, 6292), (1606, 1, 6293), (1606, 14, 6294), (1606, 90, 6295), (1606, 62, 1329), (1606, 27, 6296), (1607, 110, 1332), (1607, 1, 6297), (1607, 27, 6296), (1608, 110, 3428), (1608, 14, 3429), (1608, 1, 3430), (1608, 22, 6298), (1608, 26, 6299), (1608, 12, 6300), (1608, 90, 6301), (1608, 62, 6), (1608, 27, 6302), (1609, 110, 3434), (1609, 1, 3435), (1609, 27, 6302), (1610, 26, 6303), (1610, 110, 6304), (1610, 12, 93), (1610, 25, 94), (1610, 4, 1358), (1610, 5, 90), (1610, 10, 6292), (1610, 1, 6305), (1610, 14, 6306), (1610, 90, 6307), (1610, 62, 1329), (1610, 27, 6308), (1611, 110, 1332), (1611, 1, 6309), (1611, 27, 6308), (1612, 110, 6310), (1612, 14, 6311), (1612, 1, 6312), (1612, 12, 6313), (1612, 90, 6314), (1612, 62, 6), (1612, 27, 6315), (1613, 110, 6316), (1613, 1, 6317), (1613, 27, 6315), (1614, 110, 6318), (1614, 8, 6319), (1614, 11, 6320), (1614, 1, 6321), (1614, 10, 6322), (1614, 14, 871), (1614, 115, 6323), (1614, 87, 6324), (1614, 2, 6325), (1614, 62, 3755), (1614, 27, 6326), (1615, 26, 6327), (1615, 110, 6157), (1615, 12, 93), (1615, 25, 94), (1615, 10, 2674), (1615, 1, 6328), (1615, 14, 6329), (1615, 90, 6330), (1615, 62, 1329), (1615, 27, 6331), (1616, 110, 1332), (1616, 1, 6332), (1616, 27, 6331), (1617, 26, 6333), (1617, 110, 6334), (1617, 12, 93), (1617, 25, 94), (1617, 4, 6052), (1617, 5, 310), (1617, 10, 6335), (1617, 1, 6336), (1617, 14, 6337), (1617, 90, 6338), (1617, 62, 1329), (1617, 27, 6339), (1617, 116, 6340), (1618, 110, 1332), (1618, 1, 6341), (1618, 27, 6339), (1619, 26, 6342), (1619, 110, 3839), (1619, 12, 93), (1619, 25, 94), (1619, 4, 3774), (1619, 5, 156), (1619, 10, 4453), (1619, 1, 6343), (1619, 14, 6344), (1619, 90, 6345), (1619, 62, 1329), (1619, 27, 6346), (1620, 110, 1332), (1620, 1, 6347), (1620, 27, 6346), (1621, 26, 6348), (1621, 110, 6349), (1621, 12, 93), (1621, 25, 94), (1621, 4, 6052), (1621, 5, 90), (1621, 10, 6350), (1621, 1, 6351), (1621, 14, 6352), (1621, 90, 6353), (1621, 62, 1329), (1621, 27, 6354), (1621, 116, 6355), (1623, 110, 6357), (390, 110, 1190), (390, 14, 1185), (390, 116, 1189), (390, 1, 1188), (390, 27, 1186), (390, 90, 6239), (390, 89, 446), (1622, 26, 6240), (1622, 110, 6242), (1622, 12, 93), (1622, 25, 94), (1622, 4, 155), (1622, 5, 274), (1622, 10, 6243), (1622, 1, 6244), (1622, 14, 6245), (1622, 90, 6247), (1622, 62, 1329), (1622, 27, 6251), (1624, 110, 1332), (1624, 1, 6252), (1624, 27, 6251), (1625, 12, 286), (1625, 13, 3907), (1625, 14, 6253), (1625, 26, 2802), (1625, 1, 6256), (1625, 110, 2804), (1625, 62, 292), (1625, 27, 6257), (1627, 110, 2806), (1628, 12, 6260), (1628, 4, 4231), (1628, 5, 1204), (1628, 13, 6262), (1628, 14, 773), (1628, 10, 6265), (1628, 26, 6267), (1628, 1, 6268), (1628, 62, 292), (1628, 27, 6272), (1628, 116, 6356), (1630, 12, 286), (1630, 13, 3907), (1630, 14, 5682), (1630, 26, 6360), (1630, 1, 6361), (1630, 110, 6362), (1630, 62, 292), (1630, 27, 6363), (1632, 110, 6365), (1633, 110, 6366), (1634, 12, 6367), (1634, 4, 1204), (1634, 5, 6368), (1634, 13, 6369), (1634, 14, 6370), (1634, 10, 6371), (1634, 26, 6372), (1634, 1, 6373), (1634, 62, 292), (1634, 27, 6375), (1634, 116, 6376), (1636, 110, 6378), (1634, 110, 6379), (1628, 110, 6380), (1637, 12, 286), (1637, 4, 1270), (1637, 5, 156), (1637, 13, 3907), (1637, 14, 5682), (1637, 10, 6381), (1637, 26, 6382), (1637, 1, 6383), (1637, 110, 6384), (1637, 62, 292), (1637, 27, 6385), (1639, 110, 6387), (1640, 26, 6388), (1640, 110, 6389), (1640, 12, 507), (1640, 25, 508), (1640, 4, 6390), (1640, 5, 2368), (1640, 10, 6391), (1640, 1, 6392), (1640, 14, 6393), (1640, 90, 6394), (1640, 62, 1329), (1640, 27, 6395), (1640, 116, 6396), (1641, 110, 1332), (1641, 1, 6397), (1641, 27, 6395), (1642, 26, 6398), (1642, 110, 6399), (1642, 12, 93), (1642, 25, 94), (1642, 4, 6400), (1642, 5, 90), (1642, 10, 6401), (1642, 1, 6402), (1642, 14, 6403), (1642, 90, 6404), (1642, 62, 1329), (1642, 27, 6405), (1643, 110, 1332), (1643, 1, 6406), (1643, 27, 6405), (1644, 12, 286), (1644, 4, 2245), (1644, 5, 310), (1644, 13, 3907), (1644, 14, 6407), (1644, 10, 6408), (1644, 26, 6409), (1644, 1, 6410), (1644, 110, 6411), (1644, 62, 292), (1644, 27, 6412), (1646, 12, 1408), (1646, 13, 4013), (1646, 14, 4316), (1646, 26, 6415), (1646, 1, 6416), (1646, 110, 6417), (1646, 62, 292), (1646, 27, 6418), (1648, 12, 286), (1648, 4, 3617), (1648, 5, 90), (1648, 13, 3907), (1648, 14, 6420), (1648, 10, 6421), (1648, 26, 6422), (1648, 1, 6423), (1648, 110, 6424), (1648, 62, 292), (1648, 27, 6425), (1650, 26, 6427), (1650, 110, 6428), (1650, 12, 93), (1650, 25, 94), (1650, 4, 3774), (1650, 5, 90), (1650, 10, 3691), (1650, 1, 6429), (1650, 14, 6430), (1650, 90, 6431), (1650, 62, 1329), (1650, 27, 6432), (1650, 116, 6433), (1652, 26, 6435), (1652, 110, 6436), (1652, 12, 93), (1652, 25, 94), (1652, 4, 2022), (1652, 5, 299), (1652, 10, 6437), (1652, 1, 6438), (1652, 14, 6439), (1652, 90, 6440), (1652, 62, 1329), (1652, 27, 6441), (1654, 26, 6443), (1654, 110, 6444), (1654, 12, 93), (1654, 25, 94), (1654, 4, 2607), (1654, 5, 90), (1654, 10, 6445), (1654, 1, 6446), (1654, 14, 6447), (1654, 90, 6448), (1654, 62, 1329), (1654, 27, 6449), (1656, 12, 1408), (1656, 4, 2877), (1656, 5, 1090), (1656, 13, 4013), (1656, 14, 6451), (1656, 10, 6452), (1656, 26, 6453), (1656, 1, 6454), (1656, 110, 6455), (1656, 62, 292), (1656, 27, 6456), (1658, 12, 286), (1658, 4, 374), (1658, 5, 1969), (1658, 13, 3907), (1658, 14, 1965), (1658, 10, 6458), (1658, 26, 6459), (1658, 1, 6460), (1658, 110, 6461), (1658, 62, 292), (1658, 27, 6462), (1660, 12, 1408), (1660, 4, 6464), (1660, 5, 135), (1660, 13, 4013), (1660, 14, 6465), (1660, 10, 6466), (1660, 26, 6467), (1660, 1, 6468), (1660, 110, 6469), (1660, 62, 292), (1660, 27, 6470), (1662, 12, 286), (1662, 13, 3907), (1662, 14, 5539), (1662, 26, 5541), (1662, 1, 5542), (1662, 110, 5543), (1662, 62, 292), (1662, 27, 6472), (1662, 116, 5545), (1664, 110, 6474), (1664, 14, 6475), (1664, 1, 6476), (1664, 12, 6477), (1664, 90, 6478), (1664, 62, 6), (1664, 27, 6479), (1665, 110, 6480), (1665, 1, 6481), (1665, 27, 6479), (1629, 110, 6198), (1629, 1, 6358), (1629, 27, 6364), (1631, 12, 6374), (1631, 4, 6377), (1631, 5, 310), (1631, 13, 6386), (1631, 14, 6413), (1631, 10, 6419), (1631, 26, 6426), (1631, 1, 6434), (1631, 62, 292), (1631, 27, 6450), (1635, 110, 294), (1635, 1, 6457), (1635, 27, 6450), (1631, 110, 6463), (398, 110, 6471), (1638, 110, 6473), (1638, 14, 6482), (1638, 1, 6483), (1638, 12, 6484), (1638, 90, 6485), (1638, 62, 6), (1638, 27, 6486), (1645, 110, 6487), (1645, 1, 6488), (1645, 27, 6486), (1647, 110, 6148), (1647, 14, 6149), (1647, 1, 6150), (1647, 12, 6151), (1647, 90, 6152), (1647, 62, 6), (1647, 27, 6489), (1647, 116, 6154), (1649, 110, 6155), (1649, 1, 6156), (1649, 27, 6489), (1651, 110, 6490), (1651, 14, 6491), (1651, 26, 6492), (1651, 87, 3751), (1651, 12, 1372), (1651, 25, 6493), (1651, 4, 6494), (1651, 5, 274), (1651, 1, 6495), (1651, 10, 6496), (1651, 13, 6497), (1651, 27, 6498), (1651, 62, 6499), (1651, 90, 6500), (1653, 110, 1983), (1653, 1, 6501), (1653, 27, 6498), (1655, 110, 6502), (1655, 14, 6503), (1655, 1, 6504), (1655, 12, 6505), (1655, 90, 6506), (1655, 62, 6), (1655, 27, 6507), (1655, 116, 6508), (1657, 110, 6509), (1657, 1, 6510), (1657, 27, 6507), (1659, 26, 5546), (1659, 110, 5387), (1659, 12, 93), (1659, 25, 94), (1659, 4, 1744), (1659, 5, 156), (1659, 10, 5393), (1659, 1, 5485), (1659, 14, 5456), (1659, 90, 5566), (1659, 62, 1329), (1659, 27, 6511), (1661, 110, 1332), (1661, 1, 5568), (1661, 27, 6511), (1663, 12, 6512), (1663, 4, 274), (1663, 5, 310), (1663, 13, 6513), (1663, 14, 284), (1663, 10, 6514), (1663, 26, 6515), (1663, 1, 6516), (1663, 110, 6517), (1663, 62, 1416), (1663, 27, 6518), (1666, 110, 6519), (1666, 14, 6520), (1666, 1, 6521), (1666, 12, 6522), (1666, 90, 6523), (1666, 62, 6), (1666, 27, 6524), (1667, 110, 6525), (1667, 1, 6526), (1667, 27, 6524), (1668, 110, 6527), (1668, 14, 6528), (1668, 1, 6529), (1668, 12, 6530), (1668, 90, 6531), (1668, 62, 6), (1668, 27, 6532), (1669, 110, 1213), (1669, 14, 6442), (1669, 26, 6533), (1669, 87, 3751), (1669, 12, 3170), (1669, 25, 5624), (1669, 4, 6534), (1669, 5, 6535), (1669, 1, 6536), (1669, 10, 6537), (1669, 13, 5629), (1669, 27, 6538), (1669, 62, 6539), (1669, 90, 6540), (1670, 110, 1983), (1670, 1, 6541), (1670, 27, 6538), (1673, 26, 6543), (1673, 110, 6546), (1673, 12, 93), (1673, 25, 94), (1673, 10, 5961), (1673, 1, 6547), (1673, 14, 6548), (1673, 90, 903), (1673, 62, 1329), (1673, 27, 6549), (1674, 110, 1332), (1674, 1, 6550), (1674, 27, 6549), (1675, 110, 6551), (1675, 12, 5779), (1675, 4, 891), (1675, 14, 6552), (1675, 1, 6553), (1675, 27, 6554), (1675, 62, 5782), (1676, 110, 6555), (1676, 1, 6556), (1676, 27, 6557), (1677, 110, 6558), (1680, 1, 6567), (1680, 90, 6560), (1680, 14, 6561), (1680, 26, 6562), (1680, 13, 1944), (1680, 5, 135), (1680, 10, 6563), (1680, 12, 1074), (1680, 110, 6564), (1680, 4, 299), (1680, 62, 6565), (1680, 27, 6569), (1681, 110, 5325), (1681, 1, 6570), (1681, 27, 6571), (1682, 110, 5322), (1682, 1, 6567), (1682, 27, 6572), (1683, 110, 6573), (1683, 25, 6574), (1683, 4, 156), (1683, 5, 1090), (1683, 10, 6575), (1683, 13, 6576), (1683, 26, 6577), (1683, 1, 6578), (1683, 90, 6579), (1683, 14, 6580), (1683, 12, 6574), (1683, 62, 1264), (1683, 27, 6581), (1684, 110, 1266), (1684, 1, 6582), (1684, 27, 6581), (1685, 110, 6583), (1685, 14, 6584), (1685, 12, 6585), (1685, 25, 6586), (1685, 4, 1969), (1685, 5, 6587), (1685, 26, 6588), (1685, 87, 3751), (1685, 10, 6589), (1685, 13, 6590), (1685, 1, 6591), (1685, 27, 6592), (1685, 62, 6593), (1685, 90, 6594), (1686, 110, 1983), (1686, 1, 6595), (1686, 27, 6592), (1687, 110, 6596), (1687, 25, 1257), (1687, 4, 6597), (1687, 5, 135), (1687, 10, 6598), (1687, 13, 1260), (1687, 26, 6599), (1687, 1, 6600), (1687, 90, 6601), (1687, 14, 6602), (1687, 12, 1257), (1687, 62, 1264), (1687, 27, 6603), (1688, 110, 1266), (1688, 1, 6604), (1688, 27, 6603), (1689, 110, 6605), (1689, 14, 6606), (1689, 12, 2635), (1689, 25, 6607), (1689, 4, 5904), (1689, 5, 156), (1689, 26, 6608), (1689, 87, 3751), (1689, 10, 6609), (1689, 13, 4005), (1689, 1, 6610), (1689, 27, 6611), (1689, 62, 6612), (1689, 90, 6613), (1690, 110, 1983), (1690, 1, 6614), (1690, 27, 6611), (1691, 110, 6615), (1691, 14, 6616), (1691, 1, 6617), (1691, 12, 6618), (1691, 90, 6619), (1691, 62, 6), (1691, 27, 6620), (1692, 110, 6621), (1692, 1, 6622), (1692, 27, 6620), (1693, 110, 6623), (1693, 14, 6624), (1693, 1, 6625), (1693, 12, 6626), (1693, 90, 6627), (1693, 62, 6), (1693, 27, 6628), (1694, 110, 6629), (1694, 1, 6630), (1694, 27, 6628), (1695, 110, 6631), (1695, 14, 6632), (1695, 1, 6633), (1695, 22, 6634), (1695, 26, 6635), (1695, 12, 6636), (1695, 90, 6637), (1695, 62, 6), (1695, 27, 6638), (1695, 116, 6639), (1696, 110, 6640), (1696, 1, 6641), (1696, 27, 6638), (1697, 26, 6642), (1697, 110, 6643), (1697, 12, 93), (1697, 25, 94), (1697, 4, 6052), (1697, 5, 90), (1697, 10, 6644), (1697, 1, 6645), (1697, 14, 6646), (1697, 90, 6647), (1697, 62, 1329), (1697, 27, 6648), (1697, 116, 5843), (1698, 110, 1332), (1698, 1, 6649), (1698, 27, 6648), (1703, 118, 1187), (1703, 11, 6201), (1703, 8, 4089), (1703, 87, 3751), (1703, 90, 6269), (1703, 14, 6650), (1703, 62, 4097), (1703, 116, 6651), (1705, 110, 6654), (1705, 14, 6655), (1705, 12, 6656), (1705, 25, 6657), (1705, 4, 1090), (1705, 5, 1090), (1705, 26, 6658), (1705, 87, 3751), (1705, 10, 6659), (1705, 13, 6660), (1705, 1, 6661), (1705, 27, 6662), (1705, 62, 6593), (1705, 90, 6663), (1706, 110, 1983), (1706, 1, 6664), (1706, 27, 6662), (1707, 110, 6665), (1707, 14, 6666), (1707, 26, 6667), (1707, 87, 3751), (1707, 12, 3170), (1707, 25, 5624), (1707, 4, 6668), (1707, 5, 6669), (1707, 1, 6670), (1707, 10, 6671), (1707, 13, 5629), (1707, 27, 6672), (1707, 62, 5631), (1707, 90, 6673), (1708, 110, 1983), (1708, 1, 6674), (1708, 27, 6672), (1709, 110, 6675), (1709, 12, 6676), (1709, 5, 1969), (1710, 110, 6677), (1709, 14, 6678), (1709, 1, 6679), (1671, 110, 6542), (1671, 14, 6544), (1671, 1, 6545), (1671, 12, 6559), (1671, 90, 6566), (1671, 62, 6), (1671, 27, 6568), (1672, 110, 6688), (1672, 1, 6689), (1672, 27, 6568), (1717, 110, 6700), (1717, 12, 5099), (1717, 10, 6701), (1717, 14, 3905), (1717, 26, 6702), (1717, 1, 6703), (1717, 90, 6704), (1717, 13, 6705), (1717, 62, 6706), (1717, 27, 6707), (1719, 110, 6709), (1719, 1, 6710), (1719, 27, 6711), (1718, 26, 6708), (1718, 110, 6064), (1718, 12, 93), (1718, 25, 94), (1718, 4, 1422), (1718, 5, 274), (1718, 10, 6712), (1718, 1, 6713), (1718, 14, 6714), (1718, 90, 6715), (1718, 62, 1329), (1718, 27, 6716), (1720, 110, 1332), (1720, 1, 6717), (1720, 27, 6716), (1721, 110, 6718), (1721, 14, 6719), (1721, 12, 286), (1721, 25, 1779), (1721, 4, 3513), (1721, 5, 1204), (1721, 26, 6720), (1721, 87, 3751), (1721, 90, 6721), (1721, 10, 6722), (1721, 13, 289), (1721, 1, 6723), (1721, 27, 6724), (1721, 62, 292), (1723, 110, 6726), (1723, 14, 6727), (1723, 12, 286), (1723, 25, 1779), (1723, 4, 3513), (1723, 5, 1077), (1723, 26, 6728), (1723, 87, 3751), (1723, 90, 6729), (1723, 10, 6730), (1723, 13, 289), (1723, 1, 6731), (1723, 27, 6732), (1723, 62, 292), (1725, 110, 6734), (1725, 1, 6735), (1725, 27, 6736), (1726, 110, 6737), (1727, 110, 6738), (1728, 110, 6740), (1728, 14, 6741), (1728, 1, 6742), (1728, 12, 6743), (1728, 90, 6744), (1728, 62, 6), (1728, 27, 6745), (1729, 110, 6746), (1729, 1, 6747), (1729, 27, 6745), (1722, 110, 6725), (1722, 14, 6584), (1722, 12, 6585), (1722, 25, 6586), (1722, 4, 1969), (1722, 5, 6587), (1722, 26, 6733), (1722, 87, 3751), (1722, 10, 6748), (1722, 13, 6590), (1722, 1, 6749), (1722, 27, 6750), (1722, 62, 6612), (1722, 90, 6751), (1724, 110, 1983), (1724, 1, 6752), (1724, 27, 6750), (1732, 110, 6758), (1732, 14, 6759), (1732, 1, 6760), (1732, 22, 6761), (1732, 26, 4353), (1732, 12, 6762), (1732, 90, 4355), (1732, 62, 6), (1732, 27, 6763), (1733, 110, 6764), (1733, 1, 6765), (1733, 27, 6763), (1734, 110, 6766), (1734, 14, 6767), (1734, 1, 6768), (1734, 12, 6769), (1734, 90, 6770), (1734, 62, 6), (1734, 27, 6771), (1734, 116, 6772), (1735, 110, 6773), (1735, 1, 6774), (1735, 27, 6771), (1736, 110, 6775), (1736, 14, 6776), (1736, 8, 6777), (1736, 11, 6778), (1736, 10, 6779), (1736, 1, 6780), (1736, 27, 6781), (1736, 62, 6593), (1736, 115, 6782), (1736, 2, 6783), (1736, 3, 6784), (1736, 90, 6785), (1736, 116, 6786), (1737, 110, 1983), (1737, 1, 6787), (1737, 27, 6781), (1738, 26, 6788), (1738, 110, 6789), (1738, 12, 4581), (1738, 25, 4582), (1738, 4, 5657), (1738, 5, 1077), (1738, 10, 6790), (1738, 1, 6791), (1738, 14, 6792), (1738, 90, 6793), (1738, 62, 1329), (1738, 27, 6794), (1740, 110, 6796), (1740, 14, 6797), (1740, 1, 6798), (1740, 12, 6799), (1740, 90, 6800), (1740, 62, 6), (1740, 27, 6801), (1741, 110, 6802), (1741, 1, 6803), (1741, 27, 6801), (1742, 110, 6804), (1742, 14, 6805), (1742, 12, 1408), (1742, 25, 1409), (1742, 4, 6806), (1742, 5, 1090), (1742, 26, 6807), (1742, 87, 3751), (1742, 90, 6808), (1742, 10, 6809), (1742, 13, 1407), (1742, 1, 6810), (1742, 27, 6811), (1742, 62, 292), (1743, 110, 1983), (1743, 1, 6812), (1743, 27, 6811), (1744, 26, 6813), (1744, 110, 6814), (1744, 12, 93), (1744, 25, 94), (1744, 4, 2461), (1744, 5, 274), (1744, 10, 6815), (1744, 1, 6816), (1744, 14, 6817), (1744, 90, 6818), (1744, 62, 1329), (1744, 27, 6819), (1746, 110, 6821), (1746, 1, 6822), (1746, 27, 6823), (1747, 110, 6824), (1747, 14, 1690), (1747, 62, 6695), (1747, 27, 6826), (1747, 1, 6822), (1739, 110, 6739), (1739, 14, 6795), (1739, 1, 6820), (1739, 12, 6827), (1739, 90, 6828), (1739, 62, 6), (1739, 27, 6829), (1739, 116, 6830), (1745, 110, 6831), (1745, 1, 6832), (1745, 27, 6829), (1750, 110, 6835), (1750, 14, 6836), (1750, 1, 6837), (1750, 12, 6838), (1750, 90, 6839), (1750, 62, 6), (1750, 27, 6840), (1751, 110, 6841), (1751, 1, 6842), (1751, 27, 6840), (1755, 110, 190), (1755, 1, 6852), (1755, 27, 6853), (1756, 12, 1225), (1756, 4, 4231), (1756, 5, 1090), (1756, 13, 4389), (1756, 14, 480), (1756, 10, 1453), (1756, 26, 6848), (1756, 1, 6849), (1756, 110, 6850), (1756, 62, 1416), (1756, 27, 6854), (1757, 110, 6855), (1757, 1, 6856), (1757, 27, 6857), (1758, 110, 6858), (1758, 12, 6859), (1758, 14, 273), (1758, 1, 6860), (1758, 62, 6695), (1758, 27, 6861), (1758, 116, 6862), (1759, 110, 190), (1759, 1, 6863), (1759, 27, 6864), (1760, 12, 1225), (1760, 4, 3371), (1760, 5, 872), (1760, 13, 4389), (1760, 14, 5611), (1760, 10, 6865), (1760, 26, 6866), (1760, 1, 6867), (1760, 110, 6868), (1760, 62, 1416), (1760, 27, 6869), (1761, 110, 6870), (1761, 1, 6871), (1761, 27, 6872), (1762, 110, 6873), (1762, 12, 6874), (1762, 14, 273), (1762, 1, 6875), (1762, 62, 6695), (1762, 27, 6876), (1762, 116, 6877), (1408, 26, 5608), (1408, 110, 6527), (1408, 12, 93), (1408, 25, 94), (1408, 1, 6690), (1408, 14, 6825), (1408, 90, 6878), (1408, 62, 1329), (1408, 27, 6879), (1678, 110, 1332), (1678, 1, 6880), (1678, 27, 6879), (1763, 110, 6881), (1763, 1, 6882), (1763, 27, 6883), (1765, 110, 6887), (1765, 1, 6888), (1765, 27, 6889), (1766, 1, 6888), (1766, 27, 6890), (1766, 110, 6891), (1764, 110, 6886), (1764, 1, 6882), (1764, 27, 6885), (1764, 62, 6695), (1767, 110, 6892), (1767, 1, 6893), (1767, 27, 6894), (1768, 110, 6895), (1768, 1, 6896), (1768, 27, 6897), (1769, 110, 6898), (1769, 4, 374), (1769, 5, 310), (1769, 10, 6899), (1769, 14, 1540), (1769, 12, 6900), (1770, 110, 6901), (1770, 12, 6902), (1770, 4, 3103), (1770, 10, 6903), (1770, 14, 5620), (1771, 110, 6904), (1771, 1, 6905), (1771, 27, 6906), (1772, 110, 6907), (1772, 14, 5242), (1772, 1, 6910), (1772, 62, 6695), (1772, 27, 6911), (1772, 12, 6912), (1772, 4, 1840), (1772, 10, 6913), (1773, 110, 6914), (1773, 1, 6915), (1773, 27, 6916), (1774, 110, 6917), (1774, 12, 6918), (1774, 4, 3103), (1774, 5, 1090), (1774, 10, 6919), (1774, 14, 5620), (1774, 1, 6920), (1774, 62, 6695), (1774, 27, 6921), (1775, 110, 6922), (1775, 1, 6923), (1775, 27, 6924), (1776, 110, 6925), (1776, 12, 1075), (1776, 4, 6926), (1776, 5, 299), (1776, 14, 6928), (1776, 10, 6929), (1777, 110, 6930), (1777, 1, 6931), (1777, 27, 6932), (1778, 110, 6933), (1779, 110, 6934), (1779, 1, 6935), (1779, 27, 6936), (1780, 110, 4077), (1780, 1, 6937), (1780, 27, 6938), (1781, 115, 4073), (1781, 7, 6940), (1781, 8, 592), (1781, 14, 4075), (1781, 110, 4072), (1782, 110, 6941), (1782, 1, 6942), (1782, 27, 6943), (1783, 110, 6944), (1783, 115, 6945), (1783, 10, 6946), (1783, 14, 1540), (1783, 8, 4093), (1783, 1, 6947), (1783, 62, 6695), (1783, 27, 6948), (1784, 110, 6949), (1784, 1, 6950), (1784, 27, 6951), (1785, 110, 6952), (1785, 115, 4098), (1785, 10, 6953), (1785, 14, 4075), (1785, 8, 4093), (1785, 1, 6954), (1785, 62, 6695), (1785, 27, 6955), (1785, 7, 4074), (1786, 110, 6956), (1786, 1, 6957), (1786, 27, 6958), (1787, 110, 6959), (1788, 110, 6960), (1788, 1, 6961), (1788, 27, 6962), (1789, 110, 6963), (1789, 12, 6964), (1789, 4, 497), (1789, 5, 135), (1789, 10, 6965), (1789, 14, 6966), (1789, 1, 6967), (1789, 62, 6695), (1789, 27, 6968), (1790, 110, 6969), (1790, 1, 6970), (1790, 27, 6971), (1791, 110, 6972), (1791, 12, 6973), (1791, 4, 497), (1791, 5, 1954), (1791, 10, 6974), (1791, 14, 6966), (1792, 110, 6975), (1792, 1, 6976), (1792, 27, 6977), (1793, 115, 6979), (1793, 8, 6980), (1793, 14, 4327), (1793, 10, 6981), (1793, 110, 6982), (1794, 62, 6983), (1794, 87, 6984), (1794, 1, 6985), (1794, 110, 6986), (1794, 8, 4093), (1794, 7, 6987), (1794, 14, 4327), (1794, 11, 6988), (1794, 27, 6989), (1795, 118, 6990), (1795, 11, 6991), (1795, 8, 4093), (1795, 110, 6992), (1795, 87, 3751), (1795, 90, 6993), (1795, 14, 6994), (1795, 62, 4097), (1795, 116, 6995), (1796, 110, 4099), (1796, 1, 6996), (1796, 27, 6997), (1797, 110, 6998), (1797, 1, 6999), (1797, 27, 7000), (1798, 110, 7001), (1798, 115, 7002), (1798, 8, 7003), (1798, 14, 5154), (1798, 10, 7004), (1798, 90, 7005), (1799, 110, 7006), (1799, 22, 7007), (1800, 110, 7008), (1801, 110, 7009), (1802, 110, 7010), (1803, 110, 7011), (1804, 110, 7012), (1805, 110, 7013), (1806, 110, 7014), (1807, 110, 7015), (1808, 110, 7016), (1809, 110, 7017), (1810, 110, 7018), (1811, 110, 7019), (1812, 110, 7020), (1813, 110, 7021), (1814, 110, 7022), (1815, 110, 7023), (1816, 110, 7024), (1817, 110, 7025), (1818, 110, 7026), (1819, 110, 7027), (1820, 110, 7028), (1821, 110, 7029), (1822, 110, 7030), (1823, 110, 7031), (1824, 110, 7032), (1825, 110, 7033), (1826, 110, 7034), (1827, 110, 7035), (1828, 110, 7036), (1829, 110, 7037), (1830, 110, 7038), (1831, 110, 7039), (1832, 110, 7040), (1833, 110, 7041), (1834, 110, 7042), (1835, 110, 7043), (1836, 110, 7044), (1837, 110, 7045), (1838, 110, 7046), (1839, 110, 7047), (1840, 110, 7048), (1842, 110, 7052), (1842, 75, 7053), (1843, 110, 7051), (1844, 1, 7054), (1844, 2, 7055), (1844, 8, 7056), (1844, 10, 7057), (1844, 11, 7058), (1844, 14, 7059), (1844, 27, 7060), (1844, 62, 6612), (1844, 87, 3751), (1844, 90, 7061), (1844, 110, 7062), (1844, 115, 6979), (1845, 1, 7063), (1845, 27, 7060), (1845, 110, 1983), (1846, 1, 7054), (1846, 2, 7055), (1846, 8, 7056), (1846, 10, 7057), (1846, 11, 7058), (1846, 14, 7059), (1846, 27, 7064), (1846, 62, 6612), (1846, 87, 3751), (1846, 90, 7061), (1846, 110, 7062), (1846, 115, 6979), (1847, 1, 7063), (1847, 27, 7064), (1847, 110, 1983), (1848, 1, 7065), (1848, 2, 7055), (1848, 8, 7056), (1848, 10, 7066), (1848, 11, 7058), (1848, 14, 7059), (1848, 27, 7064), (1848, 62, 6612), (1848, 87, 3751), (1848, 90, 7067), (1848, 110, 7068), (1848, 115, 6979), (1849, 1, 7069), (1849, 27, 7064), (1849, 110, 1983), (1850, 1, 7070), (1850, 2, 7055), (1850, 8, 7056), (1850, 10, 7071), (1850, 11, 7058), (1850, 14, 7059), (1850, 27, 7064), (1850, 62, 6612), (1850, 87, 3751), (1850, 90, 7072), (1850, 110, 7073), (1850, 115, 6979), (1851, 1, 7074), (1851, 27, 7064), (1851, 110, 1983), (1852, 1, 7075), (1852, 2, 7055), (1852, 8, 7056), (1852, 10, 7076), (1852, 11, 7058), (1852, 14, 7059), (1852, 27, 7064), (1852, 62, 6612), (1852, 87, 3751), (1852, 90, 7077), (1852, 110, 7078), (1852, 115, 6979), (1853, 1, 7079), (1853, 27, 7064), (1853, 110, 1983), (1854, 1, 7080), (1854, 2, 7055), (1854, 8, 7056), (1854, 10, 7081), (1854, 11, 7058), (1854, 14, 7059), (1854, 27, 7064), (1854, 62, 6612), (1854, 87, 3751), (1854, 90, 7082), (1854, 110, 7083), (1854, 115, 6979), (1855, 1, 7084), (1855, 27, 7064), (1855, 110, 1983), (1856, 1, 7085), (1856, 2, 7055), (1856, 8, 7056), (1856, 10, 7086), (1856, 11, 7058), (1856, 14, 7059), (1856, 27, 7064), (1856, 62, 6612), (1856, 87, 3751), (1856, 90, 7087), (1856, 110, 7088), (1856, 115, 6979), (1857, 1, 7089), (1857, 27, 7064), (1857, 110, 1983), (1858, 1, 7090), (1858, 2, 7055), (1858, 8, 7056), (1858, 10, 7091), (1858, 11, 7058), (1858, 14, 7059), (1858, 27, 7064), (1858, 62, 6612), (1858, 87, 3751), (1858, 90, 7092), (1858, 110, 7093), (1858, 115, 6979), (1859, 1, 7094), (1859, 27, 7064), (1859, 110, 1983), (1860, 1, 7095), (1860, 2, 7055), (1860, 8, 7056), (1860, 10, 7096), (1860, 11, 7058), (1860, 14, 7059), (1860, 27, 7064), (1860, 62, 6612), (1860, 87, 3751), (1860, 90, 7097), (1860, 110, 7098), (1860, 115, 6979), (1861, 1, 7099), (1861, 27, 7064), (1861, 110, 1983), (1862, 1, 7100), (1862, 2, 7055), (1862, 8, 7056), (1862, 10, 7101), (1862, 11, 7058), (1862, 14, 7059), (1862, 27, 7064), (1862, 62, 6612), (1862, 87, 3751), (1862, 90, 7102), (1862, 110, 7103), (1862, 115, 6979), (1863, 1, 7104), (1863, 27, 7064), (1863, 110, 1983), (1864, 1, 7105), (1864, 2, 7055), (1864, 8, 7056), (1864, 10, 7106), (1864, 11, 7058), (1864, 14, 7059), (1864, 27, 7064), (1864, 62, 6612), (1864, 87, 3751), (1864, 90, 7107), (1864, 110, 7108), (1864, 115, 6979), (1865, 1, 7109), (1865, 27, 7064), (1865, 110, 1983), (1866, 1, 7110), (1866, 2, 7055), (1866, 8, 7056), (1866, 10, 7111), (1866, 11, 7058), (1866, 14, 7059), (1866, 27, 7064), (1866, 62, 6612), (1866, 87, 3751), (1866, 90, 7112), (1866, 110, 7113), (1866, 115, 6979), (1867, 1, 7114), (1867, 27, 7064), (1867, 110, 1983), (1868, 1, 7115), (1868, 2, 7055), (1868, 8, 7056), (1868, 10, 7116), (1868, 11, 7058), (1868, 14, 7059), (1868, 27, 7064), (1868, 62, 6612), (1868, 87, 3751), (1868, 90, 7117), (1868, 110, 7118), (1868, 115, 6979), (1869, 1, 7119), (1869, 27, 7064), (1869, 110, 1983), (1870, 1, 7120), (1870, 2, 7055), (1870, 8, 7056), (1870, 10, 7121), (1870, 11, 7058), (1870, 14, 7059), (1870, 27, 7064), (1870, 62, 6612), (1870, 87, 3751), (1870, 90, 7122), (1870, 110, 7123), (1870, 115, 6979), (1871, 1, 7124), (1871, 27, 7064), (1871, 110, 1983), (1872, 1, 7125), (1872, 2, 7055), (1872, 8, 7056), (1872, 10, 7126), (1872, 11, 7058), (1872, 14, 7059), (1872, 27, 7064), (1872, 62, 6612), (1872, 87, 3751), (1872, 90, 7127), (1872, 110, 7128), (1872, 115, 6979), (1873, 1, 7129), (1873, 27, 7064), (1873, 110, 1983), (1874, 1, 7130), (1874, 2, 7055), (1874, 8, 7056), (1874, 10, 7131), (1874, 11, 7058), (1874, 14, 7059), (1874, 27, 7064), (1874, 62, 6612), (1874, 87, 3751), (1874, 90, 7132), (1874, 110, 7133), (1874, 115, 6979), (1875, 1, 7134), (1875, 27, 7064), (1875, 110, 1983), (1876, 1, 7135), (1876, 2, 7055), (1876, 8, 7056), (1876, 10, 7136), (1876, 11, 7058), (1876, 14, 7059), (1876, 27, 7064), (1876, 62, 6612), (1876, 87, 3751), (1876, 90, 7137), (1876, 110, 7138), (1876, 115, 6979), (1877, 1, 7139), (1877, 27, 7064), (1877, 110, 1983), (1878, 1, 7140), (1878, 2, 7055), (1878, 8, 7056), (1878, 10, 7141), (1878, 11, 7058), (1878, 14, 7059), (1878, 27, 7064), (1878, 62, 6612), (1878, 87, 3751), (1878, 90, 7142), (1878, 110, 7143), (1878, 115, 6979), (1879, 1, 7144), (1879, 27, 7064), (1879, 110, 1983), (1880, 1, 7145), (1880, 2, 7055), (1880, 8, 7056), (1880, 10, 7146), (1880, 11, 7058), (1880, 14, 7059), (1880, 27, 7064), (1880, 62, 6612), (1880, 87, 3751), (1880, 90, 7147), (1880, 110, 7148), (1880, 115, 6979), (1881, 1, 7149), (1881, 27, 7064), (1881, 110, 1983), (1882, 1, 7150), (1882, 2, 7055), (1882, 8, 7056), (1882, 10, 7151), (1882, 11, 7058), (1882, 14, 7059), (1882, 27, 7064), (1882, 62, 6612), (1882, 87, 3751), (1882, 90, 7152), (1882, 110, 7153), (1882, 115, 6979), (1883, 1, 7154), (1883, 27, 7064), (1883, 110, 1983), (1884, 1, 7155), (1884, 2, 7055), (1884, 8, 7056), (1884, 10, 7156), (1884, 11, 7058), (1884, 14, 7059), (1884, 27, 7064), (1884, 62, 6612), (1884, 87, 3751), (1884, 90, 7157), (1884, 110, 7158), (1884, 115, 6979), (1885, 1, 7159), (1885, 27, 7064), (1885, 110, 1983), (1886, 1, 7160), (1886, 27, 7161), (1887, 1, 7163), (1887, 8, 7164), (1887, 14, 4327), (1887, 27, 7165), (1887, 62, 6695), (1887, 110, 6986), (1888, 1, 7167), (1888, 27, 7168), (1888, 110, 7170), (1889, 1, 7171), (1889, 27, 7172), (1889, 110, 7174), (1890, 1, 7175), (1890, 27, 7176), (1890, 110, 7178), (1891, 1, 7179), (1891, 27, 7180), (1891, 110, 7183), (1892, 1, 7184), (1892, 27, 7185), (1892, 110, 7187), (1893, 1, 7188), (1893, 27, 7189), (1893, 110, 7191), (1894, 1, 7192), (1894, 27, 7193), (1894, 110, 7195), (1895, 1, 7196), (1895, 27, 7197), (1895, 110, 7199), (1886, 110, 7201), (1896, 1, 7202), (1896, 2, 7055), (1896, 8, 7056), (1896, 10, 7203), (1896, 11, 7058), (1896, 14, 7059), (1896, 27, 7204), (1896, 62, 6612), (1896, 87, 3751), (1896, 90, 7205), (1896, 110, 7206), (1896, 115, 6979), (1896, 116, 7207), (1897, 1, 7208), (1897, 27, 7204), (1897, 110, 1983), (1898, 6, 4937), (1898, 8, 4933), (1898, 11, 7209), (1898, 14, 2112), (1898, 62, 4934), (1898, 110, 7210), (1899, 8, 4093), (1899, 11, 7211), (1899, 14, 6994), (1899, 62, 4934), (1900, 6, 5256), (1900, 8, 4933), (1900, 11, 7213), (1900, 14, 5154), (1900, 62, 4934), (1900, 110, 7214), (1901, 8, 7215), (1901, 11, 7216), (1901, 14, 273), (1901, 62, 4934), (1901, 110, 7217), (1901, 7, 7219), (1795, 4, 135), (1795, 7, 5369), (1900, 7, 5369), (1898, 7, 5369), (1899, 110, 7220), (1899, 7, 5369), (1902, 1, 7221), (1902, 4, 2548), (1902, 5, 1954), (1902, 10, 7222), (1902, 12, 2635), (1902, 13, 4005), (1902, 14, 7223), (1902, 25, 6607), (1902, 26, 7224), (1902, 27, 7225), (1902, 62, 6593), (1902, 87, 3751), (1902, 90, 7226), (1902, 110, 7227), (1902, 116, 6087), (1903, 1, 7228), (1903, 27, 7225), (1903, 110, 1983), (1916, 1, 7241), (1916, 12, 7242), (1916, 14, 7243), (1916, 27, 7244), (1916, 62, 6), (1916, 90, 7245), (1916, 110, 7246), (1917, 1, 7247), (1917, 27, 7244), (1917, 110, 7248), (1918, 1, 7249), (1918, 27, 7250), (1918, 110, 7251), (1919, 1, 7252), (1919, 4, 156), (1919, 5, 1090), (1919, 10, 7253), (1919, 12, 6585), (1919, 13, 6590), (1919, 14, 7254), (1919, 25, 6586), (1919, 26, 7255), (1919, 27, 7256), (1919, 62, 6593), (1919, 87, 3751), (1919, 90, 7257), (1919, 110, 7258), (1920, 1, 7259), (1920, 27, 7256), (1920, 110, 1983), (1921, 1, 7260), (1921, 12, 7261), (1921, 14, 7262), (1921, 27, 7263), (1921, 62, 6), (1921, 90, 7264), (1921, 110, 7265), (1922, 1, 7266), (1922, 27, 7263), (1922, 110, 7267), (1923, 1, 7268), (1923, 12, 7269), (1923, 14, 7270), (1923, 27, 7271), (1923, 62, 6), (1923, 90, 7272), (1923, 110, 7273), (1924, 1, 7274), (1924, 27, 7271), (1924, 110, 7275), (1925, 1, 6516), (1925, 27, 7276), (1925, 110, 7277), (1926, 1, 7278), (1926, 12, 7279), (1926, 14, 7280), (1926, 27, 7281), (1926, 62, 6), (1926, 90, 7282), (1926, 110, 7283), (1927, 1, 7284), (1927, 27, 7281), (1927, 110, 7285), (1928, 6, 1954), (1928, 8, 5289), (1928, 11, 7286), (1928, 14, 7287), (1928, 62, 5333), (1928, 110, 7288), (1928, 118, 7289), (1930, 110, 7293), (1932, 110, 7295), (1933, 110, 7296), (1935, 1, 7305), (1935, 2, 7306), (1935, 4, 3439), (1935, 5, 1090), (1935, 10, 7307), (1935, 12, 7308), (1935, 13, 7309), (1935, 14, 7310), (1935, 22, 7311), (1935, 25, 7308), (1935, 26, 7302), (1935, 27, 7312), (1935, 62, 660), (1935, 110, 7304), (1936, 1, 7313), (1936, 27, 7312), (1936, 110, 662), (1938, 1, 7319), (1938, 27, 7315), (1938, 110, 1983), (1937, 27, 7315), (1937, 90, 7316), (1937, 110, 7317), (1937, 116, 7318), (1937, 14, 7320), (1937, 4, 7321), (1937, 10, 7322), (1937, 26, 7323), (1937, 1, 7324), (1939, 1, 7325), (1939, 27, 7326), (1939, 110, 7327), (1940, 110, 7328), (1940, 115, 4073), (1940, 7, 7330), (1940, 8, 592), (1940, 10, 7331), (1940, 90, 7332), (1940, 14, 4075), (1941, 7, 7330), (1941, 8, 592), (1941, 14, 4075), (1941, 115, 4073), (1941, 110, 7333), (1941, 10, 7335), (1941, 90, 7336), (1942, 1, 7337), (1942, 27, 7338), (1942, 110, 7339), (1943, 1, 7340), (1943, 27, 7341), (1943, 110, 7342), (1944, 27, 7346), (1944, 14, 7348), (1944, 118, 7349), (1944, 1, 7350), (1944, 89, 7351), (1944, 90, 7352), (1944, 110, 7353), (1945, 110, 7355), (1946, 110, 7356), (1947, 62, 4097), (1947, 87, 3751), (1947, 90, 7359), (1947, 110, 7360), (1947, 118, 7361), (1949, 1, 7364), (1949, 27, 7365), (1949, 110, 7366), (1950, 110, 7367), (1951, 1, 7368), (1951, 27, 7369), (1951, 110, 5197), (1952, 1, 7370), (1952, 8, 4093), (1952, 10, 7371), (1952, 14, 480), (1952, 27, 7372), (1952, 62, 6695), (1952, 110, 7373), (1952, 115, 7374), (1953, 1, 5191), (1953, 27, 7375), (1953, 110, 5190), (1954, 110, 7376), (1954, 7, 7377), (1954, 14, 7378), (1950, 1, 5194), (1954, 1, 5194), (1955, 1, 7379), (1955, 27, 7380), (1955, 110, 7381), (1956, 110, 7383), (1956, 90, 7384), (1956, 1, 7385), (1956, 27, 7386), (1754, 1, 6851), (1754, 12, 6909), (1754, 13, 6927), (1754, 14, 6939), (1754, 25, 6978), (1754, 26, 7162), (1754, 27, 7166), (1754, 62, 292), (1754, 87, 3751), (1754, 90, 7169), (1754, 110, 7173), (1957, 1, 7177), (1957, 27, 7166), (1957, 110, 1983), (1958, 27, 7182), (1958, 110, 7194), (1959, 1, 7198), (1959, 14, 6727), (1959, 27, 7200), (1959, 32, 7212), (1959, 62, 6), (1959, 90, 7218), (1959, 92, 7314), (1959, 110, 7329), (1961, 1, 7334), (1961, 27, 7200), (1961, 110, 7343), (1962, 1, 7344), (1962, 2, 7345), (1962, 4, 3440), (1962, 5, 1954), (1962, 10, 7347), (1962, 12, 7354), (1962, 13, 7387), (1962, 14, 4415), (1962, 22, 7388), (1962, 25, 7354), (1962, 26, 7389), (1962, 27, 7390), (1962, 62, 660), (1962, 110, 7391), (1963, 1, 7392), (1963, 27, 7390), (1963, 110, 662), (1964, 1, 7393), (1964, 14, 7394), (1964, 27, 7395), (1964, 32, 7212), (1964, 62, 6), (1964, 90, 7396), (1964, 92, 7397), (1964, 110, 7398), (1966, 1, 7399), (1966, 27, 7395), (1966, 110, 7400), (1967, 1, 7401), (1967, 14, 7402), (1967, 27, 7403), (1967, 32, 7212), (1967, 62, 6), (1967, 90, 7404), (1967, 92, 7405), (1967, 110, 7406), (1969, 1, 7407), (1969, 27, 7403), (1969, 110, 7408), (1981, 1, 6096), (1981, 27, 7417), (1981, 110, 6095), (1982, 1, 7419), (1982, 14, 7420), (1982, 27, 7421), (1982, 32, 7212), (1982, 62, 6), (1982, 90, 7422), (1982, 92, 7423), (1982, 110, 7424), (1984, 1, 7425), (1984, 27, 7421), (1984, 110, 7426), (1985, 1, 7427), (1985, 4, 2368), (1985, 5, 1077), (1985, 10, 7428), (1985, 12, 286), (1985, 13, 289), (1985, 14, 7429), (1985, 25, 1779), (1985, 26, 7430), (1985, 27, 7431), (1985, 62, 292), (1985, 87, 3751), (1985, 90, 7432), (1985, 110, 7433), (1987, 110, 7435), (1988, 1, 7436), (1988, 14, 7437), (1988, 22, 7438), (1988, 27, 7439), (1988, 32, 7212), (1988, 62, 6), (1988, 90, 7440), (1988, 92, 7441), (1988, 110, 7442), (1990, 1, 7443), (1990, 27, 7439), (1990, 110, 7444), (1992, 8, 7446), (1992, 11, 7447), (1992, 14, 7448), (1992, 62, 4097), (1992, 87, 3751), (1992, 90, 7449), (1992, 110, 7450), (1992, 118, 7451), (1994, 110, 7454), (1995, 8, 4093), (1995, 11, 7455), (1995, 14, 7456), (1995, 62, 4097), (1995, 87, 3751), (1995, 90, 7457), (1995, 110, 7458), (1995, 118, 7459), (1997, 110, 7462), (1998, 8, 4093), (1998, 11, 7463), (1998, 14, 7464), (1998, 62, 4097), (1998, 87, 3751), (1998, 90, 7465), (1998, 110, 7466), (1998, 118, 7467), (2000, 110, 7470), (2001, 8, 7471), (2001, 11, 7472), (2001, 14, 1945), (2001, 62, 4097), (2001, 87, 3751), (2001, 90, 7473), (2001, 110, 7474), (2001, 118, 7475), (2003, 110, 7478), (2004, 110, 7479), (2005, 110, 7480), (2006, 110, 7481), (2007, 110, 7482), (2008, 8, 7483), (2008, 11, 7484), (2008, 14, 506), (2008, 62, 4097), (2008, 87, 3751), (2008, 90, 7485), (2008, 110, 7486), (2008, 118, 7487), (2010, 110, 7490), (2011, 110, 7491), (2012, 110, 7492), (2013, 110, 7493), (2014, 110, 7494), (2015, 8, 7495), (2015, 11, 7496), (2015, 14, 7497), (2015, 62, 4097), (2015, 87, 3751), (2015, 90, 7498), (2015, 110, 7499), (2015, 118, 7500), (2017, 110, 7503), (2018, 8, 7504), (2018, 11, 7505), (2018, 14, 7506), (2018, 62, 4097), (2018, 87, 3751), (2018, 90, 7507), (2018, 110, 7508), (2018, 118, 7509), (1404, 1, 5595), (1404, 14, 5602), (1404, 27, 5604), (1404, 32, 7212), (1404, 62, 6), (1404, 90, 5606), (1404, 92, 7186), (1404, 110, 7190), (1406, 1, 7382), (1406, 27, 5604), (1406, 110, 7434), (1905, 1, 7512), (1905, 14, 7513), (1905, 22, 7514), (1905, 27, 7515), (1905, 32, 7212), (1905, 62, 6), (1905, 90, 7516), (1905, 92, 7517), (1905, 110, 7518), (2020, 1, 7519), (2020, 27, 7515), (2020, 110, 7520), (2021, 1, 7521), (2021, 14, 5602), (2021, 27, 7522), (2021, 32, 7212), (2021, 62, 6), (2021, 90, 7523), (2021, 92, 7524), (2021, 110, 7525), (2023, 1, 7526), (2023, 27, 7522), (2023, 110, 7527), (2026, 1, 7530), (2026, 27, 7531), (2026, 110, 7532), (2027, 1, 7530), (2027, 27, 7533), (2027, 62, 6695), (2027, 110, 7534), (2027, 14, 7535), (2030, 1, 7537), (2030, 2, 7538), (2030, 8, 7539), (2030, 10, 7540), (2030, 11, 7541), (2030, 14, 7542), (2030, 27, 7543), (2030, 62, 6593), (2030, 87, 3751), (2030, 90, 7544), (2030, 115, 7546), (2031, 1, 7547), (2031, 27, 7543), (2031, 110, 1983), (2032, 1, 7548), (2032, 2, 7538), (2032, 8, 7539), (2032, 10, 7549), (2032, 11, 7541), (2032, 14, 7542), (2032, 27, 7543), (2032, 62, 6593), (2032, 87, 3751), (2032, 90, 7550), (2032, 115, 7546), (2033, 1, 7552), (2033, 27, 7543), (2033, 110, 1983), (2034, 1, 7553), (2034, 2, 7538), (2034, 8, 7539), (2034, 10, 7554), (2034, 11, 7541), (2034, 14, 7542), (2034, 27, 7543), (2034, 62, 6593), (2034, 87, 3751), (2034, 90, 7555), (2034, 115, 7546), (2035, 1, 7557), (2035, 27, 7543), (2035, 110, 1983), (2036, 1, 7558), (2036, 2, 7538), (2036, 8, 7539), (2036, 10, 7559), (2036, 11, 7541), (2036, 14, 7542), (2036, 27, 7543), (2036, 62, 6593), (2036, 87, 3751), (2036, 90, 7560), (2036, 115, 7546), (2037, 1, 7562), (2037, 27, 7543), (2037, 110, 1983), (2038, 1, 7563), (2038, 2, 7538), (2038, 8, 7539), (2038, 10, 7564), (2038, 11, 7541), (2038, 14, 7542), (2038, 27, 7543), (2038, 62, 6593), (2038, 87, 3751), (2038, 90, 7565), (2038, 115, 7546), (2039, 1, 7567), (2039, 27, 7543), (2039, 110, 1983), (2040, 1, 7568), (2040, 2, 7538), (2040, 8, 7539), (2040, 10, 7569), (2040, 11, 7541), (2040, 14, 7542), (2040, 27, 7543), (2040, 62, 6593), (2040, 87, 3751), (2040, 90, 7570), (2040, 115, 7546), (2041, 1, 7572), (2041, 27, 7543), (2041, 110, 1983), (2042, 1, 7573), (2042, 2, 7538), (2042, 8, 7539), (2042, 10, 7574), (2042, 11, 7541), (2042, 14, 7542), (2042, 27, 7543), (2042, 62, 6593), (2042, 87, 3751), (2042, 90, 7575), (2042, 115, 7546), (2043, 1, 7577), (2043, 27, 7543), (2043, 110, 1983), (2044, 1, 7578), (2044, 2, 7538), (2044, 8, 7539), (2044, 10, 7579), (2044, 11, 7541), (2044, 14, 7542), (2044, 27, 7543), (2044, 62, 6593), (2044, 87, 3751), (2044, 90, 7580), (2044, 115, 7546), (2045, 1, 7582), (2045, 27, 7543), (2045, 110, 1983), (2046, 1, 7583), (2046, 2, 7538), (2046, 8, 7539), (2046, 10, 7584), (2046, 11, 7541), (2046, 14, 7542), (2046, 27, 7543), (2046, 62, 6593), (2046, 87, 3751), (2046, 90, 7585), (2046, 115, 7546), (2047, 1, 7587), (2047, 27, 7543), (2047, 110, 1983), (2048, 1, 7588), (2048, 2, 7538), (2048, 8, 7539), (2048, 10, 7589), (2048, 11, 7541), (2048, 14, 7542), (2048, 27, 7543), (2048, 62, 6593), (2048, 87, 3751), (2048, 90, 7590), (2048, 115, 7546), (2049, 1, 7592), (2049, 27, 7543), (2049, 110, 1983), (2050, 1, 7593), (2050, 2, 7538), (2050, 8, 7539), (2050, 10, 7594), (2050, 11, 7541), (2050, 14, 7542), (2050, 27, 7543), (2050, 62, 6593), (2050, 87, 3751), (2050, 90, 7595), (2050, 115, 7546), (2051, 1, 7597), (2051, 27, 7543), (2051, 110, 1983), (2052, 1, 7598), (2052, 2, 7538), (2052, 8, 7539), (2052, 10, 7599), (2052, 11, 7541), (2052, 14, 7542), (2052, 27, 7543), (2052, 62, 6593), (2052, 87, 3751), (2052, 90, 7600), (2052, 115, 7546), (2053, 1, 7602), (2053, 27, 7543), (2053, 110, 1983), (2048, 110, 7612), (2030, 110, 7613), (2036, 110, 7614), (2032, 110, 7615), (2034, 110, 7616), (2038, 110, 7617), (2040, 110, 7618), (2044, 110, 7620), (2046, 110, 7621), (2050, 110, 7622), (2052, 110, 7623), (2054, 1, 7624), (2054, 27, 7625), (2054, 110, 7626), (2055, 1, 7627), (2055, 8, 4114), (2055, 14, 4327), (2055, 27, 7628), (2055, 62, 6695), (2056, 1, 7630), (2056, 27, 7631), (2056, 110, 7632), (2057, 110, 7633), (2042, 110, 7634), (2057, 115, 7546), (2057, 8, 7539), (2057, 10, 7636), (2057, 14, 7542), (2057, 87, 3751), (2057, 11, 7541), (2057, 1, 7630), (2055, 110, 7637), (2058, 1, 7638), (2058, 4, 288), (2058, 5, 288), (2058, 10, 7639), (2058, 12, 1074), (2058, 13, 1944), (2058, 14, 7640), (2058, 26, 7641), (2058, 27, 7642), (2058, 62, 6565), (2058, 90, 7643), (2058, 110, 7644), (2059, 1, 7645), (2059, 27, 7646), (2059, 110, 5325), (2061, 1, 7648), (2061, 27, 7649), (2061, 110, 7650), (2062, 1, 7651), (2062, 4, 89), (2062, 5, 5586), (2062, 10, 7652), (2062, 12, 286), (2062, 14, 2390), (2062, 27, 7653), (2062, 62, 6695), (2062, 110, 7654), (2063, 110, 7655), (2063, 12, 7656), (2063, 4, 1270), (2063, 5, 1954), (2063, 14, 7658), (2063, 10, 7659), (2063, 1, 7660), (2064, 1, 7661), (2064, 27, 7662), (2064, 110, 7663), (2065, 1, 7664), (2065, 14, 7665), (2065, 22, 7666), (2065, 27, 7667), (2065, 32, 7212), (2065, 62, 6), (2065, 90, 7668), (2065, 92, 7669), (2065, 110, 7670), (2067, 1, 7671), (2067, 27, 7667), (2067, 110, 7672), (2068, 110, 7673), (2070, 1, 7675), (2070, 14, 7678), (2070, 27, 7679), (2070, 62, 7680), (2070, 87, 3751), (2070, 110, 7682), (2070, 8, 5371), (2070, 7, 4090), (2070, 4, 1090), (2070, 45, 135), (2070, 115, 7685), (2070, 10, 7686), (2071, 1, 7687), (2071, 14, 7688), (2071, 22, 7689), (2071, 27, 7690), (2071, 32, 7212), (2071, 62, 6), (2071, 90, 7691), (2071, 92, 7692), (2071, 110, 7693), (2073, 1, 7694), (2073, 27, 7690), (2073, 110, 7695), (2074, 1, 7696), (2074, 14, 7697), (2074, 27, 7698), (2074, 32, 7212), (2074, 62, 6), (2074, 90, 7699), (2074, 92, 7700), (2074, 110, 7701), (2074, 116, 7702), (2076, 1, 7703), (2076, 27, 7698), (2076, 110, 7704), (2077, 1, 7705), (2077, 14, 7706), (2077, 27, 7707), (2077, 32, 7212), (2077, 62, 6), (2077, 90, 7708), (2077, 92, 7709), (2077, 110, 7710), (2079, 1, 7711), (2079, 27, 7707), (2079, 110, 7712), (2080, 1, 7713), (2080, 14, 7706), (2080, 27, 7714), (2080, 32, 7212), (2080, 62, 6), (2080, 90, 7715), (2080, 92, 7716), (2080, 110, 7717), (2080, 116, 7718), (2082, 1, 7719), (2082, 27, 7714), (2082, 110, 7720), (2083, 1, 7721), (2083, 10, 7724), (2083, 12, 3170), (2083, 13, 5629), (2083, 14, 7725), (2083, 25, 5624), (2083, 26, 7726), (2083, 27, 7727), (2083, 62, 5631), (2083, 87, 3751), (2083, 90, 7728), (2083, 110, 7729), (2084, 1, 7730), (2084, 27, 7727), (2084, 110, 1983), (1912, 110, 7239), (1913, 110, 7294), (1931, 8, 4089), (1931, 11, 7297), (1931, 14, 1540), (1931, 62, 4097), (1931, 87, 3751), (1931, 116, 7299), (1931, 118, 7300), (1931, 4, 135), (1931, 45, 135), (1703, 4, 1090), (1703, 45, 135), (2085, 110, 7556), (2086, 1, 7561), (2086, 14, 7566), (2086, 22, 7571), (2086, 27, 7576), (2086, 32, 7212), (2086, 62, 6), (2086, 90, 7581), (2086, 92, 7586), (2086, 110, 7591), (2088, 1, 7596), (2088, 27, 7576), (2088, 110, 7601), (2089, 1, 7603), (2089, 14, 7604), (2089, 27, 7605), (2089, 32, 7212), (2089, 62, 6), (2089, 90, 7606), (2089, 92, 7607), (2089, 110, 7608), (2091, 1, 7609), (2091, 27, 7605), (2091, 110, 7610), (2092, 1, 7619), (2092, 4, 1830), (2092, 5, 299), (2092, 10, 1708), (2092, 12, 93), (2092, 14, 7629), (2092, 25, 94), (2092, 26, 7635), (2092, 27, 7657), (2092, 62, 1329), (2092, 90, 7676), (2092, 110, 7677), (2093, 1, 7681), (2093, 27, 7657), (2093, 110, 1332), (2094, 1, 7683), (2094, 4, 135), (2094, 5, 135), (2094, 10, 6884), (2094, 12, 286), (2094, 13, 289), (2094, 14, 7684), (2094, 25, 1779), (2094, 26, 7731), (2094, 27, 7732), (2094, 62, 292), (2094, 87, 3751), (2094, 90, 7733), (2094, 110, 7734), (2096, 1, 7736), (2096, 4, 310), (2096, 5, 288), (2096, 10, 7737), (2096, 12, 286), (2096, 13, 289), (2096, 14, 7738), (2096, 25, 1779), (2096, 26, 7739), (2096, 27, 7740), (2096, 62, 292), (2096, 87, 3751), (2096, 90, 7741), (2096, 110, 7742), (2098, 110, 7744), (2099, 110, 7745), (2100, 1, 7746), (2100, 4, 7747), (2100, 5, 135), (2100, 10, 7748), (2100, 12, 93), (2100, 14, 7749), (2100, 25, 94), (2100, 26, 7750), (2100, 27, 7751), (2100, 62, 1329), (2100, 90, 7752), (2100, 110, 7753), (2100, 116, 7754), (2102, 1, 7756), (2102, 4, 5601), (2102, 5, 299), (2102, 10, 7757), (2102, 12, 286), (2102, 13, 289), (2102, 14, 7758), (2102, 25, 1779), (2102, 26, 7759), (2102, 27, 7760), (2102, 62, 292), (2102, 87, 3751), (2102, 90, 7761), (2102, 110, 7762), (2105, 110, 7764), (2106, 110, 7765), (2107, 1, 6026), (2107, 4, 3135), (2107, 5, 156), (2107, 10, 6024), (2107, 12, 93), (2107, 14, 6025), (2107, 25, 94), (2107, 26, 6027), (2107, 27, 7766), (2107, 62, 1329), (2107, 90, 6028), (2107, 110, 6023), (2108, 1, 6030), (2108, 27, 7766), (2108, 110, 1332), (2109, 1, 7767), (2109, 4, 3103), (2109, 5, 156), (2109, 10, 7768), (2109, 12, 1074), (2109, 13, 1944), (2109, 14, 7769), (2109, 26, 7770), (2109, 27, 7771), (2109, 62, 6565), (2109, 90, 7772), (2109, 110, 7773), (2110, 1, 7774), (2110, 4, 1090), (2110, 5, 1090), (2110, 10, 5307), (2110, 12, 286), (2110, 13, 289), (2110, 14, 7775), (2110, 25, 1779), (2110, 26, 7776), (2110, 27, 7777), (2110, 62, 292), (2110, 87, 3751), (2110, 90, 7778), (2110, 110, 7779), (2112, 1, 7781), (2112, 27, 7782), (2112, 110, 5325), (2114, 110, 7784), (1929, 1, 6259), (1929, 14, 7290), (1929, 27, 7291), (1929, 32, 7212), (1929, 62, 6), (1929, 90, 7292), (1929, 92, 7298), (1929, 110, 7409), (1970, 1, 7410), (1970, 27, 7291), (1970, 110, 7411), (1993, 1, 7452), (1993, 4, 7453), (1993, 5, 1954), (1993, 10, 7460), (1993, 12, 1372), (1993, 13, 6497), (1993, 14, 7461), (1993, 25, 6493), (1993, 26, 7468), (1993, 27, 7469), (1993, 62, 7476), (1993, 87, 3751), (1993, 90, 7477), (1993, 110, 7488), (1996, 1, 7489), (1996, 27, 7469), (1996, 110, 1983), (1999, 1, 7501), (1999, 14, 7502), (1999, 27, 7510), (1999, 32, 7212), (1999, 62, 6), (1999, 90, 7511), (1999, 92, 7611), (1999, 110, 7735), (2009, 1, 7743), (2009, 27, 7510), (2009, 110, 7755), (2016, 1, 7763), (2016, 14, 7780), (2016, 27, 7785), (2016, 32, 7212), (2016, 62, 6), (2016, 90, 7786), (2016, 92, 7787), (2016, 110, 7788), (2095, 1, 7789), (2095, 27, 7785), (2095, 110, 7790), (2060, 1, 7647), (2060, 4, 1090), (2060, 5, 274), (2060, 10, 7791), (2060, 12, 286), (2060, 13, 289), (2060, 14, 7792), (2060, 25, 1779), (2060, 26, 7793), (2060, 27, 7794), (2060, 62, 292), (2060, 87, 3751), (2060, 90, 7795), (2060, 110, 7796), (2101, 110, 7798), (2103, 1, 5787), (2103, 10, 7799), (2103, 12, 286), (2103, 13, 289), (2103, 14, 5784), (2103, 25, 1779), (2103, 26, 5786), (2103, 27, 7800), (2103, 62, 292), (2103, 87, 3751), (2103, 90, 7801), (2103, 110, 5788), (2115, 110, 7803), (2097, 1, 7797), (2097, 4, 579), (2097, 5, 872), (2097, 10, 7802), (2097, 12, 1074), (2097, 13, 1944), (2097, 14, 7804), (2097, 26, 7805), (2097, 27, 7806), (2097, 62, 6565), (2097, 90, 7807), (2097, 110, 7808), (2111, 1, 7809), (2111, 27, 7810), (2111, 110, 5325), (2116, 1, 7797), (2116, 27, 7811), (2116, 110, 5322), (2117, 1, 7812), (2117, 4, 7813), (2117, 5, 7814), (2117, 10, 7815), (2117, 12, 2559), (2117, 13, 2564), (2117, 14, 7816), (2117, 25, 2559), (2117, 26, 7817), (2117, 27, 7818), (2117, 62, 1264), (2117, 90, 7819), (2117, 110, 7820), (2118, 1, 7821), (2118, 27, 7818), (2118, 110, 1266), (2119, 1, 7822), (2119, 4, 872), (2119, 5, 310), (2119, 10, 7823), (2119, 12, 1074), (2119, 13, 1944), (2119, 14, 7824), (2119, 26, 7825), (2119, 27, 7826), (2119, 62, 6565), (2119, 90, 7827), (2119, 110, 7828), (2120, 1, 7829), (2120, 27, 7830), (2120, 110, 5325), (2121, 1, 7822), (2121, 27, 7831), (2121, 110, 5322), (2122, 1, 7832), (2122, 4, 90), (2122, 5, 135), (2122, 10, 7833), (2122, 12, 507), (2122, 14, 7834), (2122, 25, 508), (2122, 26, 7835), (2122, 27, 7836), (2122, 62, 1329), (2122, 110, 7837), (2123, 1, 7838), (2123, 27, 7836), (2123, 110, 1332), (2124, 1, 7839), (2124, 4, 7475), (2124, 5, 7840), (2124, 10, 7841), (2124, 12, 3170), (2124, 13, 5629), (2124, 14, 7842), (2124, 25, 5624), (2124, 26, 7843), (2124, 27, 7844), (2124, 62, 5631), (2124, 87, 3751), (2124, 90, 7845), (2124, 110, 7846), (2125, 1, 7847), (2125, 27, 7844), (2125, 110, 1983), (2126, 1, 7848), (2126, 14, 7849), (2126, 27, 7850), (2126, 32, 7212), (2126, 62, 6), (2126, 90, 7851), (2126, 92, 7852), (2126, 110, 7853), (2128, 1, 7854), (2128, 27, 7850), (2128, 110, 7855), (2129, 1, 7856), (2129, 4, 287), (2129, 5, 288), (2129, 10, 7857), (2129, 12, 6656), (2129, 13, 6660), (2129, 14, 7858), (2129, 25, 6657), (2129, 26, 7859), (2129, 27, 7860), (2129, 62, 6593), (2129, 87, 3751), (2129, 90, 7861), (2129, 110, 7862), (2130, 1, 7863), (2130, 27, 7860), (2130, 110, 1983), (2131, 1, 7864), (2131, 4, 288), (2131, 5, 1090), (2131, 10, 1698), (2131, 12, 1771), (2131, 13, 1770), (2131, 14, 7865), (2131, 25, 2337), (2131, 26, 7866), (2131, 27, 7867), (2131, 62, 292), (2131, 87, 3751), (2131, 90, 7868), (2131, 110, 7869), (2133, 110, 7871), (1315, 1, 7721), (1315, 4, 7722), (1315, 5, 7723), (1315, 10, 7724), (1315, 12, 3170), (1315, 13, 5629), (1315, 14, 7725), (1315, 25, 5624), (1315, 26, 7726), (1315, 27, 5287), (1315, 62, 5631), (1315, 87, 3751), (1315, 90, 7728), (1315, 110, 7729), (1704, 1, 7730), (1704, 27, 5287), (1704, 110, 1983), (1934, 1, 7651), (1934, 12, 286), (1934, 13, 289), (1934, 14, 5288), (1934, 25, 1779), (1934, 26, 6652), (1934, 27, 6653), (1934, 62, 292), (1934, 87, 3751), (1934, 90, 7301), (1934, 110, 7654), (2113, 110, 7783), (2132, 1, 7870), (2132, 10, 7873), (2132, 12, 286), (2132, 13, 289), (2132, 14, 6727), (2132, 25, 1779), (2132, 26, 7874), (2132, 27, 7875), (2132, 62, 292), (2132, 87, 3751), (2132, 90, 7876), (2132, 110, 6089), (2137, 110, 7878), (2104, 1, 7303), (2104, 2, 7306), (2104, 4, 3439), (2104, 5, 135), (2104, 10, 7877), (2104, 12, 7308), (2104, 13, 7309), (2104, 14, 7879), (2104, 22, 7880), (2104, 25, 7308), (2104, 26, 7881), (2104, 27, 7882), (2104, 62, 660), (2104, 110, 7883), (2136, 1, 7884), (2136, 27, 7882), (2136, 110, 662), (2138, 22, 7885), (2138, 48, 7886), (2138, 50, 7887), (2138, 52, 7888), (2138, 102, 7889), (2138, 110, 7890), (2138, 121, 7891), (2139, 1, 7892), (2139, 27, 7893), (2139, 110, 7894), (2140, 1, 7895), (2140, 2, 7896), (2140, 3, 7897), (2140, 8, 7898), (2140, 10, 7899), (2140, 11, 7900), (2140, 14, 7901), (2140, 27, 7902), (2140, 62, 6593), (2140, 87, 3751), (2140, 90, 7903), (2140, 110, 7904), (2140, 115, 7905), (2142, 1, 7910), (2142, 27, 7907), (2142, 110, 1983), (2144, 1, 7915), (2144, 27, 7912), (2144, 110, 1983), (2146, 1, 7920), (2146, 27, 7917), (2146, 110, 1983), (2148, 1, 7925), (2148, 27, 7922), (2148, 110, 1983), (2141, 27, 7907), (2141, 110, 7927), (2141, 116, 7909), (2143, 27, 7912), (2143, 110, 7926), (2143, 116, 7914), (2145, 27, 7917), (2145, 110, 7919), (2145, 116, 7919), (2147, 27, 7922), (2147, 110, 7924), (2147, 116, 7924), (2141, 14, 7928), (2143, 14, 7929), (2145, 14, 7930), (2147, 14, 7931), (2141, 12, 1539), (2143, 12, 1539), (2145, 12, 1539), (2147, 12, 1539), (2141, 4, 2548), (2143, 4, 1794), (2145, 4, 1660), (2141, 10, 7933), (2143, 10, 7934), (2145, 10, 7935), (2147, 10, 7936), (2147, 4, 7932), (2147, 1, 7937), (2145, 1, 7938), (2143, 1, 7939), (2141, 1, 7940), (2149, 7, 5369), (2149, 8, 5269), (2149, 11, 7941), (2149, 14, 7942), (2149, 62, 6983), (2149, 87, 6984), (2149, 110, 7943), (2149, 116, 7944), (2151, 1, 7948), (2151, 27, 7949), (2151, 110, 7950), (2152, 1, 7951), (2152, 8, 7952), (2152, 14, 4086), (2152, 27, 7953), (2152, 62, 6695), (2152, 110, 7944), (2153, 1, 7954), (2153, 4, 2245), (2153, 5, 288), (2153, 10, 7955), (2153, 12, 1074), (2153, 13, 1944), (2153, 14, 7956), (2153, 26, 7957), (2153, 27, 7958), (2153, 62, 6565), (2153, 90, 7959), (2153, 110, 7960), (2154, 1, 7961), (2154, 27, 7962), (2154, 110, 5325), (2155, 1, 7954), (2155, 27, 7963), (2155, 110, 5322), (2156, 1, 7964), (2156, 4, 1076), (2156, 5, 1954), (2156, 10, 7965), (2156, 12, 6656), (2156, 13, 6660), (2156, 14, 7966), (2156, 25, 6656), (2156, 26, 7967), (2156, 27, 7968), (2156, 62, 6593), (2156, 87, 3751), (2156, 90, 7969), (2156, 110, 7970), (2157, 1, 7971), (2157, 27, 7968), (2157, 110, 1983), (2134, 1, 7872), (2134, 4, 1660), (2134, 5, 156), (2134, 10, 7906), (2134, 12, 1074), (2134, 13, 1944), (2134, 14, 7908), (2134, 26, 7911), (2134, 27, 7913), (2134, 62, 6565), (2134, 90, 7916), (2134, 110, 7918), (2135, 1, 7921), (2135, 27, 7923), (2135, 110, 5325), (2159, 1, 7973), (2159, 4, 2245), (2159, 5, 7974), (2159, 10, 7975), (2159, 12, 7976), (2159, 13, 7977), (2159, 14, 7978), (2159, 26, 7979), (2159, 27, 7980), (2159, 62, 1416), (2159, 110, 7981), (2159, 116, 7982), (2160, 1, 7983), (2160, 4, 299), (2160, 5, 135), (2160, 10, 7984), (2160, 12, 7985), (2160, 13, 7986), (2160, 14, 7987), (2160, 25, 7988), (2160, 26, 7989), (2160, 27, 7990), (2160, 62, 6593), (2160, 87, 3751), (2160, 110, 7991), (2161, 1, 7992), (2161, 27, 7990), (2161, 110, 1983), (2163, 1, 8000), (2163, 4, 3103), (2163, 5, 274), (2163, 10, 7994), (2163, 12, 1074), (2163, 13, 1944), (2163, 14, 7995), (2163, 26, 7996), (2163, 27, 8001), (2163, 62, 6565), (2163, 90, 7998), (2163, 110, 7999), (2165, 1, 8003), (2165, 27, 8004), (2165, 110, 5325), (2167, 1, 8006), (2167, 4, 135), (2167, 5, 274), (2167, 10, 8007), (2167, 12, 8008), (2167, 13, 2508), (2167, 14, 8009), (2167, 27, 8010), (2167, 62, 8011), (2167, 110, 8012), (2169, 1, 8014), (2169, 4, 8015), (2169, 5, 8016), (2169, 10, 8017), (2169, 12, 1978), (2169, 13, 5629), (2169, 14, 8018), (2169, 25, 5624), (2169, 26, 8019), (2169, 27, 8020), (2169, 62, 5631), (2169, 87, 3751), (2169, 90, 8021), (2169, 110, 8022), (2170, 1, 8023), (2170, 27, 8020), (2170, 110, 1983), (2172, 110, 8027), (2173, 1, 8028), (2173, 2, 8029), (2173, 4, 7932), (2173, 5, 1954), (2173, 10, 8030), (2173, 12, 7308), (2173, 13, 7309), (2173, 14, 8031), (2173, 22, 8032), (2173, 25, 7308), (2173, 26, 8033), (2173, 27, 8034), (2173, 62, 660), (2173, 110, 8035), (2174, 1, 8036), (2174, 27, 8034), (2174, 110, 662), (2175, 1, 8037), (2175, 14, 8038), (2175, 27, 8039), (2175, 32, 7212), (2175, 62, 6), (2175, 90, 8040), (2175, 92, 8041), (2175, 110, 8042), (2177, 1, 8043), (2177, 27, 8039), (2177, 110, 8044), (2178, 1, 8045), (2178, 4, 8046), (2178, 5, 6587), (2178, 10, 8047), (2178, 12, 8048), (2178, 13, 8049), (2178, 14, 8050), (2178, 25, 8051), (2178, 26, 8052), (2178, 27, 8053), (2178, 62, 6593), (2178, 87, 6324), (2178, 90, 8054), (2178, 110, 8055), (2179, 1, 8056), (2179, 27, 8053), (2179, 110, 1983), (2180, 8, 8057), (2180, 14, 8059), (2180, 62, 4097), (2180, 87, 3751), (2180, 90, 8060), (2180, 110, 8061), (2180, 118, 8062), (2181, 1, 8063), (2181, 27, 8064), (2181, 110, 4099), (2182, 115, 8061), (2182, 14, 480), (2182, 8, 8057), (2180, 11, 8058), (2182, 11, 8058), (2182, 10, 8065), (2182, 110, 8066), (2182, 1, 8067), (2183, 1, 8068), (2183, 14, 8069), (2183, 27, 8070), (2183, 32, 7212), (2183, 62, 6), (2183, 90, 8071), (2183, 92, 8072), (2183, 110, 8073), (2185, 1, 8074), (2185, 27, 8070), (2185, 110, 8075), (2186, 1, 8076), (2186, 14, 8077), (2186, 27, 8078), (2186, 32, 7212), (2186, 62, 6), (2186, 90, 8079), (2186, 92, 8080), (2186, 110, 8081), (2188, 1, 8082), (2188, 27, 8078), (2188, 110, 8083), (2189, 1, 8084), (2189, 4, 3103), (2189, 5, 872), (2189, 10, 8085), (2189, 12, 4403), (2189, 13, 4405), (2189, 14, 8086), (2189, 25, 8087), (2189, 26, 8088), (2189, 27, 8089), (2189, 62, 6593), (2189, 87, 3751), (2189, 90, 8090), (2189, 110, 8091), (2190, 1, 8092), (2190, 27, 8089), (2190, 110, 1983), (1947, 11, 8095), (1947, 14, 3985), (1947, 7, 8097), (1947, 8, 7003), (2192, 110, 8098), (2193, 110, 8099), (2194, 110, 8100), (2194, 14, 8101), (2194, 12, 8102), (2195, 1, 8103), (2195, 14, 1989), (2195, 27, 8104), (2195, 32, 7212), (2195, 62, 6), (2195, 90, 8105), (2195, 92, 8106), (2195, 110, 8107), (2197, 1, 8108), (2197, 27, 8104), (2197, 110, 8109), (569, 1, 1960), (569, 14, 1961), (569, 27, 1962), (569, 32, 7212), (569, 62, 6), (569, 90, 1964), (569, 92, 7357), (569, 110, 7358), (2150, 1, 7945), (2150, 27, 1962), (2150, 110, 7946), (2168, 1, 7947), (2168, 14, 5349), (2168, 27, 8013), (2168, 32, 7212), (2168, 62, 6), (2168, 90, 8024), (2168, 92, 8025), (2168, 110, 8026), (2198, 1, 8096), (2198, 27, 8013), (2198, 110, 8110), (2199, 1, 8111), (2199, 14, 8112), (2199, 27, 8113), (2199, 32, 7212), (2199, 62, 6), (2199, 90, 8114), (2199, 92, 8115), (2199, 110, 8116), (2201, 1, 8117), (2201, 27, 8113), (2201, 110, 8118), (2202, 1, 8119), (2202, 14, 8120), (2202, 27, 8121), (2202, 32, 7212), (2202, 62, 6), (2202, 90, 8122), (2202, 92, 8123), (2202, 110, 8124), (2204, 1, 8125), (2204, 27, 8121), (2204, 110, 8126), (2205, 1, 8127), (2205, 14, 8128), (2205, 27, 8129), (2205, 32, 7212), (2205, 62, 6), (2205, 90, 8130), (2205, 92, 8131), (2205, 110, 8132), (2207, 1, 8133), (2207, 27, 8129), (2207, 110, 8134), (2208, 1, 8135), (2208, 14, 8136), (2208, 27, 8137), (2208, 32, 7212), (2208, 62, 6), (2208, 90, 8138), (2208, 92, 8139), (2208, 110, 8140), (2210, 1, 8141), (2210, 27, 8137), (2210, 110, 8142), (418, 1, 1305), (418, 14, 1304), (418, 22, 1306), (418, 27, 1309), (418, 62, 6), (418, 90, 1308), (418, 110, 1303), (2211, 1, 8143), (2211, 14, 8144), (2211, 27, 8145), (2211, 32, 7212), (2211, 62, 6), (2211, 90, 8146), (2211, 92, 8147), (2211, 110, 8148), (2213, 1, 8149), (2213, 27, 8145), (2213, 110, 8150), (1904, 1, 6213), (1904, 14, 1989), (1904, 22, 1307), (1904, 27, 7229), (1904, 32, 7212), (1904, 62, 6), (1904, 90, 6215), (1904, 92, 7230), (1904, 110, 6212), (1907, 1, 6218), (1907, 27, 7229), (1907, 110, 6217), (1908, 1, 7231), (1908, 4, 1422), (1908, 5, 299), (1908, 10, 7232), (1908, 12, 93), (1908, 14, 7233), (1908, 25, 94), (1908, 26, 7234), (1908, 27, 7235), (1908, 62, 1329), (1908, 90, 7236), (1908, 110, 7237), (1909, 1, 7238), (1909, 27, 7235), (1909, 110, 1332), (1910, 1, 7240), (1910, 4, 6400), (1910, 5, 310), (1910, 10, 7412), (1910, 12, 93), (1910, 14, 7413), (1910, 25, 94), (1910, 26, 7414), (1910, 27, 7415), (1910, 62, 1329), (1910, 90, 7416), (1910, 110, 7445), (1911, 1, 7528), (1911, 27, 7415), (1911, 110, 1332), (1914, 1, 7529), (1914, 10, 7536), (1914, 12, 93), (1914, 14, 7674), (1914, 25, 94), (1914, 26, 8151), (1914, 27, 8152), (1914, 62, 1329), (1914, 90, 8153), (1914, 110, 8154), (1971, 1, 7529), (1971, 4, 6400), (1971, 5, 310), (1971, 10, 7536), (1971, 12, 93), (1971, 14, 7674), (1971, 25, 94), (1971, 26, 8151), (1971, 27, 8156), (1971, 62, 1329), (1971, 90, 8153), (1971, 110, 8154), (1972, 1, 8157), (1972, 27, 8156), (1972, 110, 1332), (1915, 1, 8155), (1915, 14, 8158), (1915, 22, 8159), (1915, 27, 8160), (1915, 32, 7212), (1915, 62, 6), (1915, 90, 8161), (1915, 92, 8162), (1915, 110, 8163), (1974, 1, 8164), (1974, 27, 8160), (1974, 110, 8165), (1975, 1, 8166), (1975, 14, 8167), (1975, 22, 8168), (1975, 27, 8169), (1975, 32, 7212), (1975, 62, 6), (1975, 90, 8170), (1975, 92, 8171), (1975, 110, 8172), (1977, 1, 8173), (1977, 27, 8169), (1977, 110, 8174), (1978, 1, 8175), (1978, 27, 8176), (1978, 110, 8177), (1991, 1, 8178), (1991, 7, 5369), (1991, 8, 4093), (1991, 11, 8179), (1991, 14, 273), (1991, 27, 8180), (1991, 62, 6983), (1991, 87, 6984), (1991, 90, 8181), (1991, 110, 8182), (2024, 1, 8183), (2024, 14, 8184), (2024, 27, 8185), (2024, 32, 7212), (2024, 62, 6), (2024, 90, 8186), (2024, 92, 8187), (2024, 110, 869), (2028, 1, 8188), (2028, 27, 8185), (2028, 110, 8189), (2029, 1, 8190), (2029, 27, 8191), (2029, 110, 8192), (2069, 110, 8193), (2069, 14, 284), (2214, 1, 8194), (2214, 27, 8195), (2214, 110, 8196), (2215, 1, 8197), (2215, 27, 8198), (2215, 62, 8199), (2215, 90, 8200), (2215, 110, 8201), (2215, 14, 6552), (2219, 1, 8210), (2219, 14, 8211), (2219, 22, 8212), (2219, 27, 8213), (2219, 32, 7212), (2219, 62, 6), (2219, 90, 8214), (2219, 92, 8215), (2219, 110, 8216), (2221, 1, 8217), (2221, 27, 8213), (2221, 110, 8218), (2222, 1, 8219), (2222, 14, 8220), (2222, 22, 8221), (2222, 27, 8222), (2222, 32, 7212), (2222, 62, 6), (2222, 90, 8223), (2222, 92, 8224), (2222, 110, 8225), (2224, 1, 8226), (2224, 27, 8222), (2224, 110, 8227), (2225, 1, 8228), (2225, 4, 134), (2225, 5, 274), (2225, 10, 8229), (2225, 12, 93), (2225, 14, 8230), (2225, 25, 94), (2225, 26, 8231), (2225, 27, 8232), (2225, 62, 1329), (2225, 90, 8233), (2225, 110, 8234), (2226, 1, 8235), (2226, 27, 8232), (2226, 110, 1332), (2235, 1, 8268), (2235, 27, 8269), (2235, 110, 8270), (2236, 1, 8271), (2236, 4, 3617), (2236, 5, 89), (2236, 10, 8260), (2236, 12, 286), (2236, 13, 3907), (2236, 14, 8261), (2236, 26, 8262), (2236, 27, 8272), (2236, 62, 1416), (2236, 110, 8265), (2236, 116, 8266), (2240, 1, 8251), (2240, 4, 134), (2240, 5, 156), (2240, 10, 8252), (2240, 12, 93), (2240, 14, 8253), (2240, 25, 94), (2240, 26, 8254), (2240, 27, 8275), (2240, 62, 1329), (2240, 90, 8256), (2240, 110, 8257), (2241, 1, 8276), (2241, 27, 8275), (2241, 110, 1332), (2242, 1, 8236), (2242, 4, 134), (2242, 5, 274), (2242, 10, 8237), (2242, 12, 93), (2242, 14, 8230), (2242, 25, 94), (2242, 26, 8238), (2242, 27, 8277), (2242, 62, 1329), (2242, 90, 8240), (2242, 110, 8241), (2243, 1, 8278), (2243, 27, 8277), (2243, 110, 1332), (2244, 1, 8243), (2244, 4, 2022), (2244, 5, 299), (2244, 10, 8244), (2244, 12, 93), (2244, 14, 8245), (2244, 25, 94), (2244, 26, 8246), (2244, 27, 8279), (2244, 62, 1329), (2244, 90, 8248), (2244, 110, 8249), (2245, 1, 8280), (2245, 27, 8279), (2245, 110, 1332), (2246, 1, 8281), (2246, 14, 8282), (2246, 27, 8283), (2246, 32, 7212), (2246, 62, 6), (2246, 90, 8284), (2246, 92, 8285), (2246, 110, 8286), (2248, 1, 8287), (2248, 27, 8283), (2248, 110, 8288), (2249, 1, 8119), (2249, 14, 8120), (2249, 27, 8289), (2249, 32, 7212), (2249, 62, 6), (2249, 90, 8122), (2249, 92, 8123), (2249, 110, 8124), (2251, 1, 8125), (2251, 27, 8289), (2251, 110, 8126), (2252, 1, 8290), (2252, 14, 8291), (2252, 22, 8292), (2252, 27, 8293), (2252, 32, 7212), (2252, 62, 6), (2252, 90, 8294), (2252, 92, 8295), (2252, 110, 8296), (2254, 1, 8297), (2254, 27, 8293), (2254, 110, 8298), (2255, 1, 2703), (2255, 14, 2702), (2255, 22, 3633), (2255, 27, 8299), (2255, 32, 7212), (2255, 62, 6), (2255, 90, 2705), (2255, 92, 2704), (2255, 110, 2701), (2257, 1, 2708), (2257, 27, 8299), (2257, 110, 2707), (2258, 1, 8300), (2258, 14, 8301), (2258, 22, 8302), (2258, 27, 8303), (2258, 32, 7212), (2258, 62, 6), (2258, 90, 8304), (2258, 92, 8305), (2258, 110, 8306), (2260, 1, 8307), (2260, 27, 8303), (2260, 110, 8308), (2261, 1, 8309), (2261, 2, 6325), (2261, 8, 6319), (2261, 10, 8310), (2261, 11, 6320), (2261, 14, 871), (2261, 27, 8311), (2261, 62, 3755), (2261, 87, 6324), (2261, 110, 8312), (2261, 115, 6323), (2158, 110, 7972), (2158, 14, 8203), (2158, 90, 7993), (2158, 1, 7997), (2158, 32, 7212), (2158, 92, 8002), (2158, 62, 6), (2158, 27, 8005), (2158, 116, 8242), (2164, 110, 8250), (2164, 1, 8258), (2164, 27, 8005), (2166, 110, 8207), (2166, 14, 8203), (2166, 90, 8205), (2166, 1, 8202), (2166, 32, 7212), (2166, 92, 8206), (2166, 62, 6), (2166, 27, 8267), (2230, 110, 8209), (2230, 1, 8208), (2230, 27, 8267), (2232, 1, 8274), (2232, 27, 8313), (2232, 110, 8314), (1948, 1, 3355), (1948, 10, 7362), (1948, 12, 93), (1948, 14, 3354), (1948, 25, 94), (1948, 26, 3356), (1948, 27, 7363), (1948, 62, 1329), (1948, 90, 3357), (1948, 110, 3351), (2191, 1, 3359), (2191, 27, 7363), (2191, 110, 1332), (2234, 110, 8093), (2238, 1, 8094), (2238, 14, 8315), (2238, 27, 8316), (2238, 32, 7212), (2238, 62, 6), (2238, 90, 8317), (2238, 92, 8318), (2238, 110, 8319), (2238, 116, 8320), (2263, 1, 8321), (2263, 27, 8316), (2263, 110, 8322), (2264, 1, 8323), (2264, 14, 8324), (2264, 27, 8325), (2264, 32, 7212), (2264, 62, 6), (2264, 90, 8326), (2264, 92, 8327), (2264, 110, 8328), (2266, 1, 8329), (2266, 27, 8325), (2266, 110, 8330), (2267, 1, 8331), (2267, 14, 8324), (2267, 27, 8332), (2267, 32, 7212), (2267, 62, 6), (2267, 90, 8333), (2267, 92, 8334), (2267, 110, 8335), (2269, 1, 8336), (2269, 27, 8332), (2269, 110, 8337), (2270, 1, 8338), (2270, 14, 8339), (2270, 27, 8340), (2270, 32, 7212), (2270, 62, 6), (2270, 90, 8341), (2270, 92, 8342), (2270, 110, 8343), (2272, 1, 8344), (2272, 27, 8340), (2272, 110, 8345), (2273, 1, 8346), (2273, 14, 8347), (2273, 27, 8348), (2273, 32, 7212), (2273, 62, 6), (2273, 90, 8349), (2273, 92, 8350), (2273, 110, 8351), (2275, 1, 8352), (2275, 27, 8348), (2275, 110, 8353), (2276, 1, 8354), (2276, 14, 7502), (2276, 27, 8355), (2276, 32, 7212), (2276, 62, 6), (2276, 90, 8356), (2276, 92, 8357), (2276, 110, 8358), (2278, 1, 8359), (2278, 27, 8355), (2278, 110, 8360), (2279, 1, 8361), (2279, 14, 8362), (2279, 27, 8363), (2279, 32, 7212), (2279, 62, 6), (2279, 90, 8364), (2279, 92, 8365), (2279, 110, 8366), (2281, 1, 8367), (2281, 27, 8363), (2281, 110, 8368), (2162, 1, 8204), (2162, 12, 8239), (2162, 14, 8247), (2162, 27, 8255), (2162, 62, 6), (2162, 90, 8259), (2162, 110, 8263), (2217, 1, 8264), (2217, 27, 8255), (2217, 110, 8273), (2218, 1, 8369), (2218, 4, 8370), (2218, 5, 135), (2218, 12, 93), (2218, 13, 3819), (2218, 14, 8371), (2218, 22, 8372), (2218, 26, 8373), (2218, 27, 8374), (2218, 62, 6), (2218, 90, 8375), (2218, 110, 8376), (2228, 1, 8377), (2228, 27, 8374), (2228, 110, 8378), (2229, 1, 8379), (2229, 12, 8380), (2229, 14, 8381), (2229, 27, 8382), (2229, 62, 6), (2229, 90, 8383), (2229, 110, 8384), (2233, 1, 8385), (2233, 27, 8382), (2233, 110, 8386), (2237, 1, 8387), (2237, 27, 8388), (2237, 110, 8389), (2282, 1, 8395), (2282, 27, 8396), (2283, 7, 7351), (2283, 8, 4089), (2283, 11, 8399), (2283, 14, 871), (2283, 27, 8400), (2283, 62, 6983), (2283, 87, 6984), (2283, 90, 8401), (2283, 110, 8402), (2283, 1, 8390), (2284, 1, 8404), (2284, 27, 8405), (2285, 1, 8408), (2285, 27, 8409), (2287, 1, 8414), (2287, 27, 8415), (2287, 110, 8417), (2289, 1, 8422), (2289, 27, 8423), (2289, 110, 8424), (2290, 1, 8422), (2290, 110, 8425), (2291, 1, 8426), (2291, 12, 8427), (2291, 14, 8428), (2291, 27, 8429), (2291, 62, 6), (2291, 90, 8430), (2291, 110, 8431), (2293, 1, 8432), (2293, 27, 8429), (2293, 110, 8433), (2294, 1, 8434), (2294, 27, 8435), (2294, 110, 8437), (2295, 1, 8438), (2295, 27, 8439), (2295, 110, 8441), (2296, 1, 8442), (2296, 27, 8443), (2296, 110, 8445), (2297, 1, 8446), (2297, 27, 8447), (2297, 110, 8449), (2298, 1, 8450), (2298, 27, 8451), (2298, 110, 8453), (2299, 1, 8454), (2299, 27, 8455), (2299, 110, 8457), (2282, 110, 8458), (2284, 110, 8459), (2285, 110, 8460), (2300, 1, 8461), (2300, 27, 8462), (2300, 110, 8463), (2301, 1, 8464), (2301, 14, 284), (2301, 27, 8465), (2301, 62, 6695), (2301, 110, 8466), (2302, 1, 8467), (2302, 4, 287), (2302, 5, 1954), (2302, 10, 8468), (2302, 12, 8469), (2302, 13, 8470), (2302, 14, 8471), (2302, 25, 8469), (2302, 26, 8472), (2302, 27, 8473), (2302, 62, 6593), (2302, 87, 3751), (2302, 90, 8474), (2302, 110, 8475), (2302, 116, 8476), (2303, 1, 8477), (2303, 27, 8473), (2303, 110, 1983), (2304, 1, 8478), (2304, 27, 8479), (2304, 110, 8480), (2306, 1, 8482), (2306, 4, 1320), (2306, 5, 1077), (2306, 10, 8483), (2306, 12, 1074), (2306, 13, 8484), (2306, 14, 8485), (2306, 26, 8486), (2306, 27, 8487), (2306, 62, 8488), (2306, 90, 8489), (2306, 110, 8490), (2307, 1, 8491), (2307, 27, 8487), (2307, 110, 1983), (2308, 1, 8492), (2308, 4, 145), (2308, 5, 1077), (2308, 10, 8493), (2308, 12, 8494), (2308, 13, 8495), (2308, 14, 8496), (2308, 25, 8497), (2308, 26, 8498), (2308, 27, 8499), (2308, 62, 8500), (2308, 110, 8501), (2309, 1, 8502), (2309, 27, 8499), (2309, 110, 1983), (2310, 1, 8503), (2310, 4, 8504), (2310, 5, 1090), (2310, 10, 8505), (2310, 12, 1074), (2310, 13, 8484), (2310, 14, 8506), (2310, 26, 8507), (2310, 27, 8508), (2310, 62, 8488), (2310, 90, 8509), (2310, 110, 8510), (2311, 1, 8511), (2311, 27, 8508), (2311, 110, 1983), (2312, 1, 8512), (2312, 27, 8513), (2312, 110, 8514), (2313, 1, 8515), (2313, 8, 4093), (2313, 10, 8516), (2313, 14, 4086), (2313, 27, 8517), (2313, 62, 6695), (2313, 110, 8518), (2313, 115, 8519), (2314, 1, 8520), (2314, 4, 1744), (2314, 5, 872), (2314, 10, 8521), (2314, 12, 1225), (2314, 13, 8522), (2314, 14, 8523), (2314, 26, 8524), (2314, 27, 8525), (2314, 62, 8488), (2314, 90, 8526), (2314, 110, 8527), (2315, 1, 8528), (2315, 27, 8525), (2315, 110, 1983), (2316, 1, 8529), (2316, 14, 8530), (2316, 27, 8531), (2316, 62, 8532), (2316, 110, 8533), (2317, 1, 8534), (2317, 27, 8531), (2317, 110, 1983), (2318, 1, 8535), (2318, 14, 8530), (2318, 27, 8536), (2318, 62, 8532), (2318, 110, 8537), (2319, 1, 8538), (2319, 27, 8536), (2319, 110, 1983), (2320, 1, 8539), (2320, 12, 8540), (2320, 14, 8541), (2320, 27, 8542), (2320, 62, 6), (2320, 90, 8543), (2320, 110, 8544), (2320, 116, 8545), (2322, 1, 8546), (2322, 27, 8542), (2322, 110, 8547), (2323, 1, 8548), (2323, 12, 8549), (2323, 14, 8550), (2323, 27, 8551), (2323, 62, 6), (2323, 90, 8552), (2323, 110, 8553), (2324, 1, 8554), (2324, 27, 8551), (2324, 110, 8555), (2325, 1, 8556), (2325, 12, 8557), (2325, 14, 8558), (2325, 27, 8559), (2325, 62, 6), (2325, 90, 8560), (2325, 110, 8561), (2325, 116, 8562), (2327, 1, 8563), (2327, 27, 8559), (2327, 110, 8564), (2328, 1, 8565), (2328, 4, 7747), (2328, 5, 288), (2328, 10, 8566), (2328, 12, 2635), (2328, 13, 4005), (2328, 14, 8567), (2328, 25, 6607), (2328, 26, 8568), (2328, 27, 8569), (2328, 62, 6593), (2328, 87, 3751), (2328, 90, 8570), (2328, 110, 8571), (2329, 1, 8572), (2329, 27, 8569), (2329, 110, 1983), (2330, 1, 8573), (2330, 4, 155), (2330, 5, 310), (2330, 10, 8574), (2330, 12, 1225), (2330, 13, 4389), (2330, 14, 273), (2330, 22, 8575), (2330, 26, 8576), (2330, 27, 8577), (2330, 62, 6), (2330, 90, 8578), (2330, 110, 8579), (2332, 1, 8580), (2332, 27, 8577), (2332, 110, 8581), (2333, 1, 8582), (2333, 4, 299), (2333, 5, 274), (2333, 10, 8583), (2333, 12, 1074), (2333, 13, 8484), (2333, 26, 8585), (2333, 27, 8586), (2333, 62, 8488), (2333, 90, 8587), (2333, 110, 8588), (2334, 1, 8589), (2334, 27, 8586), (2334, 110, 1983), (2335, 1, 8590), (2335, 4, 299), (2335, 5, 274), (2335, 10, 8591), (2335, 12, 1074), (2335, 13, 8484), (2335, 26, 8592), (2335, 27, 8593), (2335, 62, 8488), (2335, 90, 8594), (2335, 110, 8595), (2336, 1, 8596), (2336, 27, 8593), (2336, 110, 1983), (2337, 1, 8597), (2337, 2, 8598), (2337, 3, 8599), (2337, 8, 8600), (2337, 10, 8601), (2337, 11, 8602), (2337, 14, 8603), (2337, 27, 8604), (2337, 30, 8605), (2337, 62, 6593), (2337, 87, 3751), (2337, 90, 8606), (2337, 110, 8607), (2337, 115, 8608), (2339, 1, 8610), (2339, 2, 8598), (2339, 3, 8599), (2339, 8, 8600), (2339, 10, 8611), (2339, 11, 8602), (2339, 14, 8603), (2339, 27, 8612), (2339, 30, 8605), (2339, 62, 6593), (2339, 87, 3751), (2339, 90, 8613), (2339, 110, 8614), (2339, 115, 8608), (2333, 14, 8618), (2335, 14, 8618), (2345, 110, 8619), (2346, 1, 8620), (2346, 27, 8621), (2346, 110, 8622), (2347, 1, 8623), (2347, 8, 8624), (2347, 14, 4327), (2347, 27, 8625), (2347, 62, 6695), (2347, 110, 8626), (2348, 1, 8627), (2348, 4, 3103), (2348, 5, 90), (2348, 10, 8628), (2348, 12, 4403), (2348, 13, 4405), (2348, 14, 8629), (2348, 25, 8087), (2348, 26, 8630), (2348, 27, 8631), (2348, 62, 6593), (2348, 87, 3751), (2348, 90, 8632), (2348, 110, 8633), (2349, 1, 8634), (2349, 27, 8631), (2349, 110, 1983), (2338, 1, 8397), (2338, 4, 374), (2338, 5, 891), (2338, 10, 890), (2338, 12, 286), (2338, 13, 3907), (2338, 14, 8398), (2338, 22, 8403), (2338, 26, 8406), (2338, 27, 8407), (2338, 62, 6), (2338, 90, 8410), (2338, 110, 8413), (2350, 1, 8416), (2350, 27, 8407), (2350, 110, 8418), (2351, 1, 4997), (2351, 12, 286), (2351, 13, 3907), (2351, 14, 8420), (2351, 22, 8436), (2351, 26, 8440), (2351, 27, 8444), (2351, 62, 6), (2351, 90, 8448), (2351, 110, 4995), (2353, 1, 5094), (2353, 27, 8444), (2353, 110, 5093), (2354, 1, 6066), (2354, 4, 1422), (2354, 5, 274), (2354, 12, 93), (2354, 13, 3819), (2354, 14, 8452), (2354, 22, 8456), (2354, 26, 6708), (2354, 27, 8609), (2354, 62, 6), (2354, 90, 6068), (2354, 110, 6064), (2356, 1, 8615), (2356, 27, 8609), (2356, 110, 8635), (2357, 110, 8636), (2239, 1, 8391), (2239, 4, 2789), (2239, 5, 1090), (2239, 10, 8392), (2239, 12, 8393), (2239, 13, 8394), (2239, 14, 8411), (2239, 25, 8393), (2239, 26, 8412), (2239, 27, 8421), (2239, 62, 1264), (2239, 90, 8637), (2239, 110, 8638), (2239, 116, 8639), (2286, 1, 8640), (2286, 27, 8421), (2286, 110, 1266), (2288, 1, 8641), (2288, 4, 8642), (2288, 5, 8643), (2288, 10, 8644), (2288, 12, 8645), (2288, 13, 8646), (2288, 14, 8647), (2288, 25, 8645), (2288, 26, 8648), (2288, 27, 8649), (2288, 62, 1264), (2288, 90, 8650), (2288, 110, 8651), (2358, 1, 8652), (2358, 27, 8649), (2358, 110, 1266), (2361, 1, 8660), (2361, 27, 8661), (2361, 110, 8662), (2362, 1, 8663), (2362, 5, 7974), (2362, 10, 8664), (2362, 12, 7976), (2362, 14, 2112), (2362, 27, 8665), (2362, 62, 6695), (2362, 110, 8666), (2362, 116, 8667), (2364, 110, 8669), (2364, 4, 5368), (2365, 110, 8671), (2366, 110, 8672), (2363, 110, 8673), (2368, 1, 8674), (2368, 4, 3371), (2368, 5, 891), (2368, 10, 8675), (2368, 12, 507), (2368, 14, 8676), (2368, 25, 508), (2368, 26, 8677), (2368, 27, 8678), (2368, 62, 1329), (2368, 90, 8679), (2368, 110, 8680), (2369, 1, 8681), (2369, 27, 8678), (2369, 110, 1332), (2370, 1, 8682), (2370, 4, 3371), (2370, 5, 374), (2370, 10, 8683), (2370, 12, 507), (2370, 14, 8684), (2370, 25, 508), (2370, 26, 8685), (2370, 27, 8686), (2370, 62, 1329), (2370, 110, 8687), (2371, 1, 8688), (2371, 27, 8686), (2371, 110, 1332), (2395, 1, 8743), (2395, 27, 8744), (2395, 110, 8745), (2396, 8, 4093), (2396, 14, 495), (2396, 62, 6695), (2396, 110, 8746), (2397, 110, 8481), (2398, 110, 8747), (1842, 14, 3985), (1842, 7, 8748), (2400, 1, 8749), (2400, 4, 6052), (2400, 5, 299), (2400, 12, 93), (2400, 13, 3819), (2400, 14, 8750), (2400, 22, 8751), (2400, 26, 8752), (2400, 27, 8753), (2400, 62, 6), (2400, 90, 8754), (2400, 110, 8755), (2402, 1, 8756), (2402, 27, 8753), (2402, 110, 8757), (2403, 1, 8758), (2403, 12, 8759), (2403, 14, 8760), (2403, 27, 8761), (2403, 62, 6), (2403, 90, 8762), (2403, 110, 8763), (2405, 1, 8764), (2405, 27, 8761), (2405, 110, 8765), (2406, 1, 8766), (2406, 27, 8767), (2406, 110, 8768), (2407, 110, 8769), (2408, 1, 8770), (2408, 12, 8771), (2408, 14, 8772), (2408, 27, 8773), (2408, 62, 6), (2408, 90, 8774), (2408, 110, 8775), (2410, 1, 8776), (2410, 27, 8773), (2410, 110, 8777), (2411, 1, 8778), (2411, 4, 8779), (2411, 5, 8780), (2411, 10, 8781), (2411, 12, 8782), (2411, 13, 8783), (2411, 14, 8784), (2411, 22, 8785), (2411, 25, 8782), (2411, 26, 8786), (2411, 27, 8787), (2411, 62, 8788), (2411, 87, 3751), (2411, 110, 8789), (2414, 110, 8793), (2415, 1, 8794), (2415, 4, 2022), (2415, 5, 299), (2415, 10, 1735), (2415, 12, 93), (2415, 14, 8795), (2415, 25, 94), (2415, 26, 8796), (2415, 27, 8797), (2415, 62, 1329), (2415, 90, 8798), (2415, 110, 8799), (2415, 116, 8800), (2416, 1, 8801), (2416, 27, 8797), (2416, 110, 1332), (1931, 110, 4989), (1703, 110, 4990), (1226, 1, 5048), (1226, 12, 5049), (1226, 14, 5050), (1226, 22, 5051), (1226, 27, 5052), (1226, 62, 6), (1226, 90, 5053), (1226, 110, 5054), (1244, 1, 5055), (1244, 27, 5052), (1244, 110, 5056), (1245, 1, 5057), (1245, 12, 5058), (1245, 14, 5059), (1245, 27, 5060), (1245, 62, 6), (1245, 90, 5070), (1245, 110, 5071), (2341, 1, 5072), (2341, 27, 5060), (2341, 110, 8584), (2342, 1, 7545), (2342, 2, 7551), (2342, 4, 155), (2342, 5, 135), (2342, 10, 8616), (2342, 12, 7354), (2342, 13, 7387), (2342, 14, 8617), (2342, 25, 7354), (2342, 26, 8653), (2342, 27, 8654), (2342, 62, 660), (2342, 110, 8655), (2343, 1, 8656), (2343, 27, 8654), (2343, 110, 662), (2344, 1, 8657), (2344, 4, 4390), (2344, 5, 1090), (2344, 10, 8658), (2344, 12, 8659), (2344, 13, 8668), (2344, 14, 8670), (2344, 25, 8790), (2344, 26, 8802), (2344, 27, 8803), (2344, 62, 6593), (2344, 87, 6324), (2344, 110, 8804), (2360, 110, 8807), (2412, 1, 8808), (2412, 4, 2461), (2412, 5, 135), (2412, 10, 8809), (2412, 12, 8810), (2412, 13, 8811), (2412, 14, 8812), (2412, 25, 8810), (2412, 26, 8813), (2412, 27, 8814), (2412, 62, 1264), (2412, 90, 8815), (2412, 110, 8816), (2417, 1, 8817), (2417, 27, 8814), (2417, 110, 1266), (1018, 1, 7049), (1018, 12, 7050), (1018, 14, 8689), (1018, 22, 8690), (1018, 27, 8691), (1018, 62, 6), (1018, 90, 8692), (1018, 110, 8066), (1716, 1, 8693), (1716, 27, 8691), (1716, 110, 8694), (1841, 1, 8695), (1841, 12, 8696), (1841, 14, 8697), (1841, 27, 8698), (1841, 62, 6), (1841, 90, 8699), (1841, 110, 8700), (2359, 1, 8701), (2359, 27, 8698), (2359, 110, 8702), (2373, 10, 8703), (2373, 14, 2112), (2373, 62, 5729), (2373, 90, 8704), (2373, 110, 8705), (2373, 114, 8706), (2373, 116, 7356), (2375, 1, 8707), (2375, 27, 8708), (2375, 110, 5730), (2376, 1, 8709), (2376, 4, 8504), (2376, 5, 2177), (2376, 10, 8710), (2376, 12, 8711), (2376, 13, 8712), (2376, 14, 8713), (2376, 26, 8714), (2376, 27, 8715), (2376, 62, 6706), (2377, 1, 8717), (2377, 27, 8715), (2377, 110, 1983), (2378, 1, 8718), (2378, 4, 6926), (2378, 5, 4932), (2378, 10, 8719), (2378, 12, 8711), (2378, 13, 8712), (2378, 14, 8720), (2378, 26, 8721), (2378, 27, 8722), (2378, 62, 6706), (2379, 1, 8724), (2379, 27, 8722), (2379, 110, 1983), (2380, 1, 8725), (2380, 4, 6926), (2380, 5, 8726), (2380, 10, 8727), (2380, 12, 8711), (2380, 13, 8712), (2380, 14, 8720), (2380, 26, 8728), (2380, 27, 8729), (2380, 62, 6706), (2381, 1, 8731), (2381, 27, 8729), (2381, 110, 1983), (2382, 1, 8732), (2382, 4, 4300), (2382, 5, 7813), (2382, 10, 8733), (2382, 12, 8711), (2382, 13, 8712), (2382, 14, 8734), (2382, 26, 8735), (2382, 27, 8736), (2382, 62, 6706), (2383, 1, 8738), (2383, 27, 8736), (2383, 110, 1983), (2380, 110, 8739), (2378, 110, 8740), (2382, 110, 8741), (2376, 110, 8742), (2384, 110, 8792), (2385, 1, 8805), (2385, 4, 8806), (2385, 10, 8818), (2385, 12, 5247), (2385, 13, 8819), (2385, 14, 8820), (2385, 25, 5247), (2385, 26, 8821), (2385, 27, 8822), (2385, 62, 1264), (2385, 110, 8823), (2386, 1, 8824), (2386, 27, 8822), (2386, 110, 1266), (2389, 1, 8826), (2389, 12, 8830), (2389, 14, 8831), (2389, 27, 8832), (2389, 62, 6), (2389, 90, 8833), (2389, 110, 8829), (2391, 1, 8834), (2391, 27, 8832), (2391, 110, 8835), (2393, 1, 8844), (2393, 4, 3103), (2393, 5, 135), (2393, 10, 8845), (2393, 12, 2507), (2393, 13, 2508), (2393, 14, 8846), (2393, 25, 8847), (2393, 26, 8848), (2393, 27, 8849), (2393, 62, 6593), (2393, 87, 3751), (2393, 90, 8850), (2393, 110, 8851), (2399, 110, 8853), (2413, 1, 8854), (2413, 14, 506), (2413, 27, 8857), (2413, 62, 6695), (2413, 89, 8856), (2413, 110, 8858), (2418, 110, 8859), (2419, 1, 8860), (2419, 12, 8861), (2419, 14, 8862), (2419, 27, 8863), (2419, 62, 6), (2419, 90, 8864), (2419, 110, 8865), (2420, 1, 8866), (2420, 27, 8863), (2420, 110, 8867), (2421, 1, 8868), (2421, 12, 8869), (2421, 14, 8870), (2421, 27, 8871), (2421, 62, 6), (2421, 90, 8872), (2421, 110, 8873), (2423, 1, 8874), (2423, 27, 8871), (2423, 110, 8875), (2445, 1, 8947), (2445, 27, 8948), (2445, 62, 8949), (2445, 90, 8950), (2445, 110, 8890), (2446, 110, 8951), (2447, 8, 8952), (2447, 11, 8953), (2447, 14, 8954), (2447, 62, 5333), (2447, 87, 6984), (2447, 110, 8959), (2447, 45, 1954), (2449, 1, 8960), (2449, 12, 8961), (2449, 14, 8862), (2449, 27, 8962), (2449, 62, 6), (2449, 90, 8963), (2449, 110, 8964), (2451, 1, 8965), (2451, 27, 8962), (2451, 110, 8966), (2394, 8, 8716), (2394, 11, 8723), (2394, 14, 1363), (2394, 110, 8730), (2394, 114, 8791), (2452, 110, 8852), (2394, 1, 8967), (2454, 1, 8968), (2454, 27, 8971), (2454, 110, 8970), (2453, 1, 8968), (2453, 27, 8969), (2453, 110, 8970), (2455, 110, 8972), (2456, 1, 8973), (2456, 27, 8974), (2456, 110, 8975), (2457, 110, 8976), (2458, 1, 8977), (2458, 27, 8978), (2458, 110, 8979), (2459, 1, 8977), (2459, 27, 8980), (2459, 110, 8979), (2460, 1, 8981), (2460, 4, 1830), (2460, 5, 872), (2460, 10, 8982), (2460, 12, 8983), (2460, 13, 8984), (2460, 14, 8985), (2460, 25, 8983), (2460, 26, 8986), (2460, 27, 8987), (2460, 62, 1264), (2460, 90, 8988), (2460, 110, 8989), (2461, 1, 8990), (2461, 27, 8987), (2461, 110, 1266), (2462, 1, 8991), (2462, 2, 8992), (2462, 3, 8993), (2462, 8, 8994), (2462, 10, 8995), (2462, 11, 8996), (2462, 14, 6776), (2462, 27, 8997), (2462, 30, 8998), (2462, 62, 6612), (2462, 90, 8999), (2462, 110, 9000), (2462, 115, 9001), (2463, 1, 9002), (2463, 27, 8997), (2463, 110, 1983), (2464, 1, 9003), (2464, 4, 3440), (2464, 5, 135), (2464, 10, 9004), (2464, 12, 9005), (2464, 13, 9006), (2464, 14, 9007), (2464, 26, 9008), (2464, 27, 9009), (2464, 62, 1416), (2464, 110, 9010), (2465, 1, 9011), (2465, 4, 6390), (2465, 5, 135), (2465, 10, 9012), (2465, 12, 9013), (2465, 13, 9014), (2465, 14, 9015), (2465, 26, 9016), (2465, 27, 9017), (2465, 62, 5161), (2465, 90, 9018), (2465, 110, 9019), (2466, 110, 9020), (2467, 110, 1461), (2468, 1, 9021), (2468, 2, 9022), (2468, 3, 9023), (2468, 8, 6777), (2468, 10, 9024), (2468, 11, 9025), (2468, 14, 6776), (2468, 27, 9026), (2468, 30, 4033), (2468, 62, 6593), (2468, 90, 9027), (2468, 110, 9028), (2468, 115, 9029), (2470, 110, 9031), (2471, 14, 4086), (2471, 62, 5729), (2471, 90, 9032), (2471, 110, 9033), (2472, 1, 9034), (2472, 27, 9035), (2472, 110, 5730), (2469, 1, 8737), (2469, 4, 497), (2469, 5, 1090), (2469, 10, 8855), (2469, 12, 6585), (2469, 13, 6590), (2469, 14, 8889), (2469, 25, 8895), (2469, 26, 8900), (2469, 27, 8909), (2469, 62, 6593), (2469, 87, 3751), (2469, 90, 8914), (2469, 110, 8919), (2474, 110, 8929), (2473, 110, 8924), (2475, 7, 5369), (2475, 8, 8934), (2475, 11, 8937), (2475, 14, 495), (2475, 62, 6983), (2475, 87, 6984), (2475, 110, 9030), (2475, 90, 9036), (2476, 1, 9037), (2476, 10, 9038), (2476, 12, 1074), (2476, 13, 8484), (2476, 14, 9039), (2476, 26, 1947), (2476, 27, 9040), (2476, 62, 8488), (2476, 90, 9041), (2476, 110, 1949), (2477, 1, 9042), (2477, 27, 9040), (2477, 110, 1983), (2478, 1, 9043), (2478, 4, 497), (2478, 5, 1090), (2478, 10, 9044), (2478, 12, 9045), (2478, 13, 9046), (2478, 14, 9047), (2478, 26, 9048), (2478, 27, 9049), (2478, 62, 1416), (2478, 87, 3751), (2478, 110, 9033), (2479, 110, 9050), (2480, 110, 9051), (2481, 110, 9052), (2483, 110, 9055), (2482, 110, 9054), (2484, 6, 9056), (2484, 8, 9057), (2484, 11, 9058), (2484, 14, 9059), (2484, 62, 5333), (2484, 87, 6984), (2484, 110, 9060), (2486, 110, 9063), (2487, 1, 9064), (2487, 4, 9065), (2487, 5, 135), (2487, 10, 9066), (2487, 12, 93), (2487, 14, 9067), (2487, 25, 94), (2487, 26, 9068), (2487, 27, 9069), (2487, 62, 1329), (2487, 90, 9070), (2487, 110, 9071), (2488, 1, 9072), (2488, 27, 9069), (2488, 110, 1983), (2489, 1, 9073), (2489, 12, 9074), (2489, 14, 9075), (2489, 27, 9076), (2489, 62, 6), (2489, 90, 9077), (2489, 110, 9078), (2489, 116, 9079), (2491, 1, 9080), (2491, 27, 9076), (2491, 110, 9081), (1679, 1, 6691), (1679, 12, 6692), (1679, 14, 6693), (1679, 27, 6694), (1679, 62, 6), (1679, 90, 6696), (1679, 110, 6697), (1714, 1, 6698), (1714, 27, 6694), (1714, 110, 6699), (1715, 1, 6753), (1715, 12, 6754), (1715, 14, 6755), (1715, 27, 6756), (1715, 62, 6), (1715, 90, 6757), (1715, 110, 6833), (1731, 1, 6834), (1731, 27, 6756), (1731, 110, 6843), (1748, 1, 6682), (1748, 4, 3513), (1748, 5, 2245), (1748, 10, 6844), (1748, 12, 286), (1748, 13, 3907), (1748, 14, 6845), (1748, 26, 6847), (1748, 27, 8955), (1748, 62, 6), (1748, 90, 6684), (1748, 110, 6680), (1752, 1, 6687), (1752, 27, 8955), (1752, 110, 6686), (1753, 1, 6214), (1753, 12, 8825), (1753, 14, 8827), (1753, 27, 8828), (1753, 62, 6), (1753, 90, 9053), (1753, 110, 9082), (1753, 116, 9083), (2388, 1, 9084), (2388, 27, 8828), (2388, 110, 9085), (2492, 1, 9086), (2492, 12, 9087), (2492, 14, 9088), (2492, 27, 9089), (2492, 62, 6), (2492, 90, 9090), (2492, 110, 9091), (2492, 116, 9092), (2494, 1, 9093), (2494, 27, 9089), (2494, 110, 9094), (2495, 1, 9095), (2495, 4, 9096), (2495, 5, 497), (2495, 10, 9097), (2495, 12, 507), (2495, 14, 9098), (2495, 25, 508), (2495, 26, 9099), (2495, 27, 9100), (2495, 62, 1329), (2495, 90, 9101), (2495, 110, 9102), (2496, 1, 9103), (2496, 27, 9100), (2496, 110, 1983), (2497, 1, 9104), (2497, 4, 8370), (2497, 5, 156), (2497, 10, 9105), (2497, 12, 93), (2497, 14, 9106), (2497, 25, 94), (2497, 26, 9107), (2497, 27, 9108), (2497, 62, 1329), (2497, 90, 9109), (2497, 110, 9110), (2498, 1, 9111), (2498, 27, 9108), (2498, 110, 1983), (2499, 1, 9112), (2499, 2, 9113), (2499, 4, 1204), (2499, 5, 1090), (2499, 10, 9114), (2499, 12, 9005), (2499, 14, 9115), (2499, 25, 9005), (2499, 27, 9116), (2499, 62, 660), (2499, 90, 9117), (2499, 110, 9118), (2500, 1, 9119), (2500, 27, 9116), (2500, 110, 662), (2392, 7, 8836), (2392, 8, 8837), (2392, 11, 8838), (2392, 14, 1363), (2392, 110, 8839), (2392, 114, 8840), (2424, 110, 8841), (2425, 14, 2112), (2425, 62, 5729), (2425, 90, 8842), (2425, 110, 8843), (2426, 1, 8876), (2426, 27, 8877), (2426, 110, 5730), (2427, 1, 8878), (2427, 12, 8879), (2427, 14, 8880), (2427, 27, 8881), (2427, 62, 6), (2427, 90, 8882), (2427, 110, 8883), (2429, 1, 8884), (2429, 27, 8881), (2429, 110, 8885), (2430, 1, 8886), (2430, 4, 2396), (2430, 5, 156), (2430, 10, 2589), (2430, 12, 93), (2430, 14, 8887), (2430, 25, 94), (2430, 26, 8888), (2430, 27, 8891), (2430, 62, 1329), (2430, 90, 8892), (2430, 110, 8893), (2431, 1, 8894), (2431, 27, 8891), (2431, 110, 1983), (2432, 110, 8896), (2433, 1, 8897), (2433, 14, 6552), (2433, 27, 8898), (2433, 62, 6695), (2433, 110, 8899), (2434, 1, 8901), (2434, 12, 8902), (2434, 14, 8903), (2434, 27, 8904), (2434, 62, 6), (2434, 90, 8905), (2434, 110, 8906), (2436, 1, 8907), (2436, 27, 8904), (2436, 110, 8908), (2437, 1, 8910), (2437, 12, 8911), (2437, 14, 8912), (2437, 27, 8913), (2437, 62, 6), (2437, 90, 8915), (2437, 110, 8916), (2439, 1, 8917), (2439, 27, 8913), (2439, 110, 8918), (2440, 1, 8920), (2440, 12, 8921), (2440, 14, 8912), (2440, 27, 8922), (2440, 62, 6), (2440, 90, 8923), (2440, 110, 8925), (2440, 116, 8926), (2441, 1, 8927), (2441, 27, 8922), (2441, 110, 8928), (2442, 1, 8930), (2442, 4, 8370), (2442, 5, 310), (2442, 12, 93), (2442, 13, 3819), (2442, 14, 8931), (2442, 22, 8932), (2442, 26, 8933), (2442, 27, 8935), (2442, 62, 6), (2442, 90, 8936), (2442, 110, 8938), (2442, 116, 8939), (2444, 1, 8940), (2444, 27, 8935), (2444, 110, 8941), (2448, 1, 8942), (2448, 12, 8943), (2448, 14, 8944), (2448, 27, 8945), (2448, 62, 6), (2448, 90, 8946), (2448, 110, 8956), (2448, 116, 8957), (2502, 1, 9120), (2502, 27, 8945), (2502, 110, 9121), (2503, 14, 871), (2503, 62, 5729), (2503, 90, 9122), (2503, 110, 9123), (2503, 116, 9124), (2504, 1, 9125), (2504, 27, 9126), (2504, 110, 5730), (1571, 1, 6216), (1571, 12, 6681), (1571, 14, 6683), (1571, 27, 6685), (1571, 62, 6), (1571, 90, 8958), (1571, 110, 9061), (1711, 1, 9062), (1711, 27, 6685), (1711, 110, 9127), (1712, 1, 9128), (1712, 12, 9129), (1712, 14, 9130), (1712, 27, 9131), (1712, 62, 6), (1712, 90, 9132), (1712, 110, 9133), (1712, 116, 9134), (2505, 1, 9135), (2505, 27, 9131), (2505, 110, 9136), (2506, 1, 9137), (2506, 4, 2022), (2506, 5, 90), (2506, 12, 93), (2506, 13, 3819), (2506, 14, 9138), (2506, 22, 9139), (2506, 26, 9140), (2506, 27, 9141), (2506, 62, 6), (2506, 90, 9142), (2506, 110, 9143), (2508, 1, 9144), (2508, 27, 9141), (2508, 110, 9145), (2509, 1, 9146), (2509, 4, 8046), (2509, 5, 3103), (2509, 10, 9147), (2509, 12, 507), (2509, 14, 9148), (2509, 25, 508), (2509, 26, 9149), (2509, 27, 9150), (2509, 62, 1329), (2509, 90, 9151), (2509, 110, 9152), (2510, 1, 9153), (2510, 27, 9150), (2510, 110, 1983), (2511, 1, 9154), (2511, 4, 9155), (2511, 5, 1090), (2511, 10, 9156), (2511, 12, 1359), (2511, 13, 9157), (2511, 14, 9158), (2511, 25, 1409), (2511, 26, 9159), (2511, 27, 9160), (2511, 62, 292), (2511, 87, 3751), (2511, 90, 9161), (2511, 110, 9162), (2512, 1, 9163), (2512, 27, 9160), (2512, 110, 1983), (2513, 1, 9164), (2513, 4, 8046), (2513, 5, 3103), (2513, 10, 3700), (2513, 12, 507), (2513, 14, 9148), (2513, 25, 508), (2513, 26, 9165), (2513, 27, 9166), (2513, 62, 1329), (2513, 90, 9167), (2513, 110, 9168), (2514, 1, 9169), (2514, 27, 9166), (2514, 110, 1983), (2515, 1, 9170), (2515, 10, 9171), (2515, 12, 93), (2515, 14, 9172), (2515, 25, 94), (2515, 26, 5814), (2515, 27, 9173), (2515, 62, 1329), (2515, 90, 9174), (2515, 110, 9175), (2516, 1, 9176), (2516, 27, 9173), (2516, 110, 1983), (2517, 1, 9177), (2517, 4, 2245), (2517, 5, 1077), (2517, 10, 9178), (2517, 12, 6656), (2517, 13, 6660), (2517, 14, 9179), (2517, 25, 6657), (2517, 26, 9180), (2517, 27, 9181), (2517, 62, 6593), (2517, 87, 3751), (2517, 110, 9182), (2519, 110, 9186), (2519, 12, 9188), (2519, 4, 9189), (2519, 10, 9190), (2519, 14, 9191), (2519, 1, 9192), (2519, 87, 9193), (2520, 110, 9194), (2521, 1, 9195), (2521, 12, 9196), (2521, 14, 9197), (2521, 27, 9198), (2521, 62, 6), (2521, 90, 9199), (2521, 110, 9200), (2523, 1, 9201), (2523, 27, 9198), (2523, 110, 9202), (2524, 1, 9203), (2524, 4, 156), (2524, 5, 1090), (2524, 10, 9204), (2524, 12, 9205), (2524, 13, 9206), (2524, 14, 9207), (2524, 25, 9208), (2524, 26, 9209), (2524, 27, 9210), (2524, 62, 6593), (2524, 87, 3751), (2524, 90, 9211), (2524, 110, 9212), (2524, 116, 9213), (2526, 110, 9215), (2527, 1, 9216), (2527, 8, 7446), (2527, 11, 9217), (2527, 14, 9218), (2527, 27, 9219), (2527, 62, 1416), (2527, 110, 9220), (2528, 110, 9221), (2518, 1, 9183), (2518, 4, 374), (2518, 5, 274), (2518, 10, 9184), (2518, 12, 9185), (2518, 13, 9187), (2518, 14, 9214), (2518, 25, 9222), (2518, 26, 9223), (2518, 27, 9224), (2518, 62, 9225), (2518, 90, 9226), (2518, 110, 9227), (2525, 1, 9228), (2525, 27, 9224), (2525, 110, 1983), (2529, 1, 9229), (2529, 4, 9230), (2529, 5, 1090), (2529, 10, 3352), (2529, 12, 1408), (2529, 13, 4013), (2529, 14, 9231), (2529, 22, 9232), (2529, 26, 9233), (2529, 27, 9234), (2529, 62, 6), (2529, 90, 9235), (2529, 110, 9236), (2531, 1, 9237), (2531, 27, 9234), (2531, 110, 9238), (2532, 1, 9239), (2532, 10, 9240), (2532, 12, 2635), (2532, 13, 4005), (2532, 14, 9241), (2532, 25, 6607), (2532, 26, 3852), (2532, 27, 9242), (2532, 62, 6593), (2532, 87, 3751), (2532, 90, 9243), (2532, 110, 9244), (2534, 110, 9246), (2533, 1, 3730), (2533, 4, 382), (2533, 5, 156), (2533, 10, 3728), (2533, 12, 93), (2533, 14, 3729), (2533, 25, 94), (2533, 26, 3731), (2533, 27, 9245), (2533, 62, 1329), (2533, 90, 3732), (2533, 110, 3727), (2536, 1, 3730), (2536, 4, 382), (2536, 5, 156), (2536, 10, 3728), (2536, 12, 93), (2536, 14, 3729), (2536, 25, 94), (2536, 26, 3731), (2536, 27, 9248), (2536, 62, 1329), (2536, 90, 3732), (2536, 110, 3727), (2537, 1, 9249), (2537, 27, 9248), (2537, 110, 1983), (2538, 1, 9250), (2538, 4, 155), (2538, 5, 310), (2538, 10, 9251), (2538, 12, 93), (2538, 14, 9252), (2538, 25, 94), (2538, 26, 9253), (2538, 27, 9254), (2538, 62, 1329), (2538, 90, 9255), (2538, 110, 9256), (2538, 116, 9257), (2539, 1, 9258), (2539, 27, 9254), (2539, 110, 1983), (2535, 110, 4071), (2540, 110, 9247), (2540, 12, 1539), (2540, 4, 4062), (2540, 10, 89), (2540, 14, 9259), (2541, 1, 9260), (2541, 2, 9261), (2541, 8, 9262), (2541, 10, 9263), (2541, 11, 9264), (2541, 14, 7059), (2541, 27, 9265), (2541, 62, 6593), (2541, 87, 3751), (2541, 90, 9266), (2541, 110, 9267), (2541, 115, 9268), (2543, 110, 9270), (2544, 1, 9260), (2544, 2, 9261), (2544, 8, 9262), (2544, 11, 9264), (2544, 14, 7059), (2544, 27, 9265), (2544, 62, 6593), (2544, 87, 3751), (2544, 115, 9268), (2544, 90, 9271), (2544, 10, 9272), (2544, 110, 9273), (2546, 1, 9274), (2546, 2, 9275), (2546, 8, 7056), (2546, 10, 9276), (2546, 11, 9277), (2546, 14, 9278), (2546, 27, 9279), (2546, 62, 6593), (2546, 87, 3751), (2546, 90, 9280), (2546, 110, 9281), (2546, 115, 9282), (2548, 110, 9284), (2549, 1, 9285), (2549, 7, 9286), (2549, 8, 7056), (2549, 11, 9277), (2549, 14, 1363), (2549, 27, 9287), (2549, 62, 1416), (2549, 87, 3751), (2549, 110, 9282), (2551, 1, 9288), (2551, 4, 156), (2551, 5, 135), (2551, 10, 9289), (2551, 12, 6585), (2551, 13, 6590), (2551, 14, 9290), (2551, 25, 6586), (2551, 26, 9291), (2551, 27, 9292), (2551, 62, 6593), (2551, 87, 3751), (2551, 90, 9293), (2551, 110, 9294), (2553, 110, 9296), (2555, 4, 287), (2555, 5, 1454), (2555, 10, 9297), (2555, 12, 9298), (2555, 14, 7942), (2555, 26, 9299), (2555, 62, 1458), (2555, 110, 9300), (2556, 1, 9301), (2556, 27, 9302), (2556, 110, 5395), (2557, 1, 9303), (2557, 4, 9065), (2557, 5, 135), (2557, 12, 93), (2557, 13, 3819), (2557, 14, 9304), (2557, 22, 9305), (2557, 26, 9306), (2557, 27, 9307), (2557, 62, 6), (2557, 90, 9308), (2557, 110, 9309), (2559, 1, 9310), (2559, 27, 9307), (2559, 110, 9311), (2560, 1, 9312), (2560, 10, 9313), (2560, 12, 93), (2560, 14, 9314), (2560, 25, 94), (2560, 26, 9306), (2560, 27, 9315), (2560, 62, 1329), (2560, 90, 9316), (2560, 110, 9317), (2561, 1, 9318), (2561, 27, 9315), (2561, 110, 1983), (2562, 1, 9319), (2562, 4, 2607), (2562, 5, 299), (2562, 10, 9320), (2562, 12, 93), (2562, 14, 9321), (2562, 25, 94), (2562, 26, 9322), (2562, 27, 9323), (2562, 62, 1329), (2562, 90, 9324), (2562, 110, 9325), (2563, 1, 9326), (2563, 27, 9323), (2563, 110, 1983), (2564, 1, 9327), (2564, 4, 155), (2564, 5, 299), (2564, 10, 6437), (2564, 12, 93), (2564, 14, 9328), (2564, 25, 94), (2564, 26, 9329), (2564, 27, 9330), (2564, 62, 1329), (2564, 90, 9331), (2564, 110, 9332), (2564, 116, 9333), (2565, 1, 9334), (2565, 27, 9330), (2565, 110, 1983), (2566, 1, 9335), (2566, 4, 8370), (2566, 5, 156), (2566, 10, 9336), (2566, 12, 93), (2566, 14, 9337), (2566, 25, 94), (2566, 26, 9338), (2566, 27, 9339), (2566, 62, 1329), (2566, 90, 9340), (2566, 110, 9341), (2567, 1, 9342), (2567, 27, 9339), (2567, 110, 1983), (2542, 8, 4093), (2542, 11, 9269), (2542, 14, 9283), (2542, 62, 4097), (2542, 87, 3751), (2542, 90, 9295), (2542, 110, 9343), (2542, 116, 9344), (2542, 118, 9345), (2547, 1, 9346), (2547, 27, 9347), (2547, 110, 4099), (2542, 7, 4085), (2552, 1, 9348), (2552, 4, 1076), (2552, 5, 872), (2552, 10, 9349), (2552, 12, 9350), (2552, 13, 9351), (2552, 14, 8985), (2552, 25, 9350), (2552, 26, 9352), (2552, 27, 9353), (2552, 62, 1264), (2552, 90, 9354), (2552, 110, 9355), (2568, 1, 9356), (2568, 27, 9353), (2568, 110, 1266), (2569, 1, 9357), (2569, 12, 9358), (2569, 14, 9359), (2569, 27, 9360), (2569, 62, 6), (2569, 90, 9361), (2569, 110, 9362), (2571, 1, 9363), (2571, 27, 9360), (2571, 110, 9364), (2572, 1, 9365), (2572, 12, 9366), (2572, 14, 9367), (2572, 22, 9368), (2572, 27, 9369), (2572, 62, 6), (2572, 90, 9370), (2572, 110, 9371), (2572, 116, 9372), (2574, 1, 9373), (2574, 27, 9369), (2574, 110, 9374), (2575, 1, 9375), (2575, 12, 9376), (2575, 14, 9377), (2575, 22, 9378), (2575, 27, 9379), (2575, 62, 6), (2575, 90, 9380), (2575, 110, 9381), (2576, 1, 9382), (2576, 27, 9379), (2576, 110, 9383), (2577, 1, 9384), (2577, 4, 4404), (2577, 5, 135), (2577, 10, 9385), (2577, 12, 9386), (2577, 13, 9387), (2577, 14, 9388), (2577, 25, 9389), (2577, 26, 9390), (2577, 27, 9391), (2577, 62, 6593), (2577, 87, 3751), (2577, 90, 9392), (2577, 110, 9393), (2577, 116, 9394), (2579, 110, 9396), (2578, 1, 9395), (2578, 12, 9397), (2578, 14, 9398), (2578, 22, 9399), (2578, 27, 9400), (2578, 62, 6), (2578, 90, 9401), (2578, 110, 9402), (2581, 1, 9403), (2581, 27, 9400), (2581, 110, 9404), (2584, 1, 9405), (2584, 4, 2799), (2584, 5, 299), (2584, 10, 2397), (2584, 12, 286), (2584, 13, 289), (2584, 14, 3908), (2584, 25, 1779), (2584, 26, 9406), (2584, 27, 9412), (2584, 62, 292), (2584, 87, 3751), (2584, 90, 9408), (2584, 110, 9409), (2584, 116, 9410), (2586, 110, 9413), (2587, 1, 9414), (2587, 4, 9415), (2587, 5, 1090), (2587, 10, 9416), (2587, 12, 1408), (2587, 13, 1407), (2587, 14, 773), (2587, 25, 1409), (2587, 26, 9417), (2587, 27, 9418), (2587, 62, 292), (2587, 87, 3751), (2587, 90, 9419), (2587, 110, 9420), (2588, 1, 9421), (2588, 27, 9418), (2588, 110, 1983), (2589, 1, 9422), (2589, 4, 452), (2589, 5, 1090), (2589, 10, 9423), (2589, 12, 9424), (2589, 14, 9425), (2589, 26, 9426), (2589, 110, 9427), (2590, 110, 9428), (2591, 1, 9429), (2591, 12, 9430), (2591, 14, 9431), (2591, 22, 9432), (2591, 27, 9433), (2591, 62, 6), (2591, 90, 9434), (2591, 110, 9435), (2591, 116, 9436), (2593, 1, 9437), (2593, 27, 9433), (2593, 110, 9438), (2594, 1, 9442), (2594, 4, 155), (2594, 5, 156), (2594, 12, 93), (2594, 13, 3819), (2594, 14, 3442), (2594, 26, 9443), (2594, 27, 9444), (2594, 62, 1416), (2594, 87, 3751), (2594, 110, 9445), (2596, 110, 9450), (2597, 1, 9411), (2597, 12, 9451), (2597, 14, 9452), (2597, 22, 9453), (2597, 27, 9454), (2597, 62, 6), (2597, 90, 9455), (2597, 110, 9456), (2598, 1, 9457), (2598, 27, 9454), (2598, 110, 9458), (2599, 1, 6066), (2599, 12, 93), (2599, 13, 3819), (2599, 14, 9459), (2599, 22, 9460), (2599, 26, 6708), (2599, 27, 9461), (2599, 62, 6), (2599, 90, 6068), (2599, 110, 6064), (2601, 1, 8615), (2601, 27, 9461), (2601, 110, 9462), (2602, 1, 6851), (2602, 4, 6884), (2602, 5, 135), (2602, 10, 6908), (2602, 12, 6909), (2602, 13, 6927), (2602, 14, 6939), (2602, 25, 6978), (2602, 26, 7162), (2602, 27, 9463), (2602, 62, 292), (2602, 87, 3751), (2602, 90, 7169), (2602, 110, 7173), (2603, 1, 7177), (2603, 27, 9463), (2603, 110, 1983), (2604, 1, 9464), (2604, 4, 1840), (2604, 5, 274), (2604, 10, 9465), (2604, 12, 9466), (2604, 13, 9467), (2604, 14, 9468), (2604, 25, 9469), (2604, 26, 9470), (2604, 27, 9471), (2604, 62, 3755), (2604, 87, 3751), (2604, 90, 9472), (2604, 110, 9473), (2605, 110, 9474), (2607, 1, 9480), (2607, 4, 8370), (2607, 5, 310), (2607, 10, 9481), (2607, 12, 93), (2607, 14, 9482), (2607, 25, 94), (2607, 26, 9483), (2607, 27, 9484), (2607, 62, 1329), (2607, 90, 9485), (2607, 110, 8286), (2608, 1, 9486), (2608, 27, 9484), (2608, 110, 1983), (2609, 1, 9487), (2609, 10, 9488), (2609, 12, 93), (2609, 14, 9489), (2609, 25, 94), (2609, 26, 9490), (2609, 27, 9491), (2609, 62, 1329), (2609, 90, 9492), (2609, 110, 9493), (2610, 1, 9494), (2610, 27, 9491), (2610, 110, 1983), (2611, 1, 9495), (2611, 4, 3352), (2611, 5, 135), (2611, 10, 9496), (2611, 12, 286), (2611, 13, 289), (2611, 14, 9497), (2611, 25, 1779), (2611, 26, 9498), (2611, 27, 9499), (2611, 62, 292), (2611, 87, 3751), (2611, 90, 9500), (2611, 110, 9501), (2612, 1, 9502), (2612, 27, 9499), (2612, 110, 1983), (2613, 1, 9503), (2613, 4, 287), (2613, 5, 288), (2613, 10, 3970), (2613, 12, 286), (2613, 13, 289), (2613, 14, 5539), (2613, 25, 1779), (2613, 26, 9504), (2613, 27, 9505), (2613, 62, 292), (2613, 87, 3751), (2613, 90, 9506), (2613, 110, 9507), (2615, 1, 9509), (2615, 4, 1744), (2615, 5, 90), (2615, 10, 2831), (2615, 12, 93), (2615, 14, 9510), (2615, 25, 94), (2615, 26, 9511), (2615, 27, 9512), (2615, 62, 1329), (2615, 90, 9513), (2615, 110, 9514), (2616, 1, 9515), (2616, 27, 9512), (2616, 110, 1983), (2614, 1, 9508), (2614, 4, 1204), (2614, 12, 870), (2614, 13, 9516), (2614, 14, 480), (2614, 26, 9517), (2614, 27, 9518), (2614, 62, 1416), (2614, 87, 3751), (2614, 110, 9519), (2617, 110, 9520), (2618, 1, 9521), (2618, 4, 9522), (2618, 5, 9523), (2618, 10, 9524), (2618, 12, 1978), (2618, 13, 5629), (2618, 14, 9525), (2618, 25, 5624), (2618, 26, 9526), (2618, 27, 9527), (2618, 62, 5631), (2618, 87, 3751), (2618, 90, 9528), (2618, 110, 9529), (2618, 116, 9530), (2620, 110, 9532), (2621, 1, 9533), (2621, 4, 6052), (2621, 5, 299), (2621, 10, 1349), (2621, 12, 93), (2621, 14, 9534), (2621, 25, 94), (2621, 26, 9535), (2621, 27, 9536), (2621, 62, 1329), (2621, 90, 9537), (2621, 110, 9538), (2622, 1, 9539), (2622, 27, 9536), (2622, 110, 1983), (2623, 1, 9540), (2623, 27, 9541), (2623, 62, 8199), (2623, 90, 9542), (2623, 110, 9543), (2624, 110, 9544), (2625, 110, 9545), (2624, 115, 9546), (2624, 1, 9540), (2626, 1, 9547), (2626, 4, 3352), (2626, 5, 872), (2626, 10, 9548), (2626, 12, 286), (2626, 13, 289), (2626, 14, 9130), (2626, 25, 1779), (2626, 26, 9549), (2626, 27, 9550), (2626, 62, 292), (2626, 87, 3751), (2626, 90, 9551), (2626, 110, 9552), (2628, 110, 9554), (2631, 1, 9555), (2631, 4, 9556), (2631, 5, 288), (2631, 10, 9557), (2631, 12, 507), (2631, 14, 9558), (2631, 25, 508), (2631, 26, 9559), (2631, 27, 9564), (2631, 62, 1329), (2631, 90, 9561), (2631, 110, 9562), (2632, 1, 9565), (2632, 27, 9564), (2632, 110, 1983), (2633, 1, 9566), (2633, 4, 1422), (2633, 5, 90), (2633, 10, 9567), (2633, 12, 93), (2633, 14, 9568), (2633, 25, 94), (2633, 26, 9569), (2633, 27, 9570), (2633, 62, 1329), (2633, 90, 9571), (2633, 110, 9572), (2634, 1, 9573), (2634, 27, 9570), (2634, 110, 1983), (2635, 1, 9574), (2635, 12, 9575), (2635, 14, 9576), (2635, 22, 9577), (2635, 27, 9578), (2635, 62, 6), (2635, 90, 9579), (2635, 110, 9580), (2637, 1, 9581), (2637, 27, 9578), (2637, 110, 9582), (2619, 1, 9531), (2619, 4, 2368), (2619, 5, 288), (2619, 10, 9553), (2619, 12, 2635), (2619, 13, 4005), (2619, 14, 7858), (2619, 25, 2636), (2619, 26, 9563), (2619, 27, 9583), (2619, 62, 6593), (2619, 87, 3751), (2619, 90, 9584), (2619, 110, 9585), (2630, 110, 9587), (2627, 1, 9586), (2627, 4, 310), (2627, 5, 872), (2627, 10, 9588), (2627, 12, 1074), (2627, 13, 8484), (2627, 14, 9589), (2627, 26, 9590), (2627, 27, 9591), (2627, 62, 8488), (2627, 90, 9592), (2627, 110, 9593), (2638, 1, 9594), (2638, 27, 9591), (2638, 110, 1983), (2639, 1, 9595), (2639, 12, 9596), (2639, 14, 9597), (2639, 22, 9598), (2639, 27, 9599), (2639, 62, 6), (2639, 90, 9600), (2639, 110, 9601), (2641, 1, 9602), (2641, 27, 9599), (2641, 110, 9603), (2643, 14, 9605), (2643, 110, 9604), (2643, 92, 9407), (2645, 110, 9606), (2646, 7, 9607), (2646, 8, 9608), (2646, 11, 9609), (2646, 87, 6984), (2646, 90, 9610), (2646, 110, 9611), (2646, 116, 9612), (2646, 118, 6494), (2648, 1, 9616), (2648, 12, 9617), (2648, 14, 9618), (2648, 22, 9619), (2648, 27, 9620), (2648, 62, 6), (2648, 90, 9621), (2648, 110, 9622), (2650, 1, 9623), (2650, 27, 9620), (2650, 110, 9624), (2651, 1, 9625), (2651, 12, 9626), (2651, 14, 9627), (2651, 22, 9628), (2651, 27, 9629), (2651, 62, 6), (2651, 90, 9630), (2651, 110, 9631), (2653, 1, 9632), (2653, 27, 9629), (2653, 110, 9633), (2654, 1, 9634), (2654, 12, 9635), (2654, 14, 9636), (2654, 22, 9637), (2654, 27, 9638), (2654, 62, 6), (2654, 90, 9639), (2654, 110, 9640), (2656, 1, 9641), (2656, 27, 9638), (2656, 110, 9642), (2657, 110, 9643), (2657, 115, 9644), (2657, 3, 9645), (2657, 4, 6926), (2657, 7, 4074), (2657, 8, 9646), (2658, 1, 9647), (2658, 12, 9648), (2658, 14, 9649), (2658, 22, 9650), (2658, 27, 9651), (2658, 62, 6), (2658, 90, 9652), (2660, 1, 9654), (2660, 27, 9651), (2660, 110, 9655), (2661, 1, 9656), (2661, 12, 9657), (2661, 14, 9658), (2661, 22, 9659), (2661, 27, 9660), (2661, 62, 6), (2661, 90, 9661), (2661, 110, 9662), (2663, 1, 9663), (2663, 27, 9660), (2663, 110, 9664), (2658, 110, 9665), (2664, 1, 9666), (2664, 12, 9667), (2664, 14, 9668), (2664, 22, 9669), (2664, 27, 9670), (2664, 62, 6), (2664, 90, 9671), (2664, 110, 9672), (2664, 116, 9673), (2666, 1, 9674), (2666, 27, 9670), (2666, 110, 9675), (112, 1, 9439), (2583, 1, 9440), (2583, 14, 284), (2583, 27, 9441), (2583, 62, 9446), (2583, 89, 446), (2583, 90, 9448), (2583, 110, 427), (2585, 1, 9449), (2585, 27, 9441), (2585, 110, 1983), (2595, 1, 9653), (2595, 12, 9676), (2595, 14, 9677), (2595, 22, 9678), (2595, 27, 9679), (2595, 62, 6), (2595, 90, 9680), (2595, 110, 9681), (2668, 1, 9682), (2668, 27, 9679), (2668, 110, 9683), (2669, 1, 9684), (2669, 12, 9685), (2669, 14, 9686), (2669, 22, 9687), (2669, 27, 9688), (2669, 62, 6), (2669, 90, 9689), (2669, 110, 9690), (2671, 1, 9691), (2671, 27, 9688), (2671, 110, 9692), (2672, 4, 9693), (2672, 5, 872), (2672, 10, 9694), (2672, 12, 1088), (2672, 13, 9695), (2672, 14, 9696), (2672, 26, 9697), (2672, 110, 9698), (2673, 110, 9699), (2606, 1, 431), (2606, 2, 9475), (2606, 4, 1204), (2606, 5, 310), (2606, 10, 9476), (2606, 12, 9477), (2606, 13, 9478), (2606, 14, 9479), (2606, 25, 9700), (2606, 26, 9701), (2606, 27, 9702), (2606, 62, 5537), (2606, 87, 3751), (2606, 110, 9703), (2674, 1, 9704), (2674, 27, 9702), (2674, 110, 1983), (2675, 1, 9705), (2675, 2, 9706), (2675, 4, 9707), (2675, 5, 90), (2675, 10, 9708), (2675, 12, 1236), (2675, 13, 9709), (2675, 14, 9710), (2675, 25, 1236), (2675, 26, 9711), (2675, 27, 9712), (2675, 62, 660), (2675, 110, 9713), (2676, 1, 9714), (2676, 27, 9712), (2676, 110, 662), (2677, 1, 9715), (2677, 12, 9716), (2677, 14, 9717), (2677, 27, 9719), (2677, 62, 6), (2677, 90, 9720), (2677, 110, 9721), (2678, 1, 9722), (2678, 27, 9719), (2678, 110, 9723), (2629, 110, 9560), (2679, 110, 9725), (2679, 1, 9726), (2679, 27, 9727), (2680, 110, 9728), (2681, 110, 9728), (2681, 1, 9729), (1343, 14, 9613), (1343, 6, 5420), (1215, 6, 5420), (1215, 22, 9614), (2647, 1, 9615), (2647, 4, 4004), (2647, 5, 1204), (2647, 10, 9724), (2647, 12, 4403), (2647, 13, 4405), (2647, 14, 9730), (2647, 25, 8087), (2647, 26, 9731), (2647, 27, 9736), (2647, 62, 6593), (2647, 87, 3751), (2647, 90, 9733), (2647, 110, 9734), (2684, 110, 9738), (2685, 1, 9739), (2685, 12, 9740), (2685, 14, 9741), (2685, 22, 9742), (2685, 27, 9743), (2685, 62, 6), (2685, 90, 9744), (2685, 110, 9745), (2685, 116, 9746), (2686, 1, 9747), (2686, 27, 9743), (2686, 110, 9748), (2687, 1, 9749), (2687, 12, 9750), (2687, 14, 9741), (2687, 22, 9751), (2687, 27, 9752), (2687, 62, 6), (2687, 90, 9753), (2687, 110, 9754), (2687, 116, 9755), (2688, 1, 9756), (2688, 27, 9752), (2688, 110, 9757), (2689, 1, 9758), (2689, 4, 1969), (2689, 5, 6587), (2689, 10, 9759), (2689, 12, 6585), (2689, 13, 6590), (2689, 14, 6584), (2689, 25, 6586), (2689, 26, 9760), (2689, 27, 9761), (2689, 62, 6593), (2689, 87, 3751), (2689, 90, 9762), (2689, 110, 9763), (2691, 110, 9765), (2692, 1, 9766), (2692, 4, 497), (2692, 5, 1954), (2692, 10, 9767), (2692, 12, 6585), (2692, 13, 6590), (2692, 14, 9768), (2692, 25, 8895), (2692, 26, 9769), (2692, 27, 9770), (2692, 62, 6593), (2692, 87, 3751), (2692, 90, 9771), (2692, 110, 9772), (2694, 110, 9774), (2695, 1, 9775), (2695, 4, 497), (2695, 5, 1954), (2695, 10, 9776), (2695, 12, 6585), (2695, 13, 6590), (2695, 14, 9768), (2695, 25, 8895), (2695, 26, 9777), (2695, 27, 9778), (2695, 62, 6593), (2695, 87, 3751), (2695, 90, 9779), (2695, 110, 9780), (2697, 1, 9782), (2697, 4, 497), (2697, 5, 1954), (2697, 10, 9783), (2697, 12, 6585), (2697, 13, 6590), (2697, 14, 9768), (2697, 25, 8895), (2697, 26, 9784), (2697, 27, 9785), (2697, 62, 6593), (2697, 87, 3751), (2697, 90, 9786), (2697, 110, 9787), (2699, 110, 9789), (2700, 110, 9790), (2701, 7, 7219), (2701, 8, 9791), (2701, 11, 9792), (2701, 14, 9793), (2701, 62, 5333), (2701, 87, 6984), (2701, 90, 9794), (2701, 110, 9795), (2701, 116, 9796), (2701, 118, 9797), (2702, 1, 9798), (2702, 27, 9799), (2702, 110, 9800), (2703, 1, 9801), (2703, 4, 9802), (2703, 5, 1090), (2703, 10, 9803), (2703, 12, 2341), (2703, 13, 2340), (2703, 14, 9804), (2703, 25, 2342), (2703, 26, 9805), (2703, 27, 9806), (2703, 62, 292), (2703, 87, 3751), (2703, 90, 9807), (2703, 110, 9808), (2703, 116, 9809), (2704, 1, 9810), (2704, 27, 9806), (2704, 110, 1983), (2705, 1, 6723), (2705, 10, 6722), (2705, 12, 286), (2705, 13, 289), (2705, 14, 6719), (2705, 25, 1779), (2705, 26, 6720), (2705, 27, 9812), (2705, 62, 292), (2705, 87, 3751), (2705, 90, 6721), (2705, 110, 6718), (2706, 1, 9813), (2706, 27, 9812), (2706, 110, 1983), (1723, 22, 9814), (2707, 1, 6343), (2707, 12, 93), (2707, 14, 6344), (2707, 25, 94), (2707, 26, 6342), (2707, 27, 9815), (2707, 62, 1329), (2707, 90, 6345), (2707, 110, 3839), (2708, 1, 9816), (2708, 27, 9815), (2708, 110, 1983), (2445, 14, 284), (2445, 8, 5241), (2445, 7, 9817), (2709, 110, 9820), (2709, 14, 9425), (949, 22, 9822), (1305, 22, 9823), (1748, 22, 9824), (1721, 22, 9825), (2677, 22, 9826), (415, 22, 9827), (1235, 22, 9828), (2583, 22, 9829), (1408, 22, 9830), (505, 22, 9831), (1019, 22, 9832), (1319, 22, 9833), (2577, 22, 9834), (1530, 22, 9835), (2703, 22, 9836), (2478, 22, 9837), (2495, 22, 9838), (2707, 22, 9839), (2709, 22, 9840), (2445, 22, 9841), (2497, 22, 9842), (1024, 90, 9843), (2710, 1, 9844), (2710, 12, 9845), (2710, 14, 9846), (2710, 22, 9847), (2710, 27, 9848), (2710, 62, 6), (2710, 90, 9849), (2710, 110, 9850), (2712, 1, 9851), (2712, 27, 9848), (2712, 110, 9852), (2642, 1, 4941), (2642, 12, 9735), (2642, 14, 9737), (2642, 22, 9764), (2642, 27, 9773), (2642, 62, 6), (2642, 90, 9781), (2642, 110, 9788), (2690, 1, 9853), (2690, 27, 9773), (2690, 110, 9854), (2693, 8, 9857), (2693, 62, 5333), (2693, 90, 9860), (2693, 110, 9861), (2693, 116, 9862), (2693, 1, 9866), (2698, 110, 9867), (2693, 6, 9868), (2693, 14, 1690), (2693, 11, 9858), (2693, 7, 9870), (2713, 1, 9871), (2713, 10, 9872), (2713, 12, 1074), (2713, 13, 8484), (2713, 14, 9873), (2713, 26, 9874), (2713, 27, 9875), (2713, 62, 8488), (2713, 90, 9876), (2713, 110, 6925), (2714, 1, 9877), (2714, 27, 9875), (2714, 110, 1983), (2715, 1, 9878), (2715, 12, 9879), (2715, 14, 9880), (2715, 22, 9881), (2715, 27, 9882), (2715, 62, 6), (2715, 90, 9883), (2715, 110, 9884), (2716, 1, 9885), (2716, 27, 9882), (2716, 110, 9886), (2717, 1, 9887), (2717, 4, 9888), (2717, 5, 1090), (2717, 10, 9889), (2717, 12, 2341), (2717, 13, 2340), (2717, 14, 9890), (2717, 25, 2342), (2717, 26, 9891), (2717, 27, 9892), (2717, 62, 292), (2717, 87, 3751), (2717, 90, 9893), (2717, 110, 9894), (2718, 1, 9895), (2718, 27, 9892), (2718, 110, 1983), (2719, 1, 9896), (2719, 4, 2368), (2719, 5, 6587), (2719, 10, 9897), (2719, 12, 6585), (2719, 13, 6590), (2719, 14, 9898), (2719, 25, 6586), (2719, 26, 9899), (2719, 27, 9900), (2719, 62, 6593), (2719, 87, 3751), (2719, 90, 9901), (2719, 110, 9902), (2719, 116, 9903), (2721, 110, 9905), (2722, 1, 9906), (2722, 4, 2368), (2722, 5, 6587), (2722, 10, 9907), (2722, 12, 6585), (2722, 13, 6590), (2722, 14, 9898), (2722, 25, 6586), (2722, 26, 9908), (2722, 27, 9909), (2722, 62, 6593), (2722, 87, 3751), (2722, 90, 9910), (2722, 110, 9911), (2724, 110, 9913), (2725, 1, 9914), (2725, 4, 2368), (2725, 5, 6587), (2725, 10, 9915), (2725, 12, 6585), (2725, 13, 6590), (2725, 14, 9898), (2725, 25, 6586), (2725, 26, 9916), (2725, 27, 9917), (2725, 62, 6593), (2725, 87, 3751), (2725, 90, 9918), (2725, 110, 9919), (2727, 110, 9921), (2720, 1, 6846), (2720, 3, 9447), (2720, 7, 5160), (2720, 8, 5159), (2720, 10, 9718), (2720, 11, 9811), (2720, 14, 5792), (2720, 26, 9818), (2720, 27, 9819), (2720, 62, 5161), (2720, 90, 9821), (2720, 110, 9855), (2720, 114, 9856), (2720, 116, 9859), (2726, 110, 9904), (2728, 1, 9912), (2728, 12, 9920), (2728, 14, 9922), (2728, 22, 9923), (2728, 27, 9924), (2728, 62, 6), (2728, 90, 9925), (2728, 110, 9926), (2730, 1, 9927), (2730, 27, 9924), (2730, 110, 9928), (2731, 1, 9929), (2731, 4, 5126), (2731, 5, 374), (2731, 10, 9930), (2731, 12, 1771), (2731, 13, 1770), (2731, 14, 9931), (2731, 25, 2337), (2731, 26, 9932), (2731, 27, 9933), (2731, 62, 292), (2731, 87, 3751), (2731, 90, 9934), (2731, 110, 9935), (2733, 110, 9937), (2734, 1, 9938), (2734, 12, 9939), (2734, 14, 9940), (2734, 22, 9941), (2734, 27, 9942), (2734, 62, 6), (2734, 90, 9943), (2734, 110, 9944), (2736, 1, 9945), (2736, 27, 9942), (2736, 110, 9946), (1017, 110, 9863), (2723, 1, 9869), (2723, 4, 1090), (2723, 5, 274), (2723, 10, 9936), (2723, 12, 9947), (2723, 13, 9948), (2723, 14, 9949), (2723, 25, 9947), (2723, 26, 9950), (2723, 27, 9951), (2723, 62, 660), (2723, 110, 9952), (2732, 1, 9953), (2732, 27, 9951), (2732, 110, 662), (2737, 1, 9954), (2737, 4, 1830), (2737, 5, 310), (2737, 10, 9955), (2737, 12, 1225), (2737, 13, 8522), (2737, 14, 9956), (2737, 26, 9957), (2737, 27, 9958), (2737, 62, 9959), (2737, 90, 9960), (2737, 110, 9961), (2738, 1, 9962), (2738, 27, 9958), (2738, 110, 1983), (2740, 1, 9969), (2740, 4, 1830), (2740, 5, 310), (2740, 10, 9964), (2740, 12, 1225), (2740, 13, 8522), (2740, 14, 9956), (2740, 26, 9965), (2740, 27, 9970), (2740, 62, 8488), (2740, 90, 9967), (2740, 110, 9968), (2741, 1, 9971), (2741, 27, 9970), (2741, 110, 1983), (2742, 1, 9972), (2742, 12, 9973), (2742, 14, 9974), (2742, 22, 9975), (2742, 27, 9976), (2742, 62, 6), (2742, 90, 9977), (2742, 110, 9978), (2744, 1, 9979), (2744, 27, 9976), (2744, 110, 9980), (2745, 1, 9981), (2745, 10, 9982), (2745, 12, 6585), (2745, 13, 6590), (2745, 14, 9983), (2745, 25, 8895), (2745, 26, 9984), (2745, 27, 9985), (2745, 62, 6593), (2745, 87, 3751), (2745, 90, 9986), (2745, 110, 9987), (2747, 110, 9989), (2582, 1, 4087), (2582, 12, 9732), (2582, 14, 9988), (2582, 22, 9990), (2582, 27, 9991), (2582, 62, 6), (2582, 90, 9992), (2582, 110, 9993), (2748, 1, 9994), (2748, 27, 9991), (2748, 110, 9995), (2696, 1, 9864), (2696, 12, 9865), (2696, 14, 9996), (2696, 22, 9997), (2696, 27, 9998), (2696, 62, 6), (2696, 90, 9999), (2696, 110, 10000), (2749, 1, 10001), (2749, 27, 9998), (2749, 110, 10002), (2750, 6, 10003), (2750, 7, 5369), (2750, 8, 5289), (2750, 11, 10004), (2750, 14, 10005), (2750, 87, 6984), (2750, 90, 10006), (2750, 118, 10008), (2750, 110, 10011), (2750, 45, 135), (2752, 110, 10012), (2753, 110, 10013), (2754, 1, 10014), (2754, 12, 10015), (2754, 14, 10016), (2754, 22, 10017), (2754, 27, 10018), (2754, 62, 6), (2754, 90, 10019), (2754, 110, 9410), (2755, 1, 10020), (2755, 27, 10018), (2755, 110, 10021), (2756, 1, 10022), (2756, 12, 10023), (2756, 14, 10024), (2756, 22, 10025), (2756, 27, 10026), (2756, 62, 6), (2756, 90, 10027), (2756, 110, 10028), (2758, 1, 10029), (2758, 27, 10026), (2758, 110, 10030), (2759, 1, 10031), (2759, 4, 10032), (2759, 5, 7814), (2759, 10, 10033), (2759, 12, 10034), (2759, 13, 10035), (2759, 14, 10036), (2759, 25, 10034), (2759, 26, 10037), (2759, 27, 10038), (2759, 62, 1264), (2759, 90, 10039), (2759, 110, 10040), (2760, 1, 10041), (2760, 27, 10038), (2760, 110, 1266), (2761, 7, 10042), (2761, 8, 10043), (2761, 14, 5242), (2761, 18, 10045), (2761, 62, 10046), (2761, 110, 10047), (2761, 116, 10048), (2763, 6, 10050), (2763, 7, 10051), (2763, 8, 4093), (2763, 11, 10052), (2763, 14, 10053), (2763, 62, 5333), (2763, 87, 6984), (2763, 90, 10054), (2763, 110, 10055), (2763, 118, 10056), (2765, 110, 10059), (2766, 1, 10060), (2766, 4, 2758), (2766, 5, 310), (2766, 10, 10061), (2766, 12, 10062), (2766, 14, 10063), (2766, 25, 10064), (2766, 26, 10065), (2766, 27, 10066), (2766, 62, 1329), (2766, 90, 10067), (2766, 110, 10068), (2767, 1, 10069), (2767, 27, 10066), (2767, 110, 1983), (2739, 1, 9963), (2739, 10, 9465), (2739, 12, 9966), (2739, 13, 10007), (2739, 14, 10070), (2739, 26, 9470), (2739, 27, 10071), (2739, 62, 1416), (2739, 110, 10072), (2769, 1, 10073), (2769, 4, 1744), (2769, 5, 1204), (2769, 10, 10074), (2769, 12, 10075), (2769, 13, 10076), (2769, 14, 10077), (2769, 25, 10075), (2769, 26, 10078), (2769, 27, 10079), (2769, 62, 6593), (2769, 87, 3751), (2769, 90, 10080), (2769, 110, 10081), (2771, 110, 10083), (2774, 3, 10087), (2774, 6, 10088), (2774, 7, 10089), (2774, 8, 10090), (2774, 11, 10091), (2774, 14, 1177), (2774, 18, 10092), (2774, 30, 274), (2774, 62, 10046), (2774, 110, 10093), (2774, 118, 10094), (2776, 7, 10042), (2776, 8, 10043), (2776, 11, 10044), (2776, 14, 5242), (2776, 18, 10045), (2776, 62, 10046), (2776, 110, 10047), (2776, 116, 10048), (2776, 118, 10049), (2778, 1, 10095), (2778, 4, 4300), (2778, 5, 1077), (2778, 10, 10096), (2778, 12, 1225), (2778, 13, 8522), (2778, 14, 10097), (2778, 26, 10098), (2778, 27, 10099), (2778, 62, 9959), (2778, 90, 10100), (2778, 110, 10101), (2779, 1, 10102), (2779, 27, 10099), (2779, 110, 1983), (2780, 1, 10103), (2780, 4, 1422), (2780, 5, 274), (2780, 10, 10104), (2780, 12, 93), (2780, 14, 10105), (2780, 25, 94), (2780, 26, 10106), (2780, 27, 10107), (2780, 62, 1329), (2780, 90, 10108), (2780, 110, 10109), (2781, 1, 10110), (2781, 27, 10107), (2781, 110, 1983), (2782, 1, 10111), (2782, 12, 10112), (2782, 14, 10113), (2782, 22, 10114), (2782, 27, 10115), (2782, 62, 6), (2782, 90, 10116), (2782, 110, 10117), (2784, 1, 10118), (2784, 27, 10115), (2784, 110, 10119), (2785, 1, 10120), (2785, 4, 3352), (2785, 5, 288), (2785, 10, 10121), (2785, 12, 286), (2785, 13, 289), (2785, 14, 10122), (2785, 25, 1779), (2785, 26, 10123), (2785, 27, 10124), (2785, 62, 292), (2785, 87, 3751), (2785, 90, 10125), (2785, 110, 10126), (2785, 116, 10127), (2787, 110, 10129), (2788, 1, 10130), (2788, 12, 10131), (2788, 14, 10132), (2788, 22, 10133), (2788, 27, 10134), (2788, 62, 6), (2788, 90, 10135), (2788, 110, 10136), (2790, 1, 10137), (2790, 27, 10134), (2790, 110, 10138), (2751, 1, 10009), (2751, 4, 89), (2751, 5, 135), (2751, 12, 870), (2751, 14, 9425), (2751, 22, 10010), (2751, 26, 10128), (2751, 110, 869), (2786, 110, 10139), (2764, 1, 10057), (2764, 12, 10058), (2764, 14, 10140), (2764, 22, 10141), (2764, 27, 10142), (2764, 62, 6), (2764, 90, 10143), (2764, 110, 10144), (2792, 1, 10145), (2792, 27, 10142), (2792, 110, 10146), (2770, 110, 10082), (2772, 1, 10084), (2772, 4, 288), (2772, 5, 1090), (2772, 10, 10085), (2772, 12, 10086), (2772, 13, 10147), (2772, 14, 8471), (2772, 25, 10148), (2772, 26, 10149), (2772, 27, 10150), (2772, 62, 6593), (2772, 87, 3751), (2772, 90, 10151), (2772, 110, 10152), (2772, 116, 10153), (2793, 110, 10155), (2794, 110, 10156), (2794, 90, 10157), (2794, 1, 10158), (2794, 27, 10159), (2794, 123, 10161), (2795, 110, 10162), (2797, 110, 7534), (2797, 1, 7530), (2797, 27, 10163), (2798, 110, 7532), (2773, 1, 10154), (2773, 12, 10164), (2773, 14, 10165), (2773, 22, 10166), (2773, 27, 10167), (2773, 62, 6), (2773, 90, 10168), (2773, 110, 10169), (2800, 1, 10170), (2800, 27, 10167), (2800, 110, 10171), (2801, 1, 10172), (2801, 12, 10173), (2801, 14, 10174), (2801, 22, 10175), (2801, 27, 10176), (2801, 62, 6), (2801, 90, 10177), (2801, 110, 10178), (2801, 116, 10179), (2802, 1, 10180), (2802, 27, 10176), (2802, 110, 10181), (2803, 1, 10182), (2803, 12, 10183), (2803, 14, 10174), (2803, 22, 10184), (2803, 27, 10185), (2803, 62, 6), (2803, 90, 10186), (2803, 110, 10187), (2805, 1, 10188), (2805, 27, 10185), (2805, 110, 10189), (2806, 6, 10190), (2806, 8, 4089), (2806, 11, 10192), (2806, 14, 10193), (2806, 62, 5333), (2806, 87, 6984), (2806, 90, 10194), (2806, 110, 10195), (2806, 118, 10196), (2808, 110, 10199), (2809, 1, 10200), (2809, 4, 2368), (2809, 5, 1954), (2809, 10, 10201), (2809, 12, 2635), (2809, 13, 4005), (2809, 14, 10202), (2809, 25, 2636), (2809, 26, 10203), (2809, 27, 10204), (2809, 62, 6593), (2809, 87, 3751), (2809, 90, 10205), (2809, 110, 10206), (2811, 110, 10208), (2812, 1, 10209), (2812, 4, 2560), (2812, 5, 274), (2812, 10, 10210), (2812, 12, 4581), (2812, 14, 10211), (2812, 25, 4582), (2812, 26, 10212), (2812, 27, 10213), (2812, 62, 1329), (2812, 90, 10214), (2812, 110, 10215), (2813, 1, 10216), (2813, 27, 10213), (2813, 110, 1983), (2814, 1, 10217), (2814, 12, 10218), (2814, 14, 10219), (2814, 22, 10220), (2814, 27, 10221), (2814, 62, 6), (2814, 90, 10222), (2814, 110, 10223), (2816, 1, 10224), (2816, 27, 10221), (2816, 110, 10225), (2810, 1, 10160), (2810, 2, 10207), (2810, 3, 10226), (2810, 4, 2461), (2810, 5, 274), (2810, 10, 10227), (2810, 12, 7308), (2810, 13, 7309), (2810, 14, 10228), (2810, 25, 7308), (2810, 26, 10229), (2810, 27, 10230), (2810, 62, 660), (2810, 110, 10231), (2817, 1, 10232), (2817, 27, 10230), (2817, 110, 662), (2818, 1, 10233), (2818, 4, 5126), (2818, 5, 310), (2818, 10, 10234), (2818, 12, 1074), (2818, 13, 8484), (2818, 14, 10235), (2818, 26, 10236), (2818, 27, 10237), (2818, 62, 8488), (2818, 90, 10238), (2818, 110, 10239), (2819, 1, 10240), (2819, 27, 10237), (2819, 110, 1983), (2820, 1, 10241), (2820, 12, 10242), (2820, 14, 10243), (2820, 22, 10244), (2820, 27, 10245), (2820, 62, 6), (2820, 90, 10246), (2820, 110, 10247), (2826, 6, 10259), (2826, 7, 5369), (2826, 8, 4093), (2826, 11, 10260), (2826, 14, 10261), (2826, 62, 5333), (2826, 87, 6984), (2826, 90, 10262), (2826, 110, 10263), (2826, 118, 10264), (2828, 110, 10267), (2822, 1, 10248), (2822, 4, 5601), (2822, 5, 274), (2822, 10, 10249), (2822, 12, 286), (2822, 13, 289), (2822, 14, 10268), (2822, 25, 1779), (2822, 26, 10269), (2822, 27, 10270), (2822, 62, 292), (2822, 87, 3751), (2822, 90, 10271), (2822, 110, 10272), (68, 110, 295), (2832, 1, 10281), (2832, 12, 10282), (2832, 14, 10283), (2832, 22, 10284), (2832, 27, 10285), (2832, 62, 6), (2832, 90, 10286), (2832, 110, 10287), (2833, 1, 10288), (2833, 27, 10285), (2833, 110, 10289), (2834, 1, 10290), (2834, 12, 10291), (2834, 14, 10292), (2834, 22, 10293), (2834, 27, 10294), (2834, 62, 6), (2834, 90, 10295), (2834, 110, 10296), (2836, 1, 10297), (2836, 27, 10294), (2836, 110, 10298), (1958, 1, 10299), (2837, 1, 10250), (2837, 4, 8370), (2837, 10, 10251), (2837, 12, 8810), (2837, 13, 8811), (2837, 14, 10252), (2837, 25, 8810), (2837, 26, 10253), (2837, 27, 10300), (2837, 62, 1264), (2837, 90, 10255), (2837, 110, 10256), (2838, 1, 10258), (2838, 27, 10300), (2838, 110, 1266), (2839, 1, 10301), (2839, 4, 5478), (2839, 5, 156), (2839, 10, 10302), (2839, 12, 507), (2839, 14, 10303), (2839, 25, 508), (2839, 26, 10304), (2839, 27, 10305), (2839, 62, 1329), (2839, 90, 10306), (2839, 110, 10307), (2840, 1, 10308), (2840, 27, 10305), (2840, 110, 1983), (2841, 1, 10309), (2841, 4, 3342), (2841, 5, 872), (2841, 10, 10310), (2841, 12, 8810), (2841, 13, 8811), (2841, 14, 10311), (2841, 25, 8810), (2841, 26, 10312), (2841, 27, 10313), (2841, 62, 1264), (2841, 90, 10314), (2841, 110, 10315), (2842, 1, 10316), (2842, 27, 10313), (2842, 110, 1266), (2843, 1, 10317), (2843, 4, 163), (2843, 5, 274), (2843, 10, 10318), (2843, 12, 10319), (2843, 13, 10320), (2843, 14, 10321), (2843, 25, 10319), (2843, 26, 10322), (2843, 27, 10323), (2843, 62, 6593), (2843, 87, 3751), (2843, 110, 10324), (2845, 110, 10326), (2846, 1, 10327), (2846, 4, 5586), (2846, 10, 10328), (2846, 12, 10329), (2846, 13, 10330), (2846, 14, 10331), (2846, 25, 10333), (2846, 27, 10334), (2846, 62, 10335), (2846, 110, 10336), (2847, 110, 10338), (2846, 22, 10339), (2848, 1, 8805), (2848, 4, 8806), (2848, 10, 8818), (2848, 12, 5247), (2848, 13, 8819), (2848, 14, 8820), (2848, 25, 5247), (2848, 26, 8821), (2848, 27, 10340), (2848, 62, 1264), (2848, 110, 8823), (2849, 1, 10341), (2849, 27, 10340), (2849, 110, 1266), (2850, 110, 10342), (2850, 6, 10343), (2850, 14, 10344), (2851, 110, 10345), (2844, 1, 7181), (2844, 14, 10325), (2844, 27, 10346), (2844, 107, 10347), (2844, 110, 10348), (2844, 116, 10347), (2853, 1, 7181), (2853, 27, 10350), (2853, 110, 10348), (2854, 1, 10351), (2854, 4, 5904), (2854, 5, 135), (2854, 10, 10352), (2854, 12, 8494), (2854, 13, 10353), (2854, 14, 4086), (2854, 25, 8497), (2854, 26, 10354), (2854, 27, 10355), (2854, 62, 8500), (2854, 90, 10356), (2854, 110, 10357), (2855, 1, 10358), (2855, 27, 10355), (2855, 110, 1983), (2856, 1, 10359), (2856, 4, 1076), (2856, 5, 135), (2856, 10, 10360), (2856, 12, 8494), (2856, 13, 10353), (2856, 14, 506), (2856, 25, 8497), (2856, 26, 10361), (2856, 27, 10362), (2856, 62, 8500), (2856, 110, 10363), (2857, 1, 10364), (2857, 27, 10362), (2857, 110, 1983), (2858, 1, 10365), (2858, 4, 10366), (2858, 5, 1954), (2858, 10, 10367), (2858, 12, 455), (2858, 14, 10368), (2858, 25, 456), (2858, 26, 10369), (2858, 27, 10370), (2858, 62, 1329), (2858, 90, 10371), (2858, 110, 10372), (2859, 110, 10373), (2860, 1, 10374), (2860, 2, 10375), (2860, 3, 10226), (2860, 4, 1358), (2860, 5, 135), (2860, 10, 10376), (2860, 12, 7308), (2860, 13, 7309), (2860, 14, 10377), (2860, 25, 7308), (2860, 26, 10378), (2860, 27, 10379), (2860, 62, 660), (2860, 110, 10380), (2861, 1, 10381), (2861, 27, 10379), (2861, 110, 662), (2862, 1, 10382), (2862, 4, 579), (2862, 5, 135), (2862, 10, 10383), (2862, 12, 10384), (2862, 13, 10385), (2862, 14, 8618), (2862, 22, 10386), (2862, 25, 10387), (2862, 27, 10388), (2862, 62, 10389), (2862, 90, 10390), (2862, 110, 10391), (2864, 110, 10393), (2807, 1, 10197), (2807, 12, 10198), (2807, 14, 10332), (2807, 22, 10337), (2807, 27, 10392), (2807, 62, 6), (2807, 90, 10394), (2807, 110, 8614), (2865, 1, 10395), (2865, 27, 10392), (2865, 110, 10396), (2866, 1, 10397), (2866, 27, 10398), (2866, 90, 10399), (2866, 110, 10400), (2867, 110, 10401), (2837, 22, 10402), (2823, 1, 10254), (2823, 12, 10265), (2823, 14, 10266), (2823, 22, 10403), (2823, 27, 10404), (2823, 62, 6), (2823, 90, 10405), (2823, 110, 10406), (2868, 1, 10407), (2868, 27, 10404), (2868, 110, 10408), (2869, 1, 10409), (2869, 4, 2461), (2869, 5, 135), (2869, 10, 10410), (2869, 12, 8494), (2869, 13, 10353), (2869, 14, 284), (2869, 25, 8497), (2869, 26, 10411), (2869, 27, 10412), (2869, 62, 8500), (2869, 110, 10413), (2870, 1, 10414), (2870, 27, 10412), (2870, 110, 1983), (2871, 1, 10415), (2871, 12, 10416), (2871, 14, 10417), (2871, 22, 10418), (2871, 27, 10419), (2871, 62, 6), (2871, 90, 10420), (2871, 110, 10421), (2871, 116, 10422), (2873, 1, 10423), (2873, 27, 10419), (2873, 110, 10424), (1302, 1, 296), (1302, 4, 5243), (1302, 8, 5244), (1302, 10, 5245), (1302, 14, 5246), (1302, 26, 10273), (1302, 27, 10274), (1302, 62, 8488), (1302, 84, 10275), (1302, 90, 10276), (1302, 110, 10277), (1302, 114, 10278), (2829, 1, 10279), (2829, 27, 10274), (2829, 110, 1983), (2830, 1, 10280), (2830, 10, 4769), (2830, 12, 93), (2830, 14, 10425), (2830, 25, 94), (2830, 26, 10426), (2830, 27, 10427), (2830, 62, 1329), (2830, 90, 10428), (2830, 110, 10429), (2874, 1, 10280), (2874, 4, 1422), (2874, 5, 299), (2874, 10, 4769), (2874, 12, 93), (2874, 14, 10425), (2874, 25, 94), (2874, 26, 10426), (2874, 27, 10431), (2874, 62, 1329), (2874, 90, 10428), (2874, 110, 10429), (2876, 110, 10433), (2877, 1, 8204), (2877, 12, 8239), (2877, 14, 8247), (2877, 22, 10434), (2877, 27, 10435), (2877, 62, 6), (2877, 90, 8259), (2877, 110, 8263), (2879, 1, 8264), (2879, 27, 10435), (2879, 110, 10436), (2824, 1, 10257), (2824, 10, 3667), (2824, 12, 93), (2824, 14, 9489), (2824, 25, 94), (2824, 26, 10349), (2824, 27, 10430), (2824, 62, 1329), (2824, 90, 10432), (2824, 110, 10437), (2831, 110, 10439), (2852, 1, 10440), (2852, 4, 9707), (2852, 5, 310), (2852, 10, 10441), (2852, 12, 93), (2852, 14, 10442), (2852, 25, 94), (2852, 26, 10443), (2852, 27, 10444), (2852, 62, 1329), (2852, 90, 10445), (2852, 110, 10446), (2852, 116, 10447), (2880, 110, 10449), (2883, 1, 10450), (2883, 4, 1077), (2883, 5, 90), (2883, 10, 10451), (2883, 12, 93), (2883, 14, 10452), (2883, 25, 94), (2883, 26, 10453), (2883, 27, 10458), (2883, 62, 1329), (2883, 90, 10455), (2883, 110, 10456), (2884, 1, 10459), (2884, 27, 10458), (2884, 110, 1983), (2887, 1, 10460), (2887, 10, 10461), (2887, 12, 93), (2887, 14, 10462), (2887, 25, 94), (2887, 26, 10463), (2887, 27, 10468), (2887, 62, 1329), (2887, 90, 10465), (2887, 110, 10466), (2888, 1, 10467), (2888, 27, 10468), (2888, 110, 1983), (2889, 1, 10469), (2889, 4, 10470), (2889, 5, 310), (2889, 10, 10471), (2889, 12, 10472), (2889, 13, 10473), (2889, 14, 10474), (2889, 25, 10475), (2889, 26, 10476), (2889, 27, 10477), (2889, 62, 6593), (2889, 87, 3751), (2889, 90, 10478), (2889, 110, 10479), (2891, 110, 10481), (2892, 1, 10482), (2892, 4, 9065), (2892, 5, 90), (2892, 10, 10483), (2892, 12, 93), (2892, 14, 10484), (2892, 25, 94), (2892, 26, 10485), (2892, 27, 10486), (2892, 62, 1329), (2892, 90, 10487), (2892, 110, 10488), (2893, 1, 10489), (2893, 27, 10486), (2893, 110, 1983), (2894, 1, 10490), (2894, 4, 8370), (2894, 5, 310), (2894, 10, 10491), (2894, 12, 93), (2894, 14, 10492), (2894, 25, 94), (2894, 26, 10493), (2894, 27, 10494), (2894, 62, 1329), (2894, 90, 10495), (2894, 110, 10496), (2894, 116, 10497), (2895, 1, 10498), (2895, 27, 10494), (2895, 110, 1983), (2896, 1, 10499), (2896, 4, 3513), (2896, 5, 1090), (2896, 10, 10500), (2896, 12, 286), (2896, 13, 289), (2896, 14, 10501), (2896, 25, 1779), (2896, 26, 10502), (2896, 27, 10503), (2896, 62, 292), (2896, 87, 3751), (2896, 90, 10504), (2896, 110, 10505), (2898, 110, 10507), (2899, 1, 10508), (2899, 12, 10509), (2899, 14, 10510), (2899, 22, 10511), (2899, 27, 10512), (2899, 62, 6), (2899, 90, 10513), (2899, 110, 10514), (2901, 1, 10515), (2901, 27, 10512), (2901, 110, 10516), (2902, 1, 10517), (2902, 4, 2607), (2902, 5, 274), (2902, 10, 10518), (2902, 12, 93), (2902, 14, 10519), (2902, 25, 94), (2902, 26, 10520), (2902, 27, 10521), (2902, 62, 1329), (2902, 90, 10522), (2902, 110, 10523), (2902, 116, 10524), (2903, 1, 10525), (2903, 27, 10521), (2903, 110, 1983), (2904, 1, 10526), (2904, 12, 93), (2904, 14, 10527), (2904, 25, 94), (2904, 26, 10528), (2904, 27, 10529), (2904, 62, 1329), (2904, 90, 10530), (2904, 110, 10531), (2906, 1, 10526), (2906, 4, 5478), (2906, 5, 90), (2906, 10, 6292), (2906, 12, 93), (2906, 14, 10527), (2906, 25, 94), (2906, 26, 10528), (2906, 27, 10533), (2906, 62, 1329), (2906, 90, 10530), (2906, 110, 10531), (2907, 1, 10534), (2907, 27, 10533), (2907, 110, 1983), (2908, 1, 10535), (2908, 27, 10536), (2908, 90, 10537), (2908, 110, 10538), (2908, 14, 1690), (2908, 8, 4089), (2908, 7, 10539), (2909, 1, 10540), (2909, 4, 374), (2909, 5, 90), (2909, 10, 10541), (2909, 12, 286), (2909, 13, 289), (2909, 14, 10542), (2909, 25, 1779), (2909, 26, 10543), (2909, 27, 10544), (2909, 62, 292), (2909, 87, 3751), (2909, 90, 10545), (2909, 110, 10546), (2909, 116, 10547), (2911, 110, 10549), (2825, 1, 10438), (2825, 4, 1339), (2825, 5, 135), (2825, 10, 10448), (2825, 12, 93), (2825, 14, 10457), (2825, 25, 94), (2825, 26, 10480), (2825, 27, 10506), (2825, 62, 1329), (2825, 90, 10532), (2825, 110, 10548), (2875, 1, 10550), (2875, 27, 10506), (2875, 110, 1983), (2882, 1, 10551), (2882, 4, 1339), (2882, 5, 135), (2882, 10, 10552), (2882, 12, 93), (2882, 14, 10457), (2882, 25, 94), (2882, 26, 10553), (2882, 27, 10554), (2882, 62, 1329), (2882, 90, 10555), (2882, 110, 10556), (2886, 1, 10557), (2886, 27, 10554), (2886, 110, 1983), (2905, 1, 10558), (2905, 4, 6926), (2905, 5, 135), (2905, 10, 10559), (2905, 12, 93), (2905, 14, 10560), (2905, 25, 94), (2905, 26, 10561), (2905, 27, 10566), (2905, 62, 1329), (2905, 90, 10563), (2905, 110, 10564), (2910, 1, 10567), (2910, 27, 10566), (2910, 110, 1983), (2912, 1, 10568), (2912, 4, 4004), (2912, 5, 135), (2912, 10, 10569), (2912, 12, 93), (2912, 14, 10570), (2912, 25, 94), (2912, 26, 10571), (2912, 27, 10572), (2912, 62, 1329), (2912, 90, 10573), (2912, 110, 10574), (2912, 116, 1447), (2913, 1, 10575), (2913, 27, 10572), (2913, 110, 1983), (2916, 1, 10576), (2916, 4, 452), (2916, 5, 274), (2916, 10, 10577), (2916, 12, 93), (2916, 14, 10578), (2916, 25, 94), (2916, 26, 10579), (2916, 27, 10585), (2916, 62, 1329), (2916, 90, 10581), (2916, 110, 10582), (2916, 116, 10583), (2917, 1, 10586), (2917, 27, 10585), (2917, 110, 1983), (2918, 1, 10587), (2918, 4, 10588), (2918, 5, 156), (2918, 10, 10589), (2918, 12, 1074), (2918, 13, 8484), (2918, 14, 10590), (2918, 26, 10591), (2918, 27, 10592), (2918, 62, 8488), (2918, 90, 10593), (2918, 110, 10594), (2919, 1, 10595), (2919, 27, 10592), (2919, 110, 1983), (2920, 1, 10596), (2920, 4, 3439), (2920, 5, 1077), (2920, 10, 10597), (2920, 12, 1074), (2920, 13, 8484), (2920, 14, 10598), (2920, 26, 10599), (2920, 27, 10600), (2920, 62, 8488), (2920, 90, 10601), (2920, 110, 10602), (2921, 1, 10603), (2921, 27, 10600), (2921, 110, 1983), (2922, 1, 10604), (2922, 4, 3439), (2922, 5, 135), (2922, 10, 10605), (2922, 12, 1074), (2922, 13, 8484), (2922, 14, 10606), (2922, 26, 10607), (2922, 27, 10608), (2922, 62, 8488), (2922, 90, 10609), (2922, 110, 10610), (2923, 1, 10611), (2923, 27, 10608), (2923, 110, 1983), (2924, 1, 10612), (2924, 4, 3103), (2924, 5, 135), (2924, 10, 10613), (2924, 12, 286), (2924, 13, 289), (2924, 14, 10614), (2924, 25, 1779), (2924, 26, 10615), (2924, 27, 10616), (2924, 62, 292), (2924, 87, 3751), (2924, 90, 10617), (2924, 110, 10618), (2926, 110, 10620), (2927, 1, 10621), (2927, 4, 374), (2927, 5, 1090), (2927, 10, 10622), (2927, 12, 10623), (2927, 13, 10624), (2927, 14, 10625), (2927, 27, 10626), (2927, 62, 10627), (2927, 87, 10628), (2927, 110, 10629), (2928, 110, 10630), (2930, 1, 10636), (2930, 27, 10637), (2930, 90, 10638), (2930, 107, 10639), (2930, 110, 10640), (2931, 1, 10641), (2931, 4, 1954), (2931, 5, 310), (2931, 10, 10642), (2931, 12, 10643), (2931, 13, 10644), (2931, 14, 10645), (2931, 25, 10643), (2931, 26, 10646), (2931, 27, 10647), (2931, 62, 1264), (2931, 110, 10648), (2932, 1, 10649), (2932, 27, 10647), (2932, 110, 1266), (2933, 1, 10650), (2933, 4, 89), (2933, 5, 310), (2933, 10, 10651), (2933, 12, 10652), (2933, 13, 10653), (2933, 14, 3189), (2933, 25, 10652), (2933, 26, 10654), (2933, 27, 10655), (2933, 62, 1264), (2933, 90, 10656), (2933, 110, 10657), (2934, 1, 10658), (2934, 4, 374), (2934, 5, 1090), (2934, 10, 6537), (2934, 12, 6585), (2934, 13, 6590), (2934, 14, 10659), (2934, 25, 8895), (2934, 26, 10660), (2934, 27, 10661), (2934, 62, 6593), (2934, 87, 3751), (2934, 90, 10662), (2934, 110, 10663), (2935, 1, 10664), (2935, 27, 10661), (2935, 110, 1983), (2936, 1, 10665), (2936, 4, 5126), (2936, 5, 1077), (2936, 10, 10666), (2936, 12, 10643), (2936, 13, 10644), (2936, 14, 10667), (2936, 25, 10643), (2936, 26, 10668), (2936, 27, 10669), (2936, 62, 1264), (2936, 90, 10670), (2936, 110, 10671), (2937, 1, 10672), (2937, 27, 10669), (2937, 110, 1266), (2938, 1, 10673), (2938, 4, 2548), (2938, 5, 1954), (2938, 10, 10674), (2938, 12, 10643), (2938, 13, 10644), (2938, 14, 10675), (2938, 25, 10643), (2938, 26, 10676), (2938, 27, 10677), (2938, 62, 1264), (2938, 90, 10678), (2938, 110, 10679), (2939, 1, 10680), (2939, 27, 10677), (2939, 110, 1266), (2940, 6, 10681), (2940, 7, 10682), (2940, 8, 10683), (2940, 11, 10684), (2940, 14, 10685), (2940, 62, 10686), (2940, 87, 6984), (2940, 90, 10687), (2940, 110, 10688), (2940, 118, 10689), (2942, 110, 10692), (2943, 7, 5369), (2943, 8, 10693), (2943, 11, 10694), (2943, 14, 10695), (2943, 62, 10686), (2943, 87, 6984), (2943, 90, 10696), (2943, 110, 10697), (2943, 118, 7467), (2945, 110, 10700), (2946, 6, 10701), (2946, 7, 5369), (2946, 8, 10693), (2946, 11, 10702), (2946, 14, 10695), (2946, 62, 10686), (2946, 87, 6984), (2946, 90, 10696), (2946, 110, 10703), (2946, 118, 10704), (2948, 110, 10707), (2949, 11, 10709), (2949, 14, 10710), (2949, 62, 4097), (2949, 90, 10711), (2949, 110, 10712), (2949, 118, 10713), (2951, 1, 10716), (2951, 2, 10717), (2951, 4, 6052), (2951, 5, 1204), (2951, 10, 10718), (2951, 12, 1236), (2951, 13, 9709), (2951, 14, 10719), (2951, 25, 1236), (2951, 26, 10720), (2951, 27, 10721), (2951, 62, 660), (2951, 110, 10722), (2952, 1, 10723), (2952, 27, 10721), (2952, 110, 662), (2806, 7, 4090), (1342, 7, 10724), (2949, 8, 7539), (2949, 7, 4090), (2953, 1, 10725), (2953, 2, 10726), (2953, 3, 10727), (2953, 8, 6777), (2953, 10, 10728), (2953, 11, 10729), (2953, 14, 4075), (2953, 27, 10730), (2953, 30, 10731), (2953, 62, 6593), (2953, 87, 3751), (2953, 90, 10732), (2953, 110, 7304), (2953, 115, 10727), (2955, 110, 10734), (2956, 1, 10735), (2956, 4, 3342), (2956, 5, 6587), (2956, 10, 10736), (2956, 12, 10737), (2956, 13, 10738), (2956, 14, 10739), (2956, 25, 10737), (2956, 26, 10740), (2956, 27, 10741), (2956, 62, 6593), (2956, 87, 3751), (2956, 90, 10742), (2956, 110, 10743), (2958, 110, 10745), (2959, 1, 10746), (2959, 4, 5904), (2959, 5, 1090), (2959, 10, 10747), (2959, 12, 10748), (2959, 13, 10749), (2959, 14, 10750), (2959, 25, 10751), (2959, 26, 10752), (2959, 27, 10753), (2959, 62, 6593), (2959, 87, 3751), (2959, 90, 10754), (2959, 110, 10755), (2961, 110, 10757), (2962, 1, 10758), (2962, 4, 274), (2962, 5, 1954), (2962, 10, 10759), (2962, 12, 10760), (2962, 13, 10761), (2962, 14, 10762), (2962, 25, 10763), (2962, 26, 10764), (2962, 27, 10765), (2962, 62, 6593), (2962, 87, 3751), (2962, 110, 10766), (2964, 110, 10768), (2965, 1, 10769), (2965, 4, 90), (2965, 5, 1090), (2965, 10, 10770), (2965, 12, 1074), (2965, 13, 8484), (2965, 14, 10771), (2965, 26, 10772), (2965, 27, 10773), (2965, 62, 8488), (2965, 90, 10774), (2965, 110, 10775), (2966, 1, 10776), (2966, 27, 10773), (2966, 110, 1983), (2969, 1, 10777), (2969, 4, 3439), (2969, 5, 274), (2969, 10, 10778), (2969, 12, 507), (2969, 14, 10779), (2969, 25, 508), (2969, 26, 10780), (2969, 27, 10785), (2969, 62, 1329), (2969, 90, 10782), (2969, 110, 10783), (2970, 1, 10784), (2970, 27, 10785), (2970, 110, 1983), (2971, 2, 10787), (2971, 3, 10788), (2971, 11, 10791), (2971, 14, 495), (2971, 27, 10792), (2971, 62, 6593), (2971, 87, 3751), (2971, 110, 10797), (2971, 1, 10798), (2971, 8, 4093), (2971, 7, 4090), (2973, 110, 10799), (2925, 1, 5969), (2925, 4, 5904), (2925, 5, 274), (2925, 10, 10191), (2925, 12, 1771), (2925, 13, 1770), (2925, 14, 1147), (2925, 25, 2337), (2925, 26, 5968), (2925, 27, 10634), (2925, 62, 292), (2925, 87, 3751), (2925, 90, 10708), (2925, 110, 5970), (2957, 1, 10744), (2957, 4, 299), (2957, 5, 310), (2957, 10, 10756), (2957, 12, 1074), (2957, 13, 8484), (2957, 14, 10767), (2957, 26, 10796), (2957, 27, 10800), (2957, 62, 8488), (2957, 90, 10801), (2957, 110, 10802), (2960, 1, 10803), (2960, 27, 10800), (2960, 110, 1983), (2963, 8, 7471), (2963, 11, 10804), (2963, 14, 10805), (2963, 62, 4097), (2963, 87, 3751), (2963, 110, 10806), (2963, 118, 10807), (2968, 1, 10808), (2968, 27, 10809), (2968, 110, 4099), (2972, 1, 10810), (2972, 4, 10811), (2972, 5, 274), (2972, 10, 10812), (2972, 12, 1372), (2972, 13, 6497), (2972, 14, 10813), (2972, 25, 6493), (2972, 26, 10814), (2972, 27, 10815), (2972, 62, 7476), (2972, 87, 3751), (2972, 90, 10816), (2972, 110, 10817), (2974, 1, 10818), (2974, 27, 10815), (2974, 110, 1983), (2975, 1, 10819), (2975, 4, 9065), (2975, 5, 156), (2975, 10, 10820), (2975, 12, 93), (2975, 14, 10821), (2975, 25, 94), (2975, 26, 10822), (2975, 27, 10823), (2975, 62, 1329), (2975, 90, 10824), (2975, 110, 10825), (2976, 1, 10826), (2976, 27, 10823), (2976, 110, 1983), (2977, 110, 10827), (2978, 1, 10828), (2978, 4, 10829), (2978, 5, 1454), (2978, 10, 10830), (2978, 12, 10831), (2978, 13, 10832), (2978, 14, 10833), (2978, 25, 10834), (2978, 26, 10835), (2978, 27, 10836), (2978, 62, 292), (2978, 87, 3751), (2978, 90, 10837), (2978, 110, 10838), (2980, 110, 10840), (2981, 1, 10841), (2981, 4, 7500), (2981, 5, 1090), (2981, 10, 1204), (2981, 12, 1408), (2981, 13, 1407), (2981, 14, 10842), (2981, 25, 1409), (2981, 26, 10843), (2981, 27, 10844), (2981, 62, 292), (2981, 87, 3751), (2981, 90, 10845), (2981, 110, 10846), (2982, 1, 10847), (2982, 27, 10844), (2982, 110, 1983), (2983, 1, 10848), (2983, 4, 10849), (2983, 5, 1954), (2983, 10, 10850), (2983, 12, 1372), (2983, 13, 6497), (2983, 14, 10851), (2983, 25, 6493), (2983, 26, 10852), (2983, 27, 10853), (2983, 62, 7476), (2983, 87, 3751), (2983, 90, 10854), (2983, 110, 10855), (2984, 1, 10856), (2984, 27, 10853), (2984, 110, 1983), (2985, 1, 10857), (2985, 12, 10858), (2985, 14, 3794), (2985, 22, 10859), (2985, 27, 10860), (2985, 62, 6), (2985, 90, 10861), (2985, 110, 10862), (2987, 1, 10863), (2987, 27, 10860), (2987, 110, 10864), (2988, 1, 10865), (2988, 4, 2100), (2988, 5, 90), (2988, 10, 10866), (2988, 12, 93), (2988, 14, 10867), (2988, 25, 94), (2988, 26, 10868), (2988, 27, 10869), (2988, 62, 1329), (2988, 90, 10870), (2988, 110, 10871), (2990, 1, 10865), (2990, 4, 2100), (2990, 5, 90), (2990, 10, 10866), (2990, 12, 93), (2990, 14, 10867), (2990, 25, 94), (2990, 26, 10868), (2990, 27, 10873), (2990, 62, 1329), (2990, 90, 10870), (2990, 110, 10871), (2992, 1, 10865), (2992, 4, 2100), (2992, 5, 90), (2992, 10, 10866), (2992, 12, 93), (2992, 14, 10867), (2992, 25, 94), (2992, 26, 10868), (2992, 27, 10875), (2992, 62, 1329), (2992, 90, 10870), (2992, 110, 10871), (2993, 1, 10874), (2993, 27, 10875), (2993, 110, 1983), (2994, 1, 10876), (2994, 4, 10877), (2994, 5, 10878), (2994, 10, 10879), (2994, 12, 10831), (2994, 13, 10832), (2994, 14, 10880), (2994, 25, 10834), (2994, 26, 10881), (2994, 27, 10882), (2994, 62, 292), (2994, 87, 3751), (2994, 90, 10883), (2994, 110, 10884), (2996, 110, 10886), (2997, 110, 10887), (2997, 12, 10888), (2997, 4, 8504), (2997, 5, 8504), (2997, 10, 10889), (2997, 14, 10891), (2998, 110, 10892), (2999, 110, 10893), (2999, 12, 10888), (2999, 4, 1270), (2999, 5, 5904), (2999, 10, 10894), (2999, 14, 10896), (3000, 110, 10897), (3001, 1, 10898), (3001, 12, 10899), (3001, 14, 10900), (3001, 22, 10901), (3001, 27, 10902), (3001, 62, 6), (3001, 90, 10903), (3001, 110, 10904), (3003, 1, 10905), (3003, 27, 10902), (3003, 110, 10906), (3004, 1, 10907), (3004, 12, 10908), (3004, 13, 10909), (3004, 14, 10910), (3004, 26, 10911), (3004, 27, 10912), (3004, 62, 1416), (3004, 110, 10913), (3005, 110, 10914), (3006, 1, 10915), (3006, 2, 10916), (3006, 14, 10917), (3006, 22, 10918), (3006, 27, 10919), (3006, 62, 10920), (3006, 85, 10921), (3006, 87, 3751), (3006, 90, 10922), (3006, 110, 10923), (3007, 1, 10924), (3007, 3, 10925), (3007, 4, 10926), (3007, 10, 10927), (3007, 12, 10928), (3007, 13, 10929), (3007, 14, 10930), (3007, 25, 10928), (3007, 26, 10931), (3007, 27, 10932), (3007, 62, 1264), (3007, 90, 10933), (3007, 110, 10934), (3008, 1, 10935), (3008, 27, 10932), (3008, 110, 1266), (3009, 1, 10936), (3009, 12, 10937), (3009, 14, 10938), (3009, 22, 10939), (3009, 27, 10940), (3009, 62, 6), (3009, 90, 10941), (3009, 110, 10942), (3011, 1, 10943), (3011, 27, 10940), (3011, 110, 10944), (3012, 1, 10945), (3012, 27, 10946), (3012, 110, 10947), (3013, 1, 10945), (3013, 27, 10948), (3013, 110, 10947), (3014, 1, 10949), (3014, 22, 10950), (3014, 110, 10951), (3015, 7, 4090), (3015, 8, 4089), (3015, 14, 1363), (3015, 22, 10952), (3015, 110, 10953), (3016, 1, 10954), (3016, 27, 10955), (3016, 90, 10956), (3016, 107, 10957), (3016, 110, 10958), (3016, 116, 10959), (3017, 1, 10960), (3017, 4, 10961), (3017, 5, 1090), (3017, 10, 10962), (3017, 12, 1257), (3017, 13, 1260), (3017, 14, 10963), (3017, 25, 1257), (3017, 26, 10964), (3017, 27, 10965), (3017, 62, 1264), (3017, 90, 10966), (3017, 110, 10967), (3018, 1, 10968), (3018, 27, 10965), (3018, 110, 1266), (3019, 1, 10969), (3019, 12, 10970), (3019, 14, 10971), (3019, 22, 10972), (3019, 27, 10973), (3019, 62, 6), (3019, 90, 10974), (3019, 110, 10975), (3021, 1, 10976), (3021, 27, 10973), (3021, 110, 10977), (3022, 1, 10978), (3022, 4, 2368), (3022, 5, 274), (3022, 10, 10979), (3022, 12, 1074), (3022, 13, 8484), (3022, 14, 10980), (3022, 26, 10981), (3022, 27, 10982), (3022, 62, 8488), (3022, 90, 10983), (3022, 110, 10984), (3023, 1, 10985), (3023, 27, 10982), (3023, 110, 1983), (3024, 1, 10986), (3024, 10, 7639), (3024, 12, 1074), (3024, 13, 8484), (3024, 14, 10987), (3024, 26, 10988), (3024, 27, 10989), (3024, 62, 8488), (3024, 90, 7643), (3024, 110, 7644), (3025, 1, 10990), (3025, 27, 10989), (3025, 110, 1983), (3026, 1, 10991), (3026, 4, 299), (3026, 5, 288), (3026, 10, 10992), (3026, 12, 1074), (3026, 13, 8484), (3026, 14, 10993), (3026, 26, 10994), (3026, 27, 10995), (3026, 62, 8488), (3026, 90, 10996), (3026, 110, 10997), (3027, 1, 10998), (3027, 27, 10995), (3027, 110, 1983), (3028, 1, 10999), (3028, 4, 1744), (3028, 5, 1454), (3028, 10, 11000), (3028, 12, 1451), (3028, 13, 11001), (3028, 14, 11002), (3028, 26, 11003), (3028, 27, 11004), (3028, 62, 1458), (3028, 90, 11005), (3028, 110, 11006), (3029, 1, 11007), (3029, 27, 11004), (3029, 110, 1983), (3030, 1, 11008), (3030, 12, 11009), (3030, 14, 805), (3030, 22, 11010), (3030, 27, 11011), (3030, 62, 6), (3030, 90, 11012), (3030, 110, 11013), (3031, 1, 11014), (3031, 27, 11011), (3031, 110, 11015), (3032, 1, 11016), (3032, 12, 11017), (3032, 14, 11018), (3032, 22, 11019), (3032, 27, 11020), (3032, 62, 6), (3032, 90, 11021), (3032, 110, 11022), (3034, 1, 11023), (3034, 27, 11020), (3034, 110, 11024), (3035, 1, 11025), (3035, 2, 11026), (3035, 4, 155), (3035, 5, 1090), (3035, 10, 11027), (3035, 12, 9947), (3035, 13, 9948), (3035, 14, 11028), (3035, 25, 9947), (3035, 26, 11029), (3035, 27, 11030), (3035, 62, 660), (3035, 110, 11031), (3036, 1, 11032), (3036, 27, 11030), (3036, 110, 662), (3037, 1, 11033), (3037, 12, 11034), (3037, 14, 11035), (3037, 22, 11036), (3037, 27, 11037), (3037, 62, 6), (3037, 90, 11038), (3037, 110, 11039), (3039, 1, 11040), (3039, 27, 11037), (3039, 110, 11041), (3040, 4, 3371), (3040, 12, 11042), (3040, 62, 5729), (3040, 90, 11043), (3040, 110, 11044), (3041, 1, 11045), (3041, 27, 11046), (3041, 110, 5730), (3042, 1, 11047), (3042, 4, 4609), (3042, 5, 11048), (3042, 10, 11049), (3042, 12, 11050), (3042, 13, 11051), (3042, 14, 11052), (3042, 26, 11053), (3042, 27, 11054), (3042, 62, 11055), (3042, 87, 3751), (3042, 90, 11056), (3042, 110, 11057), (3044, 110, 11059), (3045, 1, 11060), (3045, 4, 145), (3045, 5, 1077), (3045, 10, 8493), (3045, 12, 8494), (3045, 13, 8495), (3045, 14, 11061), (3045, 22, 11062), (3045, 25, 8497), (3045, 27, 11063), (3045, 62, 10389), (3045, 87, 11064), (3045, 90, 10390), (3045, 110, 8501), (3047, 1, 11060), (3047, 10, 8493), (3047, 12, 8494), (3047, 13, 8495), (3047, 14, 11061), (3047, 22, 11062), (3047, 25, 8497), (3047, 27, 11066), (3047, 62, 10389), (3047, 87, 11064), (3047, 90, 10390), (3047, 110, 8501), (3049, 110, 11068), (3050, 1, 11069), (3050, 12, 11070), (3050, 14, 11071), (3050, 22, 11072), (3050, 27, 11073), (3050, 62, 6), (3050, 90, 11074), (3050, 110, 11075), (3052, 1, 11076), (3052, 27, 11073), (3052, 110, 11077), (3053, 4, 2799), (3053, 5, 1954), (3053, 10, 11078), (3053, 12, 11079), (3053, 13, 11080), (3053, 14, 11081), (3053, 26, 11082), (3053, 62, 11083), (3053, 90, 11084), (3053, 110, 11085), (3054, 1, 11086), (3054, 27, 11087), (3054, 110, 11088), (3055, 110, 11089), (3056, 110, 11089), (3057, 110, 11089), (3058, 8, 5384), (3058, 14, 2390), (3058, 62, 6695), (3058, 110, 11090), (2881, 1, 7561), (2881, 12, 10454), (2881, 14, 7566), (2881, 22, 10464), (2881, 27, 10562), (2881, 62, 6), (2881, 90, 7581), (2881, 110, 7591), (2890, 1, 7596), (2890, 27, 10562), (2890, 110, 10565), (2914, 1, 7561), (2914, 12, 10454), (2914, 14, 7566), (2914, 22, 10464), (2914, 27, 10580), (2914, 62, 6), (2914, 90, 7581), (2914, 110, 7591), (2929, 1, 7596), (2929, 27, 10580), (2929, 110, 10565), (2941, 1, 10584), (2941, 2, 10619), (2941, 4, 532), (2941, 5, 1090), (2941, 10, 10631), (2941, 12, 9947), (2941, 13, 9948), (2941, 14, 10632), (2941, 25, 9947), (2941, 26, 10633), (2941, 27, 10635), (2941, 62, 660), (2941, 110, 10690), (2944, 1, 10691), (2944, 27, 10635), (2944, 110, 662), (2947, 1, 10698), (2947, 2, 10699), (2947, 4, 3439), (2947, 5, 1954), (2947, 10, 10705), (2947, 12, 10706), (2947, 13, 10714), (2947, 14, 10715), (2947, 25, 10706), (2947, 27, 10733), (2947, 62, 660), (2947, 90, 10781), (2947, 110, 10786), (2950, 1, 10789), (2950, 27, 10733), (2950, 110, 662), (3047, 4, 145), (3047, 5, 1077), (973, 4, 1358), (973, 5, 90), (973, 10, 1499), (2351, 4, 1270), (2351, 5, 89), (2351, 10, 8419), (1081, 4, 4350), (1081, 5, 135), (1717, 4, 1954), (1717, 5, 1954), (2560, 4, 9065), (2560, 5, 135), (2954, 110, 10790), (2713, 4, 6926), (2713, 5, 299), (2103, 4, 135), (2103, 5, 1090), (3024, 4, 288), (3024, 5, 288), (1673, 4, 2022), (1673, 5, 299), (1754, 4, 6884), (1754, 5, 135), (1754, 10, 6908), (2824, 4, 1422), (2824, 5, 299), (2476, 4, 90), (2476, 5, 1204), (1625, 4, 2799), (1625, 5, 89), (1625, 10, 2801), (1581, 4, 1270), (1581, 5, 156), (1581, 10, 5683), (1549, 4, 3774), (1549, 5, 299), (1914, 4, 6400), (1914, 5, 310), (2362, 4, 2245), (449, 4, 1358), (449, 5, 90), (449, 10, 1381), (1334, 4, 3774), (1334, 5, 310), (1408, 4, 1422), (1408, 5, 90), (1408, 10, 6292), (1559, 4, 6052), (1559, 5, 299), (937, 4, 382), (937, 5, 156), (937, 10, 3728), (2599, 4, 1422), (2599, 5, 274), (981, 4, 2799), (547, 4, 134), (547, 5, 299), (1185, 4, 2597), (1185, 5, 274), (2830, 4, 1422), (2830, 5, 299), (1538, 4, 2597), (1538, 5, 90), (1538, 10, 6099), (1615, 4, 1422), (1615, 5, 135), (1432, 4, 5586), (1432, 5, 3103), (1528, 4, 3135), (1528, 5, 156), (1419, 4, 1954), (1419, 5, 1077), (1646, 4, 6414), (1646, 5, 135), (1646, 10, 1390), (977, 4, 3774), (977, 5, 310), (1371, 4, 2858), (1371, 5, 135), (2707, 4, 3774), (2707, 5, 156), (2707, 10, 4453), (2609, 4, 1422), (2609, 5, 299), (2083, 4, 7722), (2083, 5, 7723), (2515, 4, 1294), (2515, 5, 274), (1662, 4, 287), (1662, 5, 288), (1662, 10, 5540), (1280, 4, 2022), (1280, 5, 310), (2532, 4, 3439), (2532, 5, 299), (2904, 4, 5478), (2904, 5, 90), (2904, 10, 6292), (949, 4, 3774), (949, 5, 135), (1389, 4, 1744), (1389, 5, 156), (1389, 10, 5393), (1934, 4, 89), (1934, 5, 5586), (1934, 10, 7652), (1948, 4, 3352), (1948, 5, 299), (824, 4, 3342), (824, 5, 156), (824, 10, 3343), (2739, 4, 1840), (2739, 5, 274), (2761, 11, 10044), (2761, 118, 10049), (1630, 4, 1270), (1630, 5, 156), (1630, 10, 6359), (2887, 4, 3774), (2887, 5, 299), (2705, 4, 3513), (2705, 5, 1204), (1979, 1, 6091), (1979, 14, 6090), (1979, 27, 7417), (1979, 62, 6), (1979, 90, 6093), (1979, 110, 6089), (1979, 12, 6092), (2182, 2, 7050), (2132, 4, 3513), (2132, 5, 1077)]
The 'itemData' table is funny. It's just a collection of integers, telling me
valueID stores the dataSo evidently, valueID points to another table itemDataValues which stores each of the actual pieces of data, and fieldID points to another table fields, which stores the type of data corresponding to that integer.
First, let's see what these fieldIDs actually mean:
In [7]:
print(cur.execute("select sql from sqlite_master where name = 'fields';").fetchall()[0][0])
print(cur.execute("select * from fields;").fetchall())
CREATE TABLE fields (
fieldID INTEGER PRIMARY KEY,
fieldName TEXT,
fieldFormatID INT,
FOREIGN KEY (fieldFormatID) REFERENCES fieldFormats(fieldFormatID)
)
[(1, 'url', None), (2, 'rights', None), (3, 'series', None), (4, 'volume', None), (5, 'issue', None), (6, 'edition', None), (7, 'place', None), (8, 'publisher', None), (10, 'pages', None), (11, 'ISBN', None), (12, 'publicationTitle', None), (13, 'ISSN', None), (14, 'date', None), (15, 'section', None), (18, 'callNumber', None), (19, 'archiveLocation', None), (21, 'distributor', None), (22, 'extra', None), (25, 'journalAbbreviation', None), (26, 'DOI', None), (27, 'accessDate', None), (28, 'seriesTitle', None), (29, 'seriesText', None), (30, 'seriesNumber', None), (31, 'institution', None), (32, 'reportType', None), (36, 'code', None), (40, 'session', None), (41, 'legislativeBody', None), (42, 'history', None), (43, 'reporter', None), (44, 'court', None), (45, 'numberOfVolumes', None), (46, 'committee', None), (48, 'assignee', None), (50, 'patentNumber', None), (51, 'priorityNumbers', None), (52, 'issueDate', None), (53, 'references', None), (54, 'legalStatus', None), (55, 'codeNumber', None), (59, 'artworkMedium', None), (60, 'number', None), (61, 'artworkSize', None), (62, 'libraryCatalog', None), (63, 'videoRecordingFormat', None), (64, 'interviewMedium', None), (65, 'letterType', None), (66, 'manuscriptType', None), (67, 'mapType', None), (68, 'scale', None), (69, 'thesisType', None), (70, 'websiteType', None), (71, 'audioRecordingFormat', None), (72, 'label', None), (74, 'presentationType', None), (75, 'meetingName', None), (76, 'studio', None), (77, 'runningTime', None), (78, 'network', None), (79, 'postType', None), (80, 'audioFileType', None), (81, 'version', None), (82, 'system', None), (83, 'company', None), (84, 'conferenceName', None), (85, 'encyclopediaTitle', None), (86, 'dictionaryTitle', None), (87, 'language', None), (88, 'programmingLanguage', None), (89, 'university', None), (90, 'abstractNote', None), (91, 'websiteTitle', None), (92, 'reportNumber', None), (93, 'billNumber', None), (94, 'codeVolume', None), (95, 'codePages', None), (96, 'dateDecided', None), (97, 'reporterVolume', None), (98, 'firstPage', None), (99, 'documentNumber', None), (100, 'dateEnacted', None), (101, 'publicLawNumber', None), (102, 'country', None), (103, 'applicationNumber', None), (104, 'forumTitle', None), (105, 'episodeNumber', None), (107, 'blogTitle', None), (108, 'type', None), (109, 'medium', None), (110, 'title', None), (111, 'caseName', None), (112, 'nameOfAct', None), (113, 'subject', None), (114, 'proceedingsTitle', None), (115, 'bookTitle', None), (116, 'shortTitle', None), (117, 'docketNumber', None), (118, 'numPages', None), (119, 'programTitle', None), (120, 'issuingAuthority', None), (121, 'filingDate', None), (122, 'genre', None), (123, 'archive', None)]
I'm interested in URLs, which have fieldID 1.
Now, I want to find which pieces of data are stored at those valueIDs:
In [8]:
print(cur.execute("select sql from sqlite_master where name = 'itemDataValues';").fetchall()[0][0])
print(cur.execute("select * from itemDataValues;").fetchall())
CREATE TABLE itemDataValues (
valueID INTEGER PRIMARY KEY,
value UNIQUE
)
[(1, 'What if Time Really Exists?'), (2, '2008-11-23 2008-11-23'), (3, 'http://arxiv.org/abs/0811.3772'), (4, '0811.3772'), (5, 'Despite the obvious utility of the concept, it has often been argued that time does not exist. I take the opposite perspective: let\'s imagine that time does exist, and the universe is described by a quantum state obeying ordinary time-dependent quantum mechanics. Reconciling this simple picture with the known facts about our universe turns out to be a non-trivial task, but by taking it seriously we can infer deep facts about the fundamental nature of reality. The arrow of time finds a plausible explanation in a "Heraclitean universe," described by a quantum state eternally evolving in an infinite-dimensional Hilbert space.'), (6, 'arXiv.org'), (7, '2009-02-04 21:33:03'), (8, '0811.3772 PDF'), (9, 'http://www.arxiv.org/pdf/0811.3772.pdf'), (10, '2009-02-04 21:33:04'), (11, 'Time and Causation'), (12, '2009-02-03 2009-02-03'), (13, 'http://arxiv.org/abs/0902.0559'), (14, '0902.0559'), (15, 'In this review paper, we consider the fundamental nature of time and causality, most particularly, in the context of the theories of special and general relativity. We also discuss the issue of closed timelike curves in the context of general relativity, and the associated paradoxes, the question of directionality of the time flow and, rather briefly, the problem of time in quantum gravity.'), (16, '2009-02-04 21:35:03'), (17, '0902.0559 PDF'), (18, 'http://www.arxiv.org/pdf/0902.0559.pdf'), (19, '2009-02-04 21:35:04'), (20, 'Simulating merging binary black holes with nearly extremal spins'), (21, '2010-10-13 2010-10-13'), (22, '2011-03-20 19:23:57'), (23, 'IMEX Evolution of Scalar Fields on Curved Backgrounds'), (24, '2009-05-14 May 14, 2009'), (25, '1063--1094'), (26, 'Commun. Comput. Phys.'), (27, 'Gravitational waves from black hole-neutron star binaries I: Classification of waveforms'), (28, '2009-02-02 2009-02-02'), (29, 'http://arxiv.org/abs/0902.0416'), (30, '0902.0416'), (31, "Using our new numerical-relativity code SACRA, long-term simulations for inspiral and merger of black hole (BH)-neutron star (NS) binaries are performed, focusing particularly on gravitational waveforms. As the initial conditions, BH-NS binaries in a quasiequilibrium state are prepared in a modified version of the moving-puncture approach. The BH is modeled by a nonspinning moving puncture and for the NS, a polytropic equation of state with $\\Gamma=2$ and the irrotational velocity field are employed. The mass ratio of the BH to the NS, $Q=M_{\\rm BH}/M_{\\rm NS}$, is chosen in the range between 1.5 and 5. The compactness of the NS, defined by ${\\cal C}=GM_{\\rm NS}/c^2R_{\\rm NS}$, is chosen to be between 0.145 and 0.178. For a large value of $Q$ for which the NS is not tidally disrupted and is simply swallowed by the BH, gravitational waves are characterized by inspiral, merger, and ringdown waveforms. In this case, the waveforms are qualitatively the same as that from BH-BH binaries. For a sufficiently small value of $Q \\alt 2$, the NS may be tidally disrupted before it is swallowed by the BH. In this case, the amplitude of the merger and ringdown waveforms is very low, and thus, gravitational waves are characterized by the inspiral waveform and subsequent quick damping. The difference in the merger and ringdown waveforms is clearly reflected in the spectrum shape and in the ``cut-off'' frequency above which the spectrum amplitude steeply decreases. When an NS is not tidally disrupted (e.g., for Q=5), kick velocity, induced by asymmetric gravitational wave emission, agrees approximately with that derived for the merger of BH-BH binaries, whereas for the case that the tidal disruption occurs, the kick velocity is significantly suppressed."), (32, '2009-02-04 21:35:17'), (33, 'Gravitational waves from black hole-neutron star binaries I'), (34, '0902.0416 PDF'), (35, 'http://www.arxiv.org/pdf/0902.0416.pdf'), (36, '2009-02-04 21:35:18'), (37, 'Searching for binary coalescences with inspiral templates: Detection and parameter estimation'), (38, 'http://arxiv.org/abs/0902.0307'), (39, '0902.0307'), (40, 'There has been remarkable progress in numerical relativity recently. This has led to the generation of gravitational waveform signals covering what has been traditionally termed the three phases of the coalescence of a compact binary - the inspiral, merger and ringdown. In this paper, we examine the usefulness of inspiral only templates for both detection and parameter estimation of the full coalescence waveforms generated by numerical relativity simulations. To this end, we deploy as search templates waveforms based on the effective one-body waveforms terminated at the light-ring as well as standard post-Newtonian waveforms. We find that both of these are good for detection of signals. Parameter estimation is good at low masses, but degrades as the mass of the binary system increases.'), (41, '2009-02-04 21:35:22'), (42, 'Searching for binary coalescences with inspiral templates'), (43, '0902.0307 PDF'), (44, 'http://www.arxiv.org/pdf/0902.0307.pdf'), (45, 'Brunch and South Beach Diet - Healthy Brunch Recipe and South Beach Diet'), (46, 'How pure is the tail of gravitational collapse ?'), (47, 'http://arxiv.org/abs/0902.0237'), (48, 'Class. Quantum Grav. 26 (2009) 028001'), (49, '0902.0237'), (50, 'Waves propagating in a curved spacetime develop tails. In particular, it is well established that the late-time dynamics of gravitational collapse is dominated by a power-law decaying tail of the form $Mt^{-(2l+3)}$, where $M$ is the black-hole mass. It should be emphasized, however, that in a typical evolution scenario there is a considerable time window in which the signal is no longer dominated by the black-hole quasinormal modes, but the leading order power-law tail has not yet taken over. Higher-order terms may have a considerable contribution to the signal at these intermediate times. It is therefore of interest to analyze these higher-order corrections to the leading-order power-law behavior. We show that the higher-order contamination terms die off at late times as $M^2t^{-4}\\ln(t/M)$ for spherical perturbations, and as $M^2t^{-(2l+4)}\\ln^2(t/M)$ for non-spherical $(l\\neq0)$ perturbations. These results imply that the leading-order power-law tail becomes "pure" (namely, with less than 1% contamination) only at extremely late times of the order of $10^4M$.'), (51, '2009-02-04 21:35:32'), (52, '0902.0237 PDF'), (53, 'http://www.arxiv.org/pdf/0902.0237.pdf'), (54, '2009-02-04 21:35:33'), (55, 'http://www.southbeachdiet.com/sbd/publicsite/healthy-brunch-recipe.aspx'), (56, 'An improved analytical description of inspiralling and coalescing black-hole binaries'), (57, 'http://arxiv.org/abs/0902.0136'), (58, '0902.0136'), (59, 'BrownSC-2008-17.pdf'), (60, 'http://www.global-sci.com/cgi-bin/fulltext/6/1063/full'), (61, '0902.0136 PDF'), (62, 'http://www.arxiv.org/pdf/0902.0136.pdf'), (63, 'The wave equation on axisymmetric stationary black hole backgrounds'), (64, '2009-01-26 2009-01-26'), (65, 'http://arxiv.org/abs/0901.4125'), (66, '0901.4125'), (67, 'Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein equations--a major open question in the subject. Nonetheless, it is only very recently that even the most basic boundedness and quantitative decay properties of linear waves have been proven in a suitably general class of black hole exterior spacetimes. This talk will review our current mathematical understanding of waves on black hole backgrounds, beginning with the classical boundedness theorem of Kay and Wald on exactly Schwarzschild exteriors and ending with very recent boundedness and decay theorems (proven in collaboration with Igor Rodnianski) on a wider class of spacetimes. This class of spacetimes includes in particular slowly rotating Kerr spacetimes, but in the case of the boundedness theorem is in fact much larger, encompassing general axisymmetric stationary spacetimes whose geometry is sufficiently close to Schwarzschild and whose Killing fields span the null generator of the horizon.'), (68, '2009-02-04 22:02:00'), (69, '0901.4125 PDF'), (70, 'http://www.arxiv.org/pdf/0901.4125.pdf'), (71, '2009-02-04 22:02:01'), (72, 'QND measurements for future gravitational-wave detectors'), (73, 'http://threepotato.blogspot.com/2007/11/homemade-teddy-grahams.html'), (74, '2009-02-04 22:03:08'), (75, 'Astro2010 Decadal Survey Whitepaper: Coordinated Science in the Gravitational and Electromagnetic Skies'), (76, '2009-02-10 2009-02-10'), (77, 'http://arxiv.org/abs/0902.1527'), (78, '0902.1527'), (79, 'It is widely expected that the coming decade will witness the first direct detection of gravitational waves (GWs). The ground-based LIGO and Virgo GW observatories are being upgraded to advanced sensitivity, and are expected to observe a significant binary merger rate. The launch of The Laser Interferometer Space Antenna (LISA) would extend the GW window to low frequencies, opening new vistas on dynamical processes involving massive (M >~ 10^5 M_Sun) black holes. GW events are likely to be accompanied by electromagnetic (EM) counterparts and, since information carried electromagnetically is complementary to that carried gravitationally, a great deal can be learned about an event and its environment if it becomes possible to measure both forms of radiation in concert. Measurements of this kind will mark the dawn of trans-spectral astrophysics, bridging two distinct spectral bands of information. The aim of this whitepaper is to articulate future directions in both theory and observation that are likely to impact broad astrophysical inquiries of general interest. What will EM observations reflect on the nature and diversity of GW sources? Can GW sources be exploited as complementary probes of cosmology? What cross-facility coordination will expand the science returns of gravitational and electromagnetic observations?'), (80, '2009-02-11 18:50:54'), (81, 'Astro2010 Decadal Survey Whitepaper'), (82, '0902.1527 PDF'), (83, 'http://www.arxiv.org/pdf/0902.1527.pdf'), (84, '2009-02-11 18:50:55'), (85, '0219-8916'), (86, 'Journal of Hyperbolic Differential Equations'), (87, 'Copyright (C) 2009 The American Physical Society; Please report any problems to prola@aps.org'), (88, 'Kinematical conditions in the construction of spacetime'), (89, 17), (90, 10), (91, 2529), (92, '1978-05-15 May 15, 1978'), (93, 'Physical Review D'), (94, 'Phys. Rev. D'), (95, 'http://link.aps.org/abstract/PRD/v17/p2529'), (96, '10.1103/PhysRevD.17.2529'), (97, 'We adopt the point of view that a solution of Einstein\'s equations is an evolution of given initial Cauchy data. Implementing the evolution equations necessarily requires a determination, not directly dictated by the field equations, of the kinematics of the observers in terms of which the evolution is represented. In this paper we study the observers\' kinematics (velocities and accelerations) in terms of the geometry of their congruences of world lines relative to families of time slicings of spacetime, which contrasts with the more usual approach of imposing particular "gauge" or "coordinate conditions." The types of conditions we suggest are adapted to the exact Einstein equations for general strong-field, dynamic spacetimes that have to be calculated numerically. Typically, the equations are three-dimensionally covariant, elliptic, and linear in the kinematical functions (the lapse function and shift vector) that they determine. The gravitational field enters in nonlinear form through the presence of curvature in the equations. We present a flat-space model of such elliptic equations (e.g. for maximal slicing) which suggests that this curvature leads to an exponential decrease in the proper time between time slices at late times. We show how the use of maximal slicing with minimal-distortion observers generalizes the notion of a stationary rest frame to dynamical asymptotically flat spacetimes. In cosmological spacetimes the use of minimum-distortion observers is shown to differentiate between those universes which contain only kinematic time dependence (e.g. open Kasner universe) and those in which dynamical degrees of freedom are present (e.g. mixmaster universe). We examine many examples and construct new coordinate systems in both asymptotically flat and cosmological solutions to illustrate these properties.'), (98, 'PROLA'), (99, '2009-02-15 20:03:24'), (100, 'PROLA Full Text PDF'), (101, 'http://prola.aps.org/pdf/PRD/v17/i10/p2529_1'), (102, '2009-02-15 20:03:25'), (103, 'Nonlinear gravitational-wave memory from binary black hole mergers'), (104, '2009-02-23 2009-02-23'), (105, 'http://arxiv.org/abs/0902.3660'), (106, '0902.3660'), (107, 'On Toroidal Horizons in Binary Black Hole Inspirals'), (108, '2011-10-07 2011-10-07'), (109, '0902.3660 PDF'), (110, 'http://www.arxiv.org/pdf/0902.3660.pdf'), (111, '2009-02-25 18:36:20'), (112, 'Momentum Flow in Black Hole Binaries: I. Post-Newtonian Analysis of the Inspiral and Spin-Induced Bobbing'), (113, '2009-02-24 2009-02-24'), (114, 'http://arxiv.org/abs/0902.4077'), (115, '0902.4077'), (116, 'A brief overview is presented of a new Caltech/Cornell research program that is exploring the nonlinear dynamics of curved spacetime in binary black hole collisions and mergers, and of an initial project in this program aimed at elucidating the flow of linear momentum in black-hole binaries (BBHs). The "gauge-dependence" (arbitrariness) in the localization of linear momentum in BBHs is discussed, along with the hope that the qualitative behavior of linear momentum will be gauge-independent. Harmonic coordinates are suggested as a possibly preferred foundation for fixing the gauge associated with linear momentum. For a BBH or other compact binary, the Landau-Lifshitz formalism is used to define the momenta of the binary\'s individual bodies in terms of integrals over the bodies\' surfaces or interiors, and define the momentum of the gravitational field (spacetime curvature) outside the bodies as a volume integral over the field\'s momentum density. These definitions will be used in subsequent papers that explore the internal nonlinear dynamics of BBHs via numerical relativity. This formalism is then used, in the 1.5PN approximation, to explore momentum flow between a binary\'s bodies and its gravitational field during the binary\'s orbital inspiral. Special attention is paid to momentum flow and conservation associated with synchronous spin-induced bobbing of the black holes, in the so-called "extreme-kick configuration" (where two identical black holes have their spins lying in their orbital plane and antialigned).'), (117, '2009-02-25 20:44:28'), (118, 'Momentum Flow in Black Hole Binaries'), (119, '0902.4077 PDF'), (120, 'http://www.arxiv.org/pdf/0902.4077.pdf'), (121, '2009-02-25 20:44:32'), (122, 'J. Hyper. Diff. Eqns.'), (123, 'http://arxiv.org/abs/1110.1668'), (124, '01'), (125, 161), (126, '10.1142/S0219891609001769'), (127, 'http://www.worldscinet.com/jhde/06/0601/S0219891609001769.html'), (128, 'http://arxiv.org/abs/1010.2777'), (129, '2011-03-20 19:30:50'), (130, '0801.pdf'), (131, 'High-accuracy waveforms for binary black hole inspiral, merger, and ringdown'), (132, 'http://arxiv.org/pdf/0801.1455v2'), (133, 'Physical Review D (Particles, Fields, Gravitation, and Cosmology)'), (134, 79), (135, 2), (136, '2011-03-20 19:32:03'), (137, 'A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations on Conformally Compactified Spacetimes'), (138, '10.1103/PhysRevD.79.024003'), (139, 'Scitation'), (140, 'Advances in Simulations of Generic Black-Hole Binaries'), (141, '2010-01-21 2010-01-21'), (142, 'http://arxiv.org/abs/1001.3834'), (143, 'High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants'), (144, '2008-11-15 November 15, 2008'), (145, 78), (146, '104020-23'), (147, 'http://link.aps.org/abstract/PRD/v78/e104020'), (148, '10.1103/PhysRevD.78.104020'), (149, '2009-02-27 19:39:02'), (150, 'High-accuracy numerical simulation of black-hole binaries'), (151, 'Class.Quant.Grav.27:084034,2010'), (152, 'doi:10.1088/0264-9381/27/8/084034'), (153, 'High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions'), (154, '2007-12-15 December 15, 2007'), (155, 76), (156, 12), (157, '124038-31'), (158, 'http://link.aps.org/abstract/PRD/v76/e124038'), (159, '10.1103/PhysRevD.76.124038'), (160, '2009-02-27 19:39:11'), (161, 'Testing the accuracy and stability of spectral methods in numerical relativity'), (162, '2007-01-15 January 15, 2007'), (163, 75), (164, '024006-13'), (165, 'http://link.aps.org/abstract/PRD/v75/e024006'), (166, '10.1103/PhysRevD.75.024006'), (167, '2009-02-27 19:39:17'), (168, '1001.3834'), (169, 'We review some of the recent dramatic developments in the fully nonlinear simulation of generic, highly-precessing, black-hole binaries, and introduce a new approach for generating hybrid post-Newtonian / Numerical waveforms for these challenging systems.'), (170, '2011-03-21 16:06:52'), (171, '1001.3834 PDF'), (172, 'Emergent/Quantum Gravity: Macro/Micro Structures of Spacetime'), (173, '2009-03-04 2009-03-04'), (174, 'http://arxiv.org/abs/0903.0878'), (175, '0903.0878'), (176, "Emergent gravity views spacetime as an entity emergent from a more complete theory of interacting fundamental constituents valid at much finer resolution or higher energies, usually assumed to be above the Planck energy. In this view general relativity is an effective theory valid only at long wavelengths and low energies. For any presumed known theory for the microscopic structure of spacetime, we describe common tasks of emergent gravity (`top-down'), namely, identifying the conditions and processes or mechanisms whereby the familiar macroscopic spacetime emerges with high probability and reasonable robustness. Going in the opposite direction (`bottom-up') is the task of quantum gravity, i.e., finding a theory for the microscopic structure of spacetime, which, in this new view, cannot come from quantizing the metric or connection forms because they are the collective variables which are meaningful only for the macroscopic theory, i.e., general relativity. We suggest pathways to move `up' (in energy) from the given macroscopic conditions of classical gravity and quantum field theory to the domain closer to the micro-macro interface where spacetime emerged and places to look for clues or tell-tale signs at low energy where one could infer indirectly some salient features of the micro-structure of spacetime."), (177, '2009-03-24 15:20:53'), (178, 'Emergent/Quantum Gravity'), (179, '0903.0878 PDF'), (180, 'http://www.arxiv.org/pdf/0903.0878.pdf'), (181, '2009-03-24 15:20:55'), (182, 'Model waveform accuracy standards for gravitational wave data analysis'), (183, '2008-12-15 December 15, 2008'), (184, '124020-12'), (185, 'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v78/e124020'), (186, '10.1103/PhysRevD.78.124020'), (187, '2009-04-27 20:21:26'), (188, 'http://www.arxiv.org/pdf/1001.3834.pdf'), (189, '2011-03-21 16:07:11'), (190, 'GetPDFServlet.pdf'), (191, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000012124020000001&idtype=cvips&prog=normal'), (192, '2009-04-27 20:21:39'), (193, 'Comparisons of eccentric binary black hole simulations with post-Newtonian models'), (194, '2008-06-05 2008-06-05'), (195, 'http://arxiv.org/abs/0806.1037'), (196, '0806.1037'), (197, 'We present the first comparison between numerical relativity (NR) simulations of an eccentric binary black hole system with corresponding post-Newtonian (PN) results. We evolve an equal-mass, non-spinning configuration with an initial eccentricity e = 0.1 for 21 gravitational wave cycles before merger, and find agreement in the gravitational wave phase with an adiabatic eccentric PN model with 2 PN radiation reaction within 0.1 radians for 8 cycles. The NR and PN phase difference grows to 0.8 radians by 5 cycles before merger. We find that these results can be obtained by expanding the eccentric PN expressions in terms of the frequency-related variable x = (omega M)^{2/3} with M the total mass of the binary. When using instead the mean motion n = 2 pi/P, where P is the orbital period, the comparison leads to significant disagreements with NR. We also introduce a new method for matching NR and PN waveforms, based on extrapolating parameters determined from least squares fitting as t -> -infinity.'), (198, '2009-05-07 20:28:23'), (199, '0806.1037 PDF'), (200, 'http://www.arxiv.org/pdf/0806.1037.pdf'), (201, '2009-05-07 20:28:25'), (202, 'Template banks to search for compact binaries with spinning components in gravitational wave data'), (203, '2009-04-10 2009-04-10'), (204, 'http://arxiv.org/abs/0904.1715'), (205, '0904.1715'), (206, "Gravitational waves from coalescing compact binaries are one of the most promising sources for detectors such as LIGO, Virgo and GEO600. If the components of the binary posess significant angular momentum (spin), as is likely to be the case if one component is a black hole, spin-induced precession of a binary's orbital plane causes modulation of the gravitational-wave amplitude and phase. If the templates used in a matched-filter search do not accurately model these effects then the sensitivity, and hence the detection rate, will be reduced. We investigate the ability of several search pipelines to detect gravitational waves from compact binaries with spin. We use the post-Newtonian approximation to model the inspiral phase of the signal and construct two new template banks using the phenomenological waveforms of Buonanno, Chen and Vallisneri. We compare the performance of these template banks to that of banks constructed using the stationary phase approximation to the non-spinning post-Newtonian inspiral waveform currently used by LIGO and Virgo in the search for compact binary coalescence. We find that, at the same false alarm rate, a search pipeline using phenomenological templates is no more effective than a pipeline which uses non-spinning templates. We recommend the continued use of the non-spinning stationary phase template bank until the false alarm rate associated with templates which include spin effects can be substantially reduced."), (207, '2009-05-08 20:50:57'), (208, '0904.1715 PDF'), (209, 'http://www.arxiv.org/pdf/0904.1715.pdf'), (210, '2009-05-08 20:50:59'), (211, 'The catalog of nearby black hole candidates'), (212, '2011-07-12 2011-07-12'), (213, 'http://arxiv.org/abs/1107.2244'), (214, 'Phys.Rev.D82:104057,2010'), (215, 'doi:10.1103/PhysRevD.82.104057'), (216, 'We describe in detail full numerical and perturbative techniques to compute the gravitational radiation from intermediate-mass-ratio black-hole-binary inspirals and mergers. We perform a series of full numerical simulations of nonspinning black holes with mass ratios q=1/10 and q=1/15 from different initial separations and for different finite-difference resolutions. In order to perform those full numerical runs, we adapt the gauge of the moving punctures approach with a variable damping term for the shift. We also derive an extrapolation (to infinite radius) formula for the waveform extracted at finite radius. For the perturbative evolutions we use the full numerical tracks, transformed into the Schwarzschild gauge, in the source terms of the Regge-Wheller-Zerilli Schwarzschild perturbations formalism. We then extend this perturbative formalism to take into account small intrinsic spins of the large black hole, and validate it by computing the quasinormal mode frequencies, where we find good agreement for spins |a/M|<0.3. Including the final spins improves the overlap functions when comparing full numerical and perturbative waveforms, reaching 99.5% for the leading (l,m)=(2,2) and (3,3) modes, and 98.3% for the nonleading (2,1) mode in the q=1/10 case, which includes 8 orbits before merger. For the q=1/15 case, we obtain overlaps near 99.7% for all three modes. We discuss the modeling of the full inspiral and merger based on a combined matching of post-Newtonian, full numerical, and geodesic trajectories.'), (217, '2011-03-21 16:14:26'), (218, '2011-03-21 16:14:38'), (219, 'Extreme-Mass-Ratio-Black-Hole-Binary Evolutions with Numerical Relativity'), (220, '2010-09-01 2010-09-01'), (221, 'http://arxiv.org/abs/1009.0292'), (222, 'Phys.Rev.Lett.106:041101,2011'), (223, 'doi:10.1103/PhysRevLett.106.041101'), (224, '1009.0292'), (225, 'We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100:1. Our technique for evolving such extreme mass ratios is based on the moving puncture approach with a new gauge condition and an optimal choice of the mesh refinement (plus large computational resources). We achieve a convergent set of results for simulations starting with a small nonspinning black hole just outside the ISCO that then performs over two orbits before plunging into the 100 times more massive black hole. We compute the gravitational energy and momenta radiated as well as the final remnant parameters and compare these quantities with the corresponding perturbative estimates. The results show a close agreement. We briefly discuss the relevance of this simulations for Advanced LIGO, third-generation ground based detectors, and LISA observations, and self-force computations.'), (226, '2011-03-21 16:21:20'), (227, '1009.0292 PDF'), (228, 'http://www.arxiv.org/pdf/1009.0292.pdf'), (229, '2011-03-21 16:21:24'), (230, 'Modeling Gravitational Recoil Using Numerical Relativity'), (231, '2010-11-09 2010-11-09'), (232, 'http://arxiv.org/abs/1011.2210'), (233, '1011.2210'), (234, 'We review the developments in modeling gravitational recoil from merging black-hole binaries and introduce a new set of 20 simulations to test our previously proposed empirical formula for the recoil. The configurations are chosen to represent generic binaries with unequal masses and precessing spins. Results of these simulations indicate that the recoil formula is accurate to within a few km/s in the similar mass-ratio regime for the out-of-plane recoil.'), (235, '2011-03-21 16:23:49'), (236, '1011.2210 PDF'), (237, 'http://www.arxiv.org/pdf/1011.2210.pdf'), (238, '2011-03-21 16:23:53'), (239, 'Statistical studies of Spinning Black-Hole Binaries'), (240, 'Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project'), (241, '2009-01-28 2009-01-28'), (242, 'http://arxiv.org/abs/0901.4399'), (243, '0901.4399'), (244, 'The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the Initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter-estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.'), (245, '2009-05-15 16:31:24'), (246, 'Testing gravitational-wave searches with numerical relativity waveforms'), (247, '0901.4399 PDF'), (248, 'http://www.arxiv.org/pdf/0901.4399.pdf'), (249, '2009-05-15 16:31:26'), (250, '2009-10-16 2009-10-16'), (251, 'http://arxiv.org/abs/0910.3197'), (252, 'http://link.aps.org/doi/10.1103/PhysRevD.79.024003'), (253, 'Phys.Rev.D81:084023,2010; Erratum-ibid.D82:129902,2010'), (254, 'doi:10.1103/PhysRevD.82.129902'), (255, '0910.3197'), (256, "We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions S1 and S2 and magnitudes S1=S2=0.97 for different mass ratios. Starting from a fiducial initial separation of ri=50m, we perform 3.5PN evolutions down to rf=5m. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, L. We perform 16^4 simulations for six mass ratios between q=1 and q=1/16 and compute the distribution of the angles between L and Delta and L and S, directly related to recoil velocities and total angular momentum. We find a small but statistically significant bias of the distribution towards counter-alignment of both scalar products. To study the merger of black-hole binaries, we turn to full numerical techniques. We introduce empirical formulae to describe the final remnant black hole mass, spin, and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins. We then evaluate those formulae for randomly chosen directions of the individual spins and magnitudes as well as the binary's mass ratio. We found that the magnitude of the recoil velocity distribution decays as P(v) \\exp(-v/2500km/s), <v>=630km/s, and sqrt{<v^2> - <v>^2}= 534km/s, leading to a 23% probability of recoils larger than 1000km/s, and a highly peaked angular distribution along the final orbital axis. The final black-hole spin magnitude show a universal distribution highly peaked at Sf/mf^2=0.73 and a 25 degrees misalignment with respect to the final orbital angular momentum."), (257, '2011-03-21 16:24:15'), (258, '0910.3197 PDF'), (259, 'http://www.arxiv.org/pdf/0910.3197.pdf'), (260, '2011-03-21 16:24:31'), (261, 'Phys.Rev.D80:124026,2009'), (262, 'doi:10.1103/PhysRevD.80.124026'), (263, 'Binary black-hole systems with spins aligned or anti-aligned to the orbital angular momentum provide the natural ground to start detailed studies of the influence of strong-field spin effects on gravitational wave observations of coalescing binaries. Furthermore, such systems may be the preferred end-state of the inspiral of generic supermassive binary black-hole systems. In view of this, we have computed the inspiral and merger of a large set of binary systems of equal-mass black holes with spins parallel to the orbital angular momentum but otherwise arbitrary. Our attention is particularly focused on the gravitational-wave emission so as to quantify how much spin effects contribute to the signal-to-noise ratio, to the horizon distances, and to the relative event rates for the representative ranges in masses and detectors. As expected, the signal-to-noise ratio increases with the projection of the total black hole spin in the direction of the orbital momentum. We find that equal-spin binaries with maximum spin aligned with the orbital angular momentum are more than "three times as loud" as the corresponding binaries with anti-aligned spins, thus corresponding to event rates up to 30 times larger. We also consider the waveform mismatch between the different spinning configurations and find that, within our numerical accuracy, binaries with opposite spins S_1=-S_2 cannot be distinguished whereas binaries with spin S_1=S_2 have clearly distinct gravitational-wave emissions. Finally, we derive a simple expression for the energy radiated in gravitational waves and find that the binaries always have efficiencies E_rad/M > 3.6%, which can become as large as E_rad/M = 10% for maximally spinning binaries with spins aligned with the orbital angular momentum.'), (264, '2011-03-21 16:31:47'), (265, 'Effective-one-body waveforms calibrated to numerical relativity simulations'), (266, '2011-03-21 16:32:09'), (267, '00358711'), (268, 399), (269, 'We present an analytical formalism, within the Effective-One-Body framework, which predicts gravitational-wave signals from inspiralling and coalescing black-hole binaries that agree, within numerical errors, with the results of the currently most accurate numerical relativity simulations for several different mass ratios. In the equal-mass case, the gravitational wave energy flux predicted by our formalism agrees, within numerical errors, with the most accurate numerical-relativity energy flux. We think that our formalism opens a realistic possibility of constructing a sufficiently accurate, large bank of gravitational wave templates, as needed both for detection and data analysis of (non spinning) coalescing binary black holes.'), (270, '2009-00-11 11/2009'), (271, '2249-2263'), (272, 'Accurate effective-one-body waveforms of inspiralling and coalescing black-hole binaries'), (273, '2008-00-00 2008'), (274, 4), (275, '044039-24'), (276, 'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v78/e044039'), (277, '10.1103/PhysRevD.78.044039'), (278, '2009-05-16 17:33:49'), (279, '10.1111/j.1365-2966.2009.15427.x'), (280, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2009.15427.x/abstract;jsessionid=BF1B9266CFD6F052747D05BB4714066C.d03t04'), (281, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000004044039000001&idtype=cvips&prog=normal'), (282, '2009-05-16 17:34:27'), (283, 'Comparison of high-accuracy numerical simulations of black-hole binaries with stationary-phase post-Newtonian template waveforms for initial and advanced LIGO'), (284, '2009-00-00 2009'), (285, 114006), (286, 'Classical and Quantum Gravity'), (287, 26), (288, 11), (289, '0264-9381'), (290, 'We study the effectiveness of stationary-phase approximated\npost-Newtonian waveforms currently used by ground-based\ngravitational-wave detectors to search for the coalescence of binary\nblack holes by comparing them to an accurate waveform obtained from\nnumerical simulation of an equal-mass non-spinning binary black hole\ninspiral, merger and ringdown. We perform this study for the initial-\nand advanced-LIGO detectors. We find that overlaps between the\ntemplates and signal can be improved by integrating the match filter\nto higher frequencies than used currently. We propose simple analytic\nfrequency cutoffs for both initial and advanced LIGO, which achieve\nnearly optimal matches, and can easily be extended to unequal-mass,\nspinning systems. We also find that templates that include terms in\nthe phase evolution up to 3.5 post-Newtonian (pN) order are nearly\nalways better, and rarely significantly worse, than 2.0 pN templates\ncurrently in use. For initial LIGO we recommend a strategy using\ntemplates that include a recently introduced pseudo-4.0 pN term in the\nlow-mass (M [?] 35 M[?]) region, and 3.5 pN templates allowing\nunphysical values of the symmetric reduced mass e above this. This\nstrategy always achieves overlaps within 0.3% of the optimum, for the\ndata used here. For advanced LIGO we recommend a strategy using 3.5 pN\ntemplates up to M = 12 M[?], 2.0 pN templates up to M = 21 M[?],\npseudo-4.0 pN templates up to 65 M[?], and 3.5 pN templates with\nunphysical e for higher masses. This strategy always achieves overlaps\nwithin 0.7% of the optimum for advanced LIGO.'), (291, 'http://www.iop.org/EJ/abstract/0264-9381/26/11/114006'), (292, 'Institute of Physics'), (293, '2009-05-19 15:46:20'), (294, 'IOP Full Text PDF'), (295, 'AT-errata.pdf'), (296, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/proceeding/aipcp/10.1063/1.4825543'), (297, 'Strategies for the characteristic extraction of gravitational waveforms'), (298, '2009-04-15 April 15, 2009'), (299, 8), (300, '084011-18'), (301, 'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v79/e084011'), (302, '10.1103/PhysRevD.79.084011'), (303, '2009-05-19 16:00:14'), (304, 'Mass and spin co-evolution during the alignment of a black hole in a warped accretion disc'), (305, '2011-03-21 16:33:05'), (306, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000079000008084011000001&idtype=cvips&prog=normal'), (307, '2009-05-19 16:00:28'), (308, 'Numerical relativity and asymptotic flatness'), (309, '065008'), (310, 6), (311, "It is highly plausible that the region of spacetime far from an\nisolated gravitating body is, in some sense, asymptotically\nMinkowskian. However theoretical studies of the full nonlinear theory,\ninitiated by Bondi et al (1962 Proc. R. Soc. A 269 21-51), Sachs (1962\nProc. R. Soc. A 270 103-26) and Newman and Unti (1962 J. Math. Phys. 3\n891-901), rely on careful, clever, a priori choices of a chart (and\ntetrad) and so are not readily accessible to the numerical relativist,\nwho chooses her/his chart on the basis of quite different grounds.\nThis paper seeks to close this gap. Starting from data available in a\ntypical numerical evolution, we construct a chart and tetrad which\nare, asymptotically, sufficiently close to the theoretical ones, so\nthat the key concepts of the Bondi news function, Bondi mass and its\nrate of decrease can be estimated. In particular, these estimates can\nbe expressed in the numerical relativist's chart as numerical\nrelativity recipes."), (312, 'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/26/6/065008/'), (313, '2009-05-19 16:07:21'), (314, 'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/26/6/065008/cqg9_6_065008.pdf'), (315, '2009-05-19 16:07:23'), (316, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000010104020000001&idtype=cvips&prog=normal'), (317, '2009-05-20 15:30:18'), (318, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000076000012124038000001&idtype=cvips&prog=normal'), (319, '2009-05-20 15:46:55'), (320, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000075000002024006000001&idtype=cvips&prog=normal'), (321, '2009-05-20 15:47:21'), (322, 'Quasinormal modes of black holes and black branes'), (323, 'arXiv:1110.1668'), (324, 'We examine the structure of the event horizon for numerical simulations of two black holes that begin in a quasicircular orbit, inspiral, and finally merge. We find that the spatial cross section of the merged event horizon has spherical topology (to the limit of our resolution), despite the expectation that generic binary black hole mergers in the absence of symmetries should result in an event horizon that briefly has a toroidal cross section. Using insight gained from our numerical simulations, we investigate how the choice of time slicing affects both the spatial cross section of the event horizon and the locus of points at which generators of the event horizon cross. To ensure the robustness of our conclusions, our results are checked at multiple numerical resolutions. 3D visualization data for these resolutions are available for public access online. We find that the structure of the horizon generators in our simulations is consistent with expectations, and the lack of toroidal horizons in our simulations is due to our choice of time slicing.'), (325, '2011-10-11 13:50:20'), (326, 'Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra requires solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.'), (327, '1110.1668 PDF'), (328, '0905.2975 PDF'), (329, 'http://www.arxiv.org/pdf/0905.2975.pdf'), (330, '2009-05-20 16:38:47'), (331, 'http://www.phy.olemiss.edu/~berti/QNMLeaverKerr.nb'), (332, '2009-05-20 16:40:17'), (333, 'Phys.Rev.D83:024010,2011'), (334, 'doi:10.1103/PhysRevD.83.024010'), (335, '1010.2777'), (336, 'Blending Up Smoothies - Well Blog - NYTimes.com'), (337, 'http://well.blogs.nytimes.com/2009/05/21/blending-up-smoothies/?em'), (338, '2009-05-23 00:01:26'), (339, 'Recipes for Health - Want More Fruit? Get Out the Blender. - NYTimes.com'), (340, 'http://www.nytimes.com/2009/05/18/health/nutrition/18recipehealth.html?ref=fitnessandnutrition&pagewanted=all'), (341, '2009-05-23 00:01:48'), (342, 'Recipes for Health - Strawberry Smoothie - NYTimes.com'), (343, 'http://www.nytimes.com/2009/05/19/health/nutrition/19recipehealth.html?ref=fitnessandnutrition&pagewanted=all'), (344, '2009-05-23 00:02:09'), (345, 'Recipes for Health - Pineapple Banana Mint Smoothie - NYTimes.com'), (346, 'http://www.nytimes.com/2009/05/21/health/nutrition/21recipehealth.html?ref=fitnessandnutrition&pagewanted=all'), (347, '2009-05-23 00:02:15'), (348, 'Recipes for Health - Mango Buttermilk Smoothie - NYTimes.com'), (349, 'http://www.nytimes.com/2009/05/20/health/nutrition/20recipehealth.html?ref=health&pagewanted=all'), (350, '2009-05-23 00:02:21'), (351, 'Recipes for Health - Watermelon or Cantaloupe Agua Fresca - NYTimes.com'), (352, 'http://www.nytimes.com/2009/05/22/health/nutrition/22recipehealth.html?ref=fitnessandnutrition&pagewanted=all'), (353, '2009-05-23 00:02:26'), (354, 'Samurai project: Verifying the consistency of black-hole-binary waveforms for gravitational-wave detection'), (355, '084025-17'), (356, 'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v79/e084025'), (357, '10.1103/PhysRevD.79.084025'), (358, '2009-05-27 16:47:37'), (359, 'Samurai project'), (360, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2009.15427.x/full'), (361, 'Numerical relativity simulations of binary neutron stars'), (362, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000079000008084025000001&idtype=cvips&prog=normal'), (363, '2009-05-27 16:47:56'), (364, 'Status of NINJA: the Numerical INJection Analysis project'), (365, 114008), (366, 'The 2008 NRDA conference introduced the Numerical INJection Analysis\nproject (NINJA), a new collaborative effort between the numerical\nrelativity community and the data analysis community. NINJA focuses on\nmodeling and searching for gravitational wave signatures from the\ncoalescence of binary system of compact objects. We review the scope\nof this collaboration and the components of the first NINJA project,\nwhere numerical relativity groups, shared waveforms and data analysis\nteams applied various techniques to detect them when embedded in\ncolored Gaussian noise.'), (367, 'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/26/11/114008/'), (368, '2009-05-27 16:49:27'), (369, 'Status of NINJA'), (370, 'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/26/11/114008/cqg9_11_114008.pdf'), (371, '2009-05-27 16:49:29'), (372, 'Reducing phase error in long numerical binary black hole evolutions with sixth-order finite differencing'), (373, 105006), (374, 25), (375, "We describe a modification of a fourth-order accurate\n'moving-puncture' evolution code, where by replacing spatial\nfourth-order accurate differencing operators in the bulk of the grid\nby a specific choice of sixth-order accurate stencils we gain\nsignificant improvements in accuracy. We illustrate the performance of\nthe modified algorithm with an equal-mass simulation covering nine\norbits."), (376, 'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/25/10/105006/'), (377, '2009-05-27 23:06:40'), (378, 'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/25/10/105006/cqg8_10_105006.pdf'), (379, '2009-05-27 23:06:43'), (380, 'Where post-Newtonian and numerical-relativity waveforms meet'), (381, '2008-02-15 February 15, 2008'), (382, 77), (383, '044020-15'), (384, '2009-10-01 2009-10-01'), (385, '10.1103/PhysRevD.77.044020'), (386, '2009-05-27 23:07:49'), (387, 'Mass and spin co-evolution during the alignment of a black hole in a warped accretion disc - Perego - 2009 - Monthly Notices of the Royal Astronomical Society - Wiley Online Library'), (388, '2011-03-21 16:55:44'), (389, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000077000004044020000001&idtype=cvips&prog=normal'), (390, '2009-05-27 23:08:14'), (391, 'http://link.aps.org/abstract/PRD/v77/e044020'), (392, 'Extrapolating gravitational-wave data from numerical simulations'), (393, 'Relativistic Suppression of Black Hole Recoils'), (394, '2010-03-25 2010-03-25'), (395, 'http://arxiv.org/abs/1003.4993'), (396, 'Astrophys.J. 715 (2010) 1006-1011'), (397, '1003.4993'), (398, 'Numerical-relativity simulations indicate that the black hole produced in a binary merger can recoil with a velocity up to v_max ~ 4,000 km/s with respect to the center of mass of the initial binary. This challenges the paradigm that most galaxies form through hierarchical mergers, yet retain supermassive black holes at their centers despite having escape velocities much less than v_max. Interaction with a circumbinary disk can align the binary black hole spins with their orbital angular momentum, reducing the recoil velocity of the final black hole produced in the subsequent merger. However, the effectiveness of this alignment depends on highly uncertain accretion flows near the binary black holes. In this Letter, we show that if the spin S_1 of the more massive binary black hole is even partially aligned with the orbital angular momentum L, relativistic spin precession on sub-parsec scales can align the binary black hole spins with each other. This alignment significantly reduces the recoil velocity even in the absence of gas. For example, if the angle between S_1 and L at large separations is 10 degrees while the second spin S_2 is isotropically distributed, the spin alignment discussed in this paper reduces the median recoil from 864 km/s to 273 km/s for maximally spinning black holes with a mass ratio of 9/11. This reduction will greatly increase the fraction of galaxies retaining their supermassive black holes.'), (399, '2011-03-21 17:43:12'), (400, 'Emergence of spatial structure from causal sets'), (401, '2009-04-30 2009-04-30'), (402, 'http://arxiv.org/abs/0905.0017'), (403, '0905.0017'), (404, "There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying discreteness. The causal set approach, in which the fundamental relation is based upon causality, finds it easy to reproduce timelike distances, but has a more difficult time with spatial distance, due to the unique combination of Lorentz invariance and discreteness within that approach. We describe a method to deduce spatial distances from a causal set. In addition, we sketch how one might use an important ingredient in deducing spatial distance, the `$n$-link', to deduce whether a given causal set is likely to faithfully embed into a continuum spacetime."), (405, '2009-06-02 15:50:03'), (406, '0905.0017 PDF'), (407, 'http://www.arxiv.org/pdf/0905.0017.pdf'), (408, '2009-06-02 15:50:06'), (409, 'Cooks.com - Recipe - Chicken Fettuccine'), (410, 'http://www.cooks.com/rec/view/0,1639,136189-243196,00.html'), (411, '2009-06-02 15:51:09'), (412, "Hell's Kitchen Beef Wellington Recipe : Recipezaar"), (413, 'http://www.recipezaar.com/Hells-Kitchen-Beef-Wellington-286940'), (414, '2009-06-02 15:52:04'), (415, '2009-06-02 15:53:59'), (416, '2009-06-02 15:54:15'), (417, '2009-06-02 15:54:31'), (418, 'Linearized quadrupole waves in general relativity and the motion of test particles'), (419, 745), (420, '1982-00-00 1982'), (421, 'http://link.aps.org/abstract/PRD/v26/p745'), (422, '10.1103/PhysRevD.26.745'), (423, 'We write out the explicit form of the metric for a linearized quadrupole gravitational wave in the transverse-traceless gauge. We give a collection of formulas which are useful for testing numerical codes to integrate the full nonlinear Einstein equations. We also show that a test particle initially at rest acquires no energy from a linearized gravitational wave.'), (424, '2009-06-04 14:41:27'), (425, 'http://prola.aps.org/pdf/PRD/v26/i4/p745_1'), (426, '2009-06-04 14:41:29'), (427, 'Accurate gravitational waveforms from binary black-hole systems'), (428, '1003.4993 PDF'), (429, 'http://www.arxiv.org/pdf/1003.4993.pdf'), (430, 'http://arxiv.org/abs/0910.0319'), (431, 'http://www.nature.com.proxy.library.cornell.edu/nphys/journal/v7/n6/full/nphys2011.html'), (432, '2009-06-04 14:44:00'), (433, '0910.0319'), (434, '2008-10-20 2008-10-20'), (435, 'Thesis.pdf'), (436, '2011-03-21 17:43:16'), (437, 'Final spins from the merger of precessing binary black holes'), (438, "Elizabeth's Edible: Big Saturday Morning"), (439, 'http://elizabethsedibleexperience.blogspot.com/2008/08/big-saturday-morning.html'), (440, '2009-06-04 14:48:14'), (441, '2010-02-13 2010-02-13'), (442, 'http://arxiv.org/abs/1002.2643'), (443, 'Phys.Rev.D81:084054,2010'), (444, 'doi:10.1103/PhysRevD.81.084054'), (445, '2009-06-04 14:49:18'), (446, 'California Institute of Technology'), (447, 'Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit, a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the Standard Quantum Limit significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.'), (448, 'http://gwic.ligo.org/roadmap/Roadmap_020609.pdf'), (449, '2009-06-04 16:29:07'), (450, 'GWIC Roadmap'), (451, 'Multipole expansions of gravitational radiation'), (452, 52), (453, 299), (454, '1980-04-01 April 1, 1980'), (455, 'Reviews of Modern Physics'), (456, 'Rev. Mod. Phys.'), (457, 'http://link.aps.org/abstract/RMP/v52/p299'), (458, '10.1103/RevModPhys.52.299'), (459, 'This paper brings together, into a single unified notation, the multipole formalisms for gravitational radiation which various people have constructed. It also extends the results of previous workers. More specifically:'), (460, '2009-06-04 17:34:05'), (461, 677), (462, '2008-04-20 2008-04-20'), (463, 'Chinese Recipes - Juicy Steamed Dumplings'), (464, 'http://www.chinesefooddiy.com/SteamedDumplings.htm'), (465, '2009-06-07 14:55:43'), (466, '2009-06-07 14:55:52'), (467, 'Juicy Pork Dumplings'), (468, '03684245'), (469, 'Journal of the Society for Industrial and Applied Mathematics'), (470, 'J. Soc. Indust. and Appl. Math.'), (471, '1962-00-00 1962'), (472, 768), (473, '10.1137/0110059'), (474, 'http://link.aip.org/link/SMJMAP/v10/i4/p768/s1&Agg=doi'), (475, 'Gravitational Multipole Radiation'), (476, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=SMJMAP000010000004000768000001&idtype=cvips&prog=normal'), (477, '2009-06-15 19:34:31'), (478, 'Applications of Classical Physics'), (479, '064029'), (480, '2004-00-00 2004'), (481, '2009-10-06 19:19:36'), (482, '0910.0319 PDF'), (483, 'http://www.arxiv.org/pdf/0910.0319.pdf'), (484, '2009-10-06 19:19:39'), (485, 'Data Analysis Challenges for the Einstein Telescope'), (486, '2009-10-02 2009-10-02'), (487, 'http://arxiv.org/abs/0910.0380'), (488, '0910.0380'), (489, 'The Einstein Telescope is a proposed third generation gravitational wave detector that will operate in the region of 1 Hz to a few kHz. As well as the inspiral of compact binaries composed of neutron stars or black holes, the lower frequency cut-off of the detector will open the window to a number of new sources. These will include the end stage of inspirals, plus merger and ringdown of intermediate mass black holes, where the masses of the component bodies are on the order of a few hundred solar masses. There is also the possibility of observing intermediate mass ratio inspirals, where a stellar mass compact object inspirals into a black hole which is a few hundred to a few thousand times more massive. In this article, we investigate some of the data analysis challenges for the Einstein Telescope such as the effects of increased source number, the need for more accurate waveform models and the some of the computational issues that a data analysis strategy might face.'), (490, '2009-10-06 19:19:58'), (491, '0910.0380 PDF'), (492, 'http://www.arxiv.org/pdf/0910.0380.pdf'), (493, '2009-10-06 19:20:01'), (494, 'How far away is far enough for extracting numerical waveforms, and how much do they depend on the extraction method?'), (495, '2007-00-00 2007'), (496, 'S341-S368'), (497, 24), (498, 'We present a method for extracting gravitational waves from numerical\nspacetimes which generalizes and refines one of the standard methods\nbased on the Regge-Wheeler-Zerilli perturbation formalism. At the\nanalytical level, this generalization allows a much more general class\nof slicing conditions for the background geometry, and is thus not\nrestricted to Schwarzschild-like coordinates. At the numerical level,\nour approach uses high-order multi-block methods, which improve both\nthe accuracy of our simulations and of our extraction procedure. In\nparticular, the latter is simplified since there is no need for\ninterpolation, and we can afford to extract accurate waves at large\nradii with only little additional computational effort. We then\npresent fully nonlinear three-dimensional numerical evolutions of a\ndistorted Schwarzschild black hole in Kerr-Schild coordinates with an\nodd parity perturbation and analyse the improvement that we gain from\nour generalized wave extraction, comparing our new method to the\nstandard one. In particular, we analyse in detail the quasinormal\nfrequencies of the extracted waves, using both methods. We do so by\ncomparing the extracted waves with one-dimensional high resolution\nsolutions of the corresponding generalized Regge-Wheeler equation. We\nexplicitly see that the errors in the waveforms extracted with the\nstandard method at fixed, finite extraction radii do not converge to\nzero with increasing resolution. We find that even with observers as\nfar out as R = 80M--which is larger than what is commonly used in\nstate-of-the-art simulations--the assumption in the standard method\nthat the background is close to having Schwarzschild-like coordinates\nincreases the error in the extracted waves considerably. Furthermore,\nthose errors are dominated by the extraction method itself and not by\nthe accuracy of our simulations. For extraction radii between 20M and\n80M and for the resolutions that we use in this paper, our new method\ndecreases the errors in the extracted waves, compared to the standard\nmethod, by between one and three orders of magnitude. In a general\nscenario, for example a collision of compact objects, there is no\nprecise definition of gravitational radiation at a finite distance,\nand gravitational wave extraction methods at such distances are thus\ninherently approximate. The results of this paper bring up the\npossibility that different choices in the wave extraction procedure at\na fixed and finite distance may result in relative differences in the\nwaveforms which are actually larger than the numerical errors in the\nsolution.'), (499, 'http://encompass.library.cornell.edu/cgi-bin/checkIP.cgi?access=gateway_standard%26url=http://www.iop.org/EJ/abstract/0264-9381/24/12/S22/'), (500, '2009-10-29 15:19:46'), (501, 'http://www.iop.org.proxy.library.cornell.edu/EJ/article/0264-9381/24/12/S22/cqg7_12_s22.pdf'), (502, '2009-10-29 15:20:17'), (503, 'Evolution of Binary Black-Hole Spacetimes'), (504, 95), (505, 121101), (506, '2005-00-00 2005'), (507, 'Physical Review Letters'), (508, 'Phys. Rev. Lett.'), (509, 'http://link.aps.org/abstract/PRL/v95/e121101'), (510, '10.1103/PhysRevLett.95.121101'), (511, 'We describe early success in the evolution of binary black-hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary systems for enough time to extract information about the orbit, merger, and gravitational waves emitted during the event. As an example we show results from the evolution of a binary composed of two equal mass, nonspinning black holes, through a single plunge orbit, merger, and ringdown. The resultant black hole is estimated to be a Kerr black hole with angular momentum parameter a≈0.70. At present, lack of resolution far from the binary prevents an accurate estimate of the energy emitted, though a rough calculation suggests on the order of 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.'), (512, '2009-10-29 15:34:17'), (513, '10 - Elastostatics'), (514, '11 - Elastodynamics'), (515, 'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRL/v95/i12/e121101'), (516, '13 - Vorticity'), (517, '14 - Turbulence'), (518, '2009-10-29 15:34:19'), (519, 'Inspiral, merger, and ring-down of equal-mass black-hole binaries'), (520, '17 - Convection'), (521, '18 - Magnetohydrodynamics'), (522, '2007-06-15 June 15, 2007'), (523, '124018-42'), (524, 'http://link.aps.org/abstract/PRD/v75/e124018'), (525, '10.1103/PhysRevD.75.124018'), (526, '2009-10-29 15:40:23'), (527, '1002.2643'), (528, 'The inspiral of binary black holes is governed by gravitational radiation reaction at binary separations r < 1000 M, yet it is too computationally expensive to begin numerical-relativity simulations with initial separations r > 10 M. Fortunately, binary evolution between these separations is well described by post-Newtonian equations of motion. We examine how this post-Newtonian evolution affects the distribution of spin orientations at separations r ~ 10 M where numerical-relativity simulations typically begin. Although isotropic spin distributions at r ~ 1000 M remain isotropic at r ~ 10 M, distributions that are initially partially aligned with the orbital angular momentum can be significantly distorted during the post-Newtonian inspiral. Spin precession tends to align (anti-align) the binary black hole spins with each other if the spin of the more massive black hole is initially partially aligned (anti-aligned) with the orbital angular momentum, thus increasing (decreasing) the average final spin. Spin precession is stronger for comparable-mass binaries, and could produce significant spin alignment before merger for both supermassive and stellar-mass black hole binaries. We also point out that precession induces an intrinsic accuracy limitation (< 0.03 in the dimensionless spin magnitude, < 20 degrees in the direction) in predicting the final spin resulting from the merger of widely separated binaries.'), (529, 'Accurate Evolutions of Orbiting Black-Hole Binaries without Excision'), (530, '2006-03-24 March 24, 2006'), (531, '27 - Cosmology'), (532, 96), (533, 'http://www.arxiv.org/pdf/1110.1668.pdf'), (534, '2011-10-11 13:50:36'), (535, '10.1103/PhysRevLett.96.111101'), (536, 'Beyond LISA: Exploring future gravitational wave missions'), (537, '2011-03-21 17:48:45'), (538, '1002.2643 PDF'), (539, 'Gravitational-Wave Extraction from an Inspiraling Configuration of Merging Black Holes'), (540, '111102-4'), (541, '08 - Interference'), (542, '07 - Diffraction'), (543, 'http://link.aps.org/abstract/PRL/v96/e111102'), (544, '10.1103/PhysRevLett.96.111102'), (545, '2009-10-29 15:47:09'), (546, 'http://www.arxiv.org/pdf/1002.2643.pdf'), (547, '2011-03-21 17:49:03'), (548, 'PhysRevLett_96_111102.pdf'), (549, 'Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonspinning, equal-mass black holes'), (550, '01 - Physics in Euclidean Space and Flat Spacetime: Geometric Viewpoint'), (551, '02 - Kinetic Theory'), (552, '03 - Statistical Mechanics'), (553, '04 - Statistical Thermodynamics'), (554, '05 - Random Processes'), (555, '06 - Geometric Optics'), (556, '09 - Nonlinear Optics'), (557, '12 - Foundations of Fluid Dynamics'), (558, '15 - Waves and Rotating Flows'), (559, '16 - Compressible and Supersonic Flow'), (560, '19 - The Particle Kinetics of Plasma'), (561, '20 - Waves in Cold, Dense Plasmas: Two-Fluid Formalism'), (562, '21 - Kinetic Theory of Warm Plasmas'), (563, '22 - Nonlinear Dynamics of Plasmas'), (564, '23 - From Special to General Relativity'), (565, '24 - Fundamental Concepts of General Relativity'), (566, '25 - Relativistic Stars and Black Holes'), (567, '26 - Gravitational Waves and Experimental Tests of General Relativity'), (568, 'A - A Concept-Based Outline of the Book'), (569, 'B - Some Unifying Concepts'), (570, '00 - Intro'), (571, '2009-06-15 June 15, 2009'), (572, 'Viscous Flow Reversal'), (573, 'Handbook of mathematical functions'), (574, '124028-19'), (575, 'http://link.aps.org/abstract/PRD/v79/e124028'), (576, '10.1103/PhysRevD.79.124028'), (577, '1972-12-00 December 1972'), (578, 'Motion Mountain'), (579, 22), (580, 'http://www.motionmountain.net/'), (581, 1612), (582, 661), (583, '2007-00-06 06/2007'), (584, 'L147-L150'), (585, '10.1086/518769'), (586, 'MotionMountain.pdf'), (587, '2009-01-00 January 2009'), (588, '2009-11-03 17:45:48'), (589, 'http://iopscience.iop.org.proxy.library.cornell.edu/1538-4357/661/2/L147'), (590, 'Alignment of the Spins of Supermassive Black Holes Prior to Coalescence'), (591, 'This a book is for those who would like to learn something about special and general relativity beyond the usual textbooks, about quantum field theory, the elegant Fock-Schwinger-Stueckelberg proper time formalism, the elegant description of geometry by means of Clifford algebra, about the fascinating possibilities the latter algebra offers in reformulating the existing physical theories, and quantizing them in a natural way. It is shown how Clifford algebra provides much more: it provides room for new physics, with the prospects of resolving certain long standing puzzles. The theory of branes and the idea of how a 3-brane might represent our world is discussed in detail. Much attention is paid to the elegant geometric theory of branes which employs the infinite dimensional space of functions describing branes. Clifford algebra is generalized to the infinite dimensional spaces. In short, this is a book for anybody who would like to explore how the "theory of everything" might possibly be formulated. The theory that would describe all the known phenomena, could not be formulated without taking into account "all" the theoretical tools which are available. Foundations of those tools and their functional interrelations are described in the book.'), (592, 'Kluwer Academic Publishers'), (593, '2006-10-00 Oct 2006'), (594, 'http://arxiv.org/abs/gr-qc/0610061'), (595, '0610061v2.pdf'), (596, 'http://arxiv.org/pdf/gr-qc/0610061v2'), (597, '2009-06-16 14:05:54'), (598, 'The Dynamics of General Relativity'), (599, '2011-03-21 17:49:54'), (600, '1538-4357_661_2_L147.pdf'), (601, 'Table of contents'), (602, 'The Landscape of Theoretical Physics: A Global View'), (603, '083005'), (604, '2009-06-16 15:15:20'), (605, '2004-05-19 2004-05-19'), (606, 'http://ccrg.rit.edu/~EGM2009/slides/221/EcgmEccTalk.pdf'), (607, '2009-06-16 15:27:00'), (608, "The Effect of Eccentricity on LIGO's Inspiral Searches"), (609, '2009-06-16 June 16, 2009'), (610, 'The nonlinear gravitational-wave memory in binary black hole mergers'), (611, 'EGM'), (612, 'favata-EGM2009-RIT.pdf'), (613, 'http://ccrg.rit.edu/~EGM2009/slides/225/favata-EGM2009-RIT.pdf'), (614, '2009-06-16 16:25:43'), (615, 'Post-Newtonian corrections to the gravitational-wave memory for quasi-circular, inspiralling compact binaries'), (616, '2008-11-30 2008-11-30'), (617, 'http://arxiv.org/abs/0812.0069'), (618, '0812.0069'), (619, 'The Christodoulou memory is a nonlinear contribution to the gravitational-wave field that is sourced by the gravitational-wave stress-energy tensor. For quasi-circular, inspiralling binaries, the Christodoulou memory produces a growing, non-oscillatory change in the gravitational-wave "plus" polarization, resulting in the permanent displacement of a pair of freely-falling test masses after the wave has passed. In addition to its non-oscillatory behavior, the Christodoulou memory is interesting because even though it originates from 2.5 post-Newtonian (PN) order multipole interactions, it affects the waveform at leading-(Newtonian)-order. The memory is also potentially detectable in binary black hole mergers. While the oscillatory pieces of the gravitational-wave polarizations for quasi-circular, inspiralling compact binaries have been computed to 3PN order, the memory contribution to the polarizations has only been calculated to leading-order (the next-to-leading order 0.5PN term has previously been shown to vanish). Here the calculation of the memory for quasi-circular, inspiralling binaries is extended to 3PN order. While the angular dependence of the memory is essentially unchanged, the PN correction terms tend to reduce the memory\'s magnitude. Explicit expressions are given for the memory contributions to the polarizations and the spin-weighted spherical-harmonic modes of the metric and curvature perturbations. Combined with the results of Blanchet et al. (2008), this completes the waveform to 3PN order. This paper also discusses: (i) difficulties in extracting the memory from numerical simulations, (ii) other non-oscillatory effects that enter the waveform at high PN orders, and (iii) issues concerning the observability of the memory.'), (620, '2009-06-16 16:29:59'), (621, '0812.0069 PDF'), (622, 'http://www.arxiv.org/pdf/0812.0069.pdf'), (623, '2009-06-16 16:30:02'), (624, 'Astrophys.J.696:L159-L162,2009'), (625, 'doi:10.1088/0004-637X/696/2/L159'), (626, 'Some astrophysical sources of gravitational waves can produce a "memory effect," which causes a permanent displacement of the test masses in a freely falling gravitational-wave detector. The Christodoulou memory is a particularly interesting nonlinear form of memory that arises from the gravitational-wave stress-energy tensor\'s contribution to the distant gravitational-wave field. This nonlinear memory contributes a nonoscillatory component to the gravitational-wave signal at leading (Newtonian-quadrupole) order in the waveform amplitude. Previous computations of the memory and its detectability considered only the inspiral phase of binary black hole coalescence. Using an "effective-one-body" (EOB) approach calibrated to numerical relativity simulations, as well as a simple fully analytic model, the Christodoulou memory is computed for the inspiral, merger, and ringdown. The memory will be very difficult to detect with ground-based interferometers, but is likely to be observable in supermassive black hole mergers with LISA out to a redshift of two. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to "gravitate."'), (627, '2009-06-16 16:35:02'), (628, '2009-06-16 16:35:05'), (629, 'Gravitational-wave memory revisited: memory from the merger and recoil of binary black holes'), (630, '2008-11-20 2008-11-20'), (631, 'http://arxiv.org/abs/0811.3451'), (632, '0811.3451'), (633, 'Gravitational-wave memory refers to the permanent displacement of the test masses in an idealized (freely-falling) gravitational-wave interferometer. Inspiraling binaries produce a particularly interesting form of memory--the Christodoulou memory. Although it originates from nonlinear interactions at 2.5 post-Newtonian order, the Christodoulou memory affects the gravitational-wave amplitude at leading (Newtonian) order. Previous calculations have computed this non-oscillatory amplitude correction during the inspiral phase of binary coalescence. Using an "effective-one-body" description calibrated with the results of numerical relativity simulations, the evolution of the memory during the inspiral, merger, and ringdown phases, as well as the memory\'s final saturation value, are calculated. Using this model for the memory, the prospects for its detection are examined, particularly for supermassive black hole binary coalescences that LISA will detect with high signal-to-noise ratios. Coalescing binary black holes also experience center-of-mass recoil due to the anisotropic emission of gravitational radiation. These recoils can manifest themselves in the gravitational-wave signal in the form of a "linear" memory and a Doppler shift of the quasi-normal-mode frequencies. The prospects for observing these effects are also discussed.'), (634, '2009-06-16 16:35:53'), (635, 'Gravitational-wave memory revisited'), (636, '0811.3451 PDF'), (637, 'http://www.arxiv.org/pdf/0811.3451.pdf'), (638, '2009-06-16 16:35:56'), (639, 'An Overview of Gravitational-Wave Sources'), (640, '2002-04-30 2002-04-30'), (641, 'http://arxiv.org/abs/gr-qc/0204090'), (642, 'gr-qc/0204090'), (643, 'We review current best estimates of the strength and detectability of the gravitational waves from a variety of sources, for both ground-based and space-based detectors, and we describe the information carried by the waves.'), (644, '2009-06-19 14:11:56'), (645, 'gr-qc/0204090 PDF'), (646, 'http://www.arxiv.org/pdf/gr-qc/0204090.pdf'), (647, '2009-06-19 14:11:59'), (648, '2009-06-19 16:07:52'), (649, '2009-06-19 16:08:23'), (650, 'Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences'), (651, 'Radiative Gravitational Fields in General Relativity I. General Structure of the Field outside the Source'), (652, 320), (653, 1555), (654, '00804614'), (655, 'http://www.jstor.org.clsproxy.library.caltech.edu/stable/37878'), (656, '1986-12-03 Dec. 3, 1986'), (657, '379-430'), (658, 'ArticleType: primary_article / Full publication date: Dec. 3, 1986 / Copyright © 1986 The Royal Society'), (659, 'We present a well-defined formal framework, together with appropriate mathematical tools, which allow us to implement in a constructive way, and to investigate in full mathematical details, the Bonnor-Thorne approach to gravitational radiation theory. We show how to construct, within this framework, the general radiative (formal) solution of the Einstein vacuum equations, in harmonic coordinates, which is both past-stationary and past-asymptotically Minkowskian. We investigate the structure of the latter general radiative metric (including all tails and nonlinear effects) both in the near zone and in the far zone. As a side result it is proven that post-Newtonian expansions must be done by using the gauge functions (lg c)p/cn (p, n = positive integers).'), (660, 'JSTOR'), (661, '2009-06-25 02:01:10'), (662, 'JSTOR Full Text PDF'), (663, 'http://www.jstor.org.clsproxy.library.caltech.edu/stable/pdfplus/37878.pdf'), (664, '2009-06-25 02:01:12'), (665, 'Undecidability and the problem of outcomes in quantum measurements'), (666, '2009-05-26 2009-05-26'), (667, 'http://arxiv.org/abs/0905.4222'), (668, '0905.4222'), (669, 'We argue that it is fundamentally impossible to recover information about quantum superpositions when a system has interacted with a sufficiently large number of degrees of freedom of the environment. This is due to the fact that gravity imposes fundamental limitations on how accurate measurements can be. This leads to the notion of undecidability: there is no way to tell, due to fundamental limitations, if a quantum system evolved unitarily or suffered wavefunction collapse. This in turn provides a solution to the problem of outcomes in quantum measurement by providing a sharp criterion for defining when an event has taken place. We analyze in detail in examples two situations in which in principle one could recover information about quantum coherence: a) "revivals" of coherence in the interaction of a system with the environment and b) the measurement of global observables of the system plus apparatus plus environment. We show in the examples that the fundamental limitations due to gravity and quantum mechanics in measurement prevent both revivals from occurring and the measurement of global observables. It can therefore be argued that the emerging picture provides a complete resolution to the measurement problem in quantum mechanics.'), (670, '2009-06-26 15:48:27'), (671, '0905.4222 PDF'), (672, 'http://www.arxiv.org/pdf/0905.4222.pdf'), (673, '2009-06-26 15:48:30'), (674, 'Almond-Crusted Tilapia - All Recipes'), (675, 'http://allrecipes.com/Recipe/Almond-Crusted-Tilapia/Detail.aspx'), (676, '2009-06-29 19:42:03'), (677, '2009-06-29 19:42:17'), (678, 'Easy Tilapia - All Recipes'), (679, 'http://allrecipes.com/Recipe/Easy-Tilapia/Detail.aspx'), (680, '2009-06-29 19:43:10'), (681, '2009-06-29 19:43:12'), (682, 'Tilapia with tomato sauce'), (683, 'Almond-Crusted Tilapia'), (684, 'Lemon Garlic Tilapia - All Recipes'), (685, 'http://allrecipes.com/Recipe/Lemon-Garlic-Tilapia/Detail.aspx'), (686, '2009-06-29 19:43:57'), (687, '2009-06-29 19:43:59'), (688, 'Lemon Garlic Tilapia (basic recipe)'), (689, 'Chicken Puttanesca - South Beach Diet Recipes'), (690, 'http://www.southbeachdiet.com/sbd/publicsite/recipes/Chicken-Puttanesca.aspx'), (691, '2009-07-01 19:29:23'), (692, '2009-07-01 19:29:25'), (693, 'Chocolate Meringue Kisses - South Beach Diet Recipe'), (694, 'http://www.southbeachdiet.com/sbd/publicsite/recipes/chocolate-meringue-kisses.aspx'), (695, '2009-07-01 19:35:03'), (696, '2009-07-01 19:35:05'), (697, 'Grilled Sesame Salmon - South Beach Diet Recipes'), (698, 'http://www.southbeachdiet.com/sbd/publicsite/recipes/grilled-sesame-salmon.aspx'), (699, '2009-07-01 19:38:57'), (700, '2009-07-01 19:38:59'), (701, 'Beef With Asparagus and Mushrooms - South Beach Diet Recipes'), (702, 'http://www.southbeachdiet.com/sbd/publicsite/recipes/beef-with-asparagus-and-mushrooms.aspx'), (703, '2009-07-01 19:39:49'), (704, '2009-07-01 19:39:51'), (705, 'http://arxiv.org/abs/gr-qc/0405109'), (706, 'https://nrda2009.aei.mpg.de/program/Reisswig-NRDA.pdf'), (707, '2009-07-10 16:41:41'), (708, 'Unambiguous determination of binary black hole merger waveforms at scri'), (709, '2009-07-09 July 9, 2009'), (710, 'Max-Planck-Institut für Gravitationsphysik (AEI)'), (711, 'NRDA 2009'), (712, 'Reisswig-NRDA'), (713, 'Grilling and South Beach Diet - Healthy Summer Grilling and South Beach Diet'), (714, 'http://www.southbeachdiet.com/sbd/publicsite/grilled-kebabs.aspx'), (715, '2009-07-12 19:13:44'), (716, '2009-07-12 19:13:46'), (717, 'Steak and Mushroom Kebabs'), (718, 'Beef With Asparagus and Mushrooms'), (719, 'Grilled Sesame Salmon'), (720, 'Chocolate Meringue Kisses'), (721, 'Chicken Puttanesca'), (722, 'Fourth of July Treats and South Beach Diet - What Are Healthy Fourth of July Treats and South Beach Diet'), (723, 'http://www.southbeachdiet.com/sbd/publicsite/fourth-of-july-treat.aspx'), (724, '2009-07-12 20:45:36'), (725, '2009-07-12 20:45:38'), (726, 'Strawberry-Blueberry Crunch'), (727, 'Side Dishes and South Beach Diet - Healthy Side Dishes and South Beach Diet'), (728, 'http://www.southbeachdiet.com/sbd/publicsite/savory-side-dish.aspx'), (729, '2009-07-12 20:46:34'), (730, '2009-07-12 20:46:36'), (731, 'Bean Caprese Salad'), (732, 'The Computational Power of Minkowski Spacetime'), (733, '2009-07-09 2009-07-09'), (734, 'http://arxiv.org/abs/0907.1579'), (735, '0907.1579'), (736, "The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \\emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation."), (737, '2009-07-13 12:13:08'), (738, 'http://iopscience.iop.org.proxy.library.cornell.edu/1538-4357/661/2/L147/pdf/1538-4357_661_2_L147.pdf'), (739, '2011-03-21 17:57:54'), (740, '0907.1579 PDF'), (741, 'http://www.arxiv.org/pdf/0907.1579.pdf'), (742, '2009-07-13 12:13:12'), (743, 'Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors'), (744, '2009-07-03 2009-07-03'), (745, 'http://arxiv.org/abs/0907.0700'), (746, '0907.0700'), (747, 'The two-body dynamics in general relativity has been solved perturbatively using the post-Newtonian (PN) approximation. The evolution of the orbital phase and the emitted gravitational radiation are now known to a rather high order up to O(v^8), v being the characteristic velocity of the binary. The orbital evolution, however, cannot be specified uniquely due to the inherent freedom in the choice of parameter used in the PN expansion as well as the method pursued in solving the relevant differential equations. The goal of this paper is to determine the (dis)agreement between different PN waveform families in the context of initial and advanced gravitational-wave detectors. The waveforms employed in our analysis are those that are currently used by Initial LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the Fourier-domain representation TaylorF2. We examine the overlaps of these models with one another and with the prototype effective one-body model (calibrated to numerical relativity simulations, as currently used by initial LIGO) for a number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their differences and to help us decide whether there exist preferred families that are the most appropriate as search templates. We conclude that as long as the total mass remains less than a certain upper limit M_crit, all template families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial, Enhanced and Advanced LIGO. From a purely computational point of view we recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to numerical relativity simulations be used for total binary mass M > Mcrit.'), (748, '2009-07-13 16:17:28'), (749, 599), (750, '0907.0700 PDF'), (751, 'http://www.arxiv.org/pdf/0907.0700.pdf'), (752, '2009-07-13 16:17:32'), (753, 'Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins'), (754, '2009-07-02 2009-07-02'), (755, 'http://arxiv.org/abs/0907.0462'), (756, '0907.0462'), (757, '2005-10-20 October 20, 2005'), (758, 'Black-hole binaries, gravitational waves, and numerical relativity'), (759, '2003-00-12 12/2003'), (760, '0907.0462 PDF'), (761, 'http://www.arxiv.org/pdf/0907.0462.pdf'), (762, '2009-07-13 16:21:25'), (763, 'Use and Abuse of the Model Waveform Accuracy Standards'), (764, 'http://arxiv.org/abs/0907.0457'), (765, '0907.0457'), (766, 'Accuracy standards have been developed to ensure that the waveforms used for gravitational-wave data analysis are good enough to serve their intended purposes. These standards place constraints on certain norms of the frequency-domain representations of the waveform errors. Examples are given here of possible misinterpretations and misapplications of these standards, whose effect could be to vitiate the quality control they were intended to enforce. Suggestions are given for ways to avoid these problems.'), (767, '2009-07-13 16:21:40'), (768, '1254-1259'), (769, '0907.0457 PDF'), (770, 'http://www.arxiv.org/pdf/0907.0457.pdf'), (771, '2009-07-13 16:21:44'), (772, 'The Final Remnant of Binary Black Hole Mergers: Multipolar Analysis'), (773, '2009-07-01 2009-07-01'), (774, 'http://arxiv.org/abs/0907.0280'), (775, '0907.0280'), (776, 'Methods are presented to define and compute source multipoles of dynamical horizons in numerical relativity codes, extending previous work from the isolated and dynamical horizon formalisms in a manner that allows for the consideration of horizons that are not axisymmetric. These methods are then applied to a binary black hole merger simulation, providing evidence that the final remnant is a Kerr black hole, both through the (spatially) gauge-invariant recovery of the geometry of the apparent horizon, and through a detailed extraction of quasinormal ringing modes directly from the strong-field region.'), (777, '2009-07-13 16:21:56'), (778, 'The Final Remnant of Binary Black Hole Mergers'), (779, '10.1086/379311'), (780, '0907.0280 PDF'), (781, 'http://www.arxiv.org/pdf/0907.0280.pdf'), (782, '2009-07-13 16:22:00'), (783, 'Ultra-high precision cosmology from gravitational waves'), (784, '2009-06-19 2009-06-19'), (785, 'http://arxiv.org/abs/0906.3752'), (786, '0906.3752'), (787, "We show that the Big Bang Observer (BBO), a proposed space-based gravitational-wave (GW) detector, would provide ultra-precise measurements of cosmological parameters. By detecting ~300,000 compact-star binaries, and utilizing them as standard sirens, BBO would determine the Hubble constant to 0.1%, and the dark energy parameters w_0 and w_a to ~0.01 and 0.1,resp. BBO's dark-energy figure-of-merit would be approximately an order of magnitude better than all other proposed dark energy missions. To date, BBO has been designed with the primary goal of searching for gravitational waves from inflation. To observe this inflationary background, BBO would first have to detect and subtract out ~300,000 merging compact-star binaries, out to z~5. It is precisely this foreground which would enable high-precision cosmology. BBO would determine the luminosity distance to each binary to ~percent accuracy. BBO's angular resolution would be sufficient to uniquely identify the host galaxy for most binaries; a coordinated optical/infrared observing campaign could obtain the redshifts. Combining the GW-derived distances and EM-derived redshifts for such a large sample of objects leads to extraordinarily tight constraints on cosmological parameters. Such ``standard siren'' measurements of cosmology avoid many of the systematic errors associated with other techniques. We also show that BBO would be an exceptionally powerful gravitational lensing mission, and we briefly discuss other astronomical uses of BBO."), (788, '2009-07-13 16:22:42'), (789, 'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/599/2/1254/'), (790, '0906.3752 PDF'), (791, 'http://www.arxiv.org/pdf/0906.3752.pdf'), (792, '2009-07-13 16:22:46'), (793, 'Momentum flow in black-hole binaries: II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins'), (794, '2009-07-05 2009-07-05'), (795, 'http://arxiv.org/abs/0907.0869'), (796, '0907.0869'), (797, 'Research on extracting science from binary-black-hole (BBH) simulations has often adopted a "scattering matrix" perspective: given the binary\'s initial parameters, what are the final hole\'s parameters and the emitted gravitational waveform? In contrast, we are using BBH simulations to explore the nonlinear dynamics of curved spacetime. Focusing on the head-on plunge, merger, and ringdown of a BBH with transverse, antiparallel spins, we explore numerically the momentum flow between the holes and the surrounding spacetime. We use the Landau-Lifshitz field-theory-in-flat-spacetime formulation of general relativity to define and compute the density of field energy and field momentum outside horizons and the energy and momentum contained within horizons, and we define the effective velocity of each apparent and event horizon as the ratio of its enclosed momentum to its enclosed mass-energy. We find surprisingly good agreement between the horizons\' effective and coordinate velocities. To investigate the gauge dependence of our results, we compare pseudospectral and moving-puncture evolutions of physically similar initial data; although spectral and puncture simulations use different gauge conditions, we find remarkably good agreement for our results in these two cases. We also compare our simulations with the post-Newtonian trajectories and near-field energy-momentum. [Abstract abbreviated; full abstract also mentions additional results.]'), (798, '2009-07-13 16:23:17'), (799, 'Momentum flow in black-hole binaries'), (800, 'GRO J0422+32: The Lowest Mass Black Hole?'), (801, '0907.0869 PDF'), (802, 'http://www.arxiv.org/pdf/0907.0869.pdf'), (803, '2009-07-13 16:23:21'), (804, 'Conformally curved binary black hole initial data including tidal deformations and outgoing radiation'), (805, '2009-07-06 2009-07-06'), (806, 'http://arxiv.org/abs/0907.0891'), (807, '0907.0891'), (808, '(Abridged) By asymptotically matching a post-Newtonian (PN) metric to two tidally perturbed Schwarzschild metrics, we generate approximate initial data (in the form of a 4-metric) for a nonspinning black hole binary in a circular orbit. We carry out this matching through O(v^4) in the binary\'s orbital velocity v, so the resulting data are conformally curved. Far from the holes, we use the appropriate PN metric that accounts for retardation, which we construct using the highest-order PN expressions available to compute the binary\'s past history. The data set\'s uncontrolled remainders are thus O(v^5) throughout the timeslice; we also generate an extension to the data set that has uncontrolled remainders of O(v^6) in the purely PN portion of the timeslice (i.e., not too close to the holes). The resulting data are smooth, since we join all the metrics together by smoothly interpolating between them. We perform this interpolation using transition functions constructed to avoid introducing excessive additional constraint violations. Due to their inclusion of tidal deformations and outgoing radiation, these data should substantially reduce the initial spurious ("junk") radiation observed in current simulations that use conformally flat initial data. Such reductions in the nonphysical components of the initial data will be necessary for simulations to achieve the accuracy required to supply Advanced LIGO and LISA with the templates necessary for parameter estimation.'), (809, '2009-07-13 16:24:11'), (810, '2011-03-21 18:45:39'), (811, '0907.0891 PDF'), (812, 'http://www.arxiv.org/pdf/0907.0891.pdf'), (813, '2009-07-13 16:24:15'), (814, 'The Effective One Body description of the Two-Body problem'), (815, '2009-06-09 2009-06-09'), (816, 'http://arxiv.org/abs/0906.1769'), (817, '0906.1769'), (818, 'The Effective One Body (EOB) formalism is an analytical approach which aims at providing an accurate description of the motion and radiation of coalescing binary black holes with arbitrary mass ratio. We review the basic elements of this formalism and discuss its aptitude at providing accurate template waveforms to be used for gravitational wave data analysis purposes.'), (819, '2009-07-13 16:24:33'), (820, 'GRO J0422+32'), (821, '0906.1769 PDF'), (822, 'http://www.arxiv.org/pdf/0906.1769.pdf'), (823, '2009-07-13 16:24:37'), (824, 'Post-Circular Expansion of Eccentric Binary Inspirals: Fourier-Domain Waveforms in the Stationary Phase Approximation'), (825, '2009-06-01 2009-06-01'), (826, 'http://arxiv.org/abs/0906.0313'), (827, '0906.0313'), (828, 'We lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waveforms produced by eccentric, inspiraling compact binaries in a post-circular or small-eccentricity approximation. The time-dependent, "plus" and "cross" polarizations are expanded in Bessel functions, which are then self-consistently re-expanded in a power series about zero initial eccentricity to eighth order. The stationary phase approximation is then employed to obtain explicit analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify this framework by considering Newtonian-accurate waveforms, which in the post-circular scheme give rise to higher harmonics of the orbital phase and amplitude corrections both to the amplitude and the phase of the Fourier domain waveform. Such higher harmonics lead to an effective increase in the inspiral mass reach of a detector as a function of the binary\'s eccentricity e_0 at the time when the binary enters the detector sensitivity band. Using the largest initial eccentricity allowed by our approximations (e_0 < 0.4), the mass reach is found to be enhanced up to factors of approximately 5 relative to that of circular binaries for Advanced LIGO, LISA, and the proposed Einstein Telescope at a signal-to-noise ratio of ten. A post-Newtonian generalization of the post circular scheme is also discussed, which holds the promise to provide "ready-to-use" Fourier-domain waveforms for data analysis of eccentric inspirals.'), (829, '2009-07-13 16:25:11'), (830, 'Post-Circular Expansion of Eccentric Binary Inspirals'), (831, '0004-637X_599_2_1254.pdf'), (832, '0906.0313 PDF'), (833, 'http://www.arxiv.org/pdf/0906.0313.pdf'), (834, '2009-07-13 16:25:15'), (835, 'Optimal Calibration Accuracy for Gravitational Wave Detectors'), (836, '2009-06-28 2009-06-28'), (837, 'http://arxiv.org/abs/0906.5153'), (838, '0906.5153'), (839, 'Calibration errors in the response function of a gravitational wave detector degrade its ability to detect and then to measure the properties of any detected signals. This paper derives the needed levels of calibration accuracy for each of these data-analysis tasks. The levels derived here are optimal in the sense that lower accuracy would result in missed detections and/or a loss of measurement precision, while higher accuracy would be made irrelevant by the intrinsic noise level of the detector. Calibration errors affect the data-analysis process in much the same way as errors in theoretical waveform templates. The optimal level of calibration accuracy is expressed therefore as a joint limit on modeling and calibration errors: increased accuracy in one reduces the accuracy requirement in the other.'), (840, '2009-07-13 16:25:35'), (841, 'Accurate numerical simulations of inspiralling binary neutron stars and their comparison with effective-one-body analytical models'), (842, '0906.5153 PDF'), (843, 'http://www.arxiv.org/pdf/0906.5153.pdf'), (844, '2009-07-13 16:25:39'), (845, 3069), (846, '2011-03-20 2011-03-20'), (847, '2009-07-13 16:27:21'), (848, 'Pollney-Monday.pdf'), (849, 'https://nrda2009.aei.mpg.de/program/Pollney-Monday.pdf'), (850, '2009-07-13 16:29:37'), (851, 'Status of BBH simulations (with "Llama")'), (852, '2009-07-06 July 6, 2009'), (853, 'Potsdam'), (854, '2010-11-16 November 16, 2010'), (855, 'http://link.aps.org/doi/10.1103/RevModPhys.82.3069'), (856, '10.1103/RevModPhys.82.3069'), (857, 'Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational wave forms can only be calculated through numerical simulations of Einstein’s equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit could be simulated. Recently, however, a series of dramatic advances in numerical relativity has allowed stable, robust black-hole merger simulations. This remarkable progress in the rapidly maturing field of numerical relativity and the new understanding of black-hole binary dynamics that is emerging is chronicled. Important applications of these fundamental physics results to astrophysics, to gravitational-wave astronomy, and in other areas are also discussed.'), (858, '2011-10-11 19:54:50'), (859, 'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v82/i4/p3069_1'), (860, 'http://arxiv.org/abs/1103.3874'), (861, '0907.2637 PDF'), (862, 'http://www.arxiv.org/pdf/0907.2637.pdf'), (863, '2009-07-16 18:07:41'), (864, 'Stevia - Naturally Sweet - Recipes, Cooking Tips, Articles, and leading Stevia Products'), (865, 'http://www.stevia.com/SteviaRecipes.asp?RCId=1'), (866, '2009-07-16 19:24:20'), (867, '2009-07-16 19:24:22'), (868, 'Stevia Recipes'), (869, 'Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries'), (870, 'Living Reviews in Relativity'), (871, '2006-00-00 2006'), (872, 9), (873, 'http://www.livingreviews.org/lrr-2006-4'), (874, 'lrr-2006-4Color.pdf'), (875, 'http://relativity.livingreviews.org/Articles/lrr-2006-4/download/lrr-2006-4Color.pdf'), (876, '2009-07-17 15:05:24'), (877, 'Chicken Fettuccine'), (878, '"Gravitation: an introduction to current research", Louis Witten ed. (Wiley 1962), chapter 7, pp 227--265'), (879, 'Fruit Smoothies'), (880, 'Homemade Teddy Grahams'), (881, 'Ricotta Blueberry Pancakes'), (882, "Beef Wellington -- Hell's Kitchen"), (883, 'The Minimalist - Recipes for 101 Simple Salads for the Season - NYTimes.com'), (884, 'http://www.nytimes.com/2009/07/22/dining/22mlist.html?em&pagewanted=all'), (885, '2009-07-27 02:22:02'), (886, '2009-07-27 02:22:04'), (887, 'gr-qc/0405109'), (888, '101 Salad Recipes'), (889, 'The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits'), (890, 165003), (891, 16), (892, 'The New York Times - Breaking News, World News & Multimedia'), (893, '1103.3874'), (894, '2009-07-31 20:31:41'), (895, 'Binary neutron-star systems represent one of the most promising sources of gravitational waves. In order to be able to extract important information, notably about the equation of state of matter at nuclear density, it is necessary to have in hands an accurate analytical model of the expected waveforms. Following our recent work, we here analyze more in detail two general-relativistic simulations spanning about 20 gravitational-wave cycles of the inspiral of equal-mass binary neutron stars with different compactnesses, and compare them with a tidal extension of the effective-one-body (EOB) analytical model. The latter tidally extended EOB model is analytically complete up to the 1.5 post-Newtonian level, and contains an analytically undetermined parameter representing a higher-order amplification of tidal effects. We find that, by calibrating this single parameter, the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, analytical models (either EOB, or Taylor-T4) that do not incorporate such a higher-order amplification of tidal effects, build a dephasing with respect to the numerical waveforms of several radians.'), (896, '2011-03-22 13:20:59'), (897, 'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/25/16/165003/cqg8_16_165003.pdf'), (898, '2009-07-31 20:31:44'), (899, 'Estimating Energy-Momentum and Angular Momentum Near Null Infinity'), (900, '2009-07-20 2009-07-20'), (901, 'http://arxiv.org/abs/0907.3461'), (902, '0907.3461'), (903, 'The energy-momentum and angular momentum contained in a spacelike two-surface of spherical topology are estimated by joining the two-surface to null infinity via an approximate no-incoming-radiation condition. The result is a set of gauge-invariant formulas for energy-momentum and angular momentum which should be applicable to much numerical work; it also gives estimates of the finite-size effects.'), (904, '2009-08-03 15:21:40'), (905, '1103.3874 PDF'), (906, '0907.3461 PDF'), (907, 'http://www.arxiv.org/pdf/0907.3461.pdf'), (908, '2009-08-03 15:21:44'), (909, 'Improved resummation of post-Newtonian multipolar waveforms from circularized compact binaries'), (910, 'http://www.arxiv.org/pdf/1103.3874.pdf'), (911, '2011-03-22 13:21:36'), (912, '1103.pdf'), (913, 'http://arxiv.org/pdf/1103.3874v1'), (914, '2011-03-22 13:22:27'), (915, 'Post-Newtonian factorized multipolar waveforms for spinning, nonprecessing black-hole binaries'), (916, '064003'), (917, '2011-03-01 March 01, 2011'), (918, 'http://link.aps.org/doi/10.1103/PhysRevD.83.064003'), (919, '10.1103/PhysRevD.83.064003'), (920, '2009-08-03 15:28:57'), (921, 'We generalize the factorized resummation of multipolar waveforms introduced by Damour, Iyer, and Nagar to spinning black holes. For a nonspinning test particle spiraling a Kerr black hole in the equatorial plane, we find that factorized multipolar amplitudes which replace the residual relativistic amplitude fℓm with its ℓth root, ρℓm=fℓm1/ℓ, agree quite well with the numerical amplitudes up to the Kerr-spin value q≤0.95 for orbital velocities v≤0.4. The numerical amplitudes are computed solving the Teukolsky equation with a spectral code. The agreement for prograde orbits and large spin values of the Kerr black-hole can be further improved at high velocities by properly factoring out the lower-order post-Newtonian contributions in ρℓm. The resummation procedure results in a better and systematic agreement between numerical and analytical amplitudes (and energy fluxes) than standard Taylor-expanded post-Newtonian approximants. This is particularly true for higher-order modes, such as (2,1), (3,3), (3,2), and (4,4), for which less spin post-Newtonian terms are known. We also extend the factorized resummation of multipolar amplitudes to generic mass-ratio, nonprecessing, spinning black holes. Lastly, in our study we employ new, recently computed, higher-order post-Newtonian terms in several subdominant modes and compute explicit expressions for the half and one-and-half post-Newtonian contributions to the odd-parity (current) and even-parity (odd) multipoles, respectively. Those results can be used to build more accurate templates for ground-based and space-based gravitational-wave detectors.'), (922, '2009-08-03 15:29:01'), (923, 'http://www.ehow.com/how_4822962_make-odwalla-superfood.html'), (924, '2009-08-05 12:48:23'), (925, '2009-08-05 12:48:25'), (926, 'Odwalla Superfood'), (927, 'Splenda'), (928, 'http://splenda.allrecipes.com/Recipe/Recipe.aspx?nprid=104122'), (929, '2009-08-12 21:10:58'), (930, '2009-08-12 21:11:00'), (931, 'Splenda Chocolate Frosting'), (932, 'black-holes.org—White Dwarfs'), (933, 'http://web.archive.org/web/20071231081222/http://www.black-holes.org/gwa2-1.html'), (934, '2009-08-15 01:06:17'), (935, '2009-08-15 01:06:19'), (936, 'black-holes.org—Neutron Stars, Pulsars, and their Gravitational Wave Signatures'), (937, 'http://web.archive.org/web/20071226150145/www.black-holes.org/gwa2-2.html'), (938, '2009-08-15 01:06:43'), (939, '2009-08-15 01:06:45'), (940, 'black-holes.org—Black Holes and Gravitational Waves'), (941, 'http://web.archive.org/web/20071226150150/www.black-holes.org/gwa2-3.html'), (942, '2009-08-15 01:06:56'), (943, '2009-08-15 01:06:58'), (944, 'black-holes.org—Compact Binaries of Black Holes, Neutron Stars, and White Dwarfs'), (945, 'http://web.archive.org/web/20071226150155/www.black-holes.org/gwa2-4.html'), (946, '2009-08-15 01:07:10'), (947, '2009-08-15 01:07:12'), (948, 'black-holes.org—Extreme Mass-Ratio Inspirals as Sources of Gravitational Radiation'), (949, 'http://web.archive.org/web/20071226150200/www.black-holes.org/gwa2-5.html'), (950, '2009-08-15 01:07:17'), (951, '2009-08-15 01:07:19'), (952, '2011-10-11 19:54:52'), (953, '2009-08-15 01:07:29'), (954, 'black-holes.org—Gravitational Waves from the time of the Big Bang'), (955, 'http://web.archive.org/web/20071231081226/www.black-holes.org/gwa2-7.html'), (956, '2009-08-15 01:07:45'), (957, '2009-08-15 01:07:47'), (958, 'black-holes.org—Exotic Sources of Gravitational Waves'), (959, 'http://web.archive.org/web/20071231081231/www.black-holes.org/gwa2-8.html'), (960, '2009-08-15 01:08:00'), (961, '2009-08-15 01:08:02'), (962, 'black-holes.org—Unknown Sources of Gravitational Waves'), (963, 'http://web.archive.org/web/20071231081236/www.black-holes.org/gwa2-9.html'), (964, '2009-08-15 01:08:12'), (965, '2009-08-15 01:08:14'), (966, 'Simulating eXtreme Spacetimes—A Caltech–Cornell Project'), (967, 'http://www.black-holes.org/'), (968, '2009-08-15 01:14:49'), (969, '2009-08-15 01:14:51'), (970, 'index'), (971, 'black-holes.org: Relativity and the Center of the Universe'), (972, 'http://www.black-holes.org/relativity1.html'), (973, '2009-08-15 01:15:03'), (974, '2009-08-15 01:15:05'), (975, 'rel1'), (976, "black-holes.org: Einstein's Special Theory of Relativity"), (977, 'http://www.black-holes.org/relativity2.html'), (978, '2009-08-15 01:15:13'), (979, '2009-08-15 01:15:15'), (980, 'rel2'), (981, 'black-holes.org: Special Relativity and Motion'), (982, 'http://www.black-holes.org/relativity3.html'), (983, '2009-08-15 01:15:28'), (984, '2009-08-15 01:15:30'), (985, 'rel3'), (986, 'black-holes.org: Warped Spacetime'), (987, 'http://www.black-holes.org/relativity4.html'), (988, '2009-08-15 01:15:40'), (989, '2009-08-15 01:15:42'), (990, 'rel4'), (991, 'black-holes.org: Straight Lines and Geodesics'), (992, 'http://www.black-holes.org/relativity5.html'), (993, '2009-08-15 01:15:51'), (994, '2009-08-15 01:15:53'), (995, 'rel5'), (996, 'black-holes.org: Gravity and Warped Spacetime'), (997, 'http://www.black-holes.org/relativity6.html'), (998, '2009-08-15 01:16:08'), (999, '2009-08-15 01:16:10'), (1000, 'rel6'), (1001, 'black-holes.org: Gravitational Waves'), (1002, 'http://www.black-holes.org/gwa1.html'), (1003, '2009-08-15 01:17:22'), (1004, '2009-08-15 01:17:24'), (1005, 'gwa1'), (1006, 'black-holes.org: Sources of Gravitational Radiation'), (1007, 'http://www.black-holes.org/gwa2.html'), (1008, '2009-08-15 01:17:34'), (1009, '2009-08-15 01:17:36'), (1010, 'gwa2'), (1011, 'Recipes for Health - Baked Orzo With Tomatoes, Roasted Peppers and Zucchini - NYTimes.com'), (1012, 'http://www.nytimes.com/2009/08/13/health/nutrition/13recipehealth.html?em&pagewanted=all'), (1013, '2009-08-15 22:14:07'), (1014, '2009-08-15 22:14:09'), (1015, 'Baked Orzo'), (1016, '2009-08-31 18:22:59'), (1017, '2009-08-31 18:23:01'), (1018, 'Brunch: Baked Eggs'), (1019, 'Veggie Burgers and South Beach Diet - Veggie Burger Recipe and South Beach Diet'), (1020, 'http://www.southbeachdiet.com/sbd/publicsite/veggie-burger-recipe.aspx'), (1021, '2009-08-31 18:23:59'), (1022, '2009-08-31 18:24:01'), (1023, 'Veggie Burgers'), (1024, 'Steak and South Beach Diet - Steak Recipe and South Beach Diet'), (1025, 'http://www.southbeachdiet.com/sbd/publicsite/steak-recipe.aspx'), (1026, '2009-08-31 19:07:24'), (1027, '2009-08-31 19:07:26'), (1028, 'Carne Asada'), (1029, 'Blueberries and South Beach Diet - Blueberries Recipe and South Beach Diet'), (1030, 'http://www.southbeachdiet.com/sbd/publicsite/blueberry-recipe.aspx'), (1031, '2009-08-31 20:39:38'), (1032, '2009-08-31 20:39:40'), (1033, 'Blueberry Dessert'), (1034, 'Shrimp and South Beach Diet - Tropical Shrimp Recipe and South Beach Diet'), (1035, 'http://www.southbeachdiet.com/sbd/publicsite/tropical-shrimp-recipe.aspx'), (1036, '2009-08-31 20:45:00'), (1037, '2009-08-31 20:45:02'), (1038, 'Grilled Shrimp Salad'), (1039, 'Salad and South Beach Diet - Healthy Grilled Salad and South Beach Diet'), (1040, 'http://www.southbeachdiet.com/sbd/publicsite/grilled-salad-recipe.aspx'), (1041, '2009-09-01 14:16:18'), (1042, '2009-09-01 14:16:20'), (1043, 'Beef Salad'), (1044, '2009-09-01 15:03:29'), (1045, '2009-09-01 15:03:31'), (1046, 'Shrimp Salad'), (1047, 'Seafood and South Beach Diet - Seafood Recipe and South Beach Diet'), (1048, 'http://www.southbeachdiet.com/sbd/publicsite/seafood-recipe.aspx'), (1049, '2009-09-01 15:28:18'), (1050, '2009-09-01 15:28:20'), (1051, 'Mahi Mahi'), (1052, 'Bulgur Pilaf Recipe at Epicurious.com'), (1053, 'http://www.epicurious.com/recipes/food/views/Bulgur-Pilaf-233989'), (1054, '2009-09-01 17:27:00'), (1055, '2009-09-01 17:27:02'), (1056, 'Bulgur Pilaf'), (1057, 'Shrimp Appetizer and South Beach Diet - Healthy Shrimp Appetizer Recipe and South Beach Diet'), (1058, 'http://www.southbeachdiet.com/sbd/publicsite/healthy-appetizer-recipe.aspx'), (1059, '2009-09-15 15:49:49'), (1060, '2009-09-15 15:49:51'), (1061, 'Shrimp Appetizer'), (1062, 'Salad With Walnuts and South Beach Diet - Salad With Walnuts Recipe and South Beach Diet'), (1063, 'http://www.southbeachdiet.com/sbd/publicsite/salad-with-walnuts-recipe.aspx'), (1064, '2009-09-15 15:52:42'), (1065, '2009-09-15 15:52:44'), (1066, 'Endive and Walnut Salad'), (1067, 'Oatmeal and South Beach Diet - Oatmeal Pancake Recipe and South Beach Diet'), (1068, 'http://www.southbeachdiet.com/sbd/publicsite/hearty-oatmeal-recipe.aspx'), (1069, '2009-09-15 15:56:13'), (1070, '2009-09-15 15:56:15'), (1071, 'Oatmeal Pancakes'), (1072, 'Fractional differential forms'), (1073, '2001-05-00 May 00, 2001'), (1074, 'Journal of Mathematical Physics'), (1075, 'J. Math. Phys.'), (1076, 42), (1077, 5), (1078, '2203-2212'), (1079, 'http://link.aip.org.clsproxy.library.caltech.edu/link/?JMP/42/2203/1'), (1080, '10.1063/1.1364688'), (1081, '2009-09-17 23:41:04'), (1082, '2011-03-22 23:20:49'), (1083, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i6/e064003'), (1084, 'GetPDFServlet'), (1085, 'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000042000005002203000001&idtype=cvips&prog=normal'), (1086, '2009-09-17 23:41:52'), (1087, 'On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform'), (1088, 'Proceedings of the IEEE'), (1089, 66), (1090, 1), (1091, '51-83'), (1092, '1978-01-00 January, 1978'), (1093, 'http://www.fceia.unr.edu.ar/prodivoz/Harris_1978.pdf'), (1094, 'Harris_1978.pdf'), (1095, 'Simulations of Binary Black Hole Mergers Using Spectral Methods'), (1096, '2009-09-21 2009-09-21'), (1097, 'http://arxiv.org/abs/0909.3557'), (1098, '0909.3557'), (1099, 'Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code SpEC. These improvements include the use of a new damped-wave gauge condition, a new grid structure with appropriate filtering that improves stability, and better adaptivity in conforming the grid structures to the shapes and sizes of the black holes. Simulations illustrating the success of these new methods are presented for a variety of binary black-hole systems. These include fairly ``generic\'\' systems with unequal masses (up to 2:1 mass ratios), and spins (with magnitudes up to 0.4 M^2) pointing in various directions.'), (1100, '2009-09-22 05:42:34'), (1101, '2011-03-22 23:20:50'), (1102, '0909.3557 PDF'), (1103, 'http://www.arxiv.org/pdf/0909.3557.pdf'), (1104, '2009-09-22 05:42:44'), (1105, 'Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parameterized Post-Einsteinian Framework'), (1106, '2009-09-17 2009-09-17'), (1107, 'http://arxiv.org/abs/0909.3328'), (1108, '0909.3328'), (1109, 'We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid in the weak-field, as verified by precision experiments and observations, but it need not hold in the dynamical strong-field regime where tests are lacking. Fundamental bias can cause systematic errors in the detection and parameter estimation of signals, which can lead to a mischaracterization of the universe through incorrect inferences about source event rates and populations. We propose a remedy through the introduction of the parameterized post-Einsteinian framework, which consists of the enhancement of waveform templates via the inclusion of post-Einsteinian parameters. These parameters would ostensibly be designed to interpolate between templates constructed in general relativity and well-motivated alternative theories of gravity, and also include extrapolations that follow sound theoretical principles, such as consistency with conservation laws and symmetries. As an example, we construct parameterized post-Einsteinian templates for the binary coalescence of equal-mass, non-spinning compact objects in a quasi-circular inspiral. The parametrized post-Einsteinian framework should allow matched filtered data to select a specific set of post-Einsteinian parameters without a priori assuming the validity of the former, thus either verifying general relativity or pointing to possible dynamical strong-field deviations.'), (1110, '2009-09-22 05:57:10'), (1111, 'S59-S81'), (1112, '0909.3328 PDF'), (1113, 'http://www.arxiv.org/pdf/0909.3328.pdf'), (1114, '2009-09-22 05:57:14'), (1115, '"Complete" gravitational waveforms for black-hole binaries with non-precessing spins'), (1116, '2009-09-15 2009-09-15'), (1117, 'http://arxiv.org/abs/0909.2867'), (1118, '0909.2867'), (1119, 'We present the first analytical inspiral-merger-ringdown gravitational waveforms from black-hole (BH) binaries with non-precessing spins. By matching a post-Newtonian description of the inspiral to a set of numerical calculations performed in full general relativity, we obtain a waveform family with a conveniently small number of physical parameters. The physical content of these waveforms includes the "orbital hang-up" effect, when BHs are spinning rapidly along the direction of the orbital angular momentum. These waveforms will allow us to detect a larger parameter space of BH binary coalescence, to explore various scientific questions related to GW astronomy, and could dramatically improve the expected detection rates of GW detectors.'), (1120, '2009-09-22 06:00:00'), (1121, '10.1088/0264-9381/24/12/S06'), (1122, '0909.2867 PDF'), (1123, 'http://www.arxiv.org/pdf/0909.2867.pdf'), (1124, '2009-09-22 06:00:04'), (1125, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/24/12/S06/'), (1126, 'Reducing orbital eccentricity in binary black hole simulations'), (1127, '2011-03-23 00:04:21'), (1128, '0264-9381_24_12_S06.pdf'), (1129, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/24/12/S06/pdf/0264-9381_24_12_S06.pdf'), (1130, '2011-03-23 00:05:24'), (1131, "Astrophysically realistic black holes may have spins that are nearly extremal (i.e., close to 1 in dimensionless units). Numerical simulations of binary black holes are important tools both for calibrating analytical templates for gravitational-wave detection and for exploring the nonlinear dynamics of curved spacetime. However, all previous simulations of binary-black-hole inspiral, merger, and ringdown have been limited by an apparently insurmountable barrier: the merging holes' spins could not exceed 0.93, which is still a long way from the maximum possible value in terms of the physical effects of the spin. In this paper, we surpass this limit for the first time, opening the way to explore numerically the behavior of merging, nearly extremal black holes. Specifically, using an improved initial-data method suitable for binary black holes with nearly extremal spins, we simulate the inspiral (through 12.5 orbits), merger and ringdown of two equal-mass black holes with equal spins of magnitude 0.95 antialigned with the orbital angular momentum."), (1132, '2011-03-28 19:52:31'), (1133, '1010.2777 PDF'), (1134, 'http://www.arxiv.org/pdf/1010.2777.pdf'), (1135, '2011-03-28 19:52:35'), (1136, 'Indications of de Sitter Spacetime from Classical Sequential Growth Dynamics of Causal Sets'), (1137, '2009-09-25 2009-09-25'), (1138, 'http://arxiv.org/abs/0909.4771'), (1139, '0909.4771'), (1140, "A large class of the dynamical laws for causal sets described by a classical process of sequential growth yield a cyclic universe, whose cycles of expansion and contraction are punctuated by single `origin elements' of the causal set. We present evidence that the effective dynamics of the immediate future of one of these origin elements, within the context of the sequential growth dynamics, yields an initial period of de Sitter like exponential expansion, and argue that the resulting picture has many attractive features as a model of the early universe, with the potential to solve some of the standard model puzzles without any fine tuning."), (1141, '2009-09-28 17:45:14'), (1142, 'The uncertainty in hybrid gravitational waveforms: Optimizing initial orbital frequencies for binary black-hole simulations'), (1143, '0909.4771 PDF'), (1144, 'http://www.arxiv.org/pdf/0909.4771.pdf'), (1145, '2009-09-28 17:45:18'), (1146, 'The causal set approach to quantum gravity'), (1147, '2006-01-27 2006-01-27'), (1148, 'http://arxiv.org/abs/gr-qc/0601121'), (1149, 'gr-qc/0601121'), (1150, "The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The causal set is a discrete structure which avoids this problem and provides a possible history space on which to build a ``path integral'' type quantum gravity theory. Motivation, results and open problems are discussed and some comparisons to other approaches are made. Some recent progress on recovering locality in causal sets is recounted."), (1151, '2009-09-29 02:17:51'), (1152, 'gr-qc/0601121 PDF'), (1153, 'http://www.arxiv.org/pdf/gr-qc/0601121.pdf'), (1154, '2009-09-29 02:17:54'), (1155, 'Inferring population histories using cultural data'), (1156, '2009-11-07 November 07, 2009'), (1157, 'Proceedings of the Royal Society B: Biological Sciences'), (1158, '3835-3843'), (1159, 276), (1160, 1674), (1161, 'http://rspb.royalsocietypublishing.org.clsproxy.library.caltech.edu/content/276/1674/3835.abstract'), (1162, 'The question as to whether cultures evolve in a manner analogous to that of genetic evolution can be addressed by attempting to reconstruct population histories using cultural data. As others have argued, this can only succeed if cultures are isolated enough to maintain and pass on a central core of traditions that can be modified over time. In this study we used a set of cultural data (canoe design traits from Polynesia) to look for the kinds of patterns and relationships normally found in population genetic studies. After developing new techniques to accommodate the peculiarities of cultural data, we were able to infer an ancestral region (Fiji) and a sequence of cultural origins for these Polynesian societies. In addition, we found evidence of cultural exchange, migration and a serial founder effect. Results were stronger when analyses were based on functional traits (presumably subject to natural selection and convergence) rather than symbolic or stylistic traits (probably subject to cultural selection for rapid divergence). These patterns strongly suggest that cultural evolution, while clearly affected by cultural exchange, is also subject to some of the same processes and constraints as genetic evolution.'), (1163, '10.1098/rspb.2009.1088'), (1164, 'Highwire 2.0'), (1165, '2009-10-01 22:25:05'), (1166, "This article--summarizing the authors' then novel formulation of General Relativity--appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962, which is now long out of print. Intentionally unretouched, this posting is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed--but not section nor equation numbering etc. The authors' current institutional affiliations are encoded in: arnowitt@physics.tamu.edu, deser@brandeis.edu, misner@physics.umd.edu ."), (1167, '2009-11-04 00:10:09'), (1168, 'gr-qc/0405109 PDF'), (1169, '3835.full.pdf'), (1170, 'Higher-order spin effects in the dynamics of compact binaries. II. Radiation field'), (1171, 'The distribution of feline immunodeficiency virus in tissue compartments of feral domestic cats'), (1172, 'JessPaper.pdf'), (1173, 'http://www.arxiv.org/pdf/gr-qc/0405109.pdf'), (1174, '2009-11-04 00:10:13'), (1175, "Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions"), (1176, 1701), (1177, '1974-00-00 1974'), (1178, 'http://link.aps.org/abstract/PRD/v10/p1701'), (1179, '10.1103/PhysRevD.10.1701'), (1180, "The scalar, electromagnetic, and gravitational geodesic synchrotron radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. One finds that the spectral shape depends only weakly on the angular momentum parameter a / M of the black hole, but the total radiated power drops unexpectedly for a / M≳0.95 and vanishes for a / M→1. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape upon the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating there a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric optics approximation without requiring the use of vector or tensor spherical harmonics."), (1181, '2009-11-12 01:46:03'), (1182, 'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRD/v10/i6/p1701_1'), (1183, '2009-11-12 01:46:05'), (1184, '2009-12-21 2009/12/21'), (1185, '2007-05-31 2007-05-31'), (1186, '2009-11-16 21:11:06'), (1187, 476), (1188, 'http://etd.caltech.edu/etd/available/etd-05252007-143511/'), (1189, 'Topics in numerical relativity'), (1190, 'Topics in numerical relativity: The periodic standing-wave approximation, the stability of constraints in free evolution, and the spin of dynamical black holes'), (1191, 'thesis.pdf'), (1192, 'The relationship between monopole harmonics and spin-weighted spherical harmonics'), (1193, '1985-05-00 May 00, 1985'), (1194, '1030-1033'), (1195, 'http://link.aip.org/link/?JMP/26/1030/1'), (1196, '10.1063/1.526533'), (1197, '2009-11-20 17:53:10'), (1198, '2011-03-25 2011-03-25'), (1199, 'http://arxiv.org/abs/1103.5088'), (1200, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000026000005001030000001&idtype=cvips&prog=normal'), (1201, '2009-11-20 17:53:33'), (1202, 'Note on the Bondi-Metzner-Sachs Group'), (1203, '1966-05-00 May 00, 1966'), (1204, 7), (1205, '863-870'), (1206, 'http://link.aip.org/link/?JMP/7/863/1'), (1207, '10.1063/1.1931221'), (1208, '2009-11-20 17:53:57'), (1209, '1103.5088'), (1210, 'A general method is presented for estimating the uncertainty in hybrid models of gravitational waveforms from binary black-hole systems with arbitrary physical parameters, and thence the highest allowable initial orbital frequency for a numerical-relativity simulation such that the combined analytical and numerical waveform meets some minimum desired accuracy. The key strength of this estimate is that no prior numerical simulation in the relevant region of parameter space is needed. The method is demonstrated for a selection of extreme physical parameters. It is shown that optimal initial orbital frequencies depend roughly linearly on the mass of the binary, and therefore useful accuracy criteria must depend on the mass. The results indicate that accurate estimation of the parameters of stellar-mass black-hole binaries in Advanced LIGO data or calibration of waveforms for detection will require much longer numerical simulations than are currently available or more accurate post-Newtonian approximations -- or both -- especially for comparable-mass systems with high spin.'), (1211, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000007000005000863000001&idtype=cvips&prog=normal'), (1212, '2009-11-20 18:06:33'), (1213, 'Quasi-Local Mass and Angular Momentum in General Relativity'), (1214, '1967-11-00 November 00, 1967'), (1215, '2155-2161'), (1216, 'http://link.aip.org/link/?JMP/8/2155/1'), (1217, '10.1063/1.1705135'), (1218, '2009-11-20 18:06:46'), (1219, '2011-03-29 01:01:40'), (1220, 'The uncertainty in hybrid gravitational waveforms'), (1221, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000008000011002155000001&idtype=cvips&prog=normal'), (1222, '2009-11-20 18:07:02'), (1223, 'Spin-weighted spherical harmonics and electromagnetic multipole expansions'), (1224, '1977-02-00 February 00, 1977'), (1225, 'American Journal of Physics'), (1226, 'Am. J. Phys.'), (1227, 45), (1228, '173-178'), (1229, 'http://link.aip.org/link/?AJP/45/173/1'), (1230, '10.1119/1.10649'), (1231, '2009-11-21 19:54:05'), (1232, '1103.5088 PDF'), (1233, 'http://www.arxiv.org/pdf/1103.5088.pdf'), (1234, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000045000002000173000001&idtype=cvips&prog=normal'), (1235, '2009-11-21 19:54:18'), (1236, 'The American Mathematical Monthly'), (1237, 'The Mathematics of Physical Quantities: Part I: Mathematical Models for Measurement'), (1238, '00029890'), (1239, 'http://encompass.library.cornell.edu/cgi-bin/checkIP.cgi?access=gateway_standard%26url=http://www.jstor.org/stable/2315883'), (1240, '1968-02-00 Feb., 1968'), (1241, '115-138'), (1242, 'ArticleType: primary_article / Full publication date: Feb., 1968 / Copyright © 1968 Mathematical Association of America'), (1243, ''), (1244, '2009-11-25 23:55:52'), (1245, 'The Mathematics of Physical Quantities'), (1246, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2315883.pdf'), (1247, '2009-11-25 23:55:54'), (1248, 'Teukolsky equation and Penrose wave equation'), (1249, 1736), (1250, 'http://link.aps.org/abstract/PRD/v10/p1736'), (1251, '10.1103/PhysRevD.10.1736'), (1252, "It is shown that Teukolsky's equation can be derived from a second-order wave equation for the Riemann tensor. The derivation is done in a way that emphasizes the modern tensor-analysis content of the Newman-Penrose formalism."), (1253, '2009-12-10 03:51:57'), (1254, 'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRD/v10/i6/p1736_1'), (1255, '2009-12-10 03:51:59'), (1256, 'A spinor approach to general relativity'), (1257, 'Annals of Physics'), (1258, '171-201'), (1259, '1960-06-00 June 1960'), (1260, '0003-4916'), (1261, '10.1016/0003-4916(60)90021-X'), (1262, 'http://www.sciencedirect.com/science/article/B6WB1-4DDR40K-SY/2/84503f0ab2f22e744be648b59c160096'), (1263, 'A calculus for general relativity is developed in which the basic role of tensors is taken over by spinors. The Riemann-Christoffel tensor is written in a spinor form according to a scheme of Witten. It is shown that the curvature of empty space can be uniquely characterized by a totally symmetric four-index spinor which satisfies a first order equation formally identical with one for a zero rest-mass particle of spin two. However, the derivatives used here are covariant, so that on iteration, instead of the usual wave equation, a nonlinear "source" term appears. The case when a source-free electromagnetic field is present is also considered. (No quantization is attempted here.)\nThe "gravitational density" tensor of Robinson and Bel is obtained in a natural way as a striking analogy with the spinor expression for the Maxwell stress tensor in the electromagnetic case. It is shown that the curvature tensor determines four gravitational principal null directions associated with flow of "gravitational density", which supplement the two electromagnetic null directions of Synge. The invariants and Petrov type of the curvature tensor are analyzed in terms of these, and a natural classification of curvature tensors is given.\nAn essentially coordinate-free method is outlined, by which any analytic solution of Einstein\'s field equations may, in principle, be found. As an elementary example the gravitational and gravitational-electromagnetic plane wave solutions are obtained.'), (1264, 'ScienceDirect'), (1265, '2009-12-10 03:59:03'), (1266, 'ScienceDirect Full Text PDF'), (1267, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6WB1-4DDR40K-SY-1&_cdi=6697&_user=492137&_orig=search&_coverDate=06%2F30%2F1960&_sk=999899997&view=c&wchp=dGLzVlz-zSkzS&md5=c43354e46d2de8756cfa153dd2a9350c&ie=/sdarticle.pdf'), (1268, '2009-12-10 03:59:05'), (1269, 'Rotating Black Holes: Separable Wave Equations for Gravitational and Electromagnetic Perturbations'), (1270, 29), (1271, 1114), (1272, '1972-10-16 October 16, 1972'), (1273, 'http://link.aps.org/abstract/PRL/v29/p1114'), (1274, '10.1103/PhysRevLett.29.1114'), (1275, 'Separable wave equations with source terms are presented for electromagnetic and gravitational perturbations of an uncharged, rotating black hole. These equations describe the radiative field completely, and also part of the nonradiative field. Nontrivial, source-free, stationary perturbations are shown not to exist. The barrier integral governing synchrotron radiation from particles in circular orbits is shown to be the same as for scalar radiation. Future applications (stability of rotating black holes, "spin-down," superradiant scattering, floating orbits) are outlined.'), (1276, '2009-12-10 04:02:29'), (1277, 'Rotating Black Holes'), (1278, 'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRL/v29/i16/p1114_1'), (1279, '2009-12-10 04:02:31'), (1280, 'Perturbations of a Rotating Black Hole. I. Fundamental Equations for Gravitational, Electromagnetic, and Neutrino-Field Perturbations'), (1281, 'Astrophysical Journal'), (1282, 185), (1283, '1973-10-01 October 1, 1973'), (1284, '635-648'), (1285, 'http://adsabs.harvard.edu/abs/1973ApJ...185..635T'), (1286, 'Abstract image available at:\nhttp://adsabs.harvard.edu/abs/1973ApJ...185..635T'), (1287, 'NASA ADS'), (1288, '2009-12-10 04:10:21'), (1289, '2011-03-29 01:01:54'), (1290, 'kalmus_sxs.pdf'), (1291, 'http://articles.adsabs.harvard.edu.proxy.library.cornell.edu/cgi-bin/nph-iarticle_query?1973ApJ...185..635T&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf'), (1292, '2009-12-10 04:10:43'), (1293, '2009-12-15 December 15, 2009'), (1294, 80), (1295, '124045-14'), (1296, 'http://link.aps.org/abstract/PRD/v80/e124045'), (1297, '10.1103/PhysRevD.80.124045'), (1298, '2009-12-29 17:39:59'), (1299, '2011-03-23 March 23, 2011'), (1300, 'Selected Slices of LIGO'), (1301, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000080000012124045000001&idtype=cvips&prog=normal'), (1302, '2009-12-29 17:42:27'), (1303, 'Searching for Gravitational Radiation from Binary Black Hole MACHOs in the Galactic Halo'), (1304, '2007-05-10 2007-05-10'), (1305, 'http://arxiv.org/abs/0705.1514'), (1306, 'PhD Thesis, University of Wisconsin-Milwaukee, 2004'), (1307, 'Class. Quantum Grav. 30 (2013) 075017'), (1308, "The Laser Interferometer Gravitational Wave Observatory (LIGO) is one of a new generation of detectors of gravitational radiation. The existence of gravitational radiation was first predicted by Einstein in 1916, however gravitational waves have not yet been directly observed. One source of gravitation radiation is binary inspiral. Two compact bodies orbiting each other, such as a pair of black holes, lose energy to gravitational radiation. As the system loses energy the bodies spiral towards each other. This causes their orbital speed and the amount of gravitational radiation to increase, producing a characteristic ``chirp'' waveform in the LIGO sensitive band. In this thesis, matched filtering of LIGO science data is used to search for low mass binary systems in the halo of dark matter surrounding the Milky Way. Observations of gravitational microlensing events of stars in the Large Magellanic Cloud suggest that some fraction of the dark matter in the halo may be in the form of Massive Astrophysical Compact Halo Objects (MACHOs). It has been proposed that low mass black holes formed in the early universe may be a component of the MACHO population; some fraction of these black hole MACHOs will be in binary systems and detectable by LIGO. The inspiral from a MACHO binary composed of two 0.5 solar mass black holes enters the LIGO sensitive band around 40 Hz. The chirp signal increases in amplitude and frequency, sweeping through the sensitive band to 4400 Hz in 140 seconds. By using evidence from microlensing events and theoretical predictions of the population an upper limit is placed on the rate of black hole MACHO inspirals in the galactic halo."), (1309, '2010-01-27 16:01:53'), (1310, '0705.1514 PDF'), (1311, 'http://www.arxiv.org/pdf/0705.1514.pdf'), (1312, '2010-01-27 16:01:58'), (1313, 'Archives of Virology'), (1314, 'http://dx.doi.org/10.1007/s00705-010-0598-z'), (1315, '10.1007/s00705-010-0598-z'), (1316, 'SpringerLink'), (1317, 'Physics Today'), (1318, 'Copyright (C) 2010 The American Physical Society; Please report any problems to prola@aps.org'), (1319, 'Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order'), (1320, 54), (1321, 'fulltext.pdf'), (1322, 'http://www.springerlink.com.proxy.library.cornell.edu/content/x2h84m0286018747/fulltext.pdf'), (1323, '2010-02-01 01:14:14'), (1324, 4813), (1325, '1996-10-15 October 15, 1996'), (1326, 'http://link.aps.org/doi/10.1103/PhysRevD.54.4813'), (1327, '10.1103/PhysRevD.54.4813'), (1328, 'We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order (O[(v/c)4]=O[(Gm/rc2)2]) beyond the lowest-order quadrupole approximation. We cast the Einstein equations into the form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve it formally as a retarded integral over the past null cone of the chosen field point. The part of this integral that involves the matter sources and the near-zone gravitational field is evaluated in terms of multipole moments using standard techniques; the remainder of the retarded integral, extending over the radiation zone, is evaluated in a novel way. The result is a manifestly convergent and finite procedure for calculating gravitational radiation to arbitrary orders in a post-Newtonian expansion. Through second post-Newtonian order, the radiation is also shown to propagate toward the observer along true null rays of the asymptotically Schwarzschild spacetime, despite having been derived using flat-spacetime wave equations. The method cures defects that plagued previous "brute-force" slow-motion approaches to the generation of gravitational radiation, and yields results that agree perfectly with those recently obtained by a mixed post-Minkowskian post-Newtonian method. We display explicit formulas for the gravitational waveform and the energy flux for two-body systems, both in arbitrary orbits and in circular orbits. In an appendix, we extend the formalism to bodies with finite spatial extent, and derive the spin corrections to the waveform and energy loss.'), (1329, 'APS'), (1330, '2010-02-07 06:56:57'), (1331, 'Gravitational radiation from compact binary systems'), (1332, 'APS Full Text PDF'), (1333, 'SXS video conference'), (1334, '00319228'), (1335, 'p4813_1.pdf'), (1336, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v54/i8/p4813_1'), (1337, '2010-02-07 06:58:26'), (1338, "Gravitational waves from merging compact binaries: How accurately can one extract the binary's parameters from the inspiral waveform?"), (1339, 49), (1340, 2658), (1341, '1994-03-15 March 15, 1994'), (1342, 'http://link.aps.org/doi/10.1103/PhysRevD.49.2658'), (1343, '10.1103/PhysRevD.49.2658'), (1344, 'The most promising source of gravitational waves for the planned kilometer-size laser-interferometer detectors LIGO and VIRGO are merging compact binaries, i.e., neutron-star–neutron-star (NS-NS), neutron-star–black-hole (NS-BH), and black-hole–black-hole (BH-BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the inspiral gravitational wave signals by the three-detector LIGO-VIRGO network using ‘‘advanced detectors’’ (those present a few years after initial operation). The large number of cycles in the observable waveform increases our sensitivity to those parameters that affect the inspiral rate, and thereby the evolution of the waveform’s phase. These parameters are thus measured much more accurately than parameters which affect the waveform’s polarization or amplitude. To lowest order in a post-Newtonian expansion, the evolution of the waveform’s phase depends only on the combination scrM≡(M1M2)3/5(M1+M2)-1/5 of the masses M1 and M2 of the two bodies, which is known as the ‘‘chirp mass.’’ To post-1-Newtonian order, the waveform’s phase also depends sensitively on the binary’s reduced mass μ≡M1M2/(M1+M2) allowing, in principle, a measurement of both M1 and M2 with high accuracy.'), (1345, '10.1063/1.882861'), (1346, 'Gravitational waves from merging compact binaries'), (1347, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v49/i6/p2658_1'), (1348, '2010-02-07 07:05:23'), (1349, '084020'), (1350, '2009-12-17 2009-12-17'), (1351, '10.1088/0264-9381/27/8/084020'), (1352, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/27/8/084020'), (1353, '2011-03-29 17:46:21'), (1354, 'Amazing Whole Wheat Pizza Crust Recipe - Allrecipes.com'), (1355, 'http://allrecipes.com//Recipe/amazing-whole-wheat-pizza-crust/Detail.aspx'), (1356, '2011-03-29 22:43:19'), (1357, '2011-03-29 22:43:32'), (1358, 74), (1359, 'The Astrophysical Journal Letters'), (1360, 711), (1361, 'L138-L142'), (1362, 'http://stacks.iop.org/2041-8205/711/L138'), (1363, '2010-00-00 2010'), (1364, 'HM Cancri is a candidate ultracompact binary white dwarf with an apparent orbital period of only 5.4 minutes, as suggested by X-ray and optical light-curve modulations on that period, and by the absence of longer-period variability. In this Letter, we present Keck-I spectroscopy which shows clear modulation of the helium emission lines in both radial velocity and amplitude on the 5.4 minute period and no other. The data strongly suggest that the binary is emitting He I 4471 from the irradiated face of the cooler, less massive star, and He II 4686 from a ring around the more massive star. From their relative radial velocities, we measure a mass ratio q = 0.50 +- 0.13. We conclude that the observed 5.4 minute period almost certainly represents the orbital period of an interacting binary white dwarf. We thus confirm that HM Cnc is the shortest period binary star known: a unique test for stellar evolution theory, and one of the strongest known sources of gravitational waves for LISA.'), (1365, 'Spectroscopic Evidence for a 5.4 Minute Orbital Period in HM Cancri'), (1366, 'apjl_711_2_138.pdf'), (1367, 'http://www.iop.org.proxy.library.cornell.edu/EJ/article/2041-8205/711/2/L138/apjl_711_2_138.pdf'), (1368, '2010-03-10 02:47:00'), (1369, 'Seeing and Believing: Detection, Measurement, and Inference in Experimental Physics'), (1370, 'lecture_7.pdf'), (1371, 'Gravitationally collapsed objects of very low mass'), (1372, 'Monthly Notices of the Royal Astronomical Society'), (1373, 152), (1374, '1971-00-00 1971'), (1375, 'http://adsabs.harvard.edu/abs/1971MNRAS.152...75H'), (1376, 'Abstract image available at:\nhttp://adsabs.harvard.edu/abs/1971MNRAS.152...75H'), (1377, '2010-03-16 14:51:48'), (1378, 'coleman.pdf'), (1379, 'http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1971MNRAS.152...75H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf'), (1380, '2010-03-16 14:52:11'), (1381, 104034), (1382, 'http://www.springerlink.com.proxy.library.cornell.edu/content/q0641644m2132200/'), (1383, '2010-03-16 15:38:26'), (1384, 'Black holes in cosmic bodies'), (1385, "Possible manifestations of small mass black holes (M BH<M odot) in cosmic bodies (stars, millisecond pulsars, planets, etc.) are considered. The formation of millisecond pulsars in the early proposed pulsar's model goes onto a small black hole in the centre due to accretion of neutron star matter. Within the framework of a model under consideration, the following is predicted: millisecond pulsars withP\n\nmin=0.5 ms, single optical and X-ray pulsars with the negative derivative derivative of period. Small black holes can be applied to make models of anomalies in planetary bodies (gravitational, heat, etc.). The lsquovulcanrsquo model with radiation of a microblack hole in a magnetic void (M BHsim1015 g) as the source of energy is considered. At the Earth's surface, near a vulcan, the neutrino flow from a microblack hole is estimated."), (1386, '2011-04-25 2011-04-25'), (1387, 'http://arxiv.org/abs/1104.4751'), (1388, 'A possible capture process for the solar central black hole'), (1389, 'Astronomy and Astrophysics'), (1390, 99), (1391, '1981-06-01 June 1, 1981'), (1392, '31-35'), (1393, 'http://adsabs.harvard.edu/abs/1981A%26A....99...31P'), (1394, 'Clayton et al. (1975) have proposed the existence of a small\n(approximately 0.000015 solar masses) black hole in the center of the\nsun. Their proposal is related to an attempt to account for the\ndiscrepancy between the predicted capture rate of solar neutrinos on the\nbasis of standard solar models and the capture rate actually measured.\nAn investigation is conducted regarding the possibility of a capture of\na primordial black hole, which happens to fall on the sun, by the\nmechanism of gravitational braking. Attention is given to questions of\nproblem formulation, the asymptotic orbital parameters, the law of the\nretarding force, the accretion of mass, the times required for capture\nand accretion, and the lower mass limit. It is found that, in connection\nwith the absolute lower limit obtained for the mass of the black hole,\nthe possibility of a gravitational capture of a black hole in the sun\ncannot be excluded.'), (1395, '2010-03-16 15:40:28'), (1396, "Notes from Sidney Coleman's Physics 253a"), (1397, 'http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1981A%26A....99...31P&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf'), (1398, '2010-03-16 15:40:44'), (1399, '2006-11-29 November 29, 2006'), (1400, 'http://www.springerlink.com.proxy.library.cornell.edu/content/rr6lw3j81638m34k/'), (1401, '2010-03-16 15:48:14'), (1402, 'Mini-blackhole at the Solar Center and Isotopic Abundances in the Primitive Solar Nebula'), (1403, 'http://www.springerlink.com.proxy.library.cornell.edu/content/u4p4882856l67mp8/'), (1404, '2010-03-16 15:49:05'), (1405, 'Conventional nuclear physics solution of the solar neutrino problem'), (1406, 'A basic and inherently simple alternative explanation of the solar neutrino problem is proposed based upon conventional nuclear physics. Our results for the tunneling factor, astrophysicalS-factor, and our resolution are compared with rather speculative solutions commonly attempted by accepting the customary ingredients of the standard solar model. We present a more realistic solution of nuclear Coulomb barrier tunneling together with a more precise parametric representation of the astrophysical functionS. We determineS from high-energy (>100 keV)7Be(p, gamma)8B experimental cross-section data using the new tunneling factor. This leads to a low-energy fusion cross section that is lower than previous estimates by sim26–36%, decreasing the anticipated neutrino flux close to experimentally detected values. This may resolve the missing solar neutrino flux problem.'), (1407, '0004-637X'), (1408, 'The Astrophysical Journal'), (1409, 'ApJ'), (1410, 201), (1411, '1975-00-10 10/1975'), (1412, 489), (1413, '10.1086/153910'), (1414, 'http://adsabs.harvard.edu//abs/1975ApJ...201..489C'), (1415, 'Solar models of low neutrino-counting rate - The central black hole'), (1416, 'CrossRef'), (1417, '2010-03-16 15:51:58'), (1418, 'http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1975ApJ...201..489C&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf'), (1419, '2010-03-16 15:52:03'), (1420, 'High energy neutrino astronomy'), (1421, 'Nuclear Physics B - Proceedings Supplements'), (1422, 87), (1423, '1-3'), (1424, '377-386'), (1425, '2000-06-00 June 2000'), (1426, '0920-5632'), (1427, '10.1016/S0920-5632(00)00700-3'), (1428, 'http://www.sciencedirect.com/science/article/B6TVD-40GJKJ0-2S/2/8913ed621dacaee2749de7ab4b60602e'), (1429, 'The sky survey with high energy neutrinos is complementary to the survey with photons. The method of the detection of [nu][mu] is described and the expected sensitivity to high energy neutrino sources with a kilometer-scale detector is estimated. The status of the current under-water(ice) detector projects is reported.'), (1430, '2010-03-16 15:54:12'), (1431, 'http://link.aps.org/doi/10.1103/PhysRevD.74.104034'), (1432, '10.1103/PhysRevD.74.104034'), (1433, 'Using full information when computing modes of post-Newtonian waveforms from inspiralling compact binaries in circular orbit'), (1434, 'http://www.springerlink.com.proxy.library.cornell.edu/content/t43118767q08351k/'), (1435, '2010-03-16 15:54:43'), (1436, 'The Energy Source of the Sun'), (1437, 'Motivated by the search for gravitational waves emitted by binary black holes, we investigate the gravitational radiation field of point particles with spins within the framework of the multipolar-post-Newtonian wave generation formalism. We compute: (i) the spin-orbit (SO) coupling effects in the binary’s mass and current quadrupole moments one post-Newtonian (1PN) order beyond the dominant effect, (ii) the SO contributions in the gravitational-wave energy flux, and (iii) the secular evolution of the binary’s orbital phase up to 2.5PN order. Crucial ingredients for obtaining the 2.5PN contribution in the orbital phase are the binary’s energy and the spin-precession equations, derived in paper I of this series. These results provide more accurate gravitational-wave templates to be used in the data analysis of rapidly rotating Kerr-type black-hole binaries with the ground-based detectors LIGO, Virgo, GEO 600, and TAMA300, and the space-based detector LISA.'), (1438, '2010-03-26 15:47:11'), (1439, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104034'), (1440, '2010-03-26 15:47:13'), (1441, 'Erratum: Higher-order spin effects in the dynamics of compact binaries. II. Radiation field [Phys. Rev. D 74, 104034 (2006)]'), (1442, '049903'), (1443, '2007-02-12 February 12, 2007'), (1444, 'http://link.aps.org/doi/10.1103/PhysRevD.75.049903'), (1445, '10.1103/PhysRevD.75.049903'), (1446, '2010-03-26 15:48:05'), (1447, 'Erratum'), (1448, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v75/i4/e049903'), (1449, '2010-03-26 15:48:07'), (1450, 'Edth-a Differential Operator on the Sphere'), (1451, 'Mathematical Proceedings of the Cambridge Philosophical Society'), (1452, '317-330'), (1453, 92), (1454, '02'), (1455, '10.1017/S0305004100059971'), (1456, '044016'), (1457, "Introduction. In (9) Newman and Penrose introduced a differential operator which they denoted ð, the phonetic symbol edth. This operator acts on spin weighted, or spin and conformally weighted functions on the two-sphere. It turns out to be very useful in the theory of relativity via the isomorphism of the conformal group of the sphere and the proper inhomogeneous Lorentz group (11, 4). In particular, it can be viewed (2) as an angular momentum lowering operator for a suitable representation of SO(3) and can be used to investigate the representations of the Lorentz group (4). More recently, edth has appeared in the good cut equation describing Newman's -space for an asymptotically flat space-time (10). This development is closely related to Penrose's theory of twistors and, in particular, to asymptotic twistors (14)."), (1458, 'Cambridge Journals Online'), (1459, '2010-03-26 21:46:26'), (1460, 'http://journals.cambridge.org/action/displayAbstract?aid=2086504'), (1461, 'download.pdf'), (1462, 'A tapering window for time-domain templates and simulated signals in the detection of gravitational waves from coalescing compact binaries'), (1463, 'http://physicstoday.org/resource/1/phtoad/v52/i10/p44_s1?isAuthorized=no'), (1464, 'LIGO and the Detection of Gravitational Waves'), (1465, '2011-10-11 20:01:38'), (1466, 'PTO000044.pdf'), (1467, '2008-06-07 2008-06-07'), (1468, '1003.2939 PDF'), (1469, 'http://www.arxiv.org/pdf/1003.2939.pdf'), (1470, '2010-03-27 01:10:29'), (1471, 'The gravitational-wave memory effect'), (1472, '2010-03-17 2010-03-17'), (1473, 'http://arxiv.org/abs/1003.3486'), (1474, '1003.3486'), (1475, 'The nonlinear memory effect is a slowly-growing, non-oscillatory contribution to the gravitational-wave amplitude. It originates from gravitational waves that are sourced by the previously emitted waves. In an ideal gravitational-wave interferometer a gravitational-wave with memory causes a permanent displacement of the test masses that persists after the wave has passed. Surprisingly, the nonlinear memory affects the signal amplitude starting at leading (Newtonian-quadrupole) order. Despite this fact, the nonlinear memory is not easily extracted from current numerical relativity simulations. After reviewing the linear and nonlinear memory I summarize some recent work, including: (1) computations of the memory contribution to the inspiral waveform amplitude (thus completing the waveform to third post-Newtonian order); (2) the first calculations of the nonlinear memory that include all phases of binary black hole coalescence (inspiral, merger, ringdown); and (3) realistic estimates of the detectability of the memory with LISA.'), (1476, '2010-03-27 01:13:35'), (1477, '1003.3486 PDF'), (1478, 'http://www.arxiv.org/pdf/1003.3486.pdf'), (1479, '2010-03-27 01:13:38'), (1480, 114041), (1481, '10.1088/0264-9381/25/11/114041'), (1482, 'http://iopscience.iop.org/0264-9381/25/11/114041'), (1483, 'Status of the LIGO detectors'), (1484, 'We present an up-to-date, comprehensive summary of the rates for all types of compact binary coalescence sources detectable by the Initial and Advanced versions of the ground-based gravitational-wave detectors LIGO and Virgo. Astrophysical estimates for compact-binary coalescence rates depend on a number of assumptions and unknown model parameters, and are still uncertain. The most confident among these estimates are the rate predictions for coalescing binary neutron stars which are based on extrapolations from observed binary pulsars in our Galaxy. These yield a likely coalescence rate of 100 per Myr per Milky Way Equivalent Galaxy (MWEG), although the rate could plausibly range from 1 per Myr per MWEG to 1000 per Myr per MWEG. We convert coalescence rates into detection rates based on data from the LIGO S5 and Virgo VSR2 science runs and projected sensitivities for our Advanced detectors. Using the detector sensitivities derived from these data, we find a likely detection rate of 0.02 per year for Initial LIGO-Virgo interferometers, with a plausible range between 0.0002 and 0.2 per year. The likely binary neutron-star detection rate for the Advanced LIGO-Virgo network increases to 40 events per year, with a range between 0.4 and 400 per year.'), (1485, '2011-10-11 20:05:48'), (1486, '1003.2480 PDF'), (1487, 'http://www.arxiv.org/pdf/1003.2480.pdf'), (1488, '2010-03-27 01:32:54'), (1489, 'Data formats for numerical relativity waves'), (1490, '2007-09-02 2007-09-02'), (1491, 'http://arxiv.org/abs/0709.0093'), (1492, '0709.0093'), (1493, '1104.4751'), (1494, 'We present a new numerical relativity code designed for simulations of compact binaries involving matter. The code is an upgrade of the BAM code to include general relativistic hydrodynamics and implements state-of-the-art high-resolution-shock-capturing schemes on a hierarchy of mesh refined Cartesian grids with moving boxes. We test and validate the code in a series of standard experiments involving single neutron star spacetimes. We present test evolutions of quasi-equilibrium equal-mass irrotational binary neutron star configurations in quasi-circular orbits which describe the late inspiral to merger phases. Neutron star matter is modeled as a zero-temperature fluid; thermal effects can be included by means of a simple ideal-gas prescription. We analyze the impact that the use of different values of damping parameter in the Gamma-driver shift condition has on the dynamics of the system. The use of different reconstruction schemes and their impact in the post-merger dynamics is investigated. We compute and characterize the gravitational radiation emitted by the system. Self-convergence of the waves is tested, and we consistently estimate error-bars on the numerically generated waveforms in the inspiral phase.'), (1495, '0709.0093 PDF'), (1496, 'http://www.arxiv.org/pdf/0709.0093.pdf'), (1497, '2011-04-26 15:23:19'), (1498, 'Higher-order spin effects in the dynamics of compact binaries. I. Equations of motion'), (1499, 104033), (1500, 'http://link.aps.org/doi/10.1103/PhysRevD.74.104033'), (1501, '10.1103/PhysRevD.74.104033'), (1502, 'We derive the equations of motion of spinning compact binaries including the spin-orbit (SO) coupling terms one post-Newtonian (PN) order beyond the leading-order effect. For black holes maximally spinning this corresponds to 2.5PN order. Our result for the equations of motion essentially confirms the previous result by Tagoshi, Ohashi, and Owen. We also compute the spin-orbit effects up to 2.5PN order in the conserved (Noetherian) integrals of motion, namely, the energy, the total angular momentum, the linear momentum, and the center-of-mass integral. We obtain the spin precession equations at 1PN order beyond the leading term, as well. Those results will be used in a future paper to derive the time evolution of the binary orbital phase, providing more accurate templates for LIGO-Virgo-LISA–type interferometric detectors.'), (1503, '2010-03-31 16:58:16'), (1504, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104033'), (1505, '2010-03-31 16:58:18'), (1506, 'Interaction of gravitational waves with matter'), (1507, 'Pittsburgh, PA, USA'), (1508, '2011-10-03 2011-10-03'), (1509, '2006-10-07 2006-10-07'), (1510, 'S635-S642'), (1511, '10.1088/0264-9381/23/19/S01'), (1512, '2010-04-01 13:35:20'), (1513, 'International Symposium on Time-Frequency and Time-Scale Analysis'), (1514, '024003'), (1515, '2009-01-07 January 07, 2009'), (1516, 'The first spectral numerical simulations of 16 orbits, merger, and ringdown of an equal-mass nonspinning binary black hole system are presented. Gravitational waveforms from these simulations have accumulated numerical phase errors through ringdown of ≲0.1 radian when measured from the beginning of the simulation, and ≲0.02 radian when waveforms are time and phase shifted to agree at the peak amplitude. The waveform seen by an observer at infinity is determined from waveforms computed at finite radii by an extrapolation process accurate to ≲0.01 radian in phase. The phase difference between this waveform at infinity and the waveform measured at a finite radius of r=100M is about half a radian. The ratio of final mass to initial mass is Mf/M=0.951 62±0.000 02, and the final black hole spin is Sf/Mf2=0.686 46±0.000 04.'), (1517, '2010-04-14 15:16:29'), (1518, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i2/e024003'), (1519, '2010-04-14 15:16:30'), (1520, 'Gravitational memory in binary black hole mergers'), (1521, '2010-04-23 2010-04-23'), (1522, 'http://arxiv.org/abs/1004.4209'), (1523, '1004.4209'), (1524, 'In addition to the dominant oscillatory gravitational wave signals produced during binary inspirals, a non-oscillatory component arises from the nonlinear "memory" effect, sourced by the emitted gravitational radiation. The memory grows significantly during the late inspiral and merger, modifying the signal by an almost step-function profile, and making it difficult to model by approximate methods. We use numerical evolutions of binary black holes to evaluate the nonlinear memory during late-inspiral, merger and ringdown. We identify two main components of the signal: the monotonically growing portion corresponding to the memory, and an oscillatory part which sets in roughly at the time of merger and is due to the black hole ringdown. Counter-intuitively, the ringdown is most prominent for models with the lowest total spin. Thus, the case of maximally spinning black holes anti-aligned to the orbital angular momentum exhibits the highest signal-to-noise (SNR) for interferometric detectors. The largest memory offset, however, occurs for highly spinning black holes, with an estimated value of h^tot_20 \\approx 0.24 in the maximally spinning case. These results are central to determining the detectability of nonlinear memory through pulsar timing array measurements.'), (1525, '2010-04-26 18:41:14'), (1526, '1004.4209 PDF'), (1527, 'http://www.arxiv.org/pdf/1004.4209.pdf'), (1528, '2010-04-26 18:41:17'), (1529, 'Topos Methods in the Foundations of Physics'), (1530, '2010-04-20 2010-04-20'), (1531, 'http://arxiv.org/abs/1004.3564'), (1532, '1004.3564'), (1533, 'This article gives a conceptual introduction to the topos approach to the formulation of physical theories.'), (1534, '2010-04-26 18:43:48'), (1535, '1004.3564 PDF'), (1536, 'http://www.arxiv.org/pdf/1004.3564.pdf'), (1537, '2010-04-26 18:43:51'), (1538, 'Determining the Hubble constant from gravitational wave observations'), (1539, 'Nature'), (1540, '1986-00-00 1986'), (1541, 323), (1542, 6086), (1543, '310-311'), (1544, 'http://dx.doi.org/10.1038/323310a0'), (1545, '10.1038/323310a0'), (1546, '2010-06-04 21:24:30'), (1547, 'Nature Full Text PDF'), (1548, 'http://www.nature.com/nature/journal/v323/n6086/pdf/323310a0.pdf'), (1549, '2010-06-04 21:24:32'), (1550, 'Possibility of Direct Measurement of the Acceleration of the Universe Using 0.1 Hz Band Laser Interferometer Gravitational Wave Antenna in Space'), (1551, 221103), (1552, '2001-11-09 November 09, 2001'), (1553, 'http://link.aps.org/doi/10.1103/PhysRevLett.87.221103'), (1554, '10.1103/PhysRevLett.87.221103'), (1555, 'It may be possible to construct a laser interferometer gravitational wave antenna in space with hrms∼10-27 at f∼0.1Hz in this century. Using this antenna, (1) typically 105 chirp signals of coalescing binary neutron stars per year may be detected with S/N∼104; (2) we can directly measure the acceleration of the universe by a 10 yr observation of binary neutron stars; and (3) the stochastic gravitational waves of ΩGW≳10-20 predicted by the inflation may be detected by correlation analysis. Our formula for phase shift due to accelerating motion might be applied for binary sources of LISA.'), (1556, '2010-06-04 21:25:25'), (1557, 'http://prl.aps.org/pdf/PRL/v87/i22/e221103'), (1558, '2010-06-04 21:25:27'), (1559, 629), (1560, '2005-00-08 08/2005'), (1561, '15-22'), (1562, '10.1086/431341'), (1563, 'http://iopscience.iop.org/0004-637X/629/1/15'), (1564, 'Using Gravitational‐Wave Standard Sirens'), (1565, '2010-06-04 21:26:28'), (1566, '1104.4751 PDF'), (1567, 'http://www.arxiv.org/pdf/1104.4751.pdf'), (1568, '2011-04-26 15:23:30'), (1569, '0004-637X_629_1_15.pdf'), (1570, 'A Derivation of Special Relativity from Causal Sets'), (1571, '2010-05-23 2010-05-23'), (1572, 'http://arxiv.org/abs/1005.4172'), (1573, '1005.4172'), (1574, 'We present a novel derivation of special relativity based on the information physics of events comprising a causal set. We postulate that events are fundamental, and that some events have the potential to receive information about other events, but not vice versa. This leads to the concept of a partially-ordered set of events, which is called a causal set. Quantification proceeds by selecting two chains of coordinated events, each of which represents an observer, and assigning a valuation to each chain. Events can be projected onto each chain by identifying the earliest event on the chain that can be informed about the event. In this way, each event can be quantified by a pair of numbers, referred to a pair, that derives from the valuations on the chains. Pairs can be decomposed into a sum of symmetric and antisymmetric pairs, which correspond to time-like and space-like coordinates. From this pair, we derive a scalar measure and show that this is the Minkowski metric. The Lorentz transformations follow, as well as the fact that speed is a relevant quantity relating two inertial frames, and that there exists a maximal speed, which is invariant in all inertial frames. All results follow directly from the Event Postulate and the adopted quantification scheme.'), (1575, '2010-06-04 21:49:23'), (1576, '1005.4172 PDF'), (1577, 'http://www.arxiv.org/pdf/1005.4172.pdf'), (1578, '2010-06-04 21:49:26'), (1579, 'Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries'), (1580, '2010-05-18 2010-05-18'), (1581, 'http://arxiv.org/abs/1005.3306'), (1582, '1005.3306'), (1583, 'We present a new phenomenological gravitational waveform model for the inspiral and coalescence of non-precessing spinning black hole binaries. Our approach is based on a frequency domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near the merger. An analytical formula for the dominant mode of the gravitational radiation of non-precessing black hole binaries is presented that captures the phenomenology of the hybrid waveforms. Its implementation in the current searches for gravitational waves should allow cross-checks of other inspiral-merger-ringdown waveform families and improve the reach of gravitational wave searches.'), (1584, '2010-06-04 22:05:57'), (1585, 'Matching post-Newtonian and numerical relativity waveforms'), (1586, '1005.3306 PDF'), (1587, 'http://www.arxiv.org/pdf/1005.3306.pdf'), (1588, '2010-06-04 22:06:00'), (1589, 'Possible use of self-calibration to reduce systematic uncertainties in determining distance-redshift relation via gravitational radiation from merging binaries'), (1590, '2010-05-25 2010-05-25'), (1591, 'http://arxiv.org/abs/1005.4489'), (1592, '1005.4489'), (1593, 'By observing mergers of compact objects, future gravity wave experiments would measure the luminosity distance to a large number of sources to a high precision but not their redshifts. Given the directional sensitivity of an experiment, a fraction of such sources (gold plated -- GP) can be identified optically as single objects in the direction of the source. We show that if an approximate distance-redshift relation is known then it is possible to statistically resolve those sources that have multiple galaxies in the beam. We study the feasibility of using gold plated sources to iteratively resolve the unresolved sources, obtain the self-calibrated best possible distance-redshift relation and provide an analytical expression for the accuracy achievable. We derive lower limit on the total number of sources that is needed to achieve this accuracy through self-calibration. We show that this limit depends exponentially on the beam width and give estimates for various experimental parameters representative of future gravitational wave experiments DECIGO and BBO.'), (1594, '2010-06-08 13:35:44'), (1595, '1005.4489 PDF'), (1596, 'http://www.arxiv.org/pdf/1005.4489.pdf'), (1597, '2010-06-08 13:35:47'), (1598, 'Observing gravitational wave bursts in pulsar timing measurements'), (1599, 'http://iopscience.iop.org/0264-9381/23/19/S01'), (1600, 'The Virgo status'), (1601, '2011-10-11 20:08:41'), (1602, 'http://arxiv.org/abs/1110.0408'), (1603, 'arXiv:1110.0408'), (1604, 'http://link.aps.org/doi/10.1103/PhysRevD.72.083005'), (1605, 'We develop a unified formalism for describing the interaction of gravitational waves with matter that clearly separates the effects of general relativity from those due to interactions in the matter. Using it, we derive a general expression for the dispersion of gravitational waves in matter in terms of correlation functions for the matter in flat spacetime. The self energy of a gravitational wave is shown to have contributions analogous to the paramagnetic and diamagnetic contributions to the self energy of an electromagnetic wave. We apply the formalism to some simple systems - free particles, an interacting scalar field, and a fermionic superfluid.'), (1606, '0909.0742 PDF'), (1607, 'http://www.arxiv.org/pdf/0909.0742.pdf'), (1608, '2010-06-26 16:28:07'), (1609, 402), (1610, '417-423'), (1611, 'http://dx.doi.org/10.1111/j.1365-2966.2009.15887.x'), (1612, 'We propose a novel method for observing the gravitational wave signature of supermassive black hole (SMBH) mergers. This method is based on the detection of a specific type of gravitational waves, namely gravitational wave burst with memory (BWM), using pulsar timing. We study the unique signature produced by BWM in anomalous pulsar timing residuals. We show that the present-day pulsar timing precision allows one to detect BWM due to SMBH mergers from distances of up to 1\xa0Gpc (for the case of equal mass of 108\xa0M2299 SMBH). Improvements in the precision of pulsar timing together with an increase in the number of observed pulsars should eventually lead to the detection of a BWM signal due to the SMBH merger, thereby making the proposed technique complementary to the capabilities of the planned LISA mission.'), (1613, '10.1111/j.1365-2966.2009.15887.x'), (1614, 'Wiley InterScience'), (1615, '2010-06-26 16:28:30'), (1616, '2008-02-12 February 12, 2008'), (1617, 'http://link.aps.org/doi/10.1103/PhysRevD.77.044016'), (1618, '10.1103/PhysRevD.77.044016'), (1619, 'Gravitational-wave memory and pulsar timing arrays'), (1620, '2009-09-04 2009-09-04'), (1621, 'http://arxiv.org/abs/0909.0954'), (1622, '0909.0954'), (1623, 'Pulsar timing arrays (PTAs) are designed to detect gravitational waves with periods from several months to several years, e.g. those produced by by wide supermassive black-hole binaries in the centers of distant galaxies. Here we show that PTAs are also sensitive to mergers of supermassive black holes. While these mergers occur on a timescale too short to be resolvable by a PTA, they generate a change of metric due to non-linear gravitational-wave memory which persists for the duration of the experiment and could be detected. We develop the theory of the single-source detection by PTAs, and derive the sensitivity of PTAs to the gravitational-wave memory jumps. We show that mergers of $10^8M_{\\odot}$ black holes are $2-\\sigma$-detectable (in a direction, polarization, and time-dependent way) out to co-moving distances of $\\sim 1$ billion light years. Modern prediction for black-hole merger rates imply marginal to modest chance of an individual jump detection by currently developed PTAs. The sensitivity is expected to be somewhat higher for futuristic PTA experiments with SKA.'), (1624, '2010-06-26 16:33:49'), (1625, '0909.0954 PDF'), (1626, 'http://www.arxiv.org/pdf/0909.0954.pdf'), (1627, '2010-06-26 16:33:52'), (1628, 'Search for Memory and Inspiral Gravitational Waves from Super-Massive Binary Black Holes with Pulsar Timing Arrays'), (1629, '2009-09-07 2009-09-07'), (1630, 'http://arxiv.org/abs/0909.1379'), (1631, '0909.1379'), (1632, 'The merger of a super-massive binary black hole (SBBH) is one of the most extreme events in the universe with a huge amount of energy released by gravitational radiation. Although the characteristic gravitational wave (GW) frequency around the merger event is far higher than the nHz regime optimal for pulsar timing arrays (PTAs), nonlinear GW memory might be a critical smoking gun of the merger event detectable with PTAs. In this paper, basic aspects of this interesting observation are discussed for SBBHs, and the detection numbers of their memory and inspiral GWs are estimated for ongoing and planned PTAs. We find that the expected detection number would be smaller than unity for the two-types of signals even with the Square Kilometer Array. We also provide various scaling relations that would be useful to study detection probabilities of GWs from individual SBBHs with PTAs.'), (1633, '2010-06-26 16:34:36'), (1634, '0909.1379 PDF'), (1635, 'http://www.arxiv.org/pdf/0909.1379.pdf'), (1636, '2010-06-26 16:34:39'), (1637, 'The increasing sophistication and accuracy of numerical simulations of compact binaries (especially binary black holes) presents the opportunity to test the regime in which post-Newtonian (PN) predictions for the emitted gravitational waves are accurate. In order to confront numerical results with those of post-Newtonian theory, it is convenient to compare multipolar decompositions of the two waveforms. It is pointed out here that the individual modes can be computed to higher post-Newtonian order by examining the radiative multipole moments of the system, rather than by decomposing the 2.5PN polarization waveforms. In particular, the dominant (l=2, m=±2) mode can be computed to 3PN order. Individual modes are computed to as high a post-Newtonian order as possible given previous post-Newtonian results.'), (1638, '2010-07-08 18:41:14'), (1639, 'http://prd.aps.org/pdf/PRD/v77/i4/e044016'), (1640, '2010-07-08 18:41:15'), (1641, 'Gravitational Waves from Coalescing Binary Sources'), (1642, '2010-07-08 2010-07-08'), (1643, 'http://arxiv.org/abs/1007.1358'), (1644, '1007.1358'), (1645, "Coalescing binary systems (eg pulsars, neutron stars and black holes) are the most likely sources of gravitational radiation, yet to be detected on or near Earth, where the local gravitational field is negligible and the Poincar\\'e symmetry rules. On the other hand, the general theory of gravitational waves emitted by axially symmetric rotating sources predicts the existence of a non-vanishing news function. The existence of such function implies that, for a distant observer, the asymptotic group of isometries, the BMS group, has a translational symmetry that depends on the orbit periodicity of the source, thus breaking the isotropy o the Poincar\\'e translations. These results suggest the application of the asymptotic BMS-covariant wave equation to obtain a proper theoretical basis for the gravitational waves observations."), (1646, '2010-07-09 11:17:15'), (1647, '1007.1358 PDF'), (1648, 'http://www.arxiv.org/pdf/1007.1358.pdf'), (1649, '2010-07-09 11:17:18'), (1650, 'Coalescing binary systems of compact objects to (post)5/2-Newtonian order. V. Spin effects'), (1651, 821), (1652, '1995-07-15 July 15, 1995'), (1653, 'http://link.aps.org/doi/10.1103/PhysRevD.52.821'), (1654, '10.1103/PhysRevD.52.821'), (1655, 'We examine the effects of spin-orbit and spin-spin couplings on the inspiral of a coalescing binary system of spinning compact objects and on the gravitational radiation emitted therefrom. Using a formalism developed by Blanchet, Damour, and Iyer we calculate the contributions due to the spins of the bodies to the symmetric trace-free radiative multipole moments which are used to calculate the waveform, energy loss, and angular momentum loss from the inspiraling binary. Using equations of motion which include terms due to spin-orbit and spin-spin couplings we evolve the orbit of a coalescing binary and use the orbit to calculate the emitted gravitational waveform. We find the spins of the bodies affect the waveform in several ways: (1) the spin terms contribute to the orbital decay of the binary, and thus to the accumulated phase of the gravitational waveform; (2) the spins cause the orbital plane to precess, which changes the orientation of the orbital plane with respect to an observer, thus causing the shape of the waveform to be modulated; (3) the spins contribute directly to the amplitude of the waveform. We discuss the size and importance of spin effects for the case of two coalescing neutron stars, and for the case of a neutron star orbiting a rapidly rotating 10M⊙ black hole.'), (1656, '2010-07-14 19:24:19'), (1657, 'http://prd.aps.org/pdf/PRD/v52/i2/p821_1'), (1658, '2010-07-14 19:24:36'), (1659, 'Spin effects in the inspiral of coalescing compact binaries'), (1660, 47), (1661, 'R4183'), (1662, '1993-05-15 May 15, 1993'), (1663, 'http://link.aps.org/doi/10.1103/PhysRevD.47.R4183'), (1664, '10.1103/PhysRevD.47.R4183'), (1665, 'We derive the contributions of spin-orbit and spin-spin coupling to the gravitational radiation from coalescing binary systems of spinning compact objects. We calculate spin effects in the symmetric, trace-free radiative multipoles that determine the gravitational wave form, and the rate of energy loss. Assuming a balance between energy radiated and orbital energy lost, we determine the spin effects in the evolution of the orbital frequency and orbital radius. Assuming that a laser interferometric gravitational observatory can track the gravitational-wave frequency (twice the orbital frequency) as it sweeps through its sensitive bandwidth between about 10 Hz and 1 kHz, we estimate the accuracy with which the spins of the component bodies can be determined from the gravitational-wave signal.'), (1666, '2010-07-14 19:24:59'), (1667, 'http://prd.aps.org/pdf/PRD/v47/i10/pR4183_1'), (1668, '2010-07-14 19:25:01'), (1669, 'Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit'), (1670, 67), (1671, 104025), (1672, '2003-05-30 May 30, 2003'), (1673, 'http://link.aps.org/doi/10.1103/PhysRevD.67.104025'), (1674, '10.1103/PhysRevD.67.104025'), (1675, 'Black-hole (BH) binaries with single-BH masses m=(5-20)M⊙, moving on quasicircular orbits, are among the most promising sources for first-generation ground-based gravitational-wave (GW) detectors. Until now, the development of data-analysis techniques to detect GWs from these sources has been focused mostly on nonspinning BHs. The data-analysis problem for the spinning case is complicated by the necessity to model the precession-induced modulations of the GW signal, and by the large number of parameters needed to characterize the system, including the initial directions of the spins, and the position and orientation of the binary with respect to the GW detector. In this paper we consider binaries of maximally spinning BHs, and we work in the adiabatic-inspiral regime to build families of modulated detection templates that (i) are functions of very few physical and phenomenological parameters, (ii) model remarkably well the dynamical and precessional effects on the GW signal, with fitting factors on average ≳0.97, (iii) but, however, might require increasing the detection thresholds, offsetting at least partially the gains in the fitting factors. Our detection-template families are quite promising also for the case of neutron-star–black-hole binaries, with fitting factors on average ≈0.93. For these binaries we also suggest (but do not test) a further template family, which would produce essentially exact waveforms written directly in terms of the physical spin parameters.'), (1676, '2010-07-14 20:05:13'), (1677, 'Detecting gravitational waves from precessing binaries of spinning compact objects'), (1678, 'http://prd.aps.org/pdf/PRD/v67/i10/e104025'), (1679, '2010-07-14 20:05:15'), (1680, 'Erratum: Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit [Phys. Rev. D 67, 104025 (2003)]'), (1681, '029904'), (1682, '2006-07-31 July 31, 2006'), (1683, 'http://link.aps.org/doi/10.1103/PhysRevD.74.029904'), (1684, '10.1103/PhysRevD.74.029904'), (1685, '2010-07-14 20:05:38'), (1686, 'http://prd.aps.org/pdf/PRD/v74/i2/e029904'), (1687, '2010-07-14 20:05:40'), (1688, 'Influence of spin-spin coupling on inspiraling compact binaries with M1=M2 and S1=S2'), (1689, 2438), (1690, '1996-00-00 1996'), (1691, 'http://link.aps.org/doi/10.1103/PhysRevD.54.2438'), (1692, '10.1103/PhysRevD.54.2438'), (1693, "Searching for gravitational waves with laser-interferometer detectors requires a highly accurate knowledge of the gravitational wave forms in order to construct search templates with which to cross correlate the noisy detectors' output. In this spirit, we derive here an analytic approximate formula describing the precession of an inspiraling compact binary with equal masses and equal spins, where both the spin-orbit and the spin-spin couplings are taken into account."), (1694, '2010-07-14 20:14:56'), (1695, 'http://prd.aps.org/pdf/PRD/v54/i4/p2438_1'), (1696, '2010-07-14 20:14:58'), (1697, 'Gravitational Radiation from Inspiralling Compact Binaries Completed at the Third Post-Newtonian Order'), (1698, 93), (1699, '091101'), (1700, 'http://link.aps.org/doi/10.1103/PhysRevLett.93.091101'), (1701, '10.1103/PhysRevLett.93.091101'), (1702, 'The gravitational radiation from point particle binaries is computed at the third post-Newtonian (3PN) approximation of general relativity. Three previously introduced ambiguity parameters, coming from the Hadamard self-field regularization of the 3PN source-type mass quadrupole moment, are consistently determined by means of dimensional regularization, and proved to have the values ξ=-9871/9240, κ=0, and ζ=-7/33. These results complete the derivation of the general relativistic prediction for compact binary inspiral up to 3.5PN order, and should be of use for searching and deciphering the signals in the current network of gravitational wave detectors.'), (1703, '2010-07-14 20:32:15'), (1704, 'http://prl.aps.org/pdf/PRL/v93/i9/e091101'), (1705, '2010-07-14 20:32:17'), (1706, 'Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. III. Radiation reaction for binary systems with spinning bodies'), (1707, 71), (1708, '084027'), (1709, '2005-04-26 April 26, 2005'), (1710, 'http://link.aps.org/doi/10.1103/PhysRevD.71.084027'), (1711, '10.1103/PhysRevD.71.084027'), (1712, 'Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)5] and O[(v/c)7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies. In particular we determine the effects of radiation reaction coupled to spin-orbit effects on the two-body equations of motion, and on the evolution of the spins. For a suitable definition of spin, we reproduce the standard equations of motion and spin-precession at the first post-Newtonian order. At 3.5 PN order, we determine the spin-orbit induced reaction effects on the orbital motion, but we find that radiation damping has no effect on either the magnitude or the direction of the spins. Using the equations of motion, we find that the loss of total energy and total angular momentum induced by spin-orbit effects precisely balances the radiative flux of those quantities calculated by Kidder et al. The equations of motion may be useful for evolving inspiraling orbits of compact spinning binaries.'), (1713, '2010-07-14 20:36:06'), (1714, 'http://prd.aps.org/pdf/PRD/v71/i8/e084027'), (1715, '2010-07-14 20:36:08'), (1716, 'Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling'), (1717, '064017'), (1718, '2007-03-15 March 15, 2007'), (1719, 'http://link.aps.org/doi/10.1103/PhysRevD.75.064017'), (1720, '10.1103/PhysRevD.75.064017'), (1721, 'Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)5] and O[(v/c)7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies, including spin-spin effects. In particular we determine the effects of radiation-reaction coupled to spin-spin effects on the two-body equations of motion, and on the evolution of the spins. We find that radiation damping causes a 3.5PN order, spin-spin induced precession of the individual spins. This contrasts with the case of spin-orbit coupling, where we earlier found no effect on the spins at 3.5PN order. Employing the equations of motion and of spin precession, we verify that the loss of total energy and total angular momentum induced by spin-spin effects precisely balances the radiative flux of those quantities calculated by Kidder et al.'), (1722, '2010-07-14 20:39:15'), (1723, 'http://prd.aps.org/pdf/PRD/v75/i6/e064017'), (1724, '2010-07-14 20:39:17'), (1725, 'Transition from inspiral to plunge in precessing binaries of spinning black holes'), (1726, 104005), (1727, '2006-11-02 November 02, 2006'), (1728, 'http://link.aps.org/doi/10.1103/PhysRevD.74.104005'), (1729, '10.1103/PhysRevD.74.104005'), (1730, 'We investigate the nonadiabatic dynamics of spinning black-hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular-momentum losses on quasicircular orbits. We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the effective one-body approach. We focus on the influence spin terms have on the dynamics and waveforms. We evaluate the energy and angular momentum released during the final stage of inspiral and plunge. For an equal-mass binary the energy released between 40 Hz and the frequency beyond which our analytical treatment becomes unreliable is found to be, when using the effective one-body dynamics, 0.6%M for antialigned maximally spinning black holes, 5%M for aligned maximally spinning black holes, and 1.8%M for nonspinning configurations. In confirmation of previous results, we find that, for all binaries considered, the dimensionless rotation parameter J/E2 is always smaller than unity at the end of the inspiral, so that a Kerr black hole can form right after the inspiral phase. By matching a quasinormal mode ring down to the last reliable stages of the plunge, we construct complete waveforms approximately describing the gravitational-wave signal emitted by the entire process of coalescence of precessing binaries of spinning black holes.'), (1731, '2010-07-14 21:27:36'), (1732, 'http://prd.aps.org/pdf/PRD/v74/i10/e104005'), (1733, '2010-07-14 21:27:38'), (1734, 'Estimating spinning binary parameters and testing alternative theories of gravity with LISA'), (1735, '084025'), (1736, '2005-04-19 April 19, 2005'), (1737, 'http://link.aps.org/doi/10.1103/PhysRevD.71.084025'), (1738, '10.1103/PhysRevD.71.084025'), (1739, 'We investigate the effect of spin-orbit and spin-spin couplings on the estimation of parameters for inspiralling compact binaries of massive black holes, and for neutron stars inspiralling into intermediate-mass black holes, using hypothetical data from the proposed Laser Interferometer Space Antenna (LISA). We work both in Einstein’s theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. We restrict the analysis to nonprecessing spinning binaries, i.e. to cases where the spins are aligned normal to the orbital plane. We find that the accuracy with which intrinsic binary parameters such as chirp mass and reduced mass can be estimated within general relativity is degraded by between 1 and 2 orders of magnitude. We find that the bound on the coupling parameter ωBD of scalar-tensor gravity is significantly reduced by the presence of spin couplings, while the reduction in the graviton-mass bound is milder. Using fast Monte Carlo simulations of 104 binaries, we show that inclusion of spin terms in massive black-hole binaries has little effect on the angular resolution or on distance determination accuracy. For stellar-mass inspirals into intermediate-mass black holes, the angular resolution and the distance are determined only poorly, in all cases considered. We also show that, if LISA’s low-frequency noise sensitivity can be extrapolated from 10-4 Hz to as low as 10-5 Hz, the accuracy of determining both extrinsic parameters (distance, sky location) and intrinsic parameters (chirp mass, reduced mass) of massive binaries may be greatly improved.'), (1740, '2010-07-14 21:50:10'), (1741, 'http://prd.aps.org/pdf/PRD/v71/i8/e084025'), (1742, '2010-07-14 21:50:12'), (1743, 'LISA observations of rapidly spinning massive black hole binary systems'), (1744, 70), (1745, '042001'), (1746, 'http://link.aps.org/doi/10.1103/PhysRevD.70.042001'), (1747, '10.1103/PhysRevD.70.042001'), (1748, 'Binary systems of massive black holes will be detectable by the Laser Interferometer Space Antenna (LISA) throughout the entire Universe. Observations of gravitational waves from this class of sources will have important repercussions on our understanding of the behavior of gravity in the highly nonlinear relativistic regime, the distribution and interaction of massive black holes at high redshift, and the formation and evolution of cosmic structures. It is therefore important to address how accurately LISA can measure the source parameters and explore the implications for astronomy and cosmology. Present observations and theoretical models suggest that massive black holes could be spinning, possibly rapidly in some cases. In binary systems, the relativistic spin-orbit interaction causes the orbital plane to precess in space, producing a characteristic signature on the emitted gravitational waves. In this paper we investigate the effect of spins on the gravitational wave signal registered at the LISA output—we provide ready-to-use analytical expressions of the measured signal—and the implications for parameter estimation. We consider the inspiral phase of binary systems in circular orbit undergoing the so-called “simple precession” and we approximate the gravitational radiation at the restricted post1.5-Newtonian order. We show that the presence of spins changes dramatically the signature of the signal recorded by LISA. As a consequence, the mean square errors associated with the parameter measurements are significantly smaller than the ones obtained when the effect of spins is neglected. For a binary system of two 106M⊙ black holes, the angular resolution and the relative error on the luminosity distance improve by a factor of ≈3–10; the fractional errors on the chirp mass and the reduced mass decrease by a factor of ∼10 and ∼103, respectively.'), (1749, '2010-07-14 21:50:19'), (1750, 'http://prd.aps.org/pdf/PRD/v70/i4/e042001'), (1751, '2010-07-14 21:50:21'), (1752, 'Measuring coalescing massive binary black holes with gravitational waves: The impact of spin-induced precession'), (1753, 122001), (1754, '2006-12-01 December 01, 2006'), (1755, 'http://link.aps.org/doi/10.1103/PhysRevD.74.122001'), (1756, '10.1103/PhysRevD.74.122001'), (1757, 'The coalescence of massive black holes generates gravitational waves (GWs) that will be measurable by space-based detectors such as LISA to large redshifts. The spins of a binary’s black holes have an important impact on its waveform. Specifically, geodetic and gravitomagnetic effects cause the spins to precess; this precession then modulates the waveform, adding periodic structure which encodes useful information about the binary’s members. Following pioneering work by Vecchio, we examine the impact upon GW measurements of including these precession-induced modulations in the waveform model. We find that the additional periodicity due to spin precession breaks degeneracies among certain parameters, greatly improving the accuracy with which they may be measured. In particular, mass measurements are improved tremendously, by one to several orders of magnitude. Localization of the source on the sky is also improved, though not as much—low redshift systems can be localized to an ellipse which is roughly 10-a few×10 arcminutes in the long direction and a factor of 2 smaller in the short direction. Though not a drastic improvement relative to analyses which neglect spin precession, even modest gains in source localization will greatly facilitate searches for electromagnetic counterparts to GW events. Determination of distance to the source is likewise improved: We find that relative error in measured luminosity distance is commonly ∼0.1%–0.4% at z∼1. Finally, with the inclusion of precession, we find that the magnitude of the spins themselves can typically be determined for low redshift systems with an accuracy of about 0.1%–10%, depending on the spin value, allowing accurate surveys of mass and spin evolution over cosmic time.'), (1758, '2010-07-14 21:50:30'), (1759, 'Measuring coalescing massive binary black holes with gravitational waves'), (1760, 'http://prd.aps.org/pdf/PRD/v74/i12/e122001'), (1761, '2010-07-14 21:50:32'), (1762, 'Erratum: Measuring coalescing massive binary black holes with gravitational waves: The impact of spin-induced precession [Phys. Rev. D 74, 122001 (2006)]'), (1763, '089902'), (1764, '2007-04-23 April 23, 2007'), (1765, 'http://link.aps.org/doi/10.1103/PhysRevD.75.089902'), (1766, '10.1103/PhysRevD.75.089902'), (1767, '2010-07-14 21:50:44'), (1768, 'http://prd.aps.org/pdf/PRD/v75/i8/e089902'), (1769, '2010-07-14 21:50:46'), (1770, '0305-4470'), (1771, 'Journal of Physics A: Mathematical and General'), (1772, 109901), (1773, '2008-05-02 May 02, 2008'), (1774, 'http://link.aps.org/doi/10.1103/PhysRevD.77.109901'), (1775, '10.1103/PhysRevD.77.109901'), (1776, '2010-07-14 21:51:17'), (1777, 'http://prd.aps.org/pdf/PRD/v77/i10/e109901'), (1778, '2010-07-14 21:51:19'), (1779, 'Class. Quantum Grav.'), (1780, '2007-00-03 03/2007'), (1781, '1089-1113'), (1782, '10.1088/0264-9381/24/5/005'), (1783, 'http://iopscience.iop.org/0264-9381/24/5/005'), (1784, 'Binary black hole spectroscopy'), (1785, '2010-07-14 21:55:21'), (1786, '2007-00-01 01/2007'), (1787, '155-176'), (1788, '10.1088/0264-9381/24/1/009'), (1789, 'http://iopscience.iop.org/0264-9381/24/1/009'), (1790, 'Phenomenology of amplitude-corrected post-Newtonian gravitational waveforms for compact binary inspiral: I. Signal-to-noise ratios'), (1791, '2010-07-14 21:55:33'), (1792, 'Phenomenology of amplitude-corrected post-Newtonian gravitational waveforms for compact binary inspiral'), (1793, 'Choice of filters for the detection of gravitational waves from coalescing binaries'), (1794, 44), (1795, 3819), (1796, '1991-12-15 December 15, 1991'), (1797, 'http://link.aps.org/doi/10.1103/PhysRevD.44.3819'), (1798, '10.1103/PhysRevD.44.3819'), (1799, 'Coalescing binaries are one of the most promising candidates for the detection of gravitational waves with the advent of the new generation of laser interferometric gravitational-wave detectors. Signals from coalescing binaries will most probably not stand above the broadband noise of the detector. Their detection is possible by the use of special data analysis techniques such as matched filtering which takes advantage of the fact that the wave form can be fairly well predicted. The wave form of the coalescing binary signal is known very accurately. However, the parameters of the signal are not known priori and the signal needs to be correlated with several filters which are copies of the coalescing binary wave form for different values of the parameters. In this paper we present an algorithm to choose a lattice set of filters by a criterion that every signal of a certain minimal strength is picked up by at least one filter of the set. The wave form is characterized by three parameters: the time of arrival, the mass parameter, and the phase of the signal. We show that it is enough to have just two filters corresponding to the phase of the signal. Determination of the lattice for various values of the mass parameter involves a knowledge of the cross correlation function of two chirp wave forms with different values of the parameters. It is shown that for a considerable range of the mass parameter, the peak value of the correlation function, in a certain approximation, does not depend on the absolute values of the parameters but only on their difference. This leads to a very convenient way of constructing most of the lattice. The maximum possible distance up to which we can see is restricted by the threshold of the detector. There is a further limitation on this distance brought about by the fact that we can use only a finite number of filters. The number of filters which one can use depends on the available computing power. Hence, there is an empirical relation between computing power and the distance up to which we can see. In a restricted sense, the computing power decides the number of detectable events. Numerical experiments indicate that parallel processing is a promising new approach to on-line data analysis.'), (1800, '2010-07-14 21:59:00'), (1801, 'http://prd.aps.org/pdf/PRD/v44/i12/p3819_1'), (1802, '2010-07-14 21:59:02'), (1803, 111101), (1804, '2006-03-22 March 22, 2006'), (1805, 'http://link.aps.org/doi/10.1103/PhysRevLett.96.111101'), (1806, 'We present a new algorithm for evolving orbiting black-hole binaries that does not require excision or a corotating shift. Our algorithm is based on a novel technique to handle the singular puncture conformal factor. This system, based on the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein’s equations, when used with a “precollapsed” initial lapse, is nonsingular at the start of the evolution and remains nonsingular and stable provided that a good choice is made for the gauge. As a test case, we use this technique to fully evolve orbiting black-hole binaries from near the innermost stable circular orbit regime. We show fourth-order convergence of waveforms and compute the radiated gravitational energy and angular momentum from the plunge. These results are in good agreement with those predicted by the Lazarus approach.'), (1807, '2010-07-14 22:01:04'), (1808, 'http://prl.aps.org/pdf/PRL/v96/i11/e111101'), (1809, '2010-07-14 22:01:06'), (1810, 'Self-interaction spin effects in inspiralling compact binaries'), (1811, '2005-04-25 2005-04-25'), (1812, 'http://arxiv.org/abs/astro-ph/0504538'), (1813, 'Phys.Rev. D71 (2005) 124043'), (1814, 'doi:10.1103/PhysRevD.71.124043'), (1815, 'astro-ph/0504538'), (1816, 'Gravitational radiation drives compact binaries through an inspiral phase towards a final coalescence. For binaries with\\textit{spin, mass quadrupole and magnetic dipole moments}, various contributions add to this process, which is characterized by the rate of increase $df/dt$ of the gravitational wave frequency and the accumulated number $\\mathcal{N}$ of gravitational wave cycles. We present here all contributions to $df/dt$ and $% \\mathcal{N}$ up to the second post-Newtonian order. Among them we give for the first time the contributions due to the \\textit{self-interaction of individual spins}. These are shown to be commensurable with the proper spin-spin contributions for the recently discovered J0737-3039 double pulsar, and argued to represent the first corrections to the radiation reaction in the Lense-Thirring approach.'), (1817, '2010-07-15 16:14:54'), (1818, 'astro-ph/0504538 PDF'), (1819, 'http://www.arxiv.org/pdf/astro-ph/0504538.pdf'), (1820, '2010-07-15 16:14:57'), (1821, 'Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order'), (1822, 'http://arxiv.org/abs/1007.1312'), (1823, '1007.1312'), (1824, 'Using effective field theory techniques we calculate the source multipole moments needed to obtain the spin contributions to the power radiated in gravitational waves from inspiralling compact binaries to third Post-Newtonian order (3PN). The multipoles depend linearly and quadratically on the spins and include both spin(1)spin(2) and spin(1)spin(1) components. The results in this paper provide the last missing ingredient required to determine the phase evolution to 3PN including all spin effects which we will report in a separate paper.'), (1825, '2010-07-15 16:15:15'), (1826, '1007.1312 PDF'), (1827, 'http://www.arxiv.org/pdf/1007.1312.pdf'), (1828, '2010-07-15 16:15:18'), (1829, 'Spin-spin effects in radiating compact binaries'), (1830, 61), (1831, '024035'), (1832, '1999-12-28 December 28, 1999'), (1833, 'http://link.aps.org/doi/10.1103/PhysRevD.61.024035'), (1834, '10.1103/PhysRevD.61.024035'), (1835, 'The dynamics of a binary system with two spinning components on an eccentric orbit is studied, with the inclusion of the spin-spin interaction terms appearing at the second post-Newtonian order. A generalized true anomaly parametrization properly describes the radial component of the motion. The average over one radial period of the magnitude of the orbital angular momentum L̅ is found to have no nonradiative secular change. All spin-spin terms in the secular radiative loss of the energy and magnitude of orbital angular momentum are given in terms of L̅ and other constants of the motion. Among them, self-interaction spin effects are found, representing the second post-Newtonian correction to the 3/2 post-Newtonian order Lense-Thirring approximation.'), (1836, '2010-07-15 18:47:36'), (1837, 'http://prd.aps.org/pdf/PRD/v61/i2/e024035'), (1838, '2010-07-15 18:47:38'), (1839, 'Second post-Newtonian radiative evolution of the relative orientations of angular momenta in spinning compact binaries'), (1840, 62), (1841, '024007'), (1842, '2000-06-14 June 14, 2000'), (1843, 'http://link.aps.org/doi/10.1103/PhysRevD.62.024007'), (1844, '10.1103/PhysRevD.62.024007'), (1845, 'The radiative evolution of the relative orientations of the spin and orbital angular momentum vectors S1, S2 and L, characterizing a binary system on an eccentric orbit is studied up to the second post-Newtonian order. As an intermediate result, all Burke-Thorne type instantaneous radiative changes in the spins are shown to average out over a radial period. It is proved that spin-orbit and spin-spin terms contribute to the radiative angular evolution equations, while Newtonian, first and second post-Newtonian terms together with the leading order tail terms do not. In complement to the spin-orbit contribution, given earlier, the spin-spin contribution is computed and split into two-body and self-interaction parts. The latter provide the second post-Ne wtonian order corrections to the 3/2 order Lense-Thirring description.'), (1846, '2010-07-15 18:47:40'), (1847, 'http://prd.aps.org/pdf/PRD/v62/i2/e024007'), (1848, '2010-07-15 18:47:42'), (1849, 'Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: the orbital hang-up case'), (1850, '2007-12-21 2007-12-21'), (1851, 'http://arxiv.org/abs/0712.3787'), (1852, 'Phys.Rev.D78:104007,2008'), (1853, 'doi:10.1103/PhysRevD.78.104007'), (1854, '0712.3787'), (1855, 'We compare results from numerical simulations of spinning binaries in the "orbital hangup" case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants TaylorT1, T4 and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches $M\\omega = 0.1$, the accumulated phase disagreement between NR and 2.5PN results is less than three radians, and is less than 2.5 radians when using 3.5PN results. The amplitude disagreement between NR and restricted PN results increases with the black holes\' spin, from about 6% in the equal-mass case to 12% when the black holes\' spins are $S_i/M_i^2 = 0.85$. Finally, our results suggest that the merger waveform will play an important role in estimating the spin from such inspiral waveforms.'), (1856, '2010-07-19 15:33:07'), (1857, 'Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries'), (1858, '0712.3787 PDF'), (1859, 'http://www.arxiv.org/pdf/0712.3787.pdf'), (1860, '2010-07-19 15:33:10'), (1861, 'Energy and angular momentum flow into a black hole in a binary'), (1862, '2011-10-12 20:16:12'), (1863, 'file.pdf'), (1864, 'https://tds.ego-gw.it/itf/tds/file.php?callFile=VIR-NOT-DIR-1390-304.pdf'), (1865, '2011-09-07 13:47:19'), (1866, '2010-09-00 09/2010'), (1867, '2009-08-00 08/2009'), (1868, '2010-12-00 12/2010'), (1869, 'demodulating_precession:home [The SXS Project]'), (1870, 'http://black-holes.org/wiki/demodulating_precession/home'), (1871, '2011-09-08 14:53:55'), (1872, "The Definition of Mach's Principle"), (1873, '2010-07-20 2010-07-20'), (1874, 'http://arxiv.org/abs/1007.3368'), (1875, '1007.3368'), (1876, "Two definitions of Mach's principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to general relativity and may have relevance to the problem of creating a quantum theory of gravity."), (1877, '2010-07-21 19:55:10'), (1878, '1007.3368 PDF'), (1879, 'http://www.arxiv.org/pdf/1007.3368.pdf'), (1880, '2010-07-21 19:55:13'), (1881, 'Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections'), (1882, '1994-12-08 1994-12-08'), (1883, 'http://arxiv.org/abs/gr-qc/9412027'), (1884, 'Phys.Rev.D51:5753-5767,1995'), (1885, 'doi:10.1103/PhysRevD.51.5753'), (1886, 'gr-qc/9412027'), (1887, 'A particle of mass $\\mu$ moves on a circular orbit of a nonrotating black hole of mass $M$. Under the restrictions $\\mu/M \\ll 1$ and $v \\ll 1$, where $v$ is the orbital velocity, we consider the gravitational waves emitted by such a binary system. We calculate $\\dot{E}$, the rate at which the gravitational waves remove energy from the system. The total energy loss is given by $\\dot{E} = \\dot{E}^\\infty + \\dot{E}^H$, where $\\dot{E}^\\infty$ denotes that part of the gravitational-wave energy which is carried off to infinity, while $\\dot{E}^H$ denotes the part which is absorbed by the black hole. We show that the black-hole absorption is a small effect: $\\dot{E}^H/\\dot{E} \\simeq v^8$. We also compare the wave generation formalism which derives from perturbation theory to the post-Newtonian formalism of Blanchet and Damour. Among other things we consider the corrections to the asymptotic gravitational-wave field which are due to wave-propagation (tail) effects.'), (1888, '2010-07-22 19:29:25'), (1889, 'gr-qc/9412027 PDF'), (1890, 'http://www.arxiv.org/pdf/gr-qc/9412027.pdf'), (1891, '2010-07-22 19:29:28'), (1892, 'Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole :Effects of Black Hole Absorption'), (1893, '1997-11-25 1997-11-25'), (1894, 'http://arxiv.org/abs/gr-qc/9711072'), (1895, 'Prog.Theor.Phys. 98 (1997) 829-850'), (1896, 'doi:10.1143/PTP.98.829'), (1897, 'gr-qc/9711072'), (1898, 'When a particle moves around a Kerr black hole, it radiates gravitational waves.Some of these waves are absorbed by the black hole. We calculate such absorption of gravitational waves induced by a particle of mass mu in a circular orbit on an equatorial plane around a Kerr black hole of mass M. We assume that the velocity of the particle v is much smaller than the speed of light c and calculate the energy absorption rate analytically. We adopt an analytic technique for the Teukolsky equation developed by Mano, Suzuki and Takasugi. We obtain the energy absorption rate to O((v/c)^8) compared to the lowest order. We find that the black hole absorption occurs at O((v/c)^5) beyond the Newtonian-quadrapole luminosity at infinity in the case when the black hole is rotating, which is O((v/c)^3) lower than the non-rotating case. Using the energy absorption rate, we investigate its effects on the orbital evolution of coalescing compact binaries.'), (1899, '2010-07-22 19:30:03'), (1900, 'Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole'), (1901, 'gr-qc/9711072 PDF'), (1902, 'http://www.arxiv.org/pdf/gr-qc/9711072.pdf'), (1903, '2010-07-22 19:30:06'), (1904, 'Post-Newtonian expansion of gravitational waves from a particle in circular orbit around a Schwarzschild black hole'), (1905, '1994-05-25 1994-05-25'), (1906, 'http://arxiv.org/abs/gr-qc/9405062'), (1907, 'Prog.Theor.Phys.92:745-772,1994'), (1908, 'doi:10.1143/PTP.92.745'), (1909, 'gr-qc/9405062'), (1910, 'Based upon the formalism recently developed by one of us (MS), we analytically perform the post-Newtonian expansion of gravitational waves from a test particle in circular orbit of radius $r_0$ around a Schwarzschild black hole of mass $M$. We calculate gravitational wave forms and luminosity up to $v^8$ order beyond Newtonian, where $v=(M/r_0)^{1/2}$. In particular, we give the exact analytical values of the coefficients of $\\ln v$ terms at $v^6$ and $v^8$ orders in the luminosity and confirm the numerical values obtained previously by the other of us (HT) and Nakamura. Our result is valid in the small mass limit of one body and gives an important guideline for the gravitational wave physics of coalescing compact binaries.'), (1911, '2010-07-22 19:31:23'), (1912, 'gr-qc/9405062 PDF'), (1913, 'http://www.arxiv.org/pdf/gr-qc/9405062.pdf'), (1914, '2010-07-22 19:31:26'), (1915, 'Black Hole Perturbation'), (1916, '1997-12-12 1997-12-12'), (1917, 'http://arxiv.org/abs/gr-qc/9712057'), (1918, 'Prog.Theor.Phys.Suppl.128:1-121,1997'), (1919, 'doi:10.1143/PTPS.128.1'), (1920, 'gr-qc/9712057'), (1921, 'We present analytic calculations of gravitational waves from a particle orbiting a black hole. We first review the Teukolsky formalism for dealing with the gravitational perturbation of a black hole. Then we develop a systematic method to calculate higher order post-Newtonian corrections to the gravitational waves emitted by an orbiting particle. As applications of this method, we consider orbits that are nearly circular, including exactly circular ones, slightly eccentric ones and slightly inclined orbits off the equatorial plane of a Kerr black hole and give the energy flux and angular momentum flux formulas at infinity with higher order post-Newtonian corrections. Using a different method that makes use of an analytic series representation of the solution of the Teukolsky equation, we also give a post-Newtonian expanded formula for the energy flux absorbed by a Kerr black hole for a circular orbit.'), (1922, '2010-07-22 19:31:33'), (1923, 'gr-qc/9712057 PDF'), (1924, 'http://www.arxiv.org/pdf/gr-qc/9712057.pdf'), (1925, '2010-07-22 19:31:36'), (1926, 'Towards adiabatic waveforms for inspiral into Kerr black holes: A new model of the source for the time domain perturbation equation'), (1927, '2007-11-02 November 02, 2007'), (1928, 'http://link.aps.org/doi/10.1103/PhysRevD.76.104005'), (1929, '10.1103/PhysRevD.76.104005'), (1930, 'We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional partial differential equation. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.'), (1931, '2010-07-28 13:52:15'), (1932, 'Towards adiabatic waveforms for inspiral into Kerr black holes'), (1933, 'http://prd.aps.org/pdf/PRD/v76/i10/e104005'), (1934, '2010-07-28 13:52:17'), (1935, 'On the falloff of radiated energy in black hole spacetimes'), (1936, '2010-07-26 2010-07-26'), (1937, 'http://arxiv.org/abs/1007.4596'), (1938, '1007.4596'), (1939, 'The goal of much research in relativity is to understand gravitational waves generated by a strong-field dynamical spacetime. Quantities of particular interest for many calculations are the Weyl scalar $\\psi_4$, which is simply related to the flux of gravitational waves far from the source, and the flux of energy carried to distant observers, $\\dot E$. Conservation laws guarantee that, in asympotically flat spacetimes, $\\psi_4 \\propto 1/r$ and $\\dot E \\propto 1/r^2$ as $r \\to \\infty$. Most calculations extract these quantities at some finite extraction radius. An understanding of finite radius corrections to $\\psi_4$ and $\\dot E$ allows us to more accurately infer their asymptotic values from a computation. In this paper, we show that, if the final state of the system is a black hole, then the leading correction to $\\psi_4$ is ${\\cal O}(1/r^3)$, and that to the energy flux is ${\\cal O}(1/r^4)$ --- not ${\\cal O}(1/r^2)$ and ${\\cal O}(1/r^3)$ as one might naively guess. Our argument only relies on the behavior of the curvature scalars for black hole spacetimes. Using black hole perturbation theory, we calculate the corrections to the leading falloff, showing that it is quite easy to correct for finite extraction radius effects.'), (1940, '2010-07-28 13:52:39'), (1941, '1007.4596 PDF'), (1942, 'http://www.arxiv.org/pdf/1007.4596.pdf'), (1943, '2010-07-28 13:52:42'), (1944, '00222488'), (1945, '1969-00-00 1969'), (1946, 1195), (1947, '10.1063/1.1664958'), (1948, 'http://link.aip.org/link/?JMP/10/1195/1&Agg=doi'), (1949, 'Type D Vacuum Metrics'), (1950, 'COinS'), (1951, '2010-07-28 14:05:19'), (1952, '117-120'), (1953, 'http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=721375'), (1954, 3), (1955, 891), (1956, '10.1063/1.1724303'), (1957, 'http://link.aip.org/link/JMAPAQ/v3/i5/p891/s1&Agg=doi'), (1958, 'Behavior of Asymptotically Flat Empty Spaces'), (1959, '2010-08-02 21:47:21'), (1960, 'http://arxiv.org/abs/1202.2788'), (1961, '2012-02-13 2012-02-13'), (1962, '2013-09-25 15:26:44'), (1963, 'An Approach to Gravitational Radiation by a Method of Spin Coefficients'), (1964, 'We present results from a search for gravitational-wave bursts in the data collected by the LIGO and Virgo detectors between July 7, 2009 and October 20, 2010: data are analyzed when at least two of the three LIGO-Virgo detectors are in coincident operation, with a total observation time of 207 days. The analysis searches for transients of duration < 1 s over the frequency band 64-5000 Hz, without other assumptions on the signal waveform, polarization, direction or occurrence time. All identified events are consistent with the expected accidental background. We set frequentist upper limits on the rate of gravitational-wave bursts by combining this search with the previous LIGO-Virgo search on the data collected between November 2005 and October 2007. The upper limit on the rate of strong gravitational-wave bursts at the Earth is 1.3 events per year at 90% confidence. We also present upper limits on source rate density per year and Mpc^3 for sample populations of standard-candle sources. As in the previous joint run, typical sensitivities of the search in terms of the root-sum-squared strain amplitude for these waveforms lie in the range 5 10^-22 Hz^-1/2 to 1 10^-20 Hz^-1/2. The combination of the two joint runs entails the most sensitive all-sky search for generic gravitational-wave bursts and synthesizes the results achieved by the initial generation of interferometric detectors.'), (1965, '2008-09-21 2008-09-21'), (1966, 'http://link.aps.org/doi/10.1103/PhysRevD.62.084036'), (1967, 'http://link.aps.org/doi/10.1103/PhysRevD.59.124016'), (1968, 'Consistency of Post-Newtonian Waveforms with Numerical Relativity'), (1969, 18), (1970, 264), (1971, 'Prospects of observing continuous gravitational waves from known pulsars'), (1972, '2011-03-30 2011-03-30'), (1973, '10.1098/rspa.1961.0202'), (1974, 'http://rspa.royalsocietypublishing.org/content/264/1318/309.abstract'), (1975, 'http://arxiv.org/abs/1103.5867'), (1976, 'Gravitational Waves in General Relativity. VI. The Outgoing Radiation Condition'), (1977, '1961-11-21 November 21, 1961'), (1978, 'Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences'), (1979, '309-338'), (1980, 1318), (1981, 'A covariant formulation of the outgoing radiation condition for gravitational fields is proposed. The condition is based on a detailed examination of the geometry of null lines and of the algebraic and differential properties of the Riemann tensor. It relates the absence of incoming radiation, in a gravitational field with bounded sources and Euclidean topology, to the asymptotic behaviour of the Riemann tensor. Fields that are algebraically special in the Petrov classification are highly special examples of fields obeying the suggested condition.'), (1982, '2010-08-06 13:32:14'), (1983, 'Full Text PDF'), (1984, 'http://rspa.royalsocietypublishing.org/content/264/1318/309.full.pdf'), (1985, '2010-08-06 13:32:16'), (1986, '1103.5867'), (1987, "Several searches for gravitational waves from a selection of known pulsars have been performed with data from the science runs of the LIGO gravitational wave detectors. So far these have lead to no detection, but upper limits on the gravitational wave amplitudes have been set. Here we study our intrinsic ability to detect, and estimate the gravitational wave amplitude for non-accreting pulsars. Using spin-down limits on emission as a guide we examine amplitudes that would be required to observe known pulsars with future detectors (Advanced LIGO, Advanced Virgo and the Einstein Telescope), assuming that they are triaxial stars emitting at precisely twice the known rotation frequency. Maximum allowed amplitudes depend on the stars' equation of state (e.g. a normal neutron star, a quark star, a hybrid star) and the theoretical mass quadrupoles that they can sustain. We study what range of quadrupoles, and therefore equations of state, would be consistent with being able to detect these sources. For globular cluster pulsars, with spin-downs masked by accelerations within the cluster, we examine what spin-down values gravitational wave observations would be able to set. For all pulsars we also alternatively examine what internal magnetic fields they would need to sustain observable ellipticities."), (1988, 'Decoding mode-mixing in black-hole merger ringdown'), (1989, '2012-12-21 2012-12-21'), (1990, 'http://arxiv.org/abs/1212.5553'), (1991, 'Multipolar analysis of spinning binaries'), (1992, '2007-11-07 2007-11-07'), (1993, 'http://arxiv.org/abs/0711.1097'), (1994, 'Class.Quant.Grav.25:114035,2008'), (1995, 'doi:10.1088/0264-9381/25/11/114035'), (1996, '0711.1097'), (1997, 'We present a preliminary study of the multipolar structure of gravitational radiation from spinning black hole binary mergers. We consider three different spinning binary configurations: (1) one "hang-up" run, where the black holes have equal masses and large spins initially aligned with the orbital angular momentum; (2) seven "spin-flip" runs, where the holes have a mass ratio q=4, the spins are anti-aligned with the orbital angular momentum, and the initial Kerr parameters of the holes j_1=j_2=j_i are fine-tuned to produce a Schwarzschild remnant after merger; (3) three "super-kick" runs where the mass ratio q=M_1/M_2=1, 2, 4 and the spins of the two holes are initially located on the orbital plane, pointing in opposite directions. For all of these simulations we compute the multipolar energy distribution and the Kerr parameter of the final hole. For the hang-up run, we show that including leading-order spin-orbit and spin-spin terms in a multipolar decomposition of the post-Newtonian waveforms improves the agreement with the numerical simulation.'), (1998, '2010-08-09 20:08:58'), (1999, '0711.1097 PDF'), (2000, 'http://www.arxiv.org/pdf/0711.1097.pdf'), (2001, '2010-08-09 20:09:01'), (2002, 'Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms'), (2003, '2011-03-31 12:21:40'), (2004, '1103.5867 PDF'), (2005, 'http://www.arxiv.org/pdf/1103.5867.pdf'), (2006, '2011-03-31 12:21:45'), (2007, 'Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The non-spinning case'), (2008, '2004-11-30 2004-11-30'), (2009, 'http://arxiv.org/abs/gr-qc/0411146'), (2010, 'Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries'), (2011, 'Phys.Rev. D71 (2005) 084008; Erratum-ibid. D72 (2005) 069903'), (2012, 'doi:10.1103/PhysRevD.71.084008'), (2013, 'gr-qc/0411146'), (2014, 104023), (2015, '2009-05-19 May 19, 2009'), (2016, 'http://link.aps.org/doi/10.1103/PhysRevD.79.104023'), (2017, '10.1103/PhysRevD.79.104023'), (2018, 'We provide ready-to-use time-domain gravitational waveforms for spinning compact binaries with precession effects through 1.5 post-Newtonian (PN) order in amplitude, and compute their mode decomposition using spin-weighted -2 spherical harmonics. In the presence of precession, the gravitational-wave modes (ℓ,m) contain harmonics originating from combinations of the orbital frequency and precession frequencies. We find that the gravitational radiation from binary systems with large mass asymmetry and large inclination angle can be distributed among several modes. For example, during the last stages of inspiral, for some maximally spinning configurations, the amplitude of the (2, 0) and (2, 1) modes can be comparable to the amplitude of the (2, 2) mode. If the mass ratio is not too extreme, the ℓ=3 and ℓ=4 modes are generally 1 or 2 orders of magnitude smaller than the ℓ=2 modes. Restricting ourselves to spinning, nonprecessing compact binaries, we apply the stationary-phase approximation and derive the frequency-domain gravitational waveforms including spin-orbit and spin(1)-spin(2) effects through 1.5PN and 2PN order, respectively, in amplitude, and 2.5PN order in phase. Since spin effects in the amplitude through 2PN order affect only the first and second harmonics of the orbital phase, they do not extend the mass reach of gravitational-wave detectors. However, they can interfere with other harmonics and lower or raise the signal-to-noise ratio depending on the spin orientation. These ready-to-use waveforms could be employed in the data analysis of the spinning, inspiraling binaries as well as in comparison studies at the interface between analytical and numerical relativity.'), (2019, '2010-08-09 21:24:43'), (2020, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i10/e104023'), (2021, '2010-08-09 21:24:45'), (2022, 81), (2023, '089901'), (2024, '2010-04-08 April 08, 2010'), (2025, 'http://link.aps.org/doi/10.1103/PhysRevD.81.089901'), (2026, '10.1103/PhysRevD.81.089901'), (2027, '2010-08-10 13:02:24'), (2028, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e089901'), (2029, '2010-08-10 13:02:26'), (2030, "(Abridged) We revisit the problem of parameter estimation of gravitational-wave chirp signals from inspiralling non-spinning compact binaries in the light of the recent extension of the post-Newtonian (PN) phasing formula to order $(v/c)^7$ beyond the leading Newtonian order. We study in detail the implications of higher post-Newtonian orders from 1PN up to 3.5PN in steps of 0.5PN ($\\sim v/c$), and examine their convergence. In both initial and advanced detectors the estimation of the chirp mass (${\\cal M}$) and symmetric mass ratio ($\\eta$) improve at higher PN orders but oscillate with every half-a-PN order. We compare parameter estimation in different detectors and assess their relative performance in two different ways: at a {\\it fixed SNR,} with the aim of understanding how the bandwidth improves parameter estimation, and for a {\\it fixed source}, to gauge the importance of sensitivity. Errors in parameter estimation at a fixed SNR are smaller for VIRGO than for both initial and advanced LIGO. However, for sources at a fixed distance it is advanced LIGO that achieves the lowest errors owing to its greater sensitivity. Finally, we compute the amplitude corrections due to the `frequency-sweep' in the Fourier domain representation of the waveform within the stationary phase approximation and discuss its implication on parameter estimation."), (2031, '2011-04-01 01:26:55'), (2032, 'Higher-order spin effects in the dynamics of compact binaries II. Radiation field'), (2033, '2006-05-27 2006-05-27'), (2034, 'http://arxiv.org/abs/gr-qc/0605140'), (2035, 'Phys.Rev.D74:104034,2006; Erratum-ibid.D75:049903,2007; Erratum-ibid.D81:089901,2010'), (2036, 'doi:10.1103/PhysRevD.74.104034'), (2037, 'gr-qc/0605140'), (2038, "Motivated by the search for gravitational waves emitted by binary black holes, we investigate the gravitational radiation field of point particles with spins within the framework of the multipolar-post-Newtonian wave generation formalism. We compute: (i) the spin-orbit (SO) coupling effects in the binary's mass and current quadrupole moments one post-Newtonian (1PN) order beyond the dominant effect, (ii) the SO contributions in the gravitational-wave energy flux and (iii) the secular evolution of the binary's orbital phase up to 2.5PN order. Crucial ingredients for obtaining the 2.5PN contribution in the orbital phase are the binary's energy and the spin precession equations, derived in paper I of this series. These results provide more accurate gravitational-wave templates to be used in the data analysis of rapidly rotating Kerr-type black-hole binaries with the ground-based detectors LIGO, Virgo, GEO 600 and TAMA300, and the space-based detector LISA."), (2039, '2010-08-10 13:09:43'), (2040, 'gr-qc/0605140 PDF'), (2041, 'http://www.arxiv.org/pdf/gr-qc/0605140.pdf'), (2042, '2010-08-10 13:09:51'), (2043, 'reporttemplate.pdf'), (2044, 193), (2045, '1974-00-10 10/1974'), (2046, 443), (2047, '10.1086/153180'), (2048, 'http://www.adsabs.harvard.edu/abs/1974ApJ...193..443T'), (2049, 'Perturbations of a rotating black hole. III - Interaction of the hole with gravitational and electromagnetic radiation'), (2050, '2010-08-10 19:40:45'), (2051, 'http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1974ApJ...193..443T&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf'), (2052, '2010-08-10 19:41:16'), (2053, 'A Bayesian Foundation for Physical Theories'), (2054, '2010-08-10 2010-08-10'), (2055, 'http://arxiv.org/abs/1008.1635'), (2056, '1008.1635'), (2057, "Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also leads to a well-defined procedure to select one or more theories among a family of (well-defined) candidates by ranking them according to their posterior probability distributions, which result from Bayes's theorem by incorporating to an initial prior the information extracted from a dataset, ultimately defined by experimental evidence. Examples with different levels of complexity are given and three main applications to basic cosmological questions are analysed: (i) typicality of human observers, (ii) the multiverse hypothesis and, extremely briefly, some few observations about (iii) the anthropic principle. Finally, it is demonstrated that this formulation can address problems that were out of the scope of scientific research until now by presenting the isolated worlds problem and its resolution via the presented framework."), (2058, '2010-08-16 18:49:38'), (2059, '1008.1635 PDF'), (2060, 'http://www.arxiv.org/pdf/1008.1635.pdf'), (2061, '2010-08-16 18:49:41'), (2062, 'Black-hole binaries with non-precessing spins'), (2063, '2010-07-27 2010-07-27'), (2064, 'http://arxiv.org/abs/1007.4789'), (2065, '1007.4789'), (2066, "We present gravitational waveforms for the last orbits and merger of black-hole-binary (BBH) systems along two branches of the BBH parameter space: equal-mass binaries with equal non-precessing spins, and nonspinning unequal-mass binaries. The waveforms are calculated from numerical solutions of Einstein's equations for black-hole binaries that complete between six and ten orbits before merger. Along the equal-mass spinning branch, the spin parameter of each BH is $\\chi_i = S_i/M_i^2 \\in [-0.85,0.85]$, and along the unequal-mass branch the mass ratio is $q =M_2/M_1 \\in [1,4]$. We discuss the construction of low-eccentricity puncture initial data for these cases, the properties of the final merged BH, and compare the last 8-10 GW cycles up to $M\\omega = 0.1$ with the phase and amplitude predicted by standard post-Newtonian (PN) approximants. As in previous studies, we find that the phase from the 3.5PN TaylorT4 approximant is most accurate for nonspinning binaries. For equal-mass spinning binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN order) gives the most robust performance, but it is possible to treat TaylorT4 in such a way that it gives the best accuracy for spins $\\chi_i > -0.75$. When high-order amplitude corrections are included, the PN amplitude of the $(\\ell=2,m=\\pm2)$ modes is larger than the NR amplitude by between 2-4%."), (2067, '2010-08-16 18:50:12'), (2068, '1007.4789 PDF'), (2069, 'http://www.arxiv.org/pdf/1007.4789.pdf'), (2070, '2010-08-16 18:50:19'), (2071, 'Improved Time-Domain Accuracy Standards for Model Gravitational Waveforms'), (2072, 'http://arxiv.org/abs/1008.1803'), (2073, '1008.1803'), (2074, 'Model gravitational waveforms must be accurate enough to be useful for detection of signals and measurement of their parameters, so appropriate accuracy standards are needed. Yet these standards should not be unnecessarily restrictive, making them impractical for the numerical and analytical modelers to meet. The work of Lindblom, Owen, and Brown [Phys. Rev. D 78, 124020 (2008)] is extended by deriving new waveform accuracy standards which are significantly less restrictive while still ensuring the quality needed for gravitational-wave data analysis. These new standards are formulated as bounds on certain norms of the time-domain waveform errors, which makes it possible to enforce them in situations where frequency-domain errors may be difficult or impossible to estimate reliably. These standards are less restrictive by about a factor of 20 than the previously published time-domain standards for detection, and up to a factor of 60 for measurement. These new standards should therefore be much easier to use effectively.'), (2075, '2010-08-16 18:50:34'), (2076, '1008.1803 PDF'), (2077, 'http://www.arxiv.org/pdf/1008.1803.pdf'), (2078, '2010-08-16 18:50:37'), (2079, 'General relativistic dynamics of compact binaries at the third post-Newtonian order'), (2080, 'Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing'), (2081, 'gr-qc/0411146 PDF'), (2082, 'http://www.arxiv.org/pdf/gr-qc/0411146.pdf'), (2083, '2011-04-01 01:26:59'), (2084, 'Gravitational wave background from coalescence of black hole binaries population'), (2085, '2011-04-11 2011-04-11'), (2086, 'http://arxiv.org/abs/1104.2044'), (2087, '1104.2044'), (2088, 'We compute the stochastic gravitational wave background(GWB) generated by a cosmological population of (BH-BH) binaries. Using an updated version of the SeBa population synthesis code, we simulate a large sample of binary systems. Adopting a set of "standard" conservative assumptions calibrated to reproduce the observed properties of single Wolf-Rayet stars and double pulsars, we extract fundamental statistical information on (BH-BH) physical parameters (primary and secondary BH masses, orbital separations and eccentricities, formation and merger timescales). We then derive the binary birth rate from the cosmic star formation history obtained from a numerical study which reproduces the available observations at redshifts $z < 8$. Making a significant step forward to previous calculations, where only the inspiral signal was considered, we include the contribution to the GWB coming from the merging of the two BHs and from the ring-down of the final BH. We find that the GWB from the inspiral phase is characterized by a maximum amplitude in the range $\\Omega_{\\rm GW} \\sim [0.88-1.7]\\times 10^{-7}$ at frequencies $[80 - 100]$ Hz; this signal could be detected with a (S/N)$ > 100$ by a second generation interferometer, such as Advanced LIGO/VIRGO, with 1-3 years of integration. Third generation detectors, such as the Einstein Telescope, could easily detect the GWB generated by the emission during all the three phases of the evolution. The frequency dependence and amplitude of the GWB generated during the merger and ring-down is very sensitive to the adopted core mass threshold for BH formation. This opens up the possibility to better understand the final stages of the evolution of massive stellar binaries using observational constraints on the associated gravitational wave emission.'), (2089, '2011-04-13 15:39:48'), (2090, 63), (2091, '062005'), (2092, '2001-02-26 February 26, 2001'), (2093, 'http://link.aps.org/doi/10.1103/PhysRevD.63.062005'), (2094, '10.1103/PhysRevD.63.062005'), (2095, 'The general relativistic corrections in the equations of motion and associated energy of a binary system of pointlike masses are derived at the third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian expansion of the metric in harmonic coordinates at the 3PN approximation. The metric is parametrized by appropriate nonlinear potentials, which are evaluated in the case of two point particles using a Lorentzian version of a Hadamard regularization which has been defined in previous works. Distributional forms and distributional derivatives constructed from this regularization are employed systematically. The equations of motion of the particles are geodesiclike with respect to the regularized metric. Crucial contributions to the acceleration are associated with the nondistributivity of the Hadamard regularization and the violation of the Leibniz rule by the distributional derivative. The final equations of motion at the 3PN order are invariant under global Lorentz transformations, and admit a conserved energy (neglecting the radiation reaction force at the 2.5PN order). However, they are not fully determined, as they depend on one arbitrary constant, which probably reflects a physical incompleteness of the point-mass regularization. The results of this paper should be useful when comparing theory to the observations of gravitational waves from binary systems in future detectors VIRGO and LIGO.'), (2096, '2010-08-16 19:32:12'), (2097, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i6/e062005'), (2098, '2010-08-16 19:32:14'), (2099, 'Harmonic coordinate method for simulating generic singularities'), (2100, 65), (2101, '044029'), (2102, '2002-01-28 January 28, 2002'), (2103, 'http://link.aps.org/doi/10.1103/PhysRevD.65.044029'), (2104, '10.1103/PhysRevD.65.044029'), (2105, 'This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such coordinates, the terms in Einstein’s equations with the highest number of derivatives take a form similar to that of the wave equation. The application is an exploration of the generic approach to the singularity for this type of matter. The preliminary results indicate that the dynamics as one approaches the singularity is locally the dynamics of the Kasner spacetimes.'), (2106, '2010-08-16 20:35:10'), (2107, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v65/i4/e044029'), (2108, '2010-08-16 20:35:12'), (2109, 'Gauge-invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates'), (2110, 64), (2111, '084016'), (2112, '2001-00-00 2001'), (2113, 'http://link.aps.org/doi/10.1103/PhysRevD.64.084016'), (2114, '10.1103/PhysRevD.64.084016'), (2115, 'We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the gauge-invariant part of the metric perturbations from the amplitudes obeying our generalized Regge-Wheeler and Zerilli equations, and vice-versa. We also give a general expression for the radiated energy at infinity, and establish a relation between our geometrical equations and the Teukolsky formalism. The results presented in this paper are expected to be useful for the close-limit approximation to black hole collisions, for the Cauchy perturbative matching problem, and for the study of isolated horizons.'), (2116, '2010-08-16 22:08:41'), (2117, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i8/e084016'), (2118, '2010-08-16 22:08:43'), (2119, 'Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order'), (2120, '2001-05-26 2001-05-26'), (2121, 'http://arxiv.org/abs/gr-qc/0105099'), (2122, 'Phys.Rev. D65 (2002) 061501; Erratum-ibid. D71 (2005) 129902'), (2123, 'doi:10.1103/PhysRevD.65.061501'), (2124, 'gr-qc/0105099'), (2125, "The inspiral of compact binaries, driven by gravitational-radiation reaction, is investigated through 7/2 post-Newtonian (3.5PN) order beyond the quadrupole radiation. We outline the derivation of the 3.5PN-accurate binary's center-of-mass energy and emitted gravitational flux. The analysis consistently includes the relativistic effects in the binary's equations of motion and multipole moments, as well as the contributions of tails, and tails of tails, in the wave zone. However the result is not fully determined because of some physical incompleteness, present at the 3PN order, of the model of point-particle and the associated Hadamard-type self-field regularization. The orbital phase, whose prior knowledge is crucial for searching and analyzing the inspiral signal, is computed from the standard energy balance argument."), (2126, '2010-08-18 19:09:49'), (2127, 'gr-qc/0105099 PDF'), (2128, 'http://www.arxiv.org/pdf/gr-qc/0105099.pdf'), (2129, '2010-08-18 19:09:52'), (2130, 184001), (2131, '2010-08-18 19:24:49'), (2132, 181101), (2133, 'https://www.ninja-project.org/lib/exe/fetch.php?media=nrar:internal:telecon:initialfrequencynote_boyle.pdf'), (2134, '2010-08-19 13:46:29'), (2135, 'A note on initial orbital frequencies for BBH simulations'), (2136, '2010-02-10 Feb. 10, 2010'), (2137, 'Length requirements for numerical-relativity waveforms'), (2138, '1104.2044 PDF'), (2139, 'http://www.arxiv.org/pdf/1104.2044.pdf'), (2140, '2011-04-13 15:39:49'), (2141, 'Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries'), (2142, '2011-04-15 2011-04-15'), (2143, 'http://arxiv.org/abs/1104.3079'), (2144, '1104.3079'), (2145, "We present the next-to-next-to-leading order post-Newtonian (PN) spin-orbit Hamiltonian for two self-gravitating spinning compact objects. If at least one of the objects is rapidly rotating, then the corresponding interaction is comparable in strength to a 3.5PN effect. The result in the present paper in fact completes the knowledge of the post-Newtonian Hamiltonian for binary spinning black holes up to and including 3.5PN. The Hamiltonian is checked via known results for the test-spin case and via the global Poincar\\'e algebra with the center-of-mass vector uniquely determined by an ansatz."), (2146, 'https://www.ninja-project.org/lib/exe/fetch.php?media=nrar:internal:lengthsummary.pdf'), (2147, '2010-08-19 13:48:18'), (2148, 'Considerations about the length of Athena NR simulations'), (2149, '2010-02-06 Feb. 6, 2010'), (2150, '2011-04-18 15:51:16'), (2151, 'https://www.ninja-project.org/lib/exe/fetch.php?media=nrar:internal:telecon:nr-accuracy-specification.pdf'), (2152, '2010-08-19 14:33:57'), (2153, '2007-10-29 October 29, 2007'), (2154, 'Accuracy standards required for NR waveforms for use in gravitational-wave data analysis'), (2155, '2010-02-10 2010/02/10'), (2156, 'LIGO-T0900288-v3: Advanced LIGO anticipated sensitivity curves'), (2157, 'https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=2974'), (2158, '2010-08-19 15:34:51'), (2159, '2010-08-19 15:35:03'), (2160, 'AdvLIGO noise curves.pdf'), (2161, 'https://dcc.ligo.org/public/0002/T0900288/003/AdvLIGO%20noise%20curves.pdf'), (2162, '2010-08-19 15:35:16'), (2163, '2010-01-25 Jan. 25, 2010'), (2164, '1104.3079 PDF'), (2165, 'http://www.arxiv.org/pdf/1104.3079.pdf'), (2166, '2011-04-18 15:51:18'), (2167, 'An improved, "phase-relaxed" F-statistic for gravitational-wave data analysis'), (2168, '2011-04-14 2011-04-14'), (2169, 'http://arxiv.org/abs/1104.2938'), (2170, '1104.2938'), (2171, 'Rapidly rotating, slightly non-axisymmetric neutron stars emit nearly periodic gravitational waves (GWs), quite possibly at levels detectable by ground-based GW interferometers. We refer to these sources as "GW pulsars". For any given sky position and frequency evolution, the F-statistic is the optimal (frequentist) statistic for the detection of GW pulsars. However, in "all-sky" searches for previously unknown GW pulsars, it would be computationally intractable to calculate the (fully coherent) F-statistic at every point of a (suitably fine) grid covering the parameter space: the number of gridpoints is many orders of magnitude too large for that. Here we introduce a "phase-relaxed" F-statistic, which we denote F_pr, for incoherently combining the results of fully coherent searches over short time intervals. We estimate (very roughly) that for realistic searches, our F_pr is ~10-15% more sensitive than the "semi-coherent" F-statistic that is currently used. Moreover, as a byproduct of computing F_pr, one obtains a rough determination of the time-evolving phase offset between one\'s template and the true signal imbedded in the detector noise. Almost all the ingredients that go into calculating F_pr are already implemented in LAL, so we expect that relatively little additional effort would be required to develop a search code that uses F_pr.'), (2172, '2011-04-18 16:27:30'), (2173, '1104.2938 PDF'), (2174, 'http://www.arxiv.org/pdf/1104.2938.pdf'), (2175, '2011-04-18 16:27:33'), (2176, 'Antenna patterns of interferometric detectors of gravitational waves. I - Linearly polarized waves'), (2177, 224), (2178, 'Binary-black-hole initial data with nearly extremal spins'), (2179, '084017'), (2180, '2008-10-10 October 10, 2008'), (2181, 'http://link.aps.org/doi/10.1103/PhysRevD.78.084017'), (2182, '10.1103/PhysRevD.78.084017'), (2183, 'There is a significant possibility that astrophysical black holes with nearly extremal spins exist. Numerical simulations of such systems require suitable initial data. In this paper, we examine three methods of constructing binary-black-hole initial data, focusing on their ability to generate black holes with nearly extremal spins: (i) Bowen-York initial data, including standard puncture data (based on conformal flatness and Bowen-York extrinsic curvature), (ii) standard quasiequilibrium initial data (based on the extended-conformal-thin-sandwich equations, conformal flatness, and maximal slicing), and (iii) quasiequilibrium data based on the superposition of Kerr-Schild metrics. We find that the two conformally flat methods (i) and (ii) perform similarly, with spins up to about 0.99 obtainable at the initial time. However, in an evolution, we expect the spin to quickly relax to a significantly smaller value around 0.93 as the initial geometry relaxes. For quasiequilibrium superposed Kerr-Schild data [method (iii)], we construct initial data with initial spins as large as 0.9997. We evolve superposed Kerr-Schild data sets with spins of 0.93 and 0.97 and find that the spin drops by only a few parts in 104 during the initial relaxation; therefore, we expect that superposed Kerr-Schild initial data will allow evolutions of binary black holes with relaxed spins above 0.99. Along the way to these conclusions, we also present several secondary results: the power-law coefficients with which the spin of puncture initial data approaches its maximal possible value; approximate analytic solutions for large spin puncture data; embedding diagrams for single spinning black holes in methods (i) and (ii); nonunique solutions for method (ii). All of the initial-data sets that we construct contain subextremal black holes, and when we are able to push the spin of the excision boundary surface into the superextremal regime, the excision surface is always enclosed by a second, subextremal apparent horizon. The quasilocal spin is measured by using approximate rotational Killing vectors, and the spin is also inferred from the extrema of the intrinsic scalar curvature of the apparent horizon. Both approaches are found to give consistent results, with the approximate-Killing-vector spin showing the least variation during the initial relaxation.'), (2184, '2010-08-20 21:11:49'), (2185, 'http://prd.aps.org/pdf/PRD/v78/i8/e084017'), (2186, '2010-08-20 21:11:51'), (2187, 'arXiv:0805.4192'), (2188, 'Virgo TDS'), (2189, 'https://pub3.ego-gw.it/itf/tds/index.php?callContent=2&callCode=1544'), (2190, '2010-08-21 03:14:53'), (2191, 'VIR-NOT-DIR-1390-304.pdf'), (2192, '2010-08-21 03:15:22'), (2193, 'http://link.aps.org/doi/10.1103/PhysRevLett.99.181101'), (2194, '2005-11-12 Nov. 12, 2005'), (2195, 'Virgo collaboration'), (2196, 'Order of Magnitude'), (2197, '1987-01-01 January 1, 1987'), (2198, '131-154'), (2199, 'http://adsabs.harvard.edu/abs/1987MNRAS.224..131S'), (2200, 'ps1.pdf'), (2201, 'ps1ans.pdf'), (2202, 'ps2.pdf'), (2203, 'ps2ans.pdf'), (2204, 'ps3.pdf'), (2205, 'ps3ans.pdf'), (2206, 'ps4.pdf'), (2207, 'ps4ans.pdf'), (2208, 'ps5.pdf'), (2209, 'ps5ans.pdf'), (2210, 'ps6.pdf'), (2211, 'ps7.pdf'), (2212, 'ps8.pdf'), (2213, 'The Small Scale Structure of Spacetime'), (2214, '2010-09-06 2010-09-06'), (2215, 'http://arxiv.org/abs/1009.1136'), (2216, '1009.1136'), (2217, "Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the strong-coupling limit of the Wheeler-DeWitt equation. If this description proves to be correct, it suggests a fascinating relationship between small-scale quantum spacetime and the behavior of cosmologies near an asymptotically silent singularity."), (2218, '2010-09-07 13:08:01'), (2219, '1009.1136 PDF'), (2220, 'http://www.arxiv.org/pdf/1009.1136.pdf'), (2221, '2010-09-07 13:08:23'), (2222, '1009.pdf'), (2223, 'http://arxiv.org/pdf/1009.1136v1'), (2224, '2010-09-07 13:08:24'), (2225, 'The response of a free-mass interferometric gravitational wave detector to plane gravitational waves arriving from an arbitrary direction with an arbitrary linear polarization in the long-wavelength approximation is studied. It is proved that the threshold averaged coincidence probability for two detectors equals the mean of the product of their antenna power patterns, allowing the use of threshold independent criteria for judging the likelihood of coincidences between detectors. Results on the coincidences between detectors located in the U.S.A. and in Europe for random waves from Virgo are obtained, and the implications of these results for the choice of orientation of planned detectors and for the numbers of detectors world-wide are considered.'), (2226, '2011-04-18 22:07:44'), (2227, 'Circular orbits of corotating binary black holes: Comparison between analytical and numerical results'), (2228, '2002-06-28 June 28, 2002'), (2229, '1987MNRAS_224__131S.pdf'), (2230, 'Cosmic Train Wreck by Massive Black Holes: Discovery of a kpc-Scale Triple Active Galactic Nucleus'), (2231, '2011-04-18 2011-04-18'), (2232, 'http://arxiv.org/abs/1104.3391'), (2233, '1104.3391'), (2234, 'Intermediate-mass-ratio black hole binaries: intertwining numerical and perturbative techniques'), (2235, '2010-08-25 2010-08-25'), (2236, 'http://arxiv.org/abs/1008.4360'), (2237, '1008.4360'), (2238, '10.1088/0264-9381/25/18/184001'), (2239, 'http://iopscience.iop.org/0264-9381/25/18/184001'), (2240, 'Intermediate-mass-ratio black hole binaries'), (2241, '1008.4360 PDF'), (2242, 'http://www.arxiv.org/pdf/1008.4360.pdf'), (2243, '2010-10-05 15:44:42'), (2244, 'Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order'), (2245, 13), (2246, 575), (2247, 'http://stacks.iop.org/0264-9381/13/i=4/a=002'), (2248, "The two independent `plus' and `cross' polarization waveforms associated with the gravitational waves emitted by inspiralling, non-spinning, compact binaries are presented, ready for use in the data analysis of signals received by future laser interferometer gravitational-wave detectors such as LIGO and VIRGO. The computation is based on a recently derived expression of the gravitational field at the second-post-Newtonian approximation of general relativity beyond the dominant (Newtonian) quadrupolar field. The use of these theoretical waveforms to make measurements of astrophysical parameters and to test the nature of relativistic gravity is discussed."), (2249, '0264-9381_13_4_002.pdf'), (2250, '10.1103/PhysRevLett.99.181101'), (2251, 'http://stacks.iop.org/0264-9381/25/i=16/a=165003'), (2252, 'Hierarchical galaxy mergers will lead to the formation of binary and, in particular, triple SMBHs, given that most massive galaxies harbor central SMBHs. A triple of SMBHs becomes visible as a triple Active Galactic Nucleus (AGN) when the BHs accrete large amounts of gas at the same time. Here we report the discovery of a kpc-scale triple AGN, SDSSJ1027+1749 at z = 0.066, from our systematic search for hierarchical mergers of AGNs. The galaxy contains three emission-line nuclei, two of which are offset by ~ 450 and 110 km/s in velocity and by 2.4 and 3.0 kpc in projected separation from the central nucleus. All three nuclei are classified as obscured AGNs based on optical diagnostic emission line ratios, with black hole mass estimates M_BH >~ 10^8 M_sun from stellar velocity dispersions measured in the associated stellar components. Based on dynamical friction timescale estimates, the three stellar components in SDSSJ1027+1749 will merge in ~ 40 Myr, and their associated SMBHs may evolve into a gravitationally interacting triple system in ~ 200 Myr. Our result sets a lower limit of ~ 5 x 10^(-5) for the fraction of kpc-scale triples in optically selected AGNs at z ~ 0.1.'), (2253, '2011-04-19 15:16:22'), (2254, 'General relativity predicts the gravitational wave signatures of coalescing binary black holes. Explicit waveform predictions for such systems, required for optimal analysis of observational data, have so far been achieved primarily using the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late-inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein’s equations. We compare waveform phasing from simulations of the last ∼14 cycles of gravitational radiation from equal-mass, nonspinning black holes with the corresponding 2.5PN, 3PN, and 3.5PN orbital phasing. We find phasing agreement consistent with internal error estimates for either approach, suggesting that PN waveforms for this system are effective until the last orbit prior to final merger.'), (2255, 'Cosmic Train Wreck by Massive Black Holes'), (2256, '1104.3391 PDF'), (2257, 'http://www.arxiv.org/pdf/1104.3391.pdf'), (2258, '2011-04-19 15:16:26'), (2259, 'Listening to the Universe with Gravitational-Wave Astronomy'), (2260, 'Unraveling Binary Evolution from Gravitational-Wave Signals and Source Statistics'), (2261, '2010-01-14 2010-01-14'), (2262, 'http://arxiv.org/abs/1001.2583'), (2263, '1001.2583'), (2264, 'The next generation of ground-based gravitational-wave detectors are likely to observe gravitational waves from the coalescences of compact-objects binaries. We describe the state of the art for predictions of the rate of compact-binary coalescences and report on initial efforts to develop a framework for converting gravitational-wave observations into improved constraints on astrophysical parameters.'), (2265, '2010-11-11 21:45:34'), (2266, '1001.2583 PDF'), (2267, 'http://www.arxiv.org/pdf/1001.2583.pdf'), (2268, '2010-11-11 21:45:37'), (2269, 'Virgo status'), (2270, '2011-10-11 20:14:54'), (2271, '1110.0408 PDF'), (2272, '2010-11-11 21:46:01'), (2273, 'The Distribution of Coalescing Compact Binaries in the Local Universe: Prospects for Gravitational-Wave Observations'), (2274, '2010-11-04 2010-11-04'), (2275, 'http://arxiv.org/abs/1011.1256'), (2276, '1011.1256'), (2277, 'Merging compact binaries are the most viable and best studied candidates for gravitational wave (GW) detection by the fully operational network of ground-based observatories. In anticipation of the first detections, the expected distribution of GW sources in the local universe is of considerable interest. Here we investigate the full phase space distribution of coalescing compact binaries at $z = 0$ using dark matter simulations of structure formation. The fact that these binary systems acquire large barycentric velocities at birth (``kicks") results in merger site distributions that are more diffusely distributed with respect to their putative hosts, with mergers occurring out to distances of a few Mpc from the host halo. Redshift estimates based solely on the nearest galaxy in projection can, as a result, be inaccurate. On the other hand, large offsets from the host galaxy could aid the detection of faint optical counterparts and should be considered when designing strategies for follow-up observations. The degree of isotropy in the projected sky distributions of GW sources is found to be augmented with increasing kick velocity and to be severely enhanced if progenitor systems possess large kicks as inferred from the known population of pulsars and double compact binaries. Even in the absence of observed electromagnetic counterparts, the differences in sky distributions of binaries produced by disparate kick-velocity models could be discerned by GW observatories, within the expected accuracies and detection rates of advanced LIGO--in particular with the addition of more interferometers.'), (2278, '2010-11-11 21:55:15'), (2279, 'The Distribution of Coalescing Compact Binaries in the Local Universe'), (2280, '1011.1256 PDF'), (2281, 'http://www.arxiv.org/pdf/1011.1256.pdf'), (2282, '2010-11-11 21:55:38'), (2283, 'The Mass Distribution of Stellar-Mass Black Holes'), (2284, '2010-11-05 2010-11-05'), (2285, 'http://arxiv.org/abs/1011.1459'), (2286, '1011.1459'), (2287, "We perform a Bayesian analysis of the mass distribution of stellar-mass black holes using the observed masses of 15 low-mass X-ray binary systems undergoing Roche lobe overflow and five high-mass, wind-fed X-ray binary systems. Using MCMC calculations, we model the mass distribution both parametrically---as a power law, exponential, gaussian, combination of two gaussians, or log-normal distribution---and non-parametrically---as histograms with varying numbers of bins. We provide confidence bounds on the shape of the mass distribution in the context of each model and compare the models by calculating their Bayesian evidence. The mass distribution of the low-mass systems is best fit by a power-law, while the distribution of the combined sample is best fit by the exponential model. This difference indicates that the low-mass subsample is not consistent with being drawn from the distribution of the combined population. We examine the existence of a ``gap'' between the most massive neutron stars and the least massive black holes by considering the 1% quantile from each black hole mass distribution, M_1%. The best model (the power law) fitted to the low-mass systems gives a distribution with M_1% > 4.3 MSun with 90% confidence, while the best model (the exponential) fitted to all 20 systems has M_1% > 4.5 MSun with 90% confidence. We conclude that our sample of black hole masses provides strong evidence of a gap between the maximum neutron star mass and the minimum black hole mass. Our results on the low-mass sample are in qualitative agreement with those of Ozel et al (2010), although our broad model-selection analysis more reliably reveals the best-fit underlying mass distribution. The presence of a mass gap remains theoretically unexplained."), (2288, '2010-11-11 22:01:30'), (2289, '1011.1459 PDF'), (2290, 'http://www.arxiv.org/pdf/1011.1459.pdf'), (2291, '2010-11-11 22:02:15'), (2292, 'A Very Close Binary Black Hole in a Giant Elliptical Galaxy 3C 66B and its Black Hole Merger'), (2293, '2010-11-11 2010-11-11'), (2294, 'http://arxiv.org/abs/1011.2647'), (2295, 'Astrophysical Journal, vol.724, L166, 2010'), (2296, '1011.2647'), (2297, 'Recent observational results provide possible evidence that binary black holes (BBHs) exist in the center of giant galaxies and may merge to form a supermassive black hole in the process of their evolution. We first detected a periodic flux variation on a cycle of $93\\pm1$ days from the 3-mm monitor observations of a giant elliptical galaxy \\object{3C 66B} for which an orbital motion with a period of $1.05\\pm0.03$ years had been already observed. The detected signal period being shorter than the orbital period can be explained by taking into consideration the Doppler-shifted modulation due to the orbital motion of a BBH. Assuming that the BBH has a circular orbit and that the jet axis is parallel to the binary angular momentum, our observational results demonstrate the presence of a very close BBH that has the binary orbit with an orbital period of $1.05\\pm0.03$ years, an orbital radius of $(3.9\\pm1.0) \\times 10^{-3}$ pc, an orbital separation of $(6.1^{+1.0}_{-0.9}) \\times 10^{-3}$ pc, the larger black hole mass of $(1.2^{+0.5}_{-0.2}) \\times 10^9$ $M_{\\sun}$, and the smaller black hole mass of $(7.0^{+4.7}_{-6.4}) \\times 10^8$ $M_{\\sun}$. The BBH decay time of $(5.1^{+60.5}_{-2.5})\\times 10^2$ years provides evidence for the occurrence of black hole mergers. This Letter will demonstrate the interesting possibility of black hole collisions to form a supermassive black hole in the process of evolution, one of the most spectacular natural phenomena in the universe.'), (2298, '2010-11-13 00:35:44'), (2299, '1011.2647 PDF'), (2300, 'http://www.arxiv.org/pdf/1011.2647.pdf'), (2301, '2010-11-13 00:35:47'), (2302, 'A Characteristic Extraction Tool for Gravitational Waveforms'), (2303, '2010-11-18 2010-11-18'), (2304, 'http://arxiv.org/abs/1011.4223'), (2305, '1011.4223'), (2306, 'We develop and test a characteristic waveform extraction tool which incorporates major improvements and corrections of prior versions. The extraction tool uses a characteristic evolution code to propagate numerical data on an inner worldtube supplied by a 3+1 Cauchy evolution to obtain the gravitational waveform at null infinity. Accuracy and convergence of the numerical error is demonstrated for an inspiral and merger of mass M binary black holes even for an extraction worldtube with radius as small as R=20M. The tool provides a means of unambiguous comparison between waveforms generated by evolution codes based upon different formulations of the Einstein equations and based upon different numerical approximations.'), (2307, '2010-11-21 05:12:05'), (2308, '1011.4223 PDF'), (2309, 'http://www.arxiv.org/pdf/1011.4223.pdf'), (2310, '2010-11-21 05:12:11'), (2311, 'Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform'), (2312, '2010-12-11 2010-12-11'), (2313, 'http://arxiv.org/abs/1012.2456'), (2314, '1012.2456'), (2315, 'We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses $\\mu$ and $M$ in the extreme-mass-ratio limit, $\\mu/M=\\nu\\ll 1$. We focus on the transition from quasicircular inspiral to plunge, merger and ringdown.We compare the EOB waveform to a Regge-Wheeler-Zerilli (RWZ) waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by leading-order ${\\cal O}(\\nu)$ analytically--resummed radiation reaction. The EOB and the RWZ waveforms have an initial dephasing of about $5\\times 10^{-4}$ rad and maintain then a remarkably accurate phase coherence during the long inspiral ($\\sim 33$ orbits), accumulating only about $-2\\times 10^{-3}$ rad until the last stable orbit, i.e. $\\Delta\\phi/\\phi\\sim -5.95\\times 10^{-6}$. We obtain such accuracy without calibrating the analytically-resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for LISA-oriented studies. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasi-circular corrections both in the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasi-circular parameters by requiring compatibility between EOB and RWZ waveforms at the light-ring. The resulting phase difference around merger time is as small as $\\pm 0.015$ rad, with a fractional amplitude agreement of $2.5%$. This suggest that next-to-quasi-circular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical relativity waveforms.'), (2316, '2010-12-14 09:37:09'), (2317, 'Binary black hole coalescence in the extreme-mass-ratio limit'), (2318, '1012.2456 PDF'), (2319, 'http://www.arxiv.org/pdf/1012.2456.pdf'), (2320, '2010-12-14 09:37:22'), (2321, '064004'), (2322, '2009-03-03 March 03, 2009'), (2323, 'http://link.aps.org/doi/10.1103/PhysRevD.79.064004'), (2324, '10.1103/PhysRevD.79.064004'), (2325, 'We improve and generalize a resummation method of post-Newtonian multipolar waveforms from circular (nonspinning) compact binaries introduced in Refs. 1, 2. One of the characteristic features of this resummation method is to replace the usual additive decomposition of the standard post-Newtonian approach by a multiplicative decomposition of the complex multipolar waveform hℓm into several (physically motivated) factors: (i) the Newtonian waveform, (ii) a relativistic correction coming from an “effective source,” (iii) leading-order tail effects linked to propagation on a Schwarzschild background, (iv) a residual tail dephasing, and (v) residual relativistic amplitude corrections fℓm. We explore here a new route for resumming fℓm based on replacing it by its ℓ-th root: ρℓm=fℓm1/ℓ. In the extreme-mass-ratio case, this resummation procedure results in a much better agreement between analytical and numerical waveforms than when using standard post-Newtonian approximants. We then show that our best approximants behave in a robust and continuous manner as we deform them by increasing the symmetric mass ratio ν≡m1m2/(m1+m2)2 from 0 (extreme-mass-ratio case) to 1/4 (equal-mass case). The present paper also completes our knowledge of the first post-Newtonian corrections to multipole moments by computing ready-to-use explicit expressions for the first post-Newtonian contributions to the odd-parity (current) multipoles.'), (2326, '2002-10-22 2002-10-22'), (2327, 'http://arxiv.org/abs/astro-ph/0210481'), (2328, 'Annals Phys. 303 (2003) 142-178'), (2329, 'doi:10.1016/S0003-4916(02)00025-8'), (2330, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i6/e064004'), (2331, 'astro-ph/0210481'), (2332, 'The LIGO (Laser Interferometer Gravitational-Wave Observatory) detectors have just completed their first science run, following many years of planning, research, and development. LIGO is a member of what will be a worldwide network of gravitational-wave observatories, with other members in Europe, Japan, and -- hopefully -- Australia. Plans are rapidly maturing for a low frequency, space-based gravitational-wave observatory: LISA, the Laser Interferometer Space Antenna, to be launched around 2011. The goal of these instruments is to inaugurate the field of {\\it gravitational-wave astronomy}: using gravitational-waves as a means of listening to highly relativistic dynamical processes in astrophysics. This review discusses the promise of this field, outlining why gravitational waves are worth pursuing, and what they are uniquely suited to teach us about astrophysical phenomena. We review the current state of the field, both theoretical and experimental, and then highlight some aspects of gravitational-wave science that are particularly exciting (at least to this author).'), (2333, '2011-04-19 16:42:26'), (2334, 'astro-ph/0210481 PDF'), (2335, 'http://www.arxiv.org/pdf/astro-ph/0210481.pdf'), (2336, '2011-04-19 16:42:30'), (2337, 'J. Phys. A: Math. Gen.'), (2338, '2010-12-21 15:57:10'), (2339, '2010-12-21 15:57:12'), (2340, '1742-6596'), (2341, 'Journal of Physics: Conference Series'), (2342, 'J. Phys.: Conf. Ser.'), (2343, 243), (2344, '2010-00-08 08/2010'), (2345, '012007'), (2346, '10.1088/1742-6596/243/1/012007'), (2347, 'http://iopscience.iop.org/1742-6596/243/1/012007'), (2348, 'Complete phenomenological gravitational waveforms from spinning coalescing binaries'), (2349, '2010-12-21 16:19:36'), (2350, '1742-6596_243_1_012007.pdf'), (2351, 'http://iopscience.iop.org/1742-6596/243/1/012007/pdf/1742-6596_243_1_012007.pdf'), (2352, '2010-12-21 16:20:39'), (2353, 'Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins'), (2354, 'We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins that is based on a description of the late-inspiral, merger and ringdown in full general relativity (GR). By matching a post-Newtonian description of the inspiral to a set of numerical calculations performed in full GR, we obtain a waveform family with a conveniently small number of physical parameters. The physical content of these waveforms includes the "orbital hang-up" effect, and "spin flips". These waveforms will allow us to detect a larger parameter space of BBH coalescence (including a considerable fraction of precessing binaries in the comparable-mass regime), to explore various scientific questions related to gravitational-wave astronomy, and could significantly improve the expected detection rates.'), (2355, '2010-12-21 16:23:23'), (2356, '1977-11-00 11/1977'), (2357, '1833-1836'), (2358, '10.1088/0305-4470/10/11/011'), (2359, 'http://iopscience.iop.org.proxy.library.cornell.edu/0305-4470/10/11/011'), (2360, 'On a relation between spherical and spheroidal harmonics'), (2361, '2011-05-02 14:46:18'), (2362, 'jav10i11p1833.pdf'), (2363, 'http://www.nytimes.com/2007/07/18/dining/18mini.html'), (2364, '2010-12-21 16:23:36'), (2365, '2007-07-18 2007-07-18'), (2366, 'Summer Express: 101 Simple Meals Ready in 10 Minutes or Less'), (2367, '2011-05-02 15:52:38'), (2368, 19), (2369, '2007-00-10 10/2007'), (2370, 'S689-S699'), (2371, '10.1088/0264-9381/24/19/S31'), (2372, 'http://iopscience.iop.org/0264-9381/24/19/S31/'), (2373, 'A phenomenological template family for black-hole coalescence waveforms'), (2374, '2010-12-21 16:33:31'), (2375, '2011-01-19 20:18:20'), (2376, 'http://prl.aps.org/pdf/PRL/v99/i18/e181101'), (2377, '2011-01-19 20:18:22'), (2378, '0264-9381_24_19_S31.pdf'), (2379, 'Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonprecessing, spinning, equal-mass black holes'), (2380, '084041'), (2381, '2010-04-20 April 20, 2010'), (2382, 'http://link.aps.org/doi/10.1103/PhysRevD.81.084041'), (2383, '10.1103/PhysRevD.81.084041'), (2384, 'We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical relativity simulations of spinning, nonprecessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radian and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin antialigned case, these differences can be reduced to 0.13 radian and 1% during inspiral and plunge, and to 0.4 radian and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin antialigned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30M⊙–200M⊙. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin antialigned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.'), (2385, '2010-12-21 16:46:31'), (2386, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084041'), (2387, '2010-12-21 16:46:33'), (2388, 'Transition from inspiral to plunge in binary black hole coalescences'), (2389, '064015'), (2390, '2000-00-00 2000'), (2391, 'http://link.aps.org/doi/10.1103/PhysRevD.62.064015'), (2392, '10.1103/PhysRevD.62.064015'), (2393, 'Combining recent techniques giving nonperturbative resummed estimates of the damping and conservative parts of the two-body dynamics, we describe the transition between the adiabatic phase and the plunge, in coalescing binary black holes with comparable masses moving on quasicircular orbits. We give initial dynamical data for numerical relativity investigations, with a fraction of an orbit left, and provide, for data analysis purposes, an estimate of the gravitational waveform emitted throughout the inspiral, plunge and coalescence phases.'), (2394, '2010-12-21 16:51:32'), (2395, 'Effective one-body approach to general relativistic two-body dynamics'), (2396, 59), (2397, '084006'), (2398, '1999-03-08 March 08, 1999'), (2399, 'http://link.aps.org/doi/10.1103/PhysRevD.59.084006'), (2400, '10.1103/PhysRevD.59.084006'), (2401, 'We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing binary system of compact objects. The transition from the adiabatic inspiral, driven by gravitational radiation damping, to an unstable plunge, induced by strong spacetime curvature, is predicted to occur for orbits more tightly bound than the innermost stable circular orbit in a Schwarzschild metric of mass M=m1+m2. The binding energy, angular momentum and orbital frequency of the innermost stable circular orbit for the time-symmetric two-body problem are determined as a function of the mass ratio.'), (2402, '2010-12-21 16:51:36'), (2403, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i6/e064015'), (2404, '2010-12-21 16:51:38'), (2405, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v59/i8/e084006'), (2406, '2010-12-21 16:51:39'), (2407, 'The New York Times'), (2408, '0362-4331'), (2409, 'http://www.nytimes.com/2011/01/19/dining/19mini.html?pagewanted=all'), (2410, '2011-01-14 January 14, 2011'), (2411, 'For Whole-Grain Pancakes, Try a Little Tenderness: The Minimalist'), (2412, 'Dining & Wine'), (2413, 'NYTimes.com'), (2414, '2011-01-20 18:48:37'), (2415, 'For Whole-Grain Pancakes, Try a Little Tenderness'), (2416, 'http://www.nytimes.com/2008/01/16/dining/161mrex.html?ref=dining&pagewanted=all'), (2417, '2008-01-16 January 16, 2008'), (2418, 'Recipe: Whole-Grain Pancakes'), (2419, '2011-01-20 18:48:41'), (2420, 'Recipe'), (2421, 'http://www.nytimes.com/2009/12/10/health/nutrition/10recipehealth.html?pagewanted=all'), (2422, '2009-12-10 December 10, 2009'), (2423, 'Oatmeal Buttermilk Blueberry Pancakes'), (2424, 'Health / Fitness & Nutrition'), (2425, '2011-01-20 18:48:48'), (2426, 'http://www.nytimes.com/2010/12/20/health/nutrition/20recipehealth.html?pagewanted=all'), (2427, '2010-12-20 December 20, 2010'), (2428, 'Blini at the Buffet - Recipes for Health'), (2429, '2011-01-20 18:48:54'), (2430, 'http://www.nytimes.com/2011/01/19/dining/19minirex1.html?ref=dining&pagewanted=all'), (2431, 'Bulgur-Ricotta Pancakes: Recipe'), (2432, '2011-01-20 18:49:00'), (2433, 'Bulgur-Ricotta Pancakes'), (2434, 'Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame'), (2435, '2002-09-24 2002-09-24'), (2436, 'http://arxiv.org/abs/gr-qc/0209089'), (2437, 'Class.Quant.Grav. 20 (2003) 755'), (2438, 'gr-qc/0209089'), (2439, "The equations of motion of compact binary systems and their associated Lagrangian formulation have been derived in previous works at the third post-Newtonian (3PN) approximation of general relativity in harmonic coordinates. In the present work we investigate the binary's relative dynamics in the center-of-mass frame (center of mass located at the origin of the coordinates). We obtain the 3PN-accurate expressions of the center-of-mass positions and equations of the relative binary motion. We show that the equations derive from a Lagrangian (neglecting the radiation reaction), from which we deduce the conserved center-of-mass energy and angular momentum at the 3PN order. The harmonic-coordinates center-of-mass Lagrangian is equivalent, {\\it via} a contact transformation of the particles' variables, to the center-of-mass Hamiltonian in ADM coordinates that is known from the post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the dynamical stability of circular binary orbits at the 3PN order."), (2440, '2011-01-25 17:38:10'), (2441, 'Third post-Newtonian dynamics of compact binaries'), (2442, 'gr-qc/0209089 PDF'), (2443, 'http://www.arxiv.org/pdf/gr-qc/0209089.pdf'), (2444, '2011-01-25 17:38:14'), (2445, 'Summer Express'), (2446, 'fetch.pdf'), (2447, '2011-01-28 20:47:26'), (2448, 'http://prd.aps.org/pdf/PRD/v49/i6/p2658_1'), (2449, '2011-01-28 20:47:28'), (2450, 'Observing binary inspiral in gravitational radiation: One interferometer'), (2451, 2198), (2452, '1993-03-15 March 15, 1993'), (2453, 'http://link.aps.org/doi/10.1103/PhysRevD.47.2198'), (2454, '10.1103/PhysRevD.47.2198'), (2455, "Close binary systems of compact objects with less than ten minutes remaining before coalescence are readily identifiable sources of gravitational radiation for the United States Laser Interferometer Gravitational-Wave Observatory (LIGO) and the French-Italian VIRGO gravitational-wave observatory. As a start toward assessing the full capabilities of the LIGO-VIRGO detector network, we investigate the sensitivity of individual LIGO-VIRGO-like interferometers and the precision with which they can determine the characteristics of an inspiralling binary system. Since the two interferometers of the LIGO detector share nearly the same orientation, their joint sensitivity is similar to that of a single, more sensitive interferometer. We express our results for a single interferometer of both initial and advanced LIGO design, and also for the LIGO detector in the limit that its two interferometers share exactly the same orientation. We approximate the secular evolution of a binary system as driven exclusively by its leading-order quadrupole gravitational radiation. Observations of a binary in a single interferometer are described by four characteristic quantities: an amplitude A, a chirp mass M, a time T, and a phase ψ. We find the amplitude signal-to-noise ratio (SNR) ρ of an observed binary system as a function of A and M for a particular orientation of the binary with respect to the interferometer, and also the distribution of SNR's for randomly oriented binaries at a constant distance. To assess the interferometer sensitivity, we calculate the rate at which sources are expected to be observed and the range to which they are observable. Assuming a conservative rate density for coalescing neutron-star binary systems of 8×10-8 yr-1 Mpc-3, we find that the advanced LIGO detector will observe approximately 69 yr-1 with an amplitude SNR greater than 8. Of these, approximately 7 yr-1 will be from binaries at distances greater than 950 Mpc. We give analytic and numerical results for the precision with which each of the characteristic quantities can be determined by interferometer observations. For neutron-star binaries, the fractional 1σ statistical error in the determination of A is equal to 1/ρ. For ρ>8, the fractional 1σ error in the measurement of M in the advanced LIGO detectors is less than 2×10-5, a phenomenal precision. The characteristic time is related to the moment when coalescence occurs, and can be measured in the advanced detectors with a 1σ uncertainty of less than 3×10-4 s (assuming ρ>8). We also explore the sensitivity of these results to a tunable parameter in the interferometer design (the recycling frequency). The optimum choice of the parameter is dependent on the goal of the observations, e.g., maximizing the rate of detections or maximizing the precision of measurement. We determine the optimum parameter values for these two cases. The calculations leading to the SNR and the precision of measurement assume that the interferometer observations extend over only the last several minutes of binary inspiral, during which time the orbital frequency increases from approximately 5 Hz to 500 Hz. We examine the sensitivity of our results to the elapsed time of the observation and show that observations of longer duration lead to very little improvement in the SNR or the precision of measurement."), (2456, '2011-01-28 20:47:58'), (2457, 'Observing binary inspiral in gravitational radiation'), (2458, 'http://prd.aps.org/pdf/PRD/v47/i6/p2198_1'), (2459, '2011-01-28 20:48:00'), (2460, 'Detection, measurement, and gravitational radiation'), (2461, 46), (2462, 5236), (2463, '1992-12-15 December 15, 1992'), (2464, 'http://link.aps.org/doi/10.1103/PhysRevD.46.5236'), (2465, '10.1103/PhysRevD.46.5236'), (2466, 'The optimum design, construction, and use of the Laser Interferometer Gravitational Wave Observatory (LIGO), the French-Italian Gravitational Wave Observatory (VIRGO), or the Laser Gravitational Wave Observatory (LAGOS) gravitational radiation detectors depends upon accurate calculations of their sensitivity to different sources of radiation. Here I examine how to determine the sensitivity of these instruments to sources of gravitational radiation by considering the process by which data are analyzed in a noisy detector. The problem of detection (is a signal present in the output of the detector?) is separated from that of measurement (what are the parameters that characterize the signal in the detector output?). By constructing the probability that the detector output is consistent with the presence of a signal, I show how to quantify the uncertainty that the output contains a signal and is not simply noise. Proceeding further, I construct the probability distribution that the parametrization μ that characterizes the signal has a certain value. From the distribution and its mode I determine volumes V(P) in parameter space such that μ∈V(P) with probability P [owing to the random nature of the detector noise, the volumes V(P) are always different, even for identical signals in the detector output], thus quantifying the uncertainty in the estimation of the signal parametrization. These techniques are suitable for analyzing the output of a noisy detector. If we are designing a detector, or determining the suitability of an existing detector for observing a new source, then we do not have detector output to analyze but are interested in the "most likely" response of the detector to a signal. I exploit the techniques just described to determine the "most likely" volumes V(P) for detector output that would result in a parameter probability distribution with given mode. Finally, as an example, I apply these techniques to determine the anticipated sensitivity of the LIGO and LAGOS detectors to the gravitational radiation from a perturbed Kerr black hole.'), (2467, '2011-01-28 20:48:38'), (2468, 'http://prd.aps.org/pdf/PRD/v46/i12/p5236_1'), (2469, '2011-01-28 20:48:40'), (2470, 'Efficiently enclosing the compact binary parameter space by singular-value decomposition'), (2471, '2011-01-25 2011-01-25'), (2472, 'http://arxiv.org/abs/1101.4939'), (2473, '1101.4939'), (2474, 'Gravitational-wave searches for the merger of compact binaries use matched-filtering as the method of detecting signals and estimating parameters. Such searches construct a fine mesh of filters covering a signal parameter space at high density. Previously it has been shown that singular value decomposition can reduce the effective number of filters required to search the data. Here we study how the basis provided by the singular value decomposition changes dimension as a function of template bank density. We will demonstrate that it is sufficient to use the basis provided by the singular value decomposition of a low density bank to accurately reconstruct arbitrary points within the boundaries of the template bank. Since this technique is purely numerical it may have applications to interpolating the space of numerical relativity waveforms.'), (2475, '2011-01-28 21:28:08'), (2476, '1101.4939 PDF'), (2477, 'http://www.arxiv.org/pdf/1101.4939.pdf'), (2478, '2011-01-28 21:28:11'), (2479, 'http://www.nytimes.com/1997/09/17/dining/minimalist-every-day-a-red-pepper-day.html?pagewanted=all'), (2480, '1997-09-17 September 17, 1997'), (2481, 'Minimalist; Every Day, a Red Pepper Day'), (2482, '2011-01-28 21:28:27'), (2483, 'Comparison of search templates for gravitational waves from binary inspiral'), (2484, '044023'), (2485, '2001-01-30 January 30, 2001'), (2486, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.63.044023'), (2487, '10.1103/PhysRevD.63.044023'), (2488, 'We compare the performances of the templates defined by three different types of approaches: traditional post-Newtonian templates (Taylor approximants), “resummed” post-Newtonian templates assuming the adiabatic approximation and stopping before the plunge (P approximants), and further “resummed” post-Newtonian templates going beyond the adiabatic approximation and incorporating the plunge with its transition from the inspiral (effective-one-body approximants). The signal to noise ratio is significantly enhanced (mainly because of the inclusion of the plunge signal) by using these new effective-one-body templates relative to the usual post-Newtonian ones for a total binary mass m≳30M⊙, and reaches a maximum around m∼80M⊙. Independently of the question of the plunge signal, the comparison of the various templates confirms the usefulness of using resummation methods. The paper also summarizes the key elements of the construction of various templates and thus can serve as a resource for those involved in writing inspiral search software.'), (2489, '2011-01-29 21:13:14'), (2490, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i4/e044023'), (2491, '2011-01-29 21:13:16'), (2492, 'Structure and Mass Absorption of Hypothetical Terrestrial Black Holes'), (2493, 'Physics, Astrophysics and Cosmology with Gravitational Waves'), (2494, 'http://www.livingreviews.org/lrr-2009-2'), (2495, 'lrr-2009-2Color.pdf'), (2496, 'The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission'), (2497, '1999-10-26 1999-10-26'), (2498, 'http://arxiv.org/abs/gr-qc/9910091'), (2499, 'Phys.Rev.D61:084004,2000; Erratum-ibid.D63:049902,2001; Erratum-ibid.D65:069902,2002; Erratum-ibid.D67:089901,2003; Erratum-ibid.D78:109902,2008'), (2500, 'doi:10.1103/PhysRevD.61.084004'), (2501, 'gr-qc/9910091'), (2502, "A major focus of much current research in gravitation theory is on understanding how radiation reaction drives the evolution of a binary system, particularly in the extreme mass ratio limit. Such research is of direct relevance to gravitational-wave sources for space-based detectors (such as LISA). We present here a study of the radiative evolution of circular (i.e., constant Boyer-Lindquist coordinate radius), non-equatorial Kerr black hole orbits. Recent theorems have shown that, at least in an adiabatic evolution, such orbits evolve from one circular configuration into another, changing only their radius and inclination angle. This constrains the system's evolution in such a way that the change in its Carter constant can be deduced from knowledge of gravitational wave fluxes propagating to infinity and down the black hole's horizon. Thus, in this particular case, a local radiation reaction force is not needed. In accordance with post-Newtonian weak-field predictions, we find that inclined orbits radiatively evolve to larger inclination angles (although the post-Newtonian prediction overestimates the rate of this evolution in the strong field by a factor $\\lesssim 3$). We also find that the gravitational waveforms emitted by these orbits are rather complicated, particularly when the hole is rapidly spinning, as the radiation is influenced by many harmonics of the orbital frequencies."), (2503, '2011-02-03 20:18:01'), (2504, 'gr-qc/9910091 PDF'), (2505, 'http://www.arxiv.org/pdf/gr-qc/9910091.pdf'), (2506, '2011-02-03 20:18:08'), (2507, 'Communications in Mathematical Physics'), (2508, '0010-3616, 1432-0916'), (2509, '1972-12-00 12/1972'), (2510, '283-290'), (2511, '10.1007/BF01645515'), (2512, 'http://www.springerlink.com.proxy.library.cornell.edu/content/gw6257261r015077/'), (2513, 'Energy and angular momentum flow into a black hole'), (2514, '2011-09-10 18:05:26'), (2515, 'fulltext-3.pdf'), (2516, 'Post-Newtonian factorized multipolar waveforms for spinning, non-precessing black-hole binaries'), (2517, '2010-06-02 2010-06-02'), (2518, 'http://arxiv.org/abs/1006.0431'), (2519, '1006.0431'), (2520, 'We generalize the factorized resummation of multipolar waveforms introduced by Damour, Iyer and Nagar to spinning black holes. For a nonspinning test-particle spiraling a Kerr black hole in the equatorial plane, we find that factorized multipolar amplitudes which replace the residual relativistic amplitude f_{l m} with its l-th root, \\rho_{l m} = f_{l m}^{1/l}, agree quite well with the numerical amplitudes up to the Kerr-spin value q \\leq 0.95 for orbital velocities v \\leq 0.4. The numerical amplitudes are computed solving the Teukolsky equation with a spectral code. The agreement for prograde orbits and large spin values of the Kerr black hole can be further improved at high velocities by properly factoring out the lower-order post-Newtonian contributions in \\rho_{l m}. The resummation procedure results in a better and systematic agreement between numerical and analytical amplitudes (and energy fluxes) than standard Taylor-expanded post-Newtonian approximants. This is particularly true for higher-order modes, such as (2,1), (3,3), (3,2), and (4,4) for which less spin post-Newtonian terms are known. We also extend the factorized resummation of multipolar amplitudes to generic mass-ratio, non-precessing, spinning black holes. Lastly, in our study we employ new, recently computed, higher-order post-Newtonian terms in several subdominant modes, and compute explicit expressions for the half and one-and-half post-Newtonian contributions to the odd-parity (current) and even-parity (odd) multipoles, respectively. Those results can be used to build more accurate templates for ground-based and space-based gravitational-wave detectors.'), (2521, '2011-02-03 22:28:02'), (2522, '1006.0431 PDF'), (2523, 'http://www.arxiv.org/pdf/1006.0431.pdf'), (2524, '2011-02-03 22:28:06'), (2525, 'An improved effective-one-body Hamiltonian for spinning black-hole binaries'), (2526, 'http://arxiv.org/abs/0912.3517'), (2527, 'Phys.Rev.D81:084024,2010'), (2528, 'doi:10.1103/PhysRevD.81.084024'), (2529, '0912.3517'), (2530, "Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle's spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass m, but also with a spin S*. Thus, the effective particle interacts with the effective Kerr background (having spin S_Kerr) through a geodesic-type interaction and an additional spin-dependent interaction proportional to S*. When expanded in post-Newtonian (PN) orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it reproduces all spin-orbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations."), (2531, '2011-02-03 22:33:33'), (2532, '0912.3517 PDF'), (2533, 'http://www.arxiv.org/pdf/0912.3517.pdf'), (2534, '2011-02-03 22:33:38'), (2535, 'Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions'), (2536, '2005-11-20 2005-11-20'), (2537, 'http://arxiv.org/abs/gr-qc/0511111'), (2538, 'Phys.Rev. D73 (2006) 024013; Erratum-ibid. D73 (2006) 109902'), (2539, 'doi:10.1103/PhysRevD.73.024013'), (2540, 'gr-qc/0511111'), (2541, 'Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher dimensions, quantum field theory in curved space-time and studies of D-branes. We first review analytic and numerical calculations of their eigenvalues and eigenfunctions in four dimensions, filling gaps in the existing literature when necessary. Then we compute the angular dependence of the spin-weighted spheroidal harmonics corresponding to slowly-damped quasinormal mode frequencies of the Kerr black hole, providing numerical tables and approximate formulas for their scalar products. Finally we present an exhaustive analytic and numerical study of scalar spheroidal harmonics in (n+4) dimensions.'), (2542, '2011-02-04 15:34:45'), (2543, 'gr-qc/0511111 PDF'), (2544, 'http://www.arxiv.org/pdf/gr-qc/0511111.pdf'), (2545, '2011-02-04 15:34:48'), (2546, 'Fourth-order symplectic integration'), (2547, 'Physica D: Nonlinear Phenomena'), (2548, 43), (2549, '105-117'), (2550, '1990-05-00 May 1990'), (2551, '0167-2789'), (2552, '10.1016/0167-2789(90)90019-L'), (2553, 'http://encompass.library.cornell.edu/cgi-bin/checkIP.cgi?access=gateway_standard%26url=http://www.sciencedirect.com/science/article/B6TVK-46G8PC0-15/2/ace6037c371d42f2888ad504afe77ef0'), (2554, "In this paper we present an explicit fourth-order method for the integration of Hamilton's equations. This method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state. That is, the integration step is an explicit symplectic map. Although the result is first derived for a specific type of Hamiltonian, it is shown to be quite general. In particular, the results can be applied to any Lie group."), (2555, '2011-02-07 17:13:56'), (2556, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6TVK-46G8PC0-15-1&_cdi=5537&_user=492137&_pii=016727899090019L&_origin=search&_coverDate=05%2F31%2F1990&_sk=999569998&view=c&wchp=dGLbVzW-zSkWb&md5=e0fb768f76ee1483a273048d17c6c2b3&ie=/sdarticle.pdf'), (2557, '2011-02-07 17:13:58'), (2558, 'Construction of higher order symplectic integrators'), (2559, 'Physics Letters A'), (2560, 150), (2561, '5-7'), (2562, '262-268'), (2563, '1990-11-12 November 12, 1990'), (2564, '0375-9601'), (2565, '10.1016/0375-9601(90)90092-3'), (2566, 'http://encompass.library.cornell.edu/cgi-bin/checkIP.cgi?access=gateway_standard%26url=http://www.sciencedirect.com/science/article/B6TVM-46MDCD1-X8/2/5b6430b0b57d6147fde01de18f696745'), (2567, 'For Hamiltonian systems of the form H = T(p)+V(q) a method is shown to construct explicit and time reversible symplectic integrators of higher order. For any even order there exists at least one symplectic integrator with exact coefficients. The simplest one is the 4th order integrator which agrees with one found by Forest and by Neri. For 6th and 8th orders, symplectic integrators with fewer steps are obtained, for which the coefficients are given by solving a set of simultaneous algebraic equations numerically.'), (2568, '2011-02-07 17:18:13'), (2569, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6TVM-46MDCD1-X8-2&_cdi=5538&_user=492137&_pii=0375960190900923&_origin=search&_coverDate=11%2F12%2F1990&_sk=998499994&view=c&wchp=dGLbVtb-zSkzk&md5=d39aabb1981f2d249de4dc195f55e0ae&ie=/sdarticle.pdf'), (2570, '2011-02-07 17:18:15'), (2571, '2011-05-02 2011-05-02'), (2572, 'http://math.berkeley.edu/~alanw/242papers99/markiewicz.pdf'), (2573, '2011-02-07 17:50:00'), (2574, 'Survey on symplectic integrators'), (2575, '1999-00-00 1999'), (2576, 'Fortran Codes'), (2577, 'http://www.unige.ch/~hairer/software.html'), (2578, '2011-02-07 17:51:59'), (2579, 'Gravitational-wave spectroscopy of massive black holes with the space interferometer LISA'), (2580, 73), (2581, '064030'), (2582, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.73.064030'), (2583, '10.1103/PhysRevD.73.064030'), (2584, 'Newly formed black holes are expected to emit characteristic radiation in the form of quasinormal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multimode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black-hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black-hole spin and the energy emitted in each mode, will affect our ability to do black-hole spectroscopy.'), (2585, '2011-02-07 19:34:29'), (2586, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v73/i6/e064030'), (2587, '2011-02-07 19:34:31'), (2588, 'Transition from inspiral to plunge for a compact body in a circular equatorial orbit around a massive, spinning black hole'), (2589, 124022), (2590, '2000-11-28 November 28, 2000'), (2591, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.62.124022'), (2592, '10.1103/PhysRevD.62.124022'), (2593, 'There are three regimes of gravitational-radiation-reaction-induced inspiral for a compact body with mass μ, in a circular, equatorial orbit around a Kerr black hole with mass M≫μ: (i) the adiabatic inspiral regime, in which the body gradually descends through a sequence of circular, geodesic orbits; (ii) a transition regime, near the innermost stable circular orbit (isco); (iii) the plunge regime, in which the body travels on a geodesic from slightly below the isco into the hole’s horizon. This paper gives an analytic treatment of the transition regime and shows that, with some luck, gravitational waves from the transition might be measurable by the space-based LISA mission.'), (2594, '2011-02-07 23:19:00'), (2595, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i12/e124022'), (2596, '2011-02-07 23:19:02'), (2597, 82), (2598, 124052), (2599, '2010-12-22 December 22, 2010'), (2600, 'http://link.aps.org/doi/10.1103/PhysRevD.82.124052'), (2601, '10.1103/PhysRevD.82.124052'), (2602, 'One way to produce complete inspiral-merger-ringdown gravitational waveforms from black-hole-binary systems is to connect post-Newtonian (PN) and numerical-relativity (NR) results to create “hybrid” waveforms. Hybrid waveforms are central to the construction of some phenomenological models for gravitational-wave (GW) search templates, and for tests of GW search pipelines. The dominant error source in hybrid waveforms arises from the PN contribution, and can be reduced by increasing the number of NR GW cycles that are included in the hybrid. Hybrid waveforms are considered sufficiently accurate for GW detection if their mismatch error is below 3% (i.e., a fitting factor above 0.97). We address the question of the length requirements of NR waveforms such that the final hybrid waveforms meet this requirement, considering nonspinning binaries with q=M2/M1∈[1,4] and equal-mass binaries with χ=Si/Mi2∈[-0.5,0.5]. We conclude that, for the cases we study, simulations must contain between three (in the equal-mass nonspinning case) and ten (the χ=0.5 case) orbits before merger, but there is also evidence that these are the regions of parameter space for which the least number of cycles will be needed.'), (2603, '2011-02-09 16:00:16'), (2604, 'http://prd.aps.org/pdf/PRD/v82/i12/e124052'), (2605, '2011-02-09 16:00:18'), (2606, 'Accuracy and effectualness of closed-form, frequency-domain waveforms for nonspinning black hole binaries'), (2607, 83), (2608, '024006'), (2609, '2011-01-07 January 07, 2011'), (2610, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.83.024006'), (2611, '10.1103/PhysRevD.83.024006'), (2612, 'The coalescences of binary black hole systems, here taken to be nonspinning, are among the most promising sources for gravitational wave (GW) ground-based detectors, such as LIGO and Virgo. To detect the GW signals emitted by binary black holes and measure the parameters of the source, one needs to have in hand a bank of GW templates that are both effectual (for detection) and accurate (for measurement). We study the effectualness and the accuracy of the two types of parametrized banks of templates that are directly defined in the frequency domain by means of closed-form expressions, namely, “post-Newtonian” (PN) and “phenomenological” models. In the absence of knowledge of the (continuous family of) exact waveforms, our study assumes as fiducial, target waveforms the ones generated by the most accurate version of the effective-one-body formalism, calibrated upon a few high-accuracy numerical-relativity (NR) waveforms. We find that, for initial GW detectors the use, at each point of parameter space, of the best closed-form template (among PN and phenomenological models) leads to an effectualness >97% over the entire mass range and >99% in an important fraction of parameter space; however, when considering advanced detectors, both of the closed-form frequency-domain models fail to be effectual enough in significant domains of the two-dimensional [total mass and mass ratio] parameter space. Moreover, we find that, for both initial and advanced detectors, the two closed-form frequency-domain models fail to satisfy the minimal required accuracy standard in a very large domain of the two-dimensional parameter space. In addition, a side result of our study is the determination, as a function of the mass ratio, of the maximum frequency at which a frequency-domain PN waveform can be “joined” onto a NR-calibrated effective-one-body waveform without undue loss of accuracy. In the case of mass ratios larger than 4∶1 this maximum frequency occurs well before the last stable orbit, leaving probably too many orbital cycles to be covered by current NR techniques if one wanted to construct accurate-enough hybrid PN-NR waveforms. This problem will, however, be probably greatly alleviated, or even solved, by using the effective-one-body formalism instead of PN theory.'), (2613, '2011-02-10 17:47:03'), (2614, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i2/e024006'), (2615, '2011-02-10 17:47:05'), (2616, 'Ineffectiveness of Padé resummation techniques in post-Newtonian approximations'), (2617, '044004'), (2618, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.78.044004'), (2619, '10.1103/PhysRevD.78.044004'), (2620, 'We test the resummation techniques used in developing Padé and effective one body (EOB) waveforms for gravitational wave detection. Convergence tests show that Padé approximants of the gravitational wave energy flux do not accelerate the convergence of the standard Taylor approximants even in the test mass limit, and there is no reason why Padé transformations should help in estimating parameters better in data analysis. Moreover, adding a pole to the flux seems unnecessary in the construction of these Padé-approximated flux formulas. Padé approximants may be useful in suggesting the form of fitting formulas. We compare a 15-orbit numerical waveform of the Caltech-Cornell group to the suggested Padé waveforms of Damour et al. in the equal mass, nonspinning quasicircular case. The comparison suggests that the Padé waveforms do not agree better with the numerical waveform than the standard Taylor based waveforms. Based on this result, we design a simple EOB model by modifiying the Taylor-expanded EOB model of Buonanno et al., using the Taylor series of the flux with an unknown parameter at the fourth post-Newtonian order that we fit for. The 4PN parameter incorporates higher order effects of the radiation reaction. This simple EOB model generates a waveform having a phase difference of only 0.002 radians with the numerical waveform, much smaller than 0.04 radians the phase uncertainty in the numerical data itself. An EOB Hamiltonian can make use of a Padé transformation in its construction, but this is the only place Padé transformations seem useful.'), (2621, '2011-02-10 18:12:31'), (2622, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i4/e044004'), (2623, '2011-02-10 18:12:33'), (2624, 'Gravitational waves from black hole binary inspiral and merger: The span of third post-Newtonian effective-one-body templates'), (2625, '064028'), (2626, '2003-03-31 March 31, 2003'), (2627, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.67.064028'), (2628, '10.1103/PhysRevD.67.064028'), (2629, 'We extend the description of gravitational waves emitted by binary black holes during the final stages of inspiral and merger by introducing in the third post-Newtonian (3PN) effective-one-body (EOB) templates seven new “flexibility” parameters that affect the two-body dynamics and gravitational radiation emission. The plausible ranges of these flexibility parameters, notably the parameter characterizing the fourth post-Newtonian effects in the dynamics, are estimated. Using these estimates, we show that the currently available standard 3PN bank of EOB templates does “span” the space of signals opened up by all the flexibility parameters, in that their maximized mutual overlaps are larger than 96.5%. This confirms the effectualness of 3PN EOB templates for the detection of binary black holes in gravitational-wave data from interferometric detectors. The possibility to drastically reduce the number of EOB templates using a few “universal” phasing functions is suggested.'), (2630, '2011-02-10 18:36:26'), (2631, 'Gravitational waves from black hole binary inspiral and merger'), (2632, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i6/e064028'), (2633, '2011-02-10 18:36:28'), (2634, '0001-7701'), (2635, 'General Relativity and Gravitation'), (2636, 'Gen Relat Gravit'), (2637, '1986-00-03 3/1986'), (2638, '255-270'), (2639, '10.1007/BF00765886'), (2640, 'http://www.springerlink.com.proxy.library.cornell.edu/content/g33336t216w7094n/'), (2641, 'The ADM Hamiltonian at the postlinear approximation'), (2642, '2011-02-10 20:49:22'), (2643, 'http://arxiv.org/abs/1105.0265'), (2644, 'http://www.gravity.phys.uwm.edu/conferences/gwpaw/posters/ohme.pdf'), (2645, '2011-02-11 22:28:40'), (2646, 'Accuracy of hybrid waveform families'), (2647, 'HST Observations of the Stellar Distribution Near Sgr A*'), (2648, '2011-09-09 2011-09-09'), (2649, 'http://www.arxiv.org/pdf/1110.0408.pdf'), (2650, 163001), (2651, '10.1088/0264-9381/26/16/163001'), (2652, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/26/16/163001'), (2653, '2011-02-15 15:53:11'), (2654, '0264-9381_26_16_163001.pdf'), (2655, 'Faithful Effective-One-Body waveforms of equal-mass coalescing black-hole binaries'), (2656, '2007-12-18 2007-12-18'), (2657, 'http://arxiv.org/abs/0712.3003'), (2658, 'Phys.Rev.D77:084017,2008'), (2659, 'doi:10.1103/PhysRevD.77.084017'), (2660, '0712.3003'), (2661, 'We continue the program of constructing, within the Effective-One-Body (EOB) approach, high-accuracy analytic waveforms describing the signal emitted by inspiralling and coalescing black hole binaries. Here, we compare a recently derived, resummed 3 PN-accurate EOB quadrupolar waveform to the results of a numerical simulation of the inspiral and merger of an equal-mass black hole binary. We find a remarkable agreement, both in phase and in amplitude, with a maximal dephasing which can be reduced below $\\pm 0.005$ gravitational-wave (GW) cycles over 12 GW cycles corresponding to the end of the inspiral, the plunge, the merger and the beginning of the ringdown. This level of agreement is shown for two different values of the effective 4 PN parameter a_5, and for corresponding, appropriately "flexed" values of the radiation-reaction resummation parameter v_pole. In addition, our resummed EOB amplitude agrees to better than the 1% level with the numerical-relativity one up to the late inspiral. These results, together with other recent work on the EOB-numerical-relativity comparison, confirm the ability of the EOB formalism to faithfully capture the general relativistic waveforms.'), (2662, '2011-02-15 19:53:58'), (2663, '0712.3003 PDF'), (2664, 'http://www.arxiv.org/pdf/0712.3003.pdf'), (2665, '2011-02-15 19:54:05'), (2666, 'Faithful effective-one-body waveforms of small-mass-ratio coalescing black hole binaries'), (2667, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.76.064028'), (2668, '10.1103/PhysRevD.76.064028'), (2669, 'We address the problem of constructing high-accuracy, faithful analytic waveforms describing the gravitational wave signal emitted by inspiralling and coalescing binary black holes. We work within the effective-one-body (EOB) framework and propose a methodology for improving the current (waveform) implementations of this framework based on understanding, element by element, the physics behind each feature of the waveform and on systematically comparing various EOB-based waveforms with exact waveforms obtained by numerical relativity approaches. The present paper focuses on small-mass-ratio nonspinning binary systems, which can be conveniently studied by Regge-Wheeler-Zerilli-type methods. Our results include (i) a resummed, 3 PN-accurate description of the inspiral waveform, (ii) a better description of radiation reaction during the plunge, (iii) a refined analytic expression for the plunge waveform, (iv) an improved treatment of the matching between the plunge and ring-down waveforms. This improved implementation of the EOB approach allows us to construct complete analytic waveforms which exhibit a remarkable agreement with the exact ones in modulus, frequency, and phase. In particular, the analytic and numerical waveforms stay in phase, during the whole process, within ±1.1% of a cycle. We expect that the extension of our methodology to the comparable-mass case will be able to generate comparably accurate analytic waveforms of direct use for the ground-based network of interferometric detectors of gravitational waves.'), (2670, '2011-02-15 20:16:01'), (2671, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i6/e064028'), (2672, '2011-02-15 20:16:03'), (2673, 'Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling'), (2674, '024009'), (2675, '2008-07-03 July 03, 2008'), (2676, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.78.024009'), (2677, '10.1103/PhysRevD.78.024009'), (2678, 'Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the effective one body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the “effective” Hamiltonian and the “real” one; (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta; (iii) a Kerr-type effective metric (with Padé-resummed coefficients) which depends on the choice of some basic “effective spin vector” Seff, and which is deformed by comparable-mass effects; and (iv) an additional effective spin-orbit interaction term involving another spin vector σ. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter âLSO≡cJLSO/(G(HLSO/c2)2). We find that the inclusion of NLO spin-orbit terms has a significant “moderating” effect on the dynamical characteristics of the circular orbits for large and parallel spins.'), (2679, '2011-02-15 21:50:51'), (2680, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i2/e024009'), (2681, '2011-02-15 21:50:53'), (2682, 'Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation'), (2683, '084011'), (2684, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.62.084011'), (2685, '10.1103/PhysRevD.62.084011'), (2686, 'We discuss the analytical determination of the location of the last stable orbit (LSO) in circular general relativistic orbits of two point masses. We deal with the problem of the slow convergence of post-Newtonian expansions by “resumming” them in various ways. We use several different resummation methods (including new ones) based on the consideration of gauge-invariant functions, and compare the results they give at the third post-Newtonian (3PN) approximation of general relativity. Our treatment is based on the 3PN Hamiltonian of Jaranowski and Schäfer. One of the new methods we introduce is based on the consideration of the (invariant) function linking the angular momentum and the angular frequency. We also generalize the “effective one-body” approach of Buonanno and Damour by introducing a non-minimal (i.e. “non-geodesic”) effective dynamics at the 3PN level. We find that the location of the LSO sensitively depends on the (currently unknown) value of the dimensionless quantity ωstatic which parametrizes a certain regularization ambiguity of the 3PN dynamics. We find, however, that all the analytical methods we use numerically agree among themselves if the value of this parameter is ωstatic≃-9. This suggests that the correct value of ωstatic is near -9 [the precise value ωstatic*≡-47/3+(41/64)π2=-9.3439… seems to play a special role]. If this is the case, we then show how to further improve the analytical determination of various LSO quantities by using a “Shanks” transformation to accelerate the convergence of the successive (already resummed) PN estimates.'), (2687, '2011-02-16 19:53:58'), (2688, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i8/e084011'), (2689, '2011-02-16 19:54:00'), (2690, 'Coalescence of two spinning black holes: An effective one-body approach'), (2691, 124013), (2692, '2001-11-27 November 27, 2001'), (2693, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.64.124013'), (2694, '10.1103/PhysRevD.64.124013'), (2695, 'We generalize to the case of spinning black holes a recently introduced “effective one-body” approach to the general relativistic dynamics of binary systems. We show how to approximately map the conservative part of the third post-Newtonian (3PN) dynamics of two spinning black holes of masses m1, m2 and spins S1, S2 onto the dynamics of a non-spinning particle of mass μ≡m1m2/(m1+m2) in a certain effective metric gμνeff(xλ;M,ν,a) which can be viewed either as a spin deformation [with the deformation parameter a≡Seff/M] of the recently constructed 3PN effective metric gμνeff(xλ;M,ν), or as a ν deformation [with the comparable-mass deformation parameter ν≡m1m2/(m1+m2)2] of a Kerr metric of mass M≡m1+m2 and (effective) spin Seff≡[1+3m2/(4m1)]S1+[1+3m1/(4m2)]S2. The combination of the effective one-body approach, and of a Padé definition of the crucial effective radial functions, is shown to define a dynamics with much improved post-Newtonian convergence properties, even for black hole separations of the order of 6 GM/c2. The complete (conservative) phase-space evolution equations of binary spinning black hole systems are written down and their exact and approximate first integrals are discussed. This leads to the approximate existence of a two-parameter family of “spherical orbits” (with constant radius), and of a corresponding one-parameter family of “last stable spherical orbits” (LSSO). These orbits are of special interest for forthcoming LIGO-VIRGO-GEO gravitational wave observations. The binding energy and total angular momentum of LSSO’s are studied in some detail. It is argued that for most (but not all) of the parameter space of two spinning holes the approximate (leading-order) effective one-body approach introduced here gives a reliable analytical tool for describing the dynamics of the last orbits before coalescence. This tool predicts, in a quantitative way, how certain spin orientations increase the binding energy of the LSSO. This leads to a detection bias, in LIGO-VIRGO-GEO observations, favoring spinning black hole systems, and makes it urgent to complete the conservative effective one-body dynamics given here by adding (resummed) radiation reaction effects, and by constructing gravitational waveform templates that include spin effects. Finally, our approach predicts that the spin of the final hole formed by the coalescence of two arbitrarily spinning holes never approaches extremality.'), (2696, '2011-02-16 20:08:45'), (2697, 'Coalescence of two spinning black holes'), (2698, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i12/e124013'), (2699, '2011-02-16 20:08:47'), (2700, 'ohme.pdf'), (2701, 'Search for gravitational waves from binary black hole inspiral, merger and ringdown'), (2702, '2011-02-18 2011-02-18'), (2703, 'http://arxiv.org/abs/1102.3781'), (2704, '1102.3781'), (2705, 'We present the first modeled search for gravitational waves using the complete binary black hole gravitational waveform from inspiral through the merger and ringdown for binaries with negligible component spin. We searched approximately 2 years of LIGO data taken between November 2005 and September 2007 for systems with component masses of 1-99 solar masses and total masses of 25-100 solar masses. We did not detect any plausible gravitational-wave signals but we do place upper limits on the merger rate of binary black holes as a function of the component masses in this range. We constrain the rate of mergers for binary black hole systems with component masses between 19 and 28 solar masses and negligible spin to be no more than 2.0 per Mpc^3 per Myr at 90% confidence.'), (2706, '10.1103/PhysRevD.72.083005'), (2707, '1102.3781 PDF'), (2708, 'http://www.arxiv.org/pdf/1102.3781.pdf'), (2709, '2011-02-23 02:28:41'), (2710, 'Approaching faithful templates for nonspinning binary black holes using the effective-one-body approach'), (2711, 104049), (2712, '2007-11-29 November 29, 2007'), (2713, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.76.104049'), (2714, '10.1103/PhysRevD.76.104049'), (2715, 'We present an accurate approximation of the full gravitational radiation waveforms generated in the merger of noneccentric systems of two nonspinning black holes. Utilizing information from recent numerical relativity simulations and the natural flexibility of the effective-one-body (EOB) model, we extend the latter so that it can successfully match the numerical relativity waveforms during the last stages of inspiral, merger, and ringdown. By “successfully” here, we mean with phase differences ≲8% of a gravitational-wave cycle accumulated by the end of the ringdown phase, maximizing only over time of arrival and initial phase. We obtain this result by simply adding a 4-post-Newtonian order correction in the EOB radial potential and determining the (constant) coefficient by imposing high-matching performances with numerical waveforms of mass ratios m1/m2=1, 3/2, 2 and 4, m1 and m2 being the individual black-hole masses. The final black-hole mass and spin predicted by the numerical simulations are used to determine the ringdown frequency and decay time of three quasinormal-mode damped sinusoids that are attached to the EOB inspiral-(plunge) waveform at the EOB light ring. The EOB waveforms might be tested and further improved in the future by comparison with extremely long and accurate inspiral numerical relativity waveforms. They may be already employed for coherent searches and parameter estimation of gravitational waves emitted by nonspinning coalescing binary black holes with ground-based laser-interferometer detectors.'), (2716, '2011-02-26 03:00:31'), (2717, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i10/e104049'), (2718, '2011-02-26 03:00:33'), (2719, 'Detection template families for gravitational waves from the final stages of binary\x96black-hole inspirals: Nonspinning case'), (2720, '024016'), (2721, '2003-01-17 January 17, 2003'), (2722, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.67.024016'), (2723, '10.1103/PhysRevD.67.024016'), (2724, 'We investigate the problem of detecting gravitational waves from binaries of nonspinning black holes with masses m=5–20M⊙, moving on quasicircular orbits, which are arguably the most promising sources for first-generation ground-based detectors. We analyze and compare all the currently available post-Newtonian approximations for the relativistic two-body dynamics; for these binaries, different approximations predict different waveforms. We then construct examples of detection template families that embed all the approximate models and that could be used to detect the true gravitational-wave signal (but not to characterize accurately its physical parameters). We estimate that the fitting factor for our detection families is ≳0.95 (corresponding to an event rate loss ≲15%) and we estimate that the discretization of the template family, for ∼104 templates, increases the loss to ≲20%.'), (2725, '2011-02-26 03:11:37'), (2726, 'Detection template families for gravitational waves from the final stages of binary\x96black-hole inspirals'), (2727, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i2/e024016'), (2728, '2011-02-26 03:11:39'), (2729, 'Suitability of post-Newtonian/numerical-relativity hybrid waveforms for gravitational wave detectors'), (2730, '1105.0265'), (2731, 'The prospect of mini black holes, either primordial or in planned experiments at the Large Hadron Collider, interacting with the earth motivate us to examine how they may be detected and the scope of their impact on the earth. We propose that the more massive of these objects may gravitationally bind matter without significant absorption. Since the wave functions of gravitationally bound atoms orbiting a black hole are analogous to those of electrons around a nucleus, we call such an object the Gravitationally Equivalent of an Atom (GEA). Mini black holes are expected to lose mass through quantum evaporation, which has become well accepted on purely theoretical grounds. Since all attempts to directly observe x-rays from an evaporating black hole have failed, we examine the possibility of the inverse test: search for extant mini black holes by looking for emissions from matter bound in a GEA. If quantum evaporation does not occur, then miniature black holes left over from the early universe may be stable, contribute to dark matter, and in principle be detectable through emissions associated with the bound matter. We show that small black holes-with masses below \\sim10^12 kg-can bind matter without readily absorbing it into the black hole but the emissions are too weak to be detected from earth.'), (2732, '2011-05-04 14:41:59'), (2733, '1105.0265 PDF'), (2734, 'http://www.arxiv.org/pdf/1105.0265.pdf'), (2735, '2011-05-04 14:42:00'), (2736, 'Toward an optimal search strategy of optical and gravitational wave emissions from binary neutron star coalescence'), (2737, 'http://arxiv.org/abs/1109.2175'), (2738, 'arXiv:1109.2175'), (2739, 'We present HST/NICMOS data to study the surface brightness distribution of stellar light within the inner 10" of Sgr A* at 1.4, 1.7 and 1.9 microns. We use these data to independently examine the surface brightness distribution that had been measured previously with NICMOS and to determine whether there is a drop in the surface density of stars very near Sgr A*. Our analysis confirms that a previously reported drop in the surface brightness within 0.8" of Sgr A* is an artifact of bright and massive stars near that radius. We also show that the surface brightness profile within 5" or ~0.2 pc of Sgr A* can be fitted with broken power laws. The power laws are consistent with previous measurements, in that the profile becomes shallower at small radii. For radii > 0.7" the slope is beta=-0.34\\pm0.04 where Sigma is proportional to r^beta and becomes flatter at smaller radii with beta=-0.13\\pm0.04. Modeling of the surface brightness profile gives a stellar density that increases roughly as r^-1 within the inner 1" of Sgr A*. This slope confirms earlier measurements in that it is not consistent with that expected from an old, dynamically-relaxed stellar cluster with a central supermassive black hole. Assuming that the diffuse emission is not contaminated by a faint population of young stars down to the 17.1 magnitude limit of our imaging data at 1.70$\\mu$, the shallow cusp profile is not consistent with a decline in stellar density in the inner arcsecond. In addition, converting our measured diffuse light profile to a stellar mass profile, with the assumption that the light is dominated by K0 dwarfs, the enclosed stellar mass within radius r < 0.1 pc of Sgr A* is ~ 3.2x10^4 M_solar (r/0.1 {pc})^2.1.'), (2740, '2011-09-13 13:15:05'), (2741, '1109.2175 PDF'), (2742, 'http://www.arxiv.org/pdf/1109.2175.pdf'), (2743, '2011-09-13 13:15:12'), (2744, 'Tidal Perturbations to the Gravitational Inspiral of J0651+2844'), (2745, 'Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force'), (2746, '2010-10-12 2010-10-12'), (2747, 'http://arxiv.org/abs/1010.2553'), (2748, 'Phys.Rev.D83:024028,2011'), (2749, 'doi:10.1103/PhysRevD.83.024028'), (2750, '1010.2553'), (2751, 'The innermost stable circular orbit (ISCO) delimits the transition from circular orbits to those that plunge into a black hole. In the test-mass limit, well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes. In the finite-mass case, there are a large variety of ways to define an ISCO in a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO condition of Blanchet & Iyer (2003) to the case of spinning (nonprecessing) binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass limit, and (2) it accurately approximates the recently-calculated shift in the Schwarzschild ISCO frequency due to the conservative-piece of the gravitational self-force [Barack & Sago (2009)]. The generalization of this ISCO condition to spinning binaries has the property that it also exactly reproduces the Kerr ISCO in the test-mass limit (up to the order at which PN spin corrections are currently known). The shift in the ISCO due to the spin of the test-particle is also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly reproduces the ISCO shift predicted by the Papapetrou equations for a fully-relativistic spinning particle. It is surprising that an analysis of the stability of the standard PN equations of motion is able (without any form of "resummation") to accurately describe strong-field effects of the Kerr spacetime. The ISCO frequency shift due to the conservative self-force in Kerr is also calculated from this new ISCO condition, as well as from the effective-one-body Hamiltonian of Barausse & Buonanno (2010). These results serve as a useful point-of-comparison for future gravitational self-force calculations in the Kerr spacetime.'), (2752, '2011-03-02 18:20:08'), (2753, 'Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole'), (2754, '1010.2553 PDF'), (2755, 'http://www.arxiv.org/pdf/1010.2553.pdf'), (2756, '2011-03-02 18:20:15'), (2757, 'Improved filters for gravitational waves from inspiraling compact binaries'), (2758, 57), (2759, 885), (2760, '1998-01-15 January 15, 1998'), (2761, 'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.57.885'), (2762, '10.1103/PhysRevD.57.885'), (2763, 'The order of the post-Newtonian expansion needed to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiraling compact binaries is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: (a) the introduction of two new energy-type and flux-type functions e(v) and f(v), respectively, (b) the systematic use of the Padé approximation for constructing successive approximants of e(v) and f(v). The new P-approximants are not only more effectual (larger overlaps) and more faithful (smaller biases) than the standard Taylor approximants, but also converge faster and monotonically. The presently available (v/c)5-accurate post-Newtonian results can be used to construct P-approximate wave forms that provide overlaps with the exact wave form larger than 96.5%, implying that more than 90% of potential events can be detected with the aid of P-approximants as opposed to a mere 10–15 % that would be detectable using standard post-Newtonian approximants.'), (2764, '2011-03-02 19:03:32'), (2765, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v57/i2/p885_1'), (2766, '2011-03-02 19:03:34'), (2767, 'On the unreasonable effectiveness of the post-Newtonian approximation in gravitational physics'), (2768, '2011-02-25 2011-02-25'), (2769, 'http://arxiv.org/abs/1102.5192'), (2770, '1102.5192'), (2771, "The post-Newtonian approximation is a method for solving Einstein's field equations for physical systems in which motions are slow compared to the speed of light and where gravitational fields are weak. Yet it has proven to be remarkably effective in describing certain strong-field, fast-motion systems, including binary pulsars containing dense neutron stars and binary black hole systems inspiraling toward a final merger. The reasons for this effectiveness are largely unknown. When carried to high orders in the post-Newtonian sequence, predictions for the gravitational-wave signal from inspiraling compact binaries will play a key role in gravitational-wave detection by laser-interferometric observatories."), (2772, '2011-03-06 03:18:53'), (2773, '1102.5192 PDF'), (2774, 'http://www.arxiv.org/pdf/1102.5192.pdf'), (2775, '2011-03-06 03:18:56'), (2776, 'A List of Galaxies for Gravitational Wave Searches'), (2777, '2011-03-03 2011-03-03'), (2778, 'http://arxiv.org/abs/1103.0695'), (2779, '1103.0695'), (2780, 'We present a list of galaxies within 100 Mpc, which we call the Gravitational Wave Galaxy Catalogue (GWGC), that is currently being used in follow-up searches of electromagnetic counterparts from gravitational wave searches. Due to the time constraints of rapid follow-up, a locally available catalogue of reduced, homogenized data is required. To achieve this we used four existing catalogues: an updated version of the Tully Nearby Galaxy Catalog, the Catalog of Neighboring Galaxies, the V8k catalogue and HyperLEDA. The GWGC contains information on sky position, distance, blue magnitude, major and minor diameters, position angle, and galaxy type for 53,255 galaxies. Errors on these quantities are either taken directly from the literature or estimated based on our understanding of the uncertainties associated with the measurement method. By using the PGC numbering system developed for HyperLEDA, the catalogue has a reduced level of degeneracies compared to catalogues with a similar purpose and is easily updated. We also include 150 Milky Way globular clusters. Finally, we compare the GWGC to previously used catalogues, and find the GWGC to be more complete within 100 Mpc due to our use of more up-to-date input catalogues and the fact that we have not made a blue luminosity cut.'), (2781, '2011-03-06 14:10:44'), (2782, '1103.0695 PDF'), (2783, 'http://www.arxiv.org/pdf/1103.0695.pdf'), (2784, '2011-03-06 14:10:47'), (2785, 'This document proposes data formats to exchange numerical relativity results, in particular gravitational waveforms. The primary goal is to further the interaction between gravitational-wave source modeling groups and the gravitational-wave data-analysis community. We present a simple and extendable format which is applicable to various kinds of gravitational wave sources including binaries of compact objects and systems undergoing gravitational collapse, but is nevertheless sufficiently general to be useful for other purposes.'), (2786, '2011-03-07 21:47:17'), (2787, '2011-03-07 21:47:20'), (2788, 'Search templates for gravitational waves from inspiraling binaries: Choice of template spacing'), (2789, 53), (2790, 6749), (2791, '1996-06-15 June 15, 1996'), (2792, 'http://link.aps.org/doi/10.1103/PhysRevD.53.6749'), (2793, '10.1103/PhysRevD.53.6749'), (2794, 'Gravitational waves from inspiraling, compact binaries will be searched for in the output of the LIGO-VIRGO interferometric network by the method of ‘‘matched filtering’’—i.e., by correlating the noisy output of each interferometer with a set of theoretical wave form templates. These search templates will be a discrete subset of a continuous, multiparameter family, each of which approximates a possible signal. The search might be performed hierarchically, with a first pass through the data using a low threshold and a coarsely spaced, few-parameter template set, followed by a second pass on threshold-exceeding data segments, with a higher threshold and a more finely spaced template set that might have a larger number of parameters. Alternatively, the search might involve a single pass through the data using the larger threshold and finer template set. This paper extends and generalizes the Sathyaprakash-Dhurandhar (SD) formalism for choosing the discrete, finely spaced template set used in the final (or sole) pass through the data, based on the analysis of a single interferometer. The SD formalism is rephrased in geometric language by introducing a metric on the continuous template space from which the discrete template set is drawn. This template metric is used to compute the loss of signal-to-noise ratio and reduction of event rate which result from the coarseness of the template grid. Correspondingly, the template spacing and total number N of templates are expressed, via the metric, as functions of the reduction in event rate. The theory is developed for a template family of arbitrary dimensionality (whereas the original SD formalism was restricted to a single nontrivial dimension). The theory is then applied to a simple post1-Newtonian template family with two nontrivial dimensions. For this family, the number of templates N in the finely spaced grid is related to the spacing-induced fractional loss L of event rate and to the minimum mass Mmin of the least massive star in the binaries for which one searches by N∼2×105(0.1/L)(0.2M⊙/Mmin)2.7 for the first LIGO interferometers and by N∼8×106(0.1/L)(0.2M⊙/Mmin)2.7 for advanced LIGO interferometers. This is several orders of magnitude greater than one might have expected based on Sathyaprakash’s discovery of a near degeneracy in the parameter space, the discrepancy being due to that paper’s high choice of Mmin and less stringent choice of L. The computational power P required to process the steady stream of incoming data from a single interferometer through the closely spaced set of templates is given in floating-point operations per second by P∼3×1010(0.1/L)(0.2M⊙/Mmin)2.7 for the first LIGO interferometers and by P∼4×1011(0.1/L)(0.2M⊙/Mmin)2.7 for advanced LIGO interferometers. This will be within the capabilities of LIGO-era computers, but a hierarchical search may still be desirable to reduce the required computing power. © 1996 The American Physical Society.'), (2795, '2011-03-09 17:31:38'), (2796, 'Search templates for gravitational waves from inspiraling binaries'), (2797, 'http://prd.aps.org/pdf/PRD/v53/i12/p6749_1'), (2798, '2011-03-09 17:31:40'), (2799, 27), (2800, 'The Advanced Laser Interferometer Antenna (ALIA) and the Big Bang Observer (BBO) have been proposed as follow on missions to the Laser Interferometer Space Antenna (LISA). Here we study the capabilities of these observatories, and how they relate to the science goals of the missions. We find that the Advanced Laser Interferometer Antenna in Stereo (ALIAS), our proposed extension to the ALIA mission, will go considerably further toward meeting ALIA’s main scientific goal of studying intermediate mass black holes. We also compare the capabilities of LISA to a related extension of the LISA mission, the Laser Interferometer Space Antenna in Stereo (LISAS). Additionally, we find that the initial deployment phase of the BBO would be sufficient to address the BBO’s key scientific goal of detecting the Gravitational Wave Background, while still providing detailed information about foreground sources.'), (2801, 173001), (2802, '10.1088/0264-9381/27/17/173001'), (2803, 'http://iopscience.iop.org/0264-9381/27/17/173001?fromSearchPage=true'), (2804, 'Predictions for the rates of compact binary coalescences observable by ground-based gravitational-wave detectors'), (2805, '2011-03-09 21:40:59'), (2806, '0264-9381_27_17_173001.pdf'), (2807, 'http://iopscience.iop.org/0264-9381/27/17/173001/pdf/0264-9381_27_17_173001.pdf'), (2808, '2011-03-09 21:41:01'), (2809, 716), (2810, '2010-00-06 06/2010'), (2811, '615-633'), (2812, '10.1088/0004-637X/716/1/615'), (2813, 'http://iopscience.iop.org/0004-637X/716/1/615'), (2814, 'BINARY COMPACT OBJECT COALESCENCE RATES: THE ROLE OF ELLIPTICAL GALAXIES'), (2815, '2011-03-09 22:40:37'), (2816, 'BINARY COMPACT OBJECT COALESCENCE RATES'), (2817, '0004-637X_716_1_615.pdf'), (2818, 'http://iopscience.iop.org/0004-637X/716/1/615/pdf/0004-637X_716_1_615.pdf'), (2819, '2011-03-09 22:42:07'), (2820, 589), (2821, '2003-00-05 05/2003'), (2822, 'L37-L40'), (2823, '10.1086/375713'), (2824, 'http://iopscience.iop.org/1538-4357/589/1/L37'), (2825, 'Constraints on the Binary Evolution from Chirp Mass Measurements'), (2826, '2011-03-09 22:42:38'), (2827, '1538-4357_589_1_L37.pdf'), (2828, 'http://iopscience.iop.org/1538-4357/589/1/L37/pdf/1538-4357_589_1_L37.pdf'), (2829, '2011-03-09 22:42:51'), (2830, 'Accuracy requirements for the calculation of gravitational waveforms from coalescing compact binaries in numerical relativity'), (2831, 104016), (2832, '2005-05-13 May 13, 2005'), (2833, 'http://link.aps.org/doi/10.1103/PhysRevD.71.104016'), (2834, '10.1103/PhysRevD.71.104016'), (2835, 'I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical parameter estimation in modern interferometric gravitational wave detectors. Using a post-Newtonian point particle model for the premerger phase of the binary inspiral, I calculate the maximum allowable errors for the mass and relative velocity and positions of the binary during numerical simulations of the binary inspiral. These maximum allowable errors are compared to the errors of state-of-the-art numerical simulations of multiple-orbit binary neutron star calculations in full general relativity, and are found to be smaller by several orders of magnitude. A post-Newtonian model for the error of these numerical simulations suggests that adaptive mesh refinement coupled with second-order accurate finite difference codes will not be able to robustly obtain the accuracy required for reliable gravitational wave extraction on Terabyte-scale computers. I conclude that higher-order methods (higher-order finite difference methods and/or spectral methods) combined with adaptive mesh refinement and/or multipatch technology will be needed for robustly accurate gravitational wave extraction from numerical relativity calculations of binary coalescence scenarios.'), (2836, '2011-03-09 23:29:22'), (2837, 'http://prd.aps.org/pdf/PRD/v71/i10/e104016'), (2838, '2011-03-09 23:29:24'), (2839, "Measuring gravitational waves from binary black hole coalescences. II. The waves' information and its extraction, with and without templates"), (2840, 4566), (2841, '1998-04-15 April 15, 1998'), (2842, 'http://link.aps.org/doi/10.1103/PhysRevD.57.4566'), (2843, '10.1103/PhysRevD.57.4566'), (2844, 'We discuss the extraction of information from detected binary black hole (BBH) coalescence gravitational waves by the ground-based interferometers LIGO and VIRGO, and by the space-based interferometer LISA. We focus on the merger phase that occurs after the gradual inspiral and before the ringdown. Our results are (i) if numerical relativity simulations have not produced template merger waveforms before BBH events are detected, one can study the merger waves using simple band-pass filters. For BBHs smaller than about 40M⊙ detected via their inspiral waves, the band-pass filtering signal-to-noise ratio indicates that the merger waves should typically be just barely visible in the noise for initial and advanced LIGO interferometers. (ii) We derive an optimized maximum-likelihood method for extracting a best-fit merger waveform from the noisy detector output; one “perpendicularly projects” this output onto a function space (specified using wavelets) that incorporates our (possibly sketchy) prior knowledge of the waveforms. An extension of the method allows one to extract the BBH’s two independent waveforms from outputs of several interferometers. (iii) We propose a computational strategy for numerical relativists to pursue, if they successfully produce computer codes for generating merger waveforms, but if running the codes is too expensive to permit an extensive survey of the merger parameter space. In this case, for LIGO-VIRGO data analysis purposes, it would be advantageous to do a coarse survey of the parameter space aimed at exploring several qualitative issues and at determining the ranges of the several key parameters which we describe. (iv) A complete set of templates could be used to test the nonlinear dynamics of general relativity and to measure some of the binary’s parameters via matched filtering. We estimate the number of bits of information obtainable from the merger waves (about 10–60 for LIGO-VIRGO, up to 200 for LISA), estimate the information loss due to template numerical errors or sparseness in the template grid, and infer approximate requirements on template accuracy and spacing.'), (2845, '2011-03-09 23:32:35'), (2846, 'http://prd.aps.org/pdf/PRD/v57/i8/p4566_1'), (2847, '2011-03-09 23:32:37'), (2848, 541), (2849, '2000-00-09 09/2000'), (2850, '319-328'), (2851, '10.1086/309400'), (2852, 'http://iopscience.iop.org/0004-637X/541/1/319'), (2853, 'Spin‐Orbit Misalignment in Close Binaries with Two Compact Objects'), (2854, '2011-03-11 19:00:47'), (2855, '0004-637X_541_1_319.pdf'), (2856, 'http://iopscience.iop.org/0004-637X/541/1/319/pdf/0004-637X_541_1_319.pdf'), (2857, '2011-03-11 19:01:11'), (2858, 632), (2859, '2005-00-10 10/2005'), (2860, '1035-1041'), (2861, '10.1086/444346'), (2862, 'http://iopscience.iop.org/0004-637X/632/2/1035'), (2863, 'Bounds on Expected Black Hole Spins in Inspiraling Binaries'), (2864, '2011-03-11 19:07:05'), (2865, '0004-637X_632_2_1035.pdf'), (2866, 'http://iopscience.iop.org/0004-637X/632/2/1035/pdf/0004-637X_632_2_1035.pdf'), (2867, '2011-03-11 19:07:14'), (2868, '2011-10-12 20:16:14'), (2869, 'Resonant Shattering of Neutron Star Crusts'), (2870, 'LISA. Laser Interferometer Space Antenna for the detection and observation of gravitational waves. An international project in the field of Fundamental Physics in Space'), (2871, 'Max-Planck-Institut für Quantenoptik'), (2872, 'München, Germany'), (2873, 'pubman.mpdl.mpg.de'), (2874, '1006.2834 PDF'), (2875, 'http://www.arxiv.org/pdf/1006.2834.pdf'), (2876, '2011-03-11 19:14:43'), (2877, 725), (2878, 'http://pubman.mpdl.mpg.de/pubman/faces/viewItemFullPage.jsp?itemId=escidoc:52082'), (2879, '1918-1927'), (2880, '10.1088/0004-637X/725/2/1918'), (2881, 'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/725/2/1918'), (2882, '2011-04-29 2011-04-29'), (2883, '2011-03-11 20:12:56'), (2884, 'The black-hole mass distribution in the galaxy'), (2885, '0004-637X_725_2_1918.pdf'), (2886, 'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/725/2/1918/pdf/0004-637X_725_2_1918.pdf'), (2887, '2011-03-11 20:13:22'), (2888, 'Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries'), (2889, '084036'), (2890, 'http://arxiv.org/abs/1104.5552'), (2891, '10.1103/PhysRevD.62.084036'), (2892, 'Frequency-domain filters for time-windowed gravitational waves from inspiraling compact binaries are constructed which combine the excellent performance of our previously developed time-domain P approximants with the analytic convenience of the stationary phase approximation without a serious loss in event rate. These Fourier-domain representations incorporate the “edge oscillations” due to the (assumed) abrupt shutoff of the time-domain signal caused by the relativistic plunge at the last stable orbit. These new analytic approximations, the SPP approximants, are not only effectual for detection and faithful for parameter estimation, but are also computationally inexpensive to generate (and are faster by factors up to 10, as compared to the corresponding time-domain templates). The SPP approximants should provide data analysts the Fourier-domain templates for massive black hole binaries of total mass m≲40M⊙, the most likely sources for LIGO and VIRGO.'), (2893, '2011-03-13 22:35:47'), (2894, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i8/e084036'), (2895, '2011-03-13 22:35:49'), (2896, 'The Advanced LIGO Gravitational Wave Detector'), (2897, '2011-03-14 2011-03-14'), (2898, 'http://arxiv.org/abs/1103.2728'), (2899, '1103.2728'), (2900, 'The Advanced LIGO gravitational wave detectors will be installed starting in 2011, with completion scheduled for 2015. The new detectors will improve the strain sensitivity of current instruments by a factor of ten, with a thousandfold increase in the observable volume of space. Here we describe the design and limiting noise sources of these second generation, long-baseline, laser interferometers.'), (2901, '2011-03-15 12:38:58'), (2902, '1103.2728 PDF'), (2903, 'http://www.arxiv.org/pdf/1103.2728.pdf'), (2904, '2011-03-15 12:39:04'), (2905, 'Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform'), (2906, 124016), (2907, '1999-05-18 May 18, 1999'), (2908, '1104.5552'), (2909, '10.1103/PhysRevD.59.124016'), (2910, 'We prove that the oft-used stationary-phase method gives a very accurate expression for the Fourier transform of the gravitational-wave signal produced by an inspiraling compact binary. We give three arguments. First, we analytically calculate the next-order correction to the stationary-phase approximation, and show that it is small. This calculation is essentially an application of the steepest-descent method to evaluate integrals. Second, we numerically compare the stationary-phase expression to the results obtained by fast Fourier transform. We show that the differences can be fully attributed to the windowing of the time series, and that they have nothing to do with an intrinsic failure of the stationary-phase method. And third, we show that these differences are negligible for the practical application of matched filtering.'), (2911, '2011-03-15 17:51:49'), (2912, 'Gravitational waves from inspiraling compact binaries'), (2913, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v59/i12/e124016'), (2914, '2011-03-15 17:51:51'), (2915, 'Time-Frequency and Time-Scale Analysis, 1998. Proceedings of the IEEE-SP International Symposium on'), (2916, 'On the stationary phase approximation of chirp spectra'), (2917, '1998-10-00 October 1998'), (2918, '2009-08-07 2009-08-07'), (2919, '10.1109/TFSA.1998.721375'), (2920, '00721375.pdf'), (2921, 'Observations of an optical source coincident with gravitational wave emission detected from a binary neutron star coalescence will improve the confidence of detection, provide host galaxy localisation, and test models for the progenitors of short gamma ray bursts. We employ optical observations of three short gamma ray bursts, 050724, 050709, 051221, to estimate the detection rate of a coordinated optical and gravitational wave search of neutron star mergers. Model R-band optical afterglow light curves of these bursts that include a jet-break are extrapolated for these sources at the sensitivity horizon of an Advanced LIGO/Virgo network. Using optical sensitivity limits of three telescopes, namely TAROT (m=18), Zadko (m=21) and an (8-10) meter class telescope (m=26), we approximate detection rates and cadence times for imaging. We find a median coincident detection rate of 4 yr^{-1} for the three bursts. GRB 050724 like bursts, with wide opening jet angles, offer the most optimistic rate of 13 coincident detections yr^{-1}, and would be detectable by Zadko up to five days after the trigger. Late time imaging to m=26 could detect off-axis afterglows for GRB 051221 like bursts several months after the trigger. For a broad distribution of beaming angles, the optimal strategy for identifying the optical emissions triggered by gravitational wave detectors is rapid response searches with robotic telescopes followed by deeper imaging at later times if an afterglow is not detected within several days of the trigger.'), (2922, '2011-05-04 14:43:19'), (2923, '1104.5552 PDF'), (2924, 'http://www.arxiv.org/pdf/1104.5552.pdf'), (2925, '2011-05-04 14:43:20'), (2926, 'Black Hole Accretion Disks'), (2927, '2011-04-28 2011-04-28'), (2928, 'http://arxiv.org/abs/1104.5499'), (2929, '1104.5499'), (2930, 'In this review, we summarize the present status of knowledge of black hole accretion disks by discussing in some details the fundamental concepts on which the theory rests, and by describing the most often used analytic and semi-analytic models of them. We also describe numerical simulations of black hole accretion.'), (2931, '2011-05-04 14:43:38'), (2932, '1104.5499 PDF'), (2933, 'http://www.arxiv.org/pdf/1104.5499.pdf'), (2934, '2011-05-04 14:43:39'), (2935, 'Tail-induced spin-orbit effect in the gravitational radiation of compact binaries'), (2936, 'http://arxiv.org/abs/1104.5659'), (2937, '1104.5659'), (2938, 'Gravitational waves contain tail effects which are due to the back-scattering of linear waves in the curved space-time geometry around the source. In this paper we improve the knowledge and accuracy of the two-body inspiraling post-Newtonian (PN) dynamics and gravitational-wave signal by computing the spin-orbit terms induced by tail effects. Notably, we derive those terms at 3PN order in the gravitational-wave energy flux, and 2.5PN and 3PN orders in the wave polarizations. This is then used to derive the spin-orbit tail effects in the phasing through 3PN order. Our results can be employed to carry out more accurate comparisons with numerical-relativity simulations and to improve the accuracy of analytical templates aimed at describing the all process of inspiral, merger and ringdown.'), (2939, '2011-05-04 14:44:35'), (2940, '1104.5659 PDF'), (2941, 'http://www.arxiv.org/pdf/1104.5659.pdf'), (2942, '2011-05-04 14:44:36'), (2943, 'Sky localization of complete inspiral-merger-ringdown signals for nonspinning massive black hole binaries'), (2944, 'http://arxiv.org/abs/1104.5650'), (2945, '1104.5650'), (2946, "We investigate the capability of LISA to measure the sky position of equal-mass, nonspinning black hole binaries, combining for the first time the entire inspiral-merger-ringdown signal, the effect of the LISA orbits, and the complete three-channel LISA response. We consider an ensemble of systems near the peak of LISA's sensitivity band, with total rest mass of 2\\times10^6 M\\odot, a redshift of z = 1, and randomly chosen orientations and sky positions. We find median sky localization errors of approximately \\sim3 arcminutes. This is comparable to the field of view of powerful electromagnetic telescopes, such as the James Webb Space Telescope, that could be used to search for electromagnetic signals associated with merging massive black holes. We investigate the way in which parameter errors decrease with measurement time, focusing specifically on the additional information provided during the merger-ringdown segment of the signal. We find that this information improves all parameter estimates directly, rather than through diminishing correlations with any subset of well- determined parameters. Although we have employed the baseline LISA design for this study, many of our conclusions regarding the information provided by mergers will be applicable to alternative mission designs as well."), (2947, '2011-05-04 15:09:16'), (2948, '1104.5650 PDF'), (2949, 'http://www.arxiv.org/pdf/1104.5650.pdf'), (2950, '2011-05-04 15:09:17'), (2951, 'A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries'), (2952, '2007-10-11 2007-10-11'), (2953, 'http://arxiv.org/abs/0710.2335'), (2954, 'Phys.Rev.D77:104017,2008; Erratum-ibid.D79:129901,2009'), (2955, 'doi:10.1103/PhysRevD.77.104017'), (2956, '0710.2335'), (2957, 'Gravitational waveforms from the inspiral and ring-down stages of the binary black hole coalescences can be modelled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the non-perturbative merger phase of the binary black-hole coalescence problem. This enables us to \\emph{coherently} search for all three stages of the coalescence of non-spinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspiral, merger, and ring-down stages of the coalescence of non-spinning binary black holes that follow quasi-circular inspiral. This two-dimensional template family is explicitly parametrized by the physical parameters of the binary. We show that the template family is not only \\emph{effectual} in detecting the signals from black hole coalescences, but also \\emph{faithful} in estimating the parameters of the binary. We compare the sensitivity of a search (in the context of different ground-based interferometers) using all three stages of the black hole coalescence with other template-based searches which look for individual stages separately. We find that the proposed search is significantly more sensitive than other template-based searches for a substantial mass-range, potentially bringing about remarkable improvement in the event-rate of ground-based interferometers. As part of this work, we also prescribe a general procedure to construct interpolated template banks using non-spinning black hole waveforms produced by numerical relativity.'), (2958, '2011-05-05 11:32:48'), (2959, 'A template bank for gravitational waveforms from coalescing binary black holes'), (2960, '0710.2335 PDF'), (2961, 'http://www.arxiv.org/pdf/0710.2335.pdf'), (2962, '2011-05-05 11:32:57'), (2963, 'CCC-predicted low-variance circles in CMB sky and LCDM'), (2964, 'http://arxiv.org/abs/1104.5675'), (2965, '1104.5675'), (2966, "New analysis confirms our earlier claim [1], [7] of circles of notably low temperature variance, often in concentric sets, in the cosmic microwave background (CMB), discernable in WMAP data. Their reality can be interpreted as evidence of supermassive black-hole encounters in a previous aeon, as predicted by conformal cyclic cosmology (CCC) [2]. Counter arguments [4-6] pointed out that such circles arise, at similar frequency, also in simulated data using WMAP's CMB power spectrum, plus random input. We responded [7] that if such circles contribute to CMB, this influences the power spectrum, enhancing such circles in simulations. We confirm this here, but show that if the theoretical LCDM power spectrum is used instead, then the low-variance circles disappear. This is evidence that the LCDM model gives an incomplete explanation of the CMB, missing crucial information, which is provided by incorporating low-variance circles of CCC. The excellent agreement between theoretical LCDM and observed power spectrum, even for fairly large l-values, does not reveal this discrepancy, of relevance only at larger l-values where agreement is weak. We point out various non-random aspects of the circles, seen both in the true data and in simulations with WMAP power spectrum, but not with the theoretical LCDM spectrum. We also show the spatial distribution of concentric circle sets to be very non-random in the true WMAP data (perhaps owing to large-scale mass inhomogeneities distorting CCC's circle shapes), in complete contrast with simulations with WMAP power spectrum, where such circle sets are much sparser and closer to average temperature. These features are fully consistent with CCC (and with an earlier analysis [8] that the random Gaussian component in the CMB is only around 0.2 in the total CMB signal) but do not readily fit in with the random initial fluctuations of standard inflation."), (2967, '2011-05-05 12:46:42'), (2968, '1104.5675 PDF'), (2969, 'http://www.arxiv.org/pdf/1104.5675.pdf'), (2970, '2011-05-05 12:46:48'), (2971, 'Product posets and causal automorphisms of the plane'), (2972, '2011-05-11 2011-05-11'), (2973, 'http://arxiv.org/abs/1105.2192'), (2974, '1105.2192'), (2975, 'A simple characterization of the causal automorphisms of 1+1 Minkowski spacetime is given.'), (2976, '2011-05-12 13:03:28'), (2977, '1105.2192 PDF'), (2978, 'http://www.arxiv.org/pdf/1105.2192.pdf'), (2979, '2011-05-12 13:03:30'), (2980, 'Gravitational recoil during binary black hole coalescence using the effective one body approach'), (2981, 124006), (2982, '2006-06-05 June 05, 2006'), (2983, 'http://link.aps.org/doi/10.1103/PhysRevD.73.124006'), (2984, '10.1103/PhysRevD.73.124006'), (2985, 'During the coalescence of binary black holes, gravitational waves carry linear momentum away from the source, which results in the recoil of the center of mass. Using the effective one body approach, which includes nonperturbative resummed estimates for the damping and conservative parts of the compact binary dynamics, we compute the recoil during the late inspiral and the subsequent plunge of nonspinning black holes of comparable masses moving in quasicircular orbits. Further, using a prescription that smoothly connects the plunge phase to a perturbed single black hole, we obtain an estimate for the total recoil associated with the binary black hole coalescence. We show that the crucial physical feature which determines the magnitude of the terminal recoil is the presence of a burst of linear-momentum flux emitted slightly before coalescence. When using the most natural expression for the linear-momentum flux during the plunge, together with a Taylor-expanded (v/c)4 correction factor, we find that the maximum value of the terminal recoil is ∼74 km/s and occurs for η=(m1m2)/(m1+m2)2≃0.2, i.e., for a mass ratio m2/m1≃0.38. Away from this optimal mass ratio, the recoil velocity decreases approximately proportionally to the scaling function f˜(η)=η2(1-4η)1/2(1.0912-1.04η+2.92η2). We comment, however, on the fact that the above “best-bet estimate” is subject to strong uncertainties because the location and amplitude of the crucial peak of linear-momentum flux happens at a moment during the plunge where most of the simplifying analytical assumptions underlying the effective one body approach are no longer justified. Changing the analytical way of estimating the linear-momentum flux, we find maximum recoils that range between 49 and 172 km/s.'), (2986, '2011-05-16 03:36:34'), (2987, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v73/i12/e124006'), (2988, '2011-05-16 03:36:35'), (2989, 'On the accuracy of the post-Newtonian approximation'), (2990, '2002-07-08 2002-07-08'), (2991, 'http://arxiv.org/abs/gr-qc/0207037'), (2992, 'gr-qc/0207037'), (2993, "We apply standard post-Newtonian methods in general relativity to locate the innermost circular orbit (ICO) of irrotational and corotational binary black-hole systems. We find that the post-Newtonian series converges well when the two masses are comparable. We argue that the result for the ICO which is predicted by the third post-Newtonian (3PN) approximation is likely to be very close to the ``exact'' solution, within 1% of fractional accuracy or better. The 3PN result is also in remarkable agreement with a numerical calculation of the ICO in the case of two corotating black holes moving on exactly circular orbits. The behaviour of the post-Newtonian series suggests that the gravitational dynamics of two bodies of comparable masses does not resemble that of a test particle on a Schwarzschild background. This leads us to question the validity of some post-Newtonian resummation techniques that are based on the idea that the field generated by two black holes is a deformation of the Schwarzschild space-time."), (2994, '2011-05-16 03:52:43'), (2995, 'gr-qc/0207037 PDF'), (2996, 'http://www.arxiv.org/pdf/gr-qc/0207037.pdf'), (2997, '2011-05-16 03:52:45'), (2998, 'Comparing effective-one-body gravitational waveforms to accurate numerical data'), (2999, '024043'), (3000, '2008-01-28 January 28, 2008'), (3001, 'http://link.aps.org/doi/10.1103/PhysRevD.77.024043'), (3002, '10.1103/PhysRevD.77.024043'), (3003, 'We continue the program of constructing, within the effective-one-body (EOB) approach, high-accuracy, faithful analytic waveforms describing the gravitational wave signal emitted by inspiralling and coalescing binary black holes. We present the comparable-mass version of a new, resummed 3 post-Newtonian (PN) accurate EOB quadrupolar waveform that we recently introduced in the small-mass-ratio limit. We compare the phase and the amplitude of this waveform to the recently published results of a high-accuracy numerical simulation of 15 orbits of an inspiralling equal-mass binary black hole system performed by the Caltech-Cornell group. We find a remarkable agreement, both in phase and in amplitude, between the new EOB waveform and the published numerical data. More precisely: (i) in the gravitational wave (GW) frequency domain Mω<0.08 where the phase of one of the nonresummed “Taylor approximant” (T4) waveform matches well with the numerical relativity one, we find that the EOB phase fares as well, while (ii) for higher GW frequencies, 0.08<Mω≲0.14, where the Taylor T4 approximant starts to significantly diverge from the numerical relativity phase, we show that the EOB phase continues to match well the numerical relativity one. We further propose various methods of tuning the two inspiral flexibility parameters, a5 and vpole, of the EOB waveform so as to “best fit” EOB predictions to numerical data. We find that the maximal dephasing between EOB and numerical relativity can then be reduced below 10-3 GW cycles over the entire span (30 GW cycles) of the simulation (while, without tuning them, the dephasing is <8×10-3 cycles). In addition, our resummed EOB amplitude agrees much better with the numerical relativity one than any of the previously considered nonresummed, post-Newtonian one (including a recently derived, nonresummed 3 PN-accurate one). We think that the present work, taken in conjunction with other recent works on the EOB–numerical relativity comparison confirms the ability of the EOB formalism (especially in its recently improved avatars) to faithfully capture the “real” general relativistic waveforms.'), (3004, '2011-05-16 17:44:35'), (3005, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v77/i2/e024043'), (3006, '2011-05-16 17:44:36'), (3007, 'Localizing compact binary inspirals on the sky using ground-based gravitational wave interferometers'), (3008, 153001), (3009, 'http://adsabs.harvard.edu/abs/2011arXiv1105.3184N'), (3010, 'The inspirals and mergers of compact binaries are among the most promising events for ground-based gravitational wave (GW) observatories. The detection of electromagnetic (EM) signals from these sources would provide complementary information to the GW signal. It is therefore important to determine the ability of gravitational-wave detectors to localize compact binaries on the sky, so that they can be matched to their EM counterparts. We use Markov Chain Monte Carlo techniques to study sky localization using networks of ground-based interferometers. Using a coherent-network analysis, we find that the LIGO-Virgo network can localize 50% of their ~8 sigma detected neutron star binaries to better than 50 sq.deg. with 95% confidence region. The addition of LCGT and LIGO-Australia improves this to 12 sq.deg.. Using a more conservative coincident detection threshold, we find that 50% of detected neutron star binaries are localized to 13 sq.deg. using the LIGO-Virgo network, and to 3 sq.deg. using the LIGO-Virgo-LCGT-LIGO-Australia network. Our findings suggest that the coordination of GW observatories and EM facilities offers great promise.'), (3011, '10.1088/0264-9381/26/15/153001'), (3012, 'Localizing compact binary inspirals on the sky using ground-based gravitational'), (3013, '2011-05-18 14:32:14'), (3014, '2011-05-16 2011-05-16'), (3015, 'http://arxiv.org/abs/1105.3184'), (3016, '1105.3184'), (3017, '2011-05-18 14:32:40'), (3018, '1105.3184 PDF'), (3019, 'http://www.arxiv.org/pdf/1105.3184.pdf'), (3020, '2011-05-18 14:32:41'), (3021, 'http://link.aps.org/doi/10.1103/PhysRevD.66.024007'), (3022, '10.1103/PhysRevD.66.024007'), (3023, 'We compare recent numerical results, obtained within a “helical Killing vector” approach, on circular orbits of corotating binary black holes to the analytical predictions made by the effective one-body (EOB) method (which has been recently extended to the case of spinning bodies). On the scale of the differences between the results obtained by different numerical methods, we find good agreement between numerical data and analytical predictions for several invariant functions describing the dynamical properties of circular orbits. This agreement is robust against the post-Newtonian accuracy used for the analytical estimates, as well as under choices of the resummation method for the EOB “effective potential,” and gets better as one uses a higher post-Newtonian accuracy. These findings open the way to a significant “merging” of analytical and numerical methods, i.e. to matching an EOB-based analytical description of the (early and late) inspiral, up to the beginning of the plunge, to a numerical description of the plunge and merger. We illustrate also the “flexibility” of the EOB approach, i.e. the possibility of determining some “best fit” values for the analytical parameters by comparison with numerical data.'), (3024, '2011-05-25 17:38:26'), (3025, 'Circular orbits of corotating binary black holes'), (3026, 'http://prd.aps.org/pdf/PRD/v66/i2/e024007'), (3027, '2011-05-25 17:38:27'), (3028, 'Hamiltonian of a spinning test particle in curved spacetime'), (3029, '2009-11-17 November 17, 2009'), (3030, 'http://link.aps.org/doi/10.1103/PhysRevD.80.104025'), (3031, '10.1103/PhysRevD.80.104025'), (3032, 'Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase space algebra in the Newton-Wigner spin supplementary condition, suitably generalized to curved spacetime, and find that the phase space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner canonical Hamiltonian computed in PN theory in the test particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type SKerrS (and SKerr2) through 3PN order, SKerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.'), (3033, '2011-05-27 21:20:30'), (3034, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v80/i10/e104025'), (3035, '2011-05-27 21:20:31'), (3036, 'Multimessenger Astronomy'), (3037, '2011-05-29 2011-05-29'), (3038, 'http://arxiv.org/abs/1105.5843'), (3039, '1105.5843'), (3040, 'Multimessenger astronomy incorporating gravitational radiation is a new and exciting field that will potentially provide significant results and exciting challenges in the near future. With advanced interferometric gravitational wave detectors (LCGT, LIGO, Virgo) we will have the opportunity to investigate sources of gravitational waves that are also expected to be observable through other messengers, such as electromagnetic (gamma-rays, x-rays, optical, radio) and/or neutrino emission. The LIGO-Virgo interferometer network has already been used for multimessenger searches for gravitational radiation that have produced insights on cosmic events. The simultaneous observation of electromagnetic and/or neutrino emission could be important evidence in the first direct detection of gravitational radiation. Knowledge of event time, source sky location, and the expected frequency range of the signal enhances our ability to search for the gravitational radiation signatures with an amplitude closer to the noise floor of the detector. Presented here is a summary of the status of LIGO-Virgo multimessenger detection efforts, along with a discussion of questions that might be resolved using the data from advanced or third generation gravitational wave detector networks.'), (3041, '2011-05-31 14:01:17'), (3042, '1105.5843 PDF'), (3043, 'http://www.arxiv.org/pdf/1105.5843.pdf'), (3044, '2011-05-31 14:01:18'), (3045, 'Transient solar oscillations driven by primordial black holes'), (3046, '2011-05-31 2011-05-31'), (3047, 'http://arxiv.org/abs/1106.0011'), (3048, '1106.0011'), (3049, 'Stars are transparent to the passage of primordial black holes (PBHs) and serve as seismic detectors for such objects. The gravitational field of a PBH squeezes a star and causes it to ring acoustically. We calculate the seismic signature of a PBH passing through the Sun. The background for this signal is the observed spectrum of solar oscillations excited by supersonic turbulence. We predict that PBHs more massive than 10^21 g (comparable in mass to an asteroid) are detectable by existing solar observatories. The oscillations excited by PBHs peak at large scales and high frequencies, making them potentially detectable in other stars. The discovery of PBHs would have profound implications for cosmology and high-energy physics.'), (3050, '2011-06-02 13:35:15'), (3051, '1106.0011 PDF'), (3052, 'http://www.arxiv.org/pdf/1106.0011.pdf'), (3053, '2011-06-02 13:35:54'), (3054, 'The coalescence rates of double black holes'), (3055, '2011-06-02 2011-06-02'), (3056, 'http://arxiv.org/abs/1106.0397'), (3057, '1106.0397'), (3058, 'We present the summary of the recent investigations of double black hole binaries in context of their formation and merger rates. In particular we discuss the spectrum of black hole masses, the formation scenarios in the local Universe and the estimates of detection rates for gravitational radiation detectors like LIGO and VIRGO. Our study is based on observed properties of known Galactic and extra-galactic stellar mass black holes and evolutionary predictions. We argue that the binary black holes are the most promising source of gravitational radiation.'), (3059, '2011-06-03 13:30:26'), (3060, '1106.0397 PDF'), (3061, 'http://www.arxiv.org/pdf/1106.0397.pdf'), (3062, '2011-06-03 13:30:27'), (3063, 'New Generic Ringdown Frequencies at the Birth of a Kerr Black Hole'), (3064, '2011-06-03 2011-06-03'), (3065, 'http://arxiv.org/abs/1106.0782'), (3066, '1106.0782'), (3067, 'We discuss a new ringdown frequency mode for vacuum perturbations of the Kerr black hole. We evolve initial data for the vacuum radial Teukolsky equation using a near horizon approximation, and find a frequency mode analogous to that found in a recent study of radiation generated by a plunging particle close to the Kerr horizon. We discuss our results in the context of that study. We also explore the utility of this mode by fitting a numerical waveform with a combination of the usual quasi-normal modes (QNMs) and the new oscillation frequency.'), (3068, '2011-06-07 12:48:33'), (3069, '1106.0782 PDF'), (3070, 'http://www.arxiv.org/pdf/1106.0782.pdf'), (3071, '2011-06-07 12:48:38'), (3072, 'A systematic search for massive black hole binaries in SDSS spectroscopic sample'), (3073, '2011-06-06 2011-06-06'), (3074, 'http://arxiv.org/abs/1106.1180'), (3075, '1106.1180'), (3076, 'We present the results of a systematic search for massive black hole binaries in the Sloan Digital Sky Survey spectroscopic database. We focus on bound binaries, under the assumption that one of the black holes is active. In this framework, the broad lines associated to the accreting black hole are expected to show systematic velocity shifts with respect to the narrow lines, which trace the rest-frame of the galaxy. For a sample of 54586 quasars and 3929 galaxies at redshifts 0.1<z<1.5 we brute-force model each spectrum as a mixture of two quasars at two different redshifts. The spectral model is a data-driven dimensionality reduction of the SDSS quasar spectra based on a matrix factorization. We identified 32 objects with peculiar spectra. Nine of them can be interpreted as black hole binaries. This doubles the number of known black hole binary candidates. We also report on the discovery of a new class of extreme double-peaked emitters with exceptionally broad and faint Balmer lines. For all the interesting sources, we present detailed analysis of the spectra, and discuss possible interpretations.'), (3077, '2011-06-08 14:30:45'), (3078, '1106.1180 PDF'), (3079, 'http://www.arxiv.org/pdf/1106.1180.pdf'), (3080, '2011-06-08 14:30:46'), (3081, '2009-01-00 01/2009'), (3082, '015009'), (3083, '10.1088/0264-9381/26/1/015009'), (3084, 'http://iopscience.iop.org/0264-9381/26/1/015009;jsessionid=4B3878B0EB6A43B8C484F5AD0D09795B.c3'), (3085, 'A method for estimating time–frequency characteristics of compact binary mergers to improve searches for inspiral, merger and ring-down phases separately'), (3086, '2011-06-09 00:35:24'), (3087, '0264-9381_26_1_015009.pdf'), (3088, 'Estimating the final spin of a binary black hole coalescence'), (3089, '026004'), (3090, '2008-01-17 January 17, 2008'), (3091, 'http://link.aps.org/doi/10.1103/PhysRevD.77.026004'), (3092, '10.1103/PhysRevD.77.026004'), (3093, 'We present a straightforward approach for estimating the final black hole spin of a binary black hole coalescence with arbitrary initial masses and spins. Making some simple assumptions, we estimate the final angular momentum to be the sum of the individual spins plus the orbital angular momentum of a test particle orbiting at the last stable orbit around a Kerr black hole with a spin parameter of the final black hole. The formula we obtain is able to reproduce with reasonable accuracy the results from available numerical simulations, but, more importantly, it can be used to investigate what configurations might give rise to interesting dynamics. In particular, we discuss scenarios which might give rise to a flip in the direction of the total angular momentum of the system. By studying the dependence of the final spin upon the mass ratio and initial spins, we find that our simple approach suggests that it is not possible to spin-up a black hole to extremal values through merger scenarios irrespective of the mass ratio of the objects involved.'), (3094, '2011-06-09 00:51:06'), (3095, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v77/i2/e026004'), (3096, '2011-06-09 00:51:07'), (3097, '2011-06-09 19:53:00'), (3098, '2011-06-09 19:54:07'), (3099, '1107.2244'), (3100, 'Context. In order to study the association of the origin of ultra high energy cosmic rays (UHECR) with active galactic nuclei (AGN) at all levels of their activity we require an unbiased sample of black holes. Aims. Here we describe such a sample, of about 6 000 black holes, within the local Universe, inside the GZK (Greisen Zatsepin Kuzmin) limit, around 100 Mpc. Methods. The starting point is the 2 micron all sky survey, with the next steps as: test its com- pleteness down to low flux densities, confine it to redshifts z < 0.025, limit it to early Hubble type galaxies, test with B-V colors and with the FIR/Radio ratio the possible separation in classes of sources for the ultra high energy cosmic rays, use the spheroidal stellar component - black hole mass relationship to derive black hole masses, and test them with known black hole masses. Results. The statistics are consistent with the mass function of black hole masses, with a rel- atively flat distribution to about 10^8 Msol, and thereafter a very steep spectrum. Our sample cuts off just below 10^7 Msol, indicating a gap for lower masses, below somewhere near 10^6 Msol. We construct the sky distribution for all black holes above 10^7 Msol, 10^8 Msol, and 3 x 10^8 Msol, and also show the sky distribution for the five redshift ranges 0.0 - 0.005, 0.005 - 0.0010, 0.010 - 0.015, 0.015 - 0.020, and 0.020 to 0.025.'), (3101, '2011-07-13 06:39:28'), (3102, 'Cauchy-Characteristic Matching: A New Approach to Radiation Boundary Conditions'), (3103, 23), (3104, 4303), (3105, '1996-06-03 June 03, 1996'), (3106, 'http://link.aps.org/doi/10.1103/PhysRevLett.76.4303'), (3107, '10.1103/PhysRevLett.76.4303'), (3108, 'We investigate a new methodology for computing wave generation, using Cauchy evolution in a bounded interior region and characteristic evolution in the exterior. Matching the two schemes eliminates usual difficulties such as backreflection from the outer computational boundary. Mapping radiative infinity into a finite grid domain allows a global solution. The matching interface can be close to the sources, the wave fronts can have arbitrary geometry, and strong nonlinearity can be present. The matching algorithm dramatically outperforms traditional radiation boundary conditions.'), (3109, 'Efficient algorithm for computing the time-resolved full-sky cross power in an interferometer with omnidirectional elements'), (3110, 123003), (3111, '2007-06-13 June 13, 2007'), (3112, 'http://link.aps.org/doi/10.1103/PhysRevD.75.123003'), (3113, '10.1103/PhysRevD.75.123003'), (3114, 'We derive both time- and frequency-domain algorithms for the fast, approximate, numeric evaluation of the cross-correlation integral that appears in a variety of imaging applications. These algorithms possess a number of useful features. Their operation counts are linear in the amount (duration) of data to be processed, which allows them to be run quickly on small amounts of data, thereby allowing one to resolve time dependence in the sources being imaged. The algorithms also provide means by which to systematically increase or decrease their accuracy for increases and decreases in speed, respectively; that is to say, one can choose to obtain the result to lower accuracy and thereby obtain the result more quickly or with more modest computer requirements. The frequency-domain implementation is particularly fast and, on a 32-bit 1.8 GHz Pentium-M computer, has demonstrated the ability to synthesize full-sky cross-power images for a single baseline up to harmonic order 19, with a signal-to-noise ratio of 26 dB, at speeds of over 800 k sample/s.'), (3115, '2011-06-09 12:33:38'), (3116, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v75/i12/e123003'), (3117, '2011-06-09 12:33:51'), (3118, 'Tracking the precession of compact binaries from their gravitational-wave signal'), (3119, '2010-12-13 2010-12-13'), (3120, 'http://arxiv.org/abs/1012.2879'), (3121, '1012.2879'), (3122, 'We present a simple method to track the precession of a black-hole-binary system, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitude of the $(\\ell=2,|m|=2)$ modes is maximized, which we denote the "quadrupole-aligned" frame. We demonstrate the efficacy of this method when applied to waveforms from numerical simulations. In the test case of an equal-mass nonspinning binary, our method locates the direction of the orbital angular momentum to within $(\\Delta \\theta, \\Delta \\phi) = (0.05^{\\circ},0.2^{\\circ})$. We then apply the method to a $q = M_2/M_1 = 3$ binary that exhibits significant precession. In general a spinning binary\'s orbital angular momentum $\\mathbf{L}$ is \\emph{not} orthogonal to the orbital plane. Evidence that our method locates the direction of $\\mathbf{L}$ rather than the normal of the orbital plane is provided by comparison with post-Newtonian (PN) results. Also, we observe that it accurately reproduces similar higher-mode amplitudes to a comparable non-spinning (and therefore non-precessing) binary, and that the frequency of the $(\\ell=2,|m|=2)$ modes is consistent with the "total frequency" of the binary\'s motion. The simple form of the quadrupole-aligned waveform will be useful in attempts to analytically model the inspiral-merger-ringdown (IMR) signal of precessing binaries, and in standardizing the representation of waveforms for studies of accuracy and consistency of source modelling efforts, both numerical and analytical.'), (3123, '1107.2244 PDF'), (3124, '1012.2879 PDF'), (3125, 'http://www.arxiv.org/pdf/1012.2879.pdf'), (3126, 'http://www.arxiv.org/pdf/1107.2244.pdf'), (3127, '2011-06-10 16:29:18'), (3128, 'Cauchy-Characteristic Matching'), (3129, 'http://prl.aps.org/pdf/PRL/v76/i23/p4303_1'), (3130, '2011-06-10 16:29:19'), (3131, 'Characteristic Evolution and Matching'), (3132, 'http://www.livingreviews.org/lrr-2005-10'), (3133, 'lrr-2005-10Color.pdf'), (3134, 'High-powered gravitational news'), (3135, 56), (3136, 6298), (3137, '1997-11-15 November 15, 1997'), (3138, 'http://link.aps.org/doi/10.1103/PhysRevD.56.6298'), (3139, '10.1103/PhysRevD.56.6298'), (3140, 'We describe the computation of the Bondi news for gravitational radiation. We have implemented a computer code for this problem. We discuss the theory behind it as well as the results of validation tests. Our approach uses the compactified null cone formalism, with the computational domain extending to future null infinity and with a world tube as inner boundary. We calculate the appropriate full Einstein equations in computational eth form in (a) the interior of the computational domain and (b) on the inner boundary. At future null infinity, we transform the computed data into standard Bondi coordinates and so are able to express the news in terms of its standard N+ and N× polarization components. The resulting code is stable and second-order convergent. It runs successfully even in the highly nonlinear case, and has been tested with the news as high as 400, which represents a gravitational radiation power of about 1013M⊙/sec.'), (3141, '2011-06-10 16:50:35'), (3142, 'http://prd.aps.org/pdf/PRD/v56/i10/p6298_1'), (3143, '2011-06-10 16:50:36'), (3144, 'Unambiguous Determination of Gravitational Waveforms from Binary Black Hole Mergers'), (3145, 103), (3146, 221101), (3147, '2009-11-24 November 24, 2009'), (3148, 'http://link.aps.org/doi/10.1103/PhysRevLett.103.221101'), (3149, '10.1103/PhysRevLett.103.221101'), (3150, 'Gravitational radiation is properly defined only at future null infinity (J+), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at J+ for the inspiral and merger of two equal-mass nonspinning black holes. Thus we have determined the first unambiguous merger waveforms for this problem. The implementation is general purpose and can be applied to calculate the gravitational radiation, at J+, given data at a finite radius calculated in another computation.'), (3151, '2011-06-10 16:54:37'), (3152, 'http://prl.aps.org/pdf/PRL/v103/i22/e221101'), (3153, '2011-06-10 16:54:38'), (3154, '2010-04-00 04/2010'), (3155, '075014'), (3156, '10.1088/0264-9381/27/7/075014'), (3157, 'http://iopscience.iop.org/0264-9381/27/7/075014'), (3158, 'Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity'), (3159, '2011-06-10 16:55:28'), (3160, 'Characteristic extraction in numerical relativity'), (3161, 'http://stacks.iop.org/0264-9381/26/i=15/a=153001?key=crossref.3aa1c829d5c742dd5b837526de1788eb'), (3162, '2011-06-10 16:56:08'), (3163, '0264-9381_27_7_075014.pdf'), (3164, 'http://iopscience.iop.org/0264-9381/27/7/075014/pdf/0264-9381_27_7_075014.pdf'), (3165, '2011-06-10 16:58:33'), (3166, 'Modeling multipolar gravitational-wave emission from small mass-ratio mergers'), (3167, '2011-06-12 03:26:26'), (3168, 'Some Properties of Spin-Weighted Spheroidal Harmonics'), (3169, '1977-12-02 December 02 , 1977'), (3170, 'Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences'), (3171, '71 -86'), (3172, 358), (3173, 1692), (3174, 'http://rspa.royalsocietypublishing.org/content/358/1692/71.abstract'), (3175, "We analyse the angular eigenfunctions-spin-weighted spheroidal harmonics-and eigenvalues of Teukolsky's equation. This equation describes infinitesimal scalar, electromagnetic and gravitational perturbations of rotating (Kerr) black holes. We derive analytic expressions for the eigenvalues up to sixth order in the expansion parameter for low frequencies and an analogous expansion in the high-frequency limit. Spin-weighted spheroidal harmonics form a complete and orthonormal set of functions on a prolate spheroid. They are, however, not the eigenfunctions of the natural Laplace operator on a spheroid and thus do not allow an obvious geometrical interpretation as the corresponding spin-weighted spherical harmonics."), (3176, '10.1098/rspa.1977.0187'), (3177, '2011-06-12 16:16:01'), (3178, 'Dynamic black holes through gravitational collapse: Analysis of multipole moment of the curvatures on the horizon'), (3179, '2011-06-09 2011-06-09'), (3180, 'Proc. R. Soc. Lond. A-1977-Breuer-71-86.pdf'), (3181, 'http://arxiv.org/abs/1106.1922'), (3182, '1106.1922'), (3183, 'We have investigated several properties of rapidly rotating dynamic black holes generated by gravitational collapse of rotating relativistic stars. At present, numerical simulations of the binary black hole merger are able to produce a Kerr black hole of J_final / M_final^2 up to = 0.91, of gravitational collapse from uniformly rotating stars up to J_final / M_final^2 ~ 0.75, where J_final is the total angular momentum and M_final the total gravitational mass of the hole. We have succeeded in producing a dynamic black hole of spin J_final / M_final^2 ~ 0.95 through the collapse of differentially rotating relativistic stars. We have investigated those dynamic properties through diagnosing multipole moment of the horizon, and found the following two features. Firstly, two different definitions of the angular momentum of the hole, the approximated Killing vector approach and dipole moment of the current multipole approach, make no significant difference to our computational results. Secondly, dynamic hole approaches a Kerr by gravitational radiation within the order of a rotational period of an equilibrium star, although the dynamic hole at the very forming stage deviates quite far from a Kerr. We have also discussed a new phase of quasi-periodic waves in the gravitational waveform after the ringdown in terms of multipole moment of the dynamic hole.'), (3184, '2011-06-13 13:02:23'), (3185, 'Dynamic black holes through gravitational collapse'), (3186, '1106.1922 PDF'), (3187, 'http://www.arxiv.org/pdf/1106.1922.pdf'), (3188, '2011-06-13 13:02:26'), (3189, '1977-00-00 1977'), (3190, 1849), (3191, '10.1063/1.523499'), (3192, 'http://link.aip.org/link/JMAPAQ/v18/i9/p1849/s1&Agg=doi'), (3193, 'Spin-weighted angular spheroidal functions'), (3194, '2011-06-13 14:44:31'), (3195, 'Estimating parameters of coalescing compact binaries with a detector network including LIGO Australia'), (3196, '2011-06-13 2011-06-13'), (3197, 'http://arxiv.org/abs/1106.2547'), (3198, '1106.2547'), (3199, 'One of the goals of gravitational-wave astronomy is simultaneous detection of gravitational-wave signals from merging compact-object binaries and the electromagnetic transients from these mergers. With the next generation of advanced ground-based gravitational wave detectors under construction, we examine the benefits of the proposed extension of the detector network to include a fourth site in Australia in addition to the network of Hanford, Livingston and Cascina sites. Using Bayesian parameter-estimation analyses of simulated gravitational-wave signals from a range of coalescing-binary locations and orientations, we study the improvement in parameter estimation. We find that an Australian detector can break degeneracies in several parameters; in particular, the localization of the source on the sky is improved by a factor of ~4, with more modest improvements in distance and binary inclination estimates. This enhanced ability to localize sources on the sky will be crucial in any search for electromagnetic counterparts to detected gravitational-wave signals.'), (3200, '2011-06-15 10:55:38'), (3201, '1106.2547 PDF'), (3202, 'http://www.arxiv.org/pdf/1106.2547.pdf'), (3203, '2011-06-15 10:55:44'), (3204, 'LISA detections of massive black hole inspirals: Parameter extraction errors due to inaccurate template waveforms'), (3205, 104018), (3206, '2007-11-12 November 12, 2007'), (3207, 'http://link.aps.org/doi/10.1103/PhysRevD.76.104018'), (3208, '10.1103/PhysRevD.76.104018'), (3209, 'The planned Laser Interferometer Space Antenna (LISA) is expected to detect the inspiral and merger of massive black hole binaries (MBHBs) at z≲5 with signal-to-noise ratios (SNRs) of hundreds to thousands. Because of these high SNRs, and because these SNRs accrete over periods of weeks to months, it should be possible to extract the physical parameters of these systems with high accuracy; for instance, for a ∼106M⊙ MBHBs at z=1 it should be possible to determine the two masses to ∼0.1% and the sky location to ∼1°. However, those are just the errors due to noise: there will be additional “theoretical” errors due to inaccuracies in our best model waveforms, which are still only approximate. The goal of this paper is to estimate the typical magnitude of these theoretical errors. We develop mathematical tools for this purpose, and apply them to a somewhat simplified version of the MBHB problem, in which we consider just the inspiral part of the waveform and neglect spin-induced precession, eccentricity, and PN amplitude corrections. For this simplified version, we estimate that theoretical uncertainties in sky position will typically be ∼1°, i.e., comparable to the statistical uncertainty. For the mass and spin parameters, our results suggest that while theoretical errors will be rather small absolutely, they could still dominate over statistical errors (by roughly an order of magnitude) for the strongest sources. The tools developed here should be useful for estimating the magnitude of theoretical errors in many other problems in gravitational-wave astronomy.'), (3210, '2011-06-17 18:06:47'), (3211, 'LISA detections of massive black hole inspirals'), (3212, 'http://prd.aps.org/pdf/PRD/v76/i10/e104018'), (3213, '2011-06-17 18:06:48'), (3214, 'Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism'), (3215, 'http://arxiv.org/abs/1106.1021'), (3216, '1106.1021'), (3217, 'We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios 1, 2, 3, 4, and 6, by maximizing phase and amplitude agreement of the leading (2,2) mode and of the subleading modes (2,1), (3,3), (4,4) and (5,5). Aligning the calibrated EOB waveforms and the numerical waveforms at low frequency, the phase difference of the (2,2) mode between model and numerical simulation remains below 0.1 rad throughout the evolution for all mass ratios considered. The fractional amplitude difference at peak amplitude of the (2,2) mode is 2% and grows to 12% during the ringdown. Using the Advanced LIGO noise curve we study the effectualness and measurement accuracy of the EOB model, and stress the relevance of modeling the higher-order modes for parameter estimation. We find that the effectualness, measured by the mismatch, between the EOB and numerical-relativity polarizations which include only the (2,2) mode is smaller than 0.2% for binaries with total mass 20-200 Msun and mass ratios 1, 2, 3, 4, and 6. When numerical-relativity polarizations contain the strongest seven modes, and stellar-mass black holes with masses less than 50Msun are considered, the mismatch for mass ratio 6 (1) can be as high as 5% (0.2%) when only the EOB (2,2) mode is included, and an upper bound of the mismatch is 0.5% (0.07%) when all the four subleading EOB modes calibrated in this paper are taken into account. For binaries with intermediate-mass black holes with masses greater than 50Msun the mismatches are larger. We also determine for which signal-to-noise ratios the EOB model developed here can be used to measure binary parameters with systematic biases smaller than statistical errors due to detector noise.'), (3218, '2011-06-20 04:30:19'), (3219, '1106.1021 PDF'), (3220, 'http://www.arxiv.org/pdf/1106.1021.pdf'), (3221, '2011-06-20 04:30:53'), (3222, 'Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters'), (3223, 3033), (3224, '1996-03-15 March 15, 1996'), (3225, 'http://link.aps.org/doi/10.1103/PhysRevD.53.3033'), (3226, '10.1103/PhysRevD.53.3033'), (3227, 'The detection of gravitational waves from astrophysical sources is probably one of the most keenly awaited events in the history of astrophysics. The paucity of gravitational wave sources and the relative difficulty in detecting such waves, as compared to those in the electromagnetic domain, necessitate the development of optimal data analysis techniques to detect the signal, as well as to extract the maximum possible information from the detected signals. Coalescing binary systems are one of the most promising sources of gravitational waves. This is due to the fact that such sources are easier to model and thus one can design detection strategies particularly tuned to such signals. A lot of attention has been devoted in the literature to studying such techniques and most of the work has revolved around the Weiner filtering and the maximum likelihood estimators of the parameters of the binary system. We investigate such techniques with the aid of differential geometry which provides geometric insight into the problem. Such a formalism allows us to explore the merits and faults of a detection scheme independent of the parameters chosen to represent the waveform. The formalism also generalizes the problem of choosing an optimal set of templates to detect a known waveform buried in noisy data. We stress the need for finding a set of convenient parameters for the waveform and show that even after the inclusion of the second-order post-Newtonian corrections, the waveform can essentially be detected by employing a one-dimensional lattice of templates.'), (3228, '2011-06-22 20:11:25'), (3229, 'Gravitational waves from coalescing binaries'), (3230, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v53/i6/p3033_1'), (3231, '2011-06-22 20:11:26'), (3232, 'Tidal stabilization of rigidly rotating, fully relativistic neutron stars'), (3233, 'Effective one body Hamiltonian of two spinning black-holes with next-to-next-to-leading order spin-orbit coupling'), (3234, '2011-06-21 2011-06-21'), (3235, 'http://arxiv.org/abs/1106.4349'), (3236, '1106.4349'), (3237, 'Building on the recently computed next-to-next-to-leading order (NNLO) post-Newtonian (PN) spin-orbit Hamiltonian for spinning binaries \\cite{Hartung:2011te} we extend the effective-one-body (EOB) description of the dynamics of two spinning black-holes to NNLO in the spin-orbit interaction. The calculation that is presented extends to NNLO the next-to-leading order (NLO) spin-orbit Hamiltonian computed in Ref. \\cite{Damour:2008qf}. The present EOB Hamiltonian reproduces the spin-orbit coupling through NNLO in the test-particle limit case. In addition, in the case of spins parallel or antiparallel to the orbital angular momentum, when circular orbits exist, we find that the inclusion of NNLO spin-orbit terms moderates the effect of the NLO spin-orbit coupling.'), (3238, '2011-06-23 15:18:29'), (3239, '1106.4349 PDF'), (3240, 'http://www.arxiv.org/pdf/1106.4349.pdf'), (3241, '2011-06-23 15:18:32'), (3242, 'Binary Black Hole Waveform Extraction at Null Infinity'), (3243, '2011-06-23 2011-06-23'), (3244, 'http://arxiv.org/abs/1106.4841'), (3245, 'Class. Quantum Grav. 28 (2011) 134006'), (3246, '1106.4841'), (3247, 'In this work, we present a work in progress towards an efficient and economical computational module which interfaces between Cauchy and characteristic evolution codes. Our goal is to provide a standardized waveform extraction tool for the numerical relativity community which will allow CCE to be readily applied to a generic Cauchy code. The tool provides a means of unambiguous comparison between the waveforms generated by evolution codes based upon different formulations of the Einstein equations and different numerical approximation.'), (3248, '2011-06-27 12:35:14'), (3249, '1106.4841 PDF'), (3250, 'http://www.arxiv.org/pdf/1106.4841.pdf'), (3251, '2011-06-27 12:35:26'), (3252, 'Reliability of complete gravitational waveform models for compact binary coalescences'), (3253, '2011-07-05 2011-07-05'), (3254, 'http://arxiv.org/abs/1107.0996'), (3255, '1107.0996'), (3256, 'With recent advances in post-Newtonian (PN) theory and numerical relativity (NR) it has become possible to construct inspiral-merger-ringdown gravitational waveforms from coalescing compact binaries by combining both descriptions into one complete hybrid signal. It is important to estimate the error of such waveforms. Previous studies have identified the PN contribution as the dominant source of error, which can be reduced by incorporating longer NR simulations. There are two outstanding issues that make it difficult to determine the minimum simulation length necessary to produce suitably accurate hybrids: (1) the relevant criteria for a signal search is the mismatch between the true waveform and a set of model waveforms, optimized over all waveforms in the model. For discrete hybrids this optimization is not possible. (2) these calculations require that NR waveforms already exist, while ideally we would like to know the necessary length before performing the simulation. Here we overcome these difficulties by developing a general procedure that allows us to estimate hybrid mismatch errors without numerical data, and to optimize them over all physical parameters. Using this procedure we find that, contrary to some earlier studies, ~10 NR orbits before merger allow for the construction of waveform families that are accurate enough for detection in a broad range of parameters, only excluding highly spinning, unequal-mass systems. Nonspinning binaries, even with high mass-ratio (>20) are well modeled for astrophysically reasonable component masses. In addition, the parameter bias is only of the order of 1% for total mass and symmetric mass-ratio and less than 0.1 for the dimensionless spin magnitude. We take the view that similar NR waveform lengths will remain the state of the art in the Advanced detector era, and begin to assess the limits of the science that can be done with them.'), (3257, '2011-07-09 15:12:05'), (3258, '1107.0996 PDF'), (3259, 'http://www.arxiv.org/pdf/1107.0996.pdf'), (3260, '2011-07-09 15:12:12'), (3261, 'Mergers of black-hole binaries with aligned spins: Waveform characteristics'), (3262, '2011-07-06 2011-07-06'), (3263, 'http://arxiv.org/abs/1107.1181'), (3264, '1107.1181'), (3265, 'We conduct a descriptive analysis of the multipolar structure of gravitational-radiation waveforms from equal-mass aligned-spin mergers, following an approach first presented in the complementary context of nonspinning black holes of varying mass ratio [Baker et al., Phys. Rev. D 78:044046 (2008)]. We find that, as with the nonspinning mergers, the dominant waveform mode phases evolve together in lock-step through inspiral and merger, supporting the previous waveform description in terms of an adiabatically rigid rotator driving gravitational-wave emission -- an implicit rotating source (IRS). We further apply the late-time merger-ringdown model for the rotational frequency introduced in Baker et al. (2008), along with an improved amplitude model appropriate for the dominant (2,+/- 2) modes. This provides a quantitative description of the merger-ringdown waveforms, and suggests that the major features of these waveforms can be described with reference only to the intrinsic parameters associated with the state of the final black hole formed in the merger. We provide an explicit model for the merger-ringdown radiation, and demonstrate that this model agrees to fitting factors better than 95% with the original numerical waveforms for system masses above ~ 150 MSun. This model may be directly applicable to gravitational-wave detection of intermediate-mass black hole mergers.'), (3266, '2011-07-09 15:12:14'), (3267, 'Mergers of black-hole binaries with aligned spins'), (3268, '1107.1181 PDF'), (3269, 'http://www.arxiv.org/pdf/1107.1181.pdf'), (3270, '2011-07-09 15:12:15'), (3271, 'Trapped surfaces'), (3272, '2011-07-07 2011-07-07'), (3273, 'http://arxiv.org/abs/1107.1344'), (3274, '1107.1344'), (3275, 'I review the definition and types of (closed) trapped surfaces. Surprising global properties are shown, such as their "clairvoyance" and the possibility that they enter into flat portions of the spacetime. Several results on the interplay of trapped surfaces with vector fields and with spatial hypersurfaces are presented. Applications to the quasi-local definition of Black Holes are discussed, with particular emphasis set onto marginally trapped tubes, trapping horizons and the boundary of the region with closed trapped surfaces. Finally, the core of a trapped region is introduced, and its importance discussed.'), (3276, '2011-07-09 15:12:17'), (3277, '1107.1344 PDF'), (3278, 'http://www.arxiv.org/pdf/1107.1344.pdf'), (3279, '2011-07-09 15:12:18'), (3280, 'Addressing the spin question in gravitational-wave searches: Waveform templates for inspiralling compact binaries with nonprecessing spins'), (3281, 'http://arxiv.org/abs/1107.1267'), (3282, '1107.1267'), (3283, 'This paper presents a post-Newtonian (PN) template family of gravitational waveforms from inspiralling compact binaries with non-precessing spins, where the spin effects are described by a single "reduced-spin" parameter. This template family, which reparametrizes all the spin-dependent PN terms in terms of the leading-order (1.5PN) spin-orbit coupling term in an approximate way, has very high overlaps (fitting factor > 0.99) with non-precessing binaries with arbitrary mass ratios and spins. We also show that this template family is "effectual" towards a significant fraction of generic spinning binaries in the comparable-mass regime (m_2/m_1 < 10), providing an attractive and feasible way of searching for gravitational waves (GWs) from spinning low-mass binaries. We also show that the secular (non-oscillatory) spin-dependent effects in the phase evolution (which are taken into account by the non-precessing templates) are more important than the oscillatory effects of precession in the comparable-mass (m_1 ~= m_2) regime. Hence the effectualness of non-spinning templates is particularly poor in this case, as compared to non-precessing-spin templates. For the case of binary neutron stars observable by Advanced LIGO, even small spins (L_N . S/m^2 ~= 0.1) will cause significant de-phasing with non-spinning templates. This is contrary to the expectation that neutron-star spins may not be relevant for GW detection.'), (3284, '2011-07-09 15:12:20'), (3285, 'Addressing the spin question in gravitational-wave searches'), (3286, '1107.1267 PDF'), (3287, 'http://www.arxiv.org/pdf/1107.1267.pdf'), (3288, '2011-07-09 15:12:21'), (3289, '2011-07-13 06:39:33'), (3290, 'Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects'), (3291, '2007-03-15 2007-03-15'), (3292, 'http://arxiv.org/abs/gr-qc/0703086'), (3293, 'Phys.Rev.D77:042001,2008'), (3294, 'doi:10.1103/PhysRevD.77.042001'), (3295, 'gr-qc/0703086'), (3296, 'The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond--Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.'), (3297, '2011-07-14 11:00:57'), (3298, 'gr-qc/0703086 PDF'), (3299, 'http://www.arxiv.org/pdf/gr-qc/0703086.pdf'), (3300, '2011-07-14 11:01:04'), (3301, 'Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral'), (3302, '2009-11-18 2009-11-18'), (3303, 'http://arxiv.org/abs/0911.3535'), (3304, 'Phys.Rev.D81:123016,2010'), (3305, 'doi:10.1103/PhysRevD.81.123016'), (3306, '0911.3535'), (3307, "The early part of the gravitational wave signal of binary neutron star inspirals can potentially yield robust information on the nuclear equation of state. The influence of a star's internal structure on the waveform is characterized by a single parameter: the tidal deformability lambda, which measures the star's quadrupole deformation in response to the companion's perturbing tidal field. We calculate lambda for a wide range of equations of state and find that the value of lambda spans an order of magnitude for the range of equation of state models considered. An analysis of the feasibility of discriminating between neutron star equations of state with gravitational wave observations of the early part of the inspiral reveals that the measurement error in lambda increases steeply with the total mass of the binary. Comparing the errors with the expected range of lambda, we find that Advanced LIGO observations of binaries at a distance of 100 Mpc will probe only unusually stiff equations of state, while the proposed Einstein Telescope is likely to see a clean tidal signature."), (3308, '2011-07-14 17:58:23'), (3309, '0911.3535 PDF'), (3310, 'http://www.arxiv.org/pdf/0911.3535.pdf'), (3311, '2011-07-14 17:58:27'), (3312, 'Constraining neutron star tidal Love numbers with gravitational wave detectors'), (3313, '2007-09-12 2007-09-12'), (3314, 'http://arxiv.org/abs/0709.1915'), (3315, 'Phys.Rev.D77:021502,2008'), (3316, 'doi:10.1103/PhysRevD.77.021502'), (3317, '0709.1915'), (3318, "Ground-based gravitational wave detectors may be able to constrain the nuclear equation of state using the early, low frequency portion of the signal of detected neutron star - neutron star inspirals. In this early adiabatic regime, the influence of a neutron star's internal structure on the phase of the waveform depends only on a single parameter lambda of the star related to its tidal Love number, namely the ratio of the induced quadrupole moment to the perturbing tidal gravitational field. We analyze the information obtainable from gravitational wave frequencies smaller than a cutoff frequency of 400 Hz, where corrections to the internal-structure signal are less than 10 percent. For an inspiral of two non-spinning 1.4 solar mass neutron stars at a distance of 50 Mpc, LIGO II detectors will be able to constrain lambda to lambda < 2.0 10^{37} g cm^2 s^2 with 90% confidence. Fully relativistic stellar models show that the corresponding constraint on radius R for 1.4 solar mass neutron stars would be R < 13.6 km (15.3 km) for a n=0.5 (n=1.0) polytrope."), (3319, '2011-07-14 18:08:24'), (3320, '0709.1915 PDF'), (3321, 'http://www.arxiv.org/pdf/0709.1915.pdf'), (3322, '2011-07-14 18:08:26'), (3323, 'Extending the effective-one-body Hamiltonian of black-hole binaries to include next-to-next-to-leading spin-orbit couplings'), (3324, '2011-07-14 2011-07-14'), (3325, 'http://arxiv.org/abs/1107.2904'), (3326, '1107.2904'), (3327, 'In the effective-one-body (EOB) approach the dynamics of two compact objects of masses m1 and m2 and spins S1 and S2 is mapped into the dynamics of one test particle of mass mu = m1 m2/(m1+m2) and spin S* moving in a deformed Kerr metric with mass M = m1+m2 and spin Skerr. In a previous paper we computed an EOB Hamiltonian for spinning black-hole binaries that (i) when expanded in post-Newtonian orders, reproduces the leading order spin-spin coupling and the leading and next-to-leading order spin-orbit couplings for any mass ratio, and (iii) reproduces all spin-orbit couplings in the test-particle limit. Here we extend this EOB Hamiltonian to include next-to-next-to-leading spin-orbit couplings for any mass ratio. We discuss two classes of EOB Hamiltonians that differ by the way the spin variables are mapped between the effective and real descriptions. We also investigate the main features of the dynamics when the motion is equatorial, such as the existence of the innermost stable circular orbit and of a peak in the orbital frequency during the plunge subsequent to the inspiral.'), (3328, '2011-07-15 08:49:02'), (3329, '1107.2904 PDF'), (3330, 'http://www.arxiv.org/pdf/1107.2904.pdf'), (3331, '2011-07-15 08:49:04'), (3332, 'Numerical simulations of black-hole binaries and gravitational wave emission'), (3333, 'http://arxiv.org/abs/1107.2819'), (3334, '1107.2819'), (3335, 'We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in three major areas of BH physics: (i) BHs as sources of gravitational waves (GWs), (ii) astrophysical systems involving BHs, and (iii) BHs in high-energy physics. We conclude with a list of the most urgent tasks for numerical relativity in these three areas.'), (3336, '2011-07-15 08:50:27'), (3337, '1107.2819 PDF'), (3338, 'http://www.arxiv.org/pdf/1107.2819.pdf'), (3339, '2011-07-15 08:50:29'), (3340, '2011-10-11 21:22:15'), (3341, '2011-07-15 19:55:28'), (3342, 58), (3343, 124031), (3344, '1998-11-23 November 23, 1998'), (3345, 'http://link.aps.org/doi/10.1103/PhysRevD.58.124031'), (3346, '10.1103/PhysRevD.58.124031'), (3347, 'It is shown analytically that an external tidal gravitational field increases the secular stability of a fully general relativistic, rigidly rotating neutron star that is near marginal stability, protecting it against gravitational collapse. This stabilization is shown to result from the simple fact that the energy δM(Q,R) required to raise a tide on such a star, divided by the square of the tide’s quadrupole moment Q, is a decreasing function of the star’s radius R,(d/dR)[δM(Q,R)/Q2]<0 (where, as R changes, the star’s structure is changed in accordance with the star’s fundamental mode of radial oscillation). If (d/dR)[δM(Q,R)/Q2] were positive, the tidal coupling would destabilize the star. As an application, a rigidly rotating, marginally secularly stable neutron star in an inspiraling binary system will be protected against secular collapse, and against dynamical collapse, by tidal interaction with its companion. The “local-asymptotic-rest-frame” tools used in the analysis are somewhat unusual and may be powerful in other studies of neutron stars and black holes interacting with an external environment. As a by-product of the analysis, in an appendix the influence of tidal interactions on mass-energy conservation is elucidated.'), (3348, '2011-07-25 11:00:53'), (3349, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i12/e124031'), (3350, '2011-07-25 11:00:54'), (3351, 'Laws of motion and precession for black holes and other bodies'), (3352, 31), (3353, 1815), (3354, '1985-04-15 April 15, 1985'), (3355, 'http://link.aps.org/doi/10.1103/PhysRevD.31.1815'), (3356, '10.1103/PhysRevD.31.1815'), (3357, 'Laws of motion and precession are derived for a Kerr black hole or any other body which is far from all other sources of gravity (‘‘isolated body’’) and has multipole moments that change slowly with time. Previous work by D’Eath and others has shown that to high accuracy the body moves along a geodesic of the surrounding spacetime geometry, and Fermi-Walker transports its angular-momentum vector. This paper derives the largest corrections to the geodesic law of motion and Fermi-Walker law of transport. These corrections are due to coupling of the body’s angular momentum and quadrupole moment to the Riemann curvature of the surrounding spacetime. The resulting laws of motion and precession are identical to those that have been derived previously, by many researchers, for test bodies with negligible self-gravity. However, the derivation given here is valid for any isolated body, regardless of the strength of its self-gravity. These laws of motion and precession can be converted into equations of motion and precession by combining them with an approximate solution to the Einstein field equations for the surrounding spacetime. As an example, the conversion is carried out for two gravitationally bound systems of bodies with sizes much less than their separations. The resulting equations of motion and precession are derived accurately through post1.5-Newtonian order. For the special case of two Kerr black holes orbiting each other, these equations of motion and precession (which include couplings of the holes’ spins and quadrupole moments to spacetime curvature) reduce to equations previously derived by D’Eath. The precession due to coupling of a black hole’s quadrupole moment to surrounding curvature may be large enough, if the hole lives at the center of a very dense star cluster, for observational detection by its effects on extragalactic radio jets. Unless the hole rotates very slowly, this quadrupole-induced precession is far larger than the spin-down of the hole by tidal distortion (‘‘horizon viscosity’’). When the hole is in orbit around a massive companion, the quadrupole-induced precession is far smaller than geodetic precession.'), (3358, '2011-07-25 11:03:35'), (3359, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v31/i8/p1815_1'), (3360, '2011-07-25 11:03:37'), (3361, 'Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries'), (3362, '2011-07-21 2011-07-21'), (3363, 'http://arxiv.org/abs/1107.4294'), (3364, '1107.4294'), (3365, 'We present the next-to-next-to-leading order post-Newtonian (PN) spin(1)-spin(2) Hamiltonian for two self-gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincare algebra with the center-of-mass vector uniquely determined by an ansatz.'), (3366, '2011-07-25 11:33:08'), (3367, '1107.4294 PDF'), (3368, 'http://www.arxiv.org/pdf/1107.4294.pdf'), (3369, '2011-07-25 11:33:10'), (3370, 'Gauge invariance of general relativistic tidal heating'), (3371, 60), (3372, 104054), (3373, '1999-10-28 October 28, 1999'), (3374, 'http://link.aps.org/doi/10.1103/PhysRevD.60.104054'), (3375, '10.1103/PhysRevD.60.104054'), (3376, 'When a self-gravitating body (e.g., a neutron star or black hole) interacts with an external tidal field (e.g., that of a binary companion), the interaction can do work on the body, changing its mass-energy. The details of this “tidal heating” are analyzed using the Landau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the work done on the body is gauge invariant, while the body-tidal-field interaction energy contained within the body’s local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, where the interaction energy is shown to depend on how one localizes gravitational energy, but the work done on the body is independent of that localization.'), (3377, '2011-07-25 14:30:31'), (3378, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v60/i10/e104054'), (3379, '2011-07-25 14:30:32'), (3380, 'Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order'), (3381, 'http://arxiv.org/abs/1107.4322'), (3382, '1107.4322'), (3383, 'We calculate the next-to-next-to-leading order (NNLO) spin1-spin2 dynamics of a compact binary evaluated at fourth post-Newtonian (PN) order. We use an effective field theory (EFT) approach, and first demonstrate here the ability of the EFT approach to go at NNLO in the PN corrections of spin effects. The NNLO spin1-spin2 interaction sector includes contributions from diagrams, which are not pure spin1-spin2 diagrams, as they arise from other sectors. These diagrams contribute through the leading order spin accelerations and precessions, that should be first taken into account here. The EFT calculation is carried out in terms of the nonrelativistic gravitational (NRG) fields. The fact that the spin is derivative-coupled adds significantly to the complexity of computations. In particular, for the irreducible two-loop diagrams, which are the most complicated in this sector, irreducible two-loop tensor integrals up to order 4 are encountered. Moreover, not all of the benefits of the NRG fields apply to spin interactions, as all possible diagram topologies are realized at each order of G included. Still, the NRG fields remain advantageous, and thus there was no use of automated computations in this work. Our final result can be reduced, and a NNLO spin1-spin2 Hamiltonian can be derived from it.'), (3384, '2011-07-25 14:53:14'), (3385, '1107.4322 PDF'), (3386, 'http://www.arxiv.org/pdf/1107.4322.pdf'), (3387, '2011-07-25 14:53:18'), (3388, 'LISA technology and instrumentation'), (3389, '2011-07-25 15:34:04'), (3390, 'Black-hole hair loss: learning about binary progenitors from ringdown signals'), (3391, 'http://arxiv.org/abs/1107.0854'), (3392, '1107.0854'), (3393, 'Perturbed Kerr black holes emit gravitational radiation, which (for the practical purposes of gravitational-wave astronomy) consists of a superposition of damped sinusoids termed quasi-normal modes. The frequencies and time-constants of the modes depend only on the mass and spin of the black hole - a consequence of the no-hair theorem. It has been proposed that a measurement of two or more quasi-normal modes could be used to confirm that the source is a black hole and to test if general relativity continues to hold in ultra-strong gravitational fields. In this paper we propose a practical approach to testing general relativity with quasi-normal modes. We will also argue that the relative amplitudes of the various quasi-normal modes encode important information about the origin of the perturbation that caused them. This helps in inferring the nature of the perturbation from an observation of the emitted quasi-normal modes. In particular, we will show that the relative amplitudes of the different quasi-normal modes emitted in the process of the merger of a pair of nonspinning black holes can be used to measure the component masses of the progenitor binary.'), (3394, '2011-07-25 15:43:52'), (3395, 'Black-hole hair loss'), (3396, '1107.0854 PDF'), (3397, 'http://www.arxiv.org/pdf/1107.0854.pdf'), (3398, '2011-07-25 15:44:16'), (3399, 'The mass function of black holes at 1<4.5: comparison of models with observations'), (3400, '2011-07-01 July 1, 2011'), (3401, 'http://adsabs.harvard.edu/abs/2011arXiv1107.4916N'), (3402, 'In this paper, we compare the observationally derived black hole mass function (BHMF) of luminous broad-line quasars (BLQSOs) at 1<4.5 drawn from the Sloan Digital Sky Survey (SDSS) presented in Kelly et al. (2010), with models of merger driven BH growth in the context of standard hierarchical structure formation models. In the models, we explore two distinct black hole seeding prescriptions at the highest redshifts: "light seeds" - remnants of Population III stars and "massive seeds" that form from the direct collapse of pre-galactic disks. The subsequent merger triggered mass build-up of the black hole population is tracked over cosmic time under the assumption of a fixed accretion rate as well as rates drawn from the distribution derived by Merloni & Heinz. Our model snapshots are compared to the SDSS derived BHMFs of BLQSOs. Our key findings are that the duty cycle of SMBHs powering BLQSOs increases with increasing redshift for all models and models with Pop III remnants as black hole seeds are unable to fit the observationally derived BHMFs for BLQSOs, lending strong support for the massive seeding model (abridged).'), (3403, '2011-07-26 14:37:26'), (3404, 'The mass function of black holes at 1<4.5'), (3405, 'The mass function of black holes at 1<z<4.5: comparison of models with obs'), (3406, '2011-07-26 14:37:27'), (3407, 'The mass function of black holes at 1<z<4.5: comparison of models with observations'), (3408, '2011-07-25 2011-07-25'), (3409, 'http://arxiv.org/abs/1107.4916'), (3410, '1107.4916'), (3411, 'In this paper, we compare the observationally derived black hole mass function (BHMF) of luminous broad-line quasars (BLQSOs) at 1<z<4.5 drawn from the Sloan Digital Sky Survey (SDSS) presented in Kelly et al. (2010), with models of merger driven BH growth in the context of standard hierarchical structure formation models. In the models, we explore two distinct black hole seeding prescriptions at the highest redshifts: "light seeds" - remnants of Population III stars and "massive seeds" that form from the direct collapse of pre-galactic disks. The subsequent merger triggered mass build-up of the black hole population is tracked over cosmic time under the assumption of a fixed accretion rate as well as rates drawn from the distribution derived by Merloni & Heinz. Our model snapshots are compared to the SDSS derived BHMFs of BLQSOs. Our key findings are that the duty cycle of SMBHs powering BLQSOs increases with increasing redshift for all models and models with Pop III remnants as black hole seeds are unable to fit the observationally derived BHMFs for BLQSOs, lending strong support for the massive seeding model (abridged).'), (3412, '2011-07-26 14:37:47'), (3413, 'The mass function of black holes at 1<z<4.5'), (3414, '1107.4916 PDF'), (3415, 'http://www.arxiv.org/pdf/1107.4916.pdf'), (3416, '2011-07-26 14:37:48'), (3417, 'Cosmological post-Newtonian expansions to arbitrary order'), (3418, '2009-08-19 2009-08-19'), (3419, 'http://arxiv.org/abs/0908.2836'), (3420, 'Commun.Math.Phys.295:431-463,2010'), (3421, 'doi:10.1007/s00220-009-0931-0'), (3422, '0908.2836'), (3423, 'We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter $\\ep=v_T/c$ $(0<\\ep < \\ep_0)$, where $c$ is the speed of light, and $v_T$ is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab $M\\cong [0,T)\\times \\Tbb^3$, and converge as $\\ep \\searrow 0$ to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter $\\ep$ to any specified order with expansion coefficients that satisfy $\\ep$-independent (nonlocal) symmetric hyperbolic equations.'), (3424, '2011-07-26 16:26:46'), (3425, '0908.2836 PDF'), (3426, 'http://www.arxiv.org/pdf/0908.2836.pdf'), (3427, '2011-07-26 16:26:47'), (3428, 'Implicit-explicit (IMEX) evolution of single black holes'), (3429, '2011-05-19 2011-05-19'), (3430, 'http://arxiv.org/abs/1105.3922'), (3431, '1105.3922'), (3432, 'Numerical simulations of binary black holes---an important predictive tool for the detection of gravitational waves---are computationally expensive, especially for binaries with high mass ratios or with rapidly spinning constituent holes. Existing codes for evolving binary black holes rely on explicit timestepping methods for which the timestep size is limited by the Courant-Friedrichs-Lewy condition. In explicit evolutions of binary black holes, the timestep size is typically orders of magnitude smaller than the relevant physical timescales. Implicit timestepping methods allow for larger timesteps and often reduce the total computational cost. However, fully implicit methods can be difficult to implement for nonlinear evolution systems like the Einstein equations. Therefore, in this paper we explore implicit-explicit (IMEX) methods and use them for the first time to evolve black-hole spacetimes. Specifically, as a first step toward IMEX evolution of a full binary-black-hole spacetime, we develop an IMEX algorithm of the generalized harmonic formulation of the Einstein equations and use this algorithm to evolve stationary and perturbed single-black-hole spacetimes. Numerical experiments explore the stability and computational efficiency of our method.'), (3433, '2011-07-26 16:47:24'), (3434, '1105.3922 PDF'), (3435, 'http://www.arxiv.org/pdf/1105.3922.pdf'), (3436, '2011-07-26 16:47:25'), (3437, 'Journal of Physics A: Mathematical and Theoretical'), (3438, 'J. Phys. A: Math. Theor.'), (3439, 40), (3440, 50), (3441, '1751-8113'), (3442, '2007-12-00 12/2007'), (3443, '15071-15082'), (3444, '10.1088/1751-8113/40/50/011'), (3445, 'http://iopscience.iop.org/1751-8121/40/50/011?fromSearchPage=true'), (3446, 'Transformation of complex spherical harmonics under rotations'), (3447, '2011-07-26 21:58:06'), (3448, '1751-8121_40_50_011.pdf'), (3449, 'Molecular Simulation'), (3450, 'Mol. Simulation'), (3451, '0892-7022'), (3452, '1989-08-00 8/1989'), (3453, '271-281'), (3454, '10.1080/08927028908031380'), (3455, 'http://www.tandfonline.com.proxy.library.cornell.edu/doi/abs/10.1080/08927028908031380'), (3456, 'Reorientational Correlation Functions, Quaternions and Wigner Rotation Matrices'), (3457, '2011-07-27 03:08:11'), (3458, '08927028908031380.pdf'), (3459, 'European Journal of Physics'), (3460, 'Eur. J. Phys.'), (3461, '0143-0807'), (3462, '1984-07-00 07/1984'), (3463, '163-171'), (3464, '10.1088/0143-0807/5/3/008'), (3465, 'http://iopscience.iop.org.proxy.library.cornell.edu/0143-0807/5/3/008'), (3466, 'Quaternions and spherical harmonics'), (3467, '2011-07-27 05:12:00'), (3468, '0143-0807_5_3_008.pdf'), (3469, 'Revealing the physics of r-modes in low-mass X-ray binaries'), (3470, 'http://arxiv.org/abs/1107.5064'), (3471, '1107.5064'), (3472, 'We consider the astrophysical constraints on the gravitational-wave driven r-mode instability in accreting neutron stars in low-mass X-ray binaries. We use recent results on superfluid and superconducting properties to infer the core temperature in these neutron stars and show the diversity of the observed population. Simple theoretical models indicate that many of these systems reside inside the r-mode instability region. However, this is in clear disagreement with expectations, especially for the systems containing the most rapidly rotating neutron stars. The inconsistency highlights the need to re-evaluate our understanding of the many areas of physics relevant to the r-mode instability. We summarize the current status of our understanding, and we discuss directions for future research which could resolve this dilemma.'), (3473, '2011-07-27 14:57:57'), (3474, '1107.5064 PDF'), (3475, 'http://www.arxiv.org/pdf/1107.5064.pdf'), (3476, '2011-07-27 14:57:59'), (3477, 'Transformation of the multipolar components of gravitational radiation under rotations and boosts'), (3478, '044024'), (3479, 'http://link.aps.org/doi/10.1103/PhysRevD.78.044024'), (3480, '10.1103/PhysRevD.78.044024'), (3481, 'We study the transformation of multipolar decompositions of gravitational radiation under rotations and boosts. Rotations to the remnant black hole’s frame simplify the waveforms from the merger of generic spinning black hole binaries. Boosts may be important to get an accurate gravitational-wave phasing, especially for configurations leading to large recoil velocities of the remnant. As a test of the formalism we revisit the classic problem of point particles falling into a Schwarzschild black hole. Then we highlight by specific examples the importance of choosing the right frame in numerical simulations of unequal mass, spinning binary black-hole mergers.'), (3482, '2011-07-27 20:11:16'), (3483, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i4/e044024'), (3484, '2011-07-27 20:11:17'), (3485, 'Measuring a cosmological distance-redshift relationship using only gravitational wave observations of binary neutron star coalescences'), (3486, '2011-07-28 2011-07-28'), (3487, 'http://arxiv.org/abs/1107.5725'), (3488, '1107.5725'), (3489, "Detection of gravitational waves from the inspiral phase of binary neutron star coalescence will allow us to measure the effects of the tidal coupling in such systems. These effects will be measurable using 3rd generation gravitational wave detectors, e.g. the Einstein Telescope, which will be capable of detecting inspiralling binary neutron star systems out to redshift z=4. Tidal effects provide additional contributions to the phase evolution of the gravitational wave signal that break a degeneracy between the system's mass parameters and redshift and thereby allowing for the simultaneous measurement of both the effective distance and the redshift for individual sources. Using the population of O(10^3-10^7) detectable binary neutron star systems predicted for the Einstein Telescope the luminosity distance--redshift relation can be probed independently of the cosmological distance ladder and independently of electromagnetic observations. We present the results of a Fisher information analysis applied to waveforms assuming a subset of possible neutron equations of state. We conclude that the redshift of such systems can be determined to O(10%) for z>1 and in the most optimistic case accuracies of 2% can be achieved."), (3490, '2011-07-29 14:25:08'), (3491, '1107.5725 PDF'), (3492, 'http://www.arxiv.org/pdf/1107.5725.pdf'), (3493, '2011-07-29 14:25:09'), (3494, 'Post-1-Newtonian tidal effects in the gravitational waveform from binary inspirals'), (3495, '084051'), (3496, '2011-04-28 April 28, 2011'), (3497, 'http://link.aps.org/doi/10.1103/PhysRevD.83.084051'), (3498, '10.1103/PhysRevD.83.084051'), (3499, 'The gravitational wave signal from an inspiralling binary neutron star system will contain detailed information about tidal coupling in the system, and thus, about the internal physics of the neutron stars. To extract this information will require highly accurate models for the gravitational waveform. We present here a calculation of the gravitational wave signal from a binary with quadrupolar tidal interactions which includes all post-1-Newtonian–order effects in both the conservative dynamics and wave generation. We consider stars with adiabatically induced quadrupoles moving in circular orbits, and work to linear order in the stars’ quadrupole moments. We find that post-1-Newtonian corrections increase the tidal signal by approximately 20% at gravitational wave frequencies of 400 Hz.'), (3500, '2011-07-29 14:27:34'), (3501, 'http://prd.aps.org/pdf/PRD/v83/i8/e084051'), (3502, '2011-07-29 14:27:35'), (3503, '1976-06-00 06/1976'), (3504, '897-904'), (3505, '10.1088/0305-4470/9/6/010'), (3506, 'http://iopscience.iop.org.proxy.library.cornell.edu/0305-4470/9/6/010;jsessionid=299AED68BAF264E81DA887573DC6A0AC.c3'), (3507, 'Baker-Campbell-Hausdorff formulae and spherical and hyperbolic rotations'), (3508, '2011-08-02 17:56:58'), (3509, '0305-4470_9_6_010.pdf'), (3510, 'quadframe.pdf'), (3511, 'Demodulation of Gravitational Waveforms from Precessing Black Hole Binaries'), (3512, '2011-07-26 July 26, 2011'), (3513, 30), (3514, '1989-00-00 1989'), (3515, 2035), (3516, '10.1063/1.528242'), (3517, 'http://link.aip.org/link/JMAPAQ/v30/i9/p2035/s1&Agg=doi'), (3518, 'Dynkin’s method of computing the terms of the Baker–Campbell–Hausdorff series'), (3519, '2011-08-03 18:29:00'), (3520, 'JMathPhys_30_2035.pdf'), (3521, 'Beyond Fisher: exact sampling distributions of the maximum-likelihood estimator in gravitational-wave parameter estimation'), (3522, '2011-08-04 2011-08-04'), (3523, 'http://arxiv.org/abs/1108.1158'), (3524, '1108.1158'), (3525, 'In gravitational-wave astronomy, data analysts often wish to characterize the expected parameter-estimation accuracy of future observations. The semianalytical Fisher-matrix formalism provides lower bounds on the spread of the maximum-likelihood estimator across noise realizations; it also provides the leading-order width of the posterior probability density. However, the Fisher matrix is limited to the high-SNR limit, which is often not realized in practice. By contrast, Bayesian-inference Monte Carlos characterize the full posterior as a function of noise for any SNR, but they are usually too computationally costly to repeat for a representative sample of noise realizations. In this article, I describe a semianalytical technique to exactly map the sampling distribution of the maximum-likelihood estimator across noise realizations at any SNR, generating an intermediate amount of information with significantly less computation. This technique can be applied to any estimation problem characterized by additive Gaussian noise.'), (3526, '2011-08-06 17:17:59'), (3527, 'Beyond Fisher'), (3528, '1108.1158 PDF'), (3529, 'http://www.arxiv.org/pdf/1108.1158.pdf'), (3530, '2011-08-06 17:18:18'), (3531, 'Precision measurement of the Hubble constant using gravitational waves'), (3532, '2011-08-05 2011-08-05'), (3533, 'http://arxiv.org/abs/1108.1317'), (3534, '1108.1317'), (3535, 'The precise measurement of the Hubble constant $H_0$ is one of the foundations of the current cosmological paradigm. Due to correlations between $H_0$ and the remaining cosmological parameters, a precise measurement of $H_0$ is critical in view of future high redshift surveys. Second generation ground-based laser interferometers are expected to deliver a wealth of gravitational waves (GW) events from coalescing compact binaries up to a redshift of about 0.3. Being free of the systematics affecting electromagnetic measurements, GW offer the possibility of an independent measurement of $H_0$ with great accuracy. This \\emph{Letter} presents a general method based on Bayesian inference aimed at estimating the value of the cosmological parameters for any GW event. In contrast to earlier work, this framework does not require the precise identification of the putative optical counterpart, but it considers all the potential galaxy hosts consistent with the recovered sky position and distance posterior distributions. When applied to the worldwide network of second generation interferometers, 50 GW events will yield a measurement of $H_0$ with an uncertainty of few percent.'), (3536, '2011-08-08 19:31:20'), (3537, '1108.1317 PDF'), (3538, 'http://www.arxiv.org/pdf/1108.1317.pdf'), (3539, '2011-08-08 19:31:23'), (3540, 'Gravitational waves from spinning black hole-neutron star binaries: dependence on black hole spins and on neutron star equations of state'), (3541, 'http://arxiv.org/abs/1108.1189'), (3542, '1108.1189'), (3543, 'We study the merger of black hole (BH)-neutron star (NS) binaries with a variety of BH spins aligned or anti-aligned with the orbital angular momentum, and with the mass ratio in the range MBH/MNS = 2--5, where MBH and MNS are the mass of the BH and NS, respectively. We model NS matter by systematically parametrized piecewise polytropic equations of state. The initial condition is computed in the puncture framework adopting an isolated horizon framework to estimate the BH spin and assuming an irrotational velocity field for the fluid inside the NS. Dynamical simulations are performed in full general relativity by an adaptive mesh refinement code, SACRA. The treatment of hydrodynamic equations and estimation of the disk mass are improved. We find that the NS is tidally disrupted irrespective of the mass ratio when the BH has a moderately large prograde spin, whereas only binaries with low mass ratios, MBH/MNS <~ 3 or small compactnesses of the NSs, bring the tidal disruption when the BH spin is zero or retrograde. The mass of the remnant disk is accordingly large as >~ 0.1 Msun, which is required by central engines of short gamma-ray bursts, if the BH spin is prograde. Information of the tidal disruption is reflected in a clear relation between the compactness of the NS and an appropriately defined "cutoff frequency" in the gravitational-wave spectrum, above which the spectrum damps exponentially. We find that the tidal disruption of the NS and excitation of the quasinormal mode of the remnant BH occur in a compatible manner in high mass-ratio binaries with the prograde BH spin. The correlation between the compactness and the cutoff frequency still holds for such cases. It is also suggested by extrapolation that the merger of an extremely spinning BH and an irrotational NS binary does not lead to formation of an overspinning BH.'), (3544, '2011-08-08 19:48:50'), (3545, 'Gravitational waves from spinning black hole-neutron star binaries'), (3546, '1108.1189 PDF'), (3547, 'http://www.arxiv.org/pdf/1108.1189.pdf'), (3548, '2011-08-08 19:49:15'), (3549, 'lcot_errors.pdf'), (3550, 'Errors and Omissions in Marc Alexa’s “Linear Combination of Transformations”'), (3551, 'http://www.cbloom.com/3d/techdocs/lcot_errors.pdf'), (3552, '2011-09-13 2011-09-13'), (3553, '2011-08-09'), (3554, 'Scientific Potential of Einstein Telescope'), (3555, 'http://arxiv.org/abs/1108.1423'), (3556, '1108.1423'), (3557, "Einstein gravitational-wave Telescope (ET) is a design study funded by the European Commission to explore the technological challenges of and scientific benefits from building a third generation gravitational wave detector. The three-year study, which concluded earlier this year, has formulated the conceptual design of an observatory that can support the implementation of new technology for the next two to three decades. The goal of this talk is to introduce the audience to the overall aims and objectives of the project and to enumerate ET's potential to influence our understanding of fundamental physics, astrophysics and cosmology."), (3558, '2011-08-09 16:58:19'), (3559, '1108.1423 PDF'), (3560, 'http://www.arxiv.org/pdf/1108.1423.pdf'), (3561, '2011-08-09 16:58:27'), (3562, 'Hangup Kicks: Still Larger Recoils by Partial Spin/Orbit Alignment of Black-Hole Binaries'), (3563, '2011-08-09 2011-08-09'), (3564, 'http://arxiv.org/abs/1108.2009'), (3565, '1108.2009'), (3566, 'We revisit the scenario of the gravitational radiation recoil acquired by the final remnant of a black-hole-binary merger by studying a set of configurations that have components of the spin both aligned with the orbital angular momentum and in the orbital plane. We perform a series of 24 new full numerical simulations for equal-mass and equal-spin-magnitude binaries, but with different spin orientations. We extend previous recoil fitting formulas to include nonlinear terms in the spins and successfully include both the new and known results. For this new formula the predicted maximum velocity approaches 5000km/s. More importantly, from the astrophysical point of view, it reaches this maximum for spins partially aligned with the orbital angular momentum. The optimal configuration is near an equipartition of the hangup and superkick contributions. This newly discovered contribution to the recoil leads to an important increase of the probabilities of large recoils in generic astrophysical mergers. We measure these probabilities for the case of accretion-aligned spins and find non-negligible probabilities for supermassive black hole encounters leading to recoil velocities of several thousand km/s.'), (3567, '2011-08-12 21:33:58'), (3568, 'Hangup Kicks'), (3569, '1108.2009 PDF'), (3570, 'http://www.arxiv.org/pdf/1108.2009.pdf'), (3571, '2011-08-12 21:34:02'), (3572, 'Coalescence Rate of Supermassive Black Hole Binaries Derived from Cosmological Simulations: Detection Rates for LISA and ET'), (3573, '2011-08-12 2011-08-12'), (3574, 'http://arxiv.org/abs/1108.2638'), (3575, '1108.2638'), (3576, 'The coalescence history of massive black holes has been derived from cosmological simulations, in which the evolution of those objects and that of the host galaxies are followed in a consistent way. The present study indicates that supermassive black holes having masses greater than $\\sim 10^{9} M_{\\odot}$ underwent up to 500 merger events along their history. The derived coalescence rate per comoving volume and per mass interval permitted to obtain an estimate of the expected detection rate distribution of gravitational wave signals ("ring-down") along frequencies accessible by the planned interferometers either in space (LISA) or in the ground (Einstein). For LISA, in its original configuration, a total detection rate of about $15 yr^{-1}$ is predicted for events having a signal-to-noise ratio equal to 10, expected to occur mainly in the frequency range $4-9 mHz$. For the Einstein gravitational wave telescope, one event each 14 months down to one event each 4 years is expected with a signal-to-noise ratio of 5, occurring mainly in the frequency interval $10-20 Hz$. The detection of these gravitational signals and their distribution in frequency would be in the future an important tool able to discriminate among different scenarios explaining the origin of supermassive black holes.'), (3577, '2011-08-15 16:43:17'), (3578, 'Coalescence Rate of Supermassive Black Hole Binaries Derived from Cosmological Simulations'), (3579, '1108.2638 PDF'), (3580, 'http://www.arxiv.org/pdf/1108.2638.pdf'), (3581, '2011-08-15 16:43:22'), (3582, 'Black hole Spin in Sw J1644+57 and Sw J2058+05'), (3583, '2011-08-15 2011-08-15'), (3584, 'http://arxiv.org/abs/1108.3115'), (3585, '1108.3115'), (3586, 'Recently a hard X-ray transient event, Sw J1644+57, was discovered by the Swift satellite, which marks the onset of a relativistic jet from a supermassive black hole, likely triggered by a tidal disruption event (TDE). Another candidate in the same category, Sw J2058+05, was also reported. The low event rate suggests that only a small fraction of TDEs launch relativistic jets. A common speculation is that these rare events are related to rapidly spinning black holes. We attribute jet launching to the Blandford-Znajek mechanism, and use the available data to constrain the black hole spin parameter for the two events. It is found that the two black holes indeed carry a moderate to high spin, suggesting that black hole spin is likely the crucial factor behind the Sw J1644+57 - like events.'), (3587, '2011-08-17 10:47:13'), (3588, '1108.3115 PDF'), (3589, 'http://www.arxiv.org/pdf/1108.3115.pdf'), (3590, '2011-08-17 10:47:15'), (3591, 'The gravitational-wave memory from eccentric binaries'), (3592, 'http://arxiv.org/abs/1108.3121'), (3593, '1108.3121'), (3594, 'The nonlinear gravitational-wave memory causes a time-varying but nonoscillatory correction to the gravitational-wave polarizations. It arises from gravitational-waves that are sourced by gravitational-waves. Previous considerations of the nonlinear memory effect have focused on quasicircular binaries. Here I consider the nonlinear memory from Newtonian orbits with arbitrary eccentricity. Expressions for the waveform polarizations and spin-weighted spherical-harmonic modes are derived for elliptic, hyperbolic, parabolic, and radial orbits. In the hyperbolic, parabolic, and radial cases the nonlinear memory provides a 2.5 post-Newtonian (PN) correction to the leading-order waveforms. This is in contrast to the elliptical and quasicircular cases, where the nonlinear memory corrects the waveform at leading (0PN) order. This difference in PN order arises from the fact that the memory builds up over a short "scattering" timescale in the hyperbolic case, as opposed to a much longer radiation-reaction timescale in the elliptical case. The nonlinear memory corrections presented here complete our knowledge of the leading-order (Peters-Mathews) waveforms for elliptical orbits. These calculations are also relevant for binaries with quasicircular orbits in the present epoch which had, in the past, large eccentricities. Because the nonlinear memory depends sensitively on the past evolution of a binary, I discuss the effect of this early-time eccentricity on the value of the late-time memory in nearly-circularized binaries. I also discuss the observability of large "memory jumps" in a binary\'s past that could arise from its formation in a capture process. Lastly, I provide estimates of the signal-to-noise ratio of the linear and nonlinear memories from hyperbolic and parabolic binaries.'), (3595, '2011-08-17 13:49:59'), (3596, '1108.3121 PDF'), (3597, 'http://www.arxiv.org/pdf/1108.3121.pdf'), (3598, '2011-08-17 13:50:00'), (3599, 'Inspiral-Merger-Ringdown Waveforms for Black-Hole Binaries with Nonprecessing Spins'), (3600, 106), (3601, 241101), (3602, '2011-06-15 June 15, 2011'), (3603, 'http://link.aps.org/doi/10.1103/PhysRevLett.106.241101'), (3604, '10.1103/PhysRevLett.106.241101'), (3605, 'We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with nonprecessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime, thus significantly improving the expected detection rates.'), (3606, '2011-08-17 13:58:12'), (3607, 'http://prl.aps.org/pdf/PRL/v106/i24/e241101'), (3608, '2011-08-17 13:58:13'), (3609, 'Reducing orbital eccentricity of precessing black-hole binaries'), (3610, '2011-05-19 May 19, 2011'), (3611, 'http://link.aps.org/doi/10.1103/PhysRevD.83.104034'), (3612, '10.1103/PhysRevD.83.104034'), (3613, 'Building initial conditions for generic binary black-hole evolutions which are not affected by initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure which consists of evolving the binary black hole for a couple of orbits, estimating the resulting eccentricity, and then restarting the simulation with corrected initial conditions. The presence of spins can complicate this procedure. As predicted by post-Newtonian theory, spin-spin interactions and precession prevent the binary from moving along an adiabatic sequence of spherical orbits, inducing oscillations in the radial separation and in the orbital frequency. For single-spin binary black holes these oscillations are a direct consequence of monopole-quadrupole interactions. However, spin-induced oscillations occur at approximately twice the orbital frequency, and therefore can be distinguished and disentangled from the initial spurious eccentricity which occurs at approximately the orbital frequency. Taking this into account, we develop a new eccentricity-removal procedure based on the derivative of the orbital frequency and find that it is rather successful in reducing the eccentricity measured in the orbital frequency to values less than 10-4 when moderate spins are present. We test this new procedure using numerical-relativity simulations of binary black holes with mass ratios 1.5 and 3, spin magnitude 0.5, and various spin orientations. The numerical simulations exhibit spin-induced oscillations in the dynamics at approximately twice the orbital frequency. Oscillations of similar frequency are also visible in the gravitational-wave phase and frequency of the dominant l=2, m=2 mode.'), (3614, '2011-08-17 14:03:27'), (3615, 'http://prd.aps.org/pdf/PRD/v83/i10/e104034'), (3616, '2011-08-17 14:03:28'), (3617, 28), (3618, '2011-07-00 07/2011'), (3619, 134002), (3620, '10.1088/0264-9381/28/13/134002'), (3621, 'http://iopscience.iop.org/0264-9381/28/13/134002/'), (3622, '2011-08-17 14:06:27'), (3623, '0264-9381_28_13_134002.pdf'), (3624, '1979-10-00 10/1979'), (3625, '149-175'), (3626, '10.1007/BF00756587'), (3627, 'http://arxiv.org/abs/1109.2744'), (3628, 'The gravitational interaction: Spin, rotation, and quantum effects-a review'), (3629, 'arXiv:1109.2744'), (3630, 'The gravitational interaction'), (3631, 'http://www.springerlink.com.proxy.library.cornell.edu/content/j640q10u51044755/'), (3632, '2011-08-19 05:02:17'), (3633, 'Phys.Rev.D83:122005,2011'), (3634, 'doi:10.1103/PhysRevD.83.122005'), (3635, '2011-08-23 17:17:53'), (3636, '2011-08-23 17:21:47'), (3637, 'Intermediate-mass-ratio black hole binaries II: Modeling Trajectories and Gravitational Waveforms'), (3638, '2011-08-22 2011-08-22'), (3639, 'http://arxiv.org/abs/1108.4421'), (3640, '1108.4421'), (3641, 'We revisit the scenario of small-mass-ratio (q) black-hole binaries; performing new, more accurate, simulations of mass ratios 10:1 and 100:1 for initially nonspinning black holes. We propose fitting functions for the trajectories of the two black holes as a function of time and mass ratio (in the range 1/100 < q < 1/10$) that combine aspects of post-Newtonian trajectories at smaller orbital frequencies and plunging geodesics at larger frequencies. We then use these trajectories to compute waveforms via black hole perturbation theory. Using the advanced LIGO noise curve, we see a match of ~99.5% for the leading (l,m)=(2,2) mode between the numerical relativity and perturbative waveforms. Nonleading modes have similarly high matches. We thus prove the feasibility of efficiently generating a bank of gravitational waveforms in the intermediate-mass-ratio regime using only a sparse set of full numerical simulations.'), (3642, '2011-08-24 07:01:59'), (3643, 'Intermediate-mass-ratio black hole binaries II'), (3644, '1108.4421 PDF'), (3645, 'http://www.arxiv.org/pdf/1108.4421.pdf'), (3646, '2011-08-24 07:02:12'), (3647, 'Dynamical Tides in Compact White Dwarf Binaries: Tidal Synchronization and Dissipation'), (3648, '2011-08-24 2011-08-24'), (3649, 'http://arxiv.org/abs/1108.4910'), (3650, '1108.4910'), (3651, 'In compact white dwarf (WD) binary systems (with periods ranging from minutes to hours), dynamical tides involving the excitation and dissipation of gravity waves play a dominant role in determining the physical conditions of the WDs prior to mass transfer or binary merger. We calculate the amplitude of the tidally excited gravity waves as a function of the tidal forcing frequency \\omega=2(\\Omega-\\Omega_s) (where \\Omega is the orbital frequency and \\Omega_s is the spin frequency) for several realistic carbon-oxygen WD models, assuming that the waves are efficiently dissipated in the outer layer of the star by nonlinear effects or radiative damping. The mechanism of wave excitation in WDs is complex due to the sharp features associated with composition changes inside the WD, and in our WD models gravity waves are launched just below the helium-carbon boundary. We find that the tidal torque on the WD and the related tidal energy transfer rate, \\dot E_{\\rm tide}, depend on \\omega in an erratic way. On average, \\dot E_{\\rm tide} scales approximately as \\Omega^5\\omega^5 for a large range of tidal frequencies. We also study the effects of dynamical tides on the long-term evolution of WD binaries. Above a critical orbital frequency \\Omega_c, corresponding to an orbital period of order one hour (depending on WD models), dynamical tides efficiently drive \\Omega_s toward \\Omega, although a small, almost constant degree of asynchronization (\\Omega-\\Omega_s\\sim {\\rm constant}) is maintained even at the smallest binary periods. While the orbital decay is always dominated by gravitational radiation, the tidal energy transfer can induce significant phase error in the low-frequency gravitational waveforms, detectable by the planned LISA project. Tidal dissipation may also lead to significant heating of the WD envelope and brightening of the system long before binary merger.'), (3652, '2011-08-25 17:07:41'), (3653, 'Dynamical Tides in Compact White Dwarf Binaries'), (3654, '1108.4910 PDF'), (3655, 'http://www.arxiv.org/pdf/1108.4910.pdf'), (3656, '2011-08-25 17:07:45'), (3657, 'Hubble without the Hubble: cosmology using advanced gravitational-wave detectors alone'), (3658, '2011-08-25 2011-08-25'), (3659, 'http://arxiv.org/abs/1108.5161'), (3660, '1108.5161'), (3661, 'We propose a novel approach to measuring the Hubble constant using gravitational-wave signals from compact binaries by exploiting the narrowness of the distribution of masses of the underlying neutron-star population. The Advanced LIGO gravitational wave detector is due to come online in 2015 with a factor of ~10 sensitivity increase over its predecessor. The volume-averaged range at which an inspiraling double-neutron-star binary can be detected should increase from ~15 Mpc to ~200 Mpc, providing a thousand-fold gain in the volume sensitivity of the detector. Incorporating AdLIGO into a global network (through AdVirgo or LIGO-Australia) will boost the directional sensitivity and permit source distance determination. In this paper, we explore what we can learn about the background cosmology and the mass distribution of neutron stars from the set of neutron star (NS) mergers detected by such a network. We use a Bayesian formalism to analyse catalogues of NS-NS inspiral detections. We find that it is possible to constrain the Hubble constant, H_0, and the parameters of the NS mass function using gravitational-wave data alone, without relying on electromagnetic counterparts. Under reasonable assumptions, we will be able to determine H_0 to +/- 10% using ~100 observations, provided the Gaussian half-width of the underlying double NS mass distribution is less than 0.04 M_{\\odot}. The expected precision depends linearly on the intrinsic width of the NS mass function, but has only a weak dependence on H_0 near the default parameter values. Finally, we consider what happens if, for some fraction of our data catalogue, we have an electromagnetically measured redshift. The detection, and cataloguing, of these compact object mergers will allow precision astronomy, and provide a determination of H_0 which is independent of the local distance scale.'), (3662, '2011-08-26 13:58:28'), (3663, 'Hubble without the Hubble'), (3664, '1108.5161 PDF'), (3665, 'http://www.arxiv.org/pdf/1108.5161.pdf'), (3666, '2011-08-26 13:58:33'), (3667, '084004'), (3668, '10.1088/0264-9381/27/8/084004'), (3669, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/27/8/084004'), (3670, 'Status of LCGT'), (3671, '2011-08-29 14:59:19'), (3672, '0264-9381_27_8_084004.pdf'), (3673, 'Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications'), (3674, '2011-08-27 2011-08-27'), (3675, 'http://arxiv.org/abs/1108.5486'), (3676, '1108.5486'), (3677, 'When one splits spacetime into space plus time, the Weyl curvature tensor (vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free (STF) tensors: (i) the Weyl tensor\'s so-called "electric" part or tidal field, and (ii) the Weyl tensor\'s so-called "magnetic" part or frame-drag field. Being STF, the tidal field and frame-drag field each have three orthogonal eigenvector fields which can be depicted by their integral curves. We call the integral curves of the tidal field\'s eigenvectors tendex lines, we call each tendex line\'s eigenvalue its tendicity, and we give the name tendex to a collection of tendex lines with large tendicity. The analogous quantities for the frame-drag field are vortex lines, their vorticities, and vortexes. We build up physical intuition into these concepts by applying them to a variety of weak-gravity phenomena: a spinning, gravitating point particle, two such particles side by side, a plane gravitational wave, a point particle with a dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a slow-motion binary system made of nonspinning point particles. [Abstract is abbreviated; full abstract also mentions additional results.]'), (3678, '2011-08-30 19:56:35'), (3679, '1108.5486 PDF'), (3680, 'http://www.arxiv.org/pdf/1108.5486.pdf'), (3681, '2011-08-30 19:56:50'), (3682, 'Interpolating compact binary waveforms using the singular value decomposition'), (3683, '2011-08-29 2011-08-29'), (3684, 'http://arxiv.org/abs/1108.5618'), (3685, '1108.5618'), (3686, 'Compact binary systems with total masses between tens and hundreds of solar masses will produce gravitational waves during their merger phase that are detectable by second-generation ground-based gravitational-wave detectors. In order to model the gravitational waveform of the merger epoch of compact binary coalescence, the full Einstein equations must be solved numerically for the entire mass and spin parameter space. However, this is computationally expensive. Several models have been proposed to interpolate the results of numerical relativity simulations. In this paper we propose a numerical interpolation scheme that stems from the singular value decomposition. This algorithm shows promise in allowing one to construct arbitrary waveforms within a certain parameter space given a sufficient density of numerical simulations covering the same parameter space. We also investigate how similar approaches could be used to interpolate waveforms in the context of parameter estimation.'), (3687, '2011-08-30 19:57:27'), (3688, '1108.5618 PDF'), (3689, 'http://www.arxiv.org/pdf/1108.5618.pdf'), (3690, '2011-08-30 19:57:32'), (3691, 104020), (3692, '2001-10-26 October 26, 2001'), (3693, 'http://link.aps.org/doi/10.1103/PhysRevD.64.104020'), (3694, '10.1103/PhysRevD.64.104020'), (3695, 'As a black hole in a binary spirals in gradually from large separation, energy and angular momentum flow not only to infinity but also into or out of the hole. In addition, the hole’s horizon area increases slowly during this process. In this paper, the changes in the black hole’s mass, spin, and horizon area during inspiral are calculated for a hole in a circular binary with a companion body of possibly comparable mass. When the binary is composed of equal mass black holes that have spins aligned with the orbital angular momentum and are rapidly rotating (with spins 99.8% of their maximal values), it is found that the fractional increase in the surface area of each hole’s horizon is 1% by the time the binary spirals down to a separation b of 6M (where M is the binary’s total mass), and 7% down to b=2M. The flow of energy and angular momentum into the black holes’ horizons changes the number of gravitational-wave cycles in the LIGO band by no more than a tenth of a cycle by the time the binary reaches b=2M. The results obtained in this paper are relevant for the detection and analysis of gravitational waves from binary systems containing a black hole.'), (3696, '2011-09-01 13:58:07'), (3697, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i10/e104020'), (3698, '2011-09-01 13:58:08'), (3699, 'Tidal Interaction in Binary-Black-Hole Inspiral'), (3700, 231101), (3701, '2001-11-16 November 16, 2001'), (3702, 'http://link.aps.org/doi/10.1103/PhysRevLett.87.231101'), (3703, '10.1103/PhysRevLett.87.231101'), (3704, 'Tidal torque may lead to important effects in the strong field interaction at the end point of the inspiral of two rapidly rotating black holes. We point out here that in such a case the exchange of spin and orbital angular momentum may significantly affect the energy and waveform of late stage gravitational waves, and may play an important role in the shedding of excess angular momentum. We argue that numerical relativity, the only tool for determining the importance of tidal torque, should be more specifically focused on binary configurations with aligned, large, angular momenta.'), (3705, '2011-09-01 14:42:35'), (3706, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v87/i23/e231101'), (3707, '2011-09-01 14:42:36'), (3708, 'Reversible and Irreversible Transformations in Black-Hole Physics'), (3709, 1596), (3710, '1970-11-30 November 30, 1970'), (3711, 'http://link.aps.org/doi/10.1103/PhysRevLett.25.1596'), (3712, '10.1103/PhysRevLett.25.1596'), (3713, 'The concepts of irreducible mass and of reversible and irreversible transformations in black holes are introduced, leading to the formula E2=mir2+(L2/4mir2)+p2 for a black hole of linear momentum p and angular momentum L.'), (3714, '2011-09-01 14:55:17'), (3715, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v25/i22/p1596_1'), (3716, '2011-09-01 14:55:18'), (3717, 'Hybrid method for understanding black-hole mergers: Inspiralling case'), (3718, '2011-08-31 2011-08-31'), (3719, 'http://arxiv.org/abs/1109.0081'), (3720, '1109.0081'), (3721, 'We adapt a method of matching post-Newtonian and black-hole-perturbation theories on a timelike surface (which proved useful for understanding head-on black-hole-binary collisions) to treat equal-mass, inspiralling black-hole binaries. We first introduce a radiation-reaction potential into this method, and we show that it leads to a self-consistent set of equations that describe the simultaneous evolution of the waveform and of the timelike matching surface. This allows us to produce a full inspiral-merger-ringdown waveform of the l=2, m=2,-2 modes of the gravitational waveform of an equal-mass black-hole-binary inspiral. These modes match those of numerical-relativity simulations well in phase, though less well in amplitude for the inspiral. As a second application of this method, we study a merger of black holes with spins antialigned in the orbital plane (the "superkick" configuration). During the ringdown of the superkick, the phases of the mass- and current-quadrupole radiation become locked together, because they evolve at the same quasinormal mode frequencies. We argue that this locking begins during merger, and we show that if the spins of the black holes evolve via geodetic precession in the perturbed black-hole spacetime of our model, then the spins precess at the orbital frequency during merger. In turn, this gives rise to the correct behavior of the radiation, and produces a kick similar to that observed in numerical simulations.'), (3722, '2011-09-02 18:11:00'), (3723, 'Hybrid method for understanding black-hole mergers'), (3724, '1109.0081 PDF'), (3725, 'http://www.arxiv.org/pdf/1109.0081.pdf'), (3726, '2011-09-02 18:11:01'), (3727, 'Exploring black hole superkicks'), (3728, 124047), (3729, '2008-06-27 June 27, 2008'), (3730, 'http://link.aps.org/doi/10.1103/PhysRevD.77.124047'), (3731, '10.1103/PhysRevD.77.124047'), (3732, 'Recent calculations of the recoil velocity in black-hole binary mergers have found kick velocities of ≈2500 km/s for equal-mass binaries with antialigned initial spins in the orbital plane. In general the dynamics of spinning black holes can be extremely complicated and are difficult to analyze and understand. In contrast, the “superkick” configuration is an example with a high degree of symmetry that also exhibits exciting physics. We exploit the simplicity of this test case to study more closely the role of spin in black-hole recoil and find that the recoil is with good accuracy proportional to the difference between the (l=2,m=±2) modes of Ψ4, the major contribution to the recoil occurs within 30M before and after the merger, and that this is after the time at which a standard post-Newtonian treatment breaks down. We also discuss consequences of the (l=2,m=±2) asymmetry in the gravitational wave signal for the angular dependence of the signal-to-noise ratio and the mismatch of the gravitational wave signals corresponding to the north and south poles.'), (3733, '2011-09-02 18:40:38'), (3734, 'http://prd.aps.org/pdf/PRD/v77/i12/e124047'), (3735, '2011-09-02 18:40:44'), (3736, 'Anatomy of the binary black hole recoil: A multipolar analysis'), (3737, '044031'), (3738, '2008-02-19 February 19, 2008'), (3739, 'http://link.aps.org/doi/10.1103/PhysRevD.77.044031'), (3740, '10.1103/PhysRevD.77.044031'), (3741, 'We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole coalescence, for both unequal masses and nonzero, nonprecessing spins. We show that multipole moments up to and including ℓ=4 are sufficient to accurately reproduce the final recoil velocity (within ≃2%) and that only a few dominant modes contribute significantly to it (within ≃5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an “effective Newtonian” formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulas with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasinormal modes. Analytic formulas, obtained by expressing the multipole moments in terms of the fundamental quasinormal modes of a Kerr black hole, are able to explain the onset and amount of “antikick” for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and nonplanar kicks for equal-mass spinning black holes.'), (3742, '2011-09-02 18:54:15'), (3743, 'Anatomy of the binary black hole recoil'), (3744, 'http://prd.aps.org/pdf/PRD/v77/i4/e044031'), (3745, '2011-09-02 18:54:16'), (3746, 'http://onlinelibrary.wiley.com/doi/10.1111/j.2153-3490.1970.tb01933.x/abstract'), (3747, '10.1111/j.2153-3490.1970.tb01933.x'), (3748, 'Tellus'), (3749, '2153-3490'), (3750, 'A simple finite‐difference grid with non‐constant intervals'), (3751, 'en'), (3752, '1970-02-01 1970/02/01'), (3753, '26-31'), (3754, 'A finite difference network with non-uniform grid intervals, hi, such that hi = hi-1 + O(h2i-1) is presented. The use of the grid network for two specific choices of hi - hi-1 for a linear boundary layer problem shows that it has distinct advantages in computational efficiency and in accuracy of representation of the analytical solution.'), (3755, 'Wiley Online Library'), (3756, '2011-09-02 21:44:47'), (3757, 'The recently discovered J0651+2844 is a detached, eclipsing white dwarf binary with an orbital period of 765 s. We investigate the prospects for the detection of gravitational radiation from this system and estimate the effect of the tidal deformation of the low-mass component on the period evolution of the system. Because of the high inclination of the system, the amplitude of the gravitational waves at Earth will be as much as a factor of two lower than that from an optimally oriented system. The dominant contribution of tidal corrections to the period evolution comes from the increase in rotational energy of the components as they spin up to remain tied to the orbital period. This contribution results in an advance of the timing of the eclipses by an additional 0.3 s after one year.'), (3758, '2011-09-14 12:52:35'), (3759, '1109.2744 PDF'), (3760, 'j.2153-3490.1970.tb01933.x.pdf'), (3761, 'http://www.arxiv.org/pdf/1109.2744.pdf'), (3762, '2011-09-14 12:52:37'), (3763, '2011-10-13 2011-10-13'), (3764, 'Quasi-Normal Modes of Stars and Black Holes'), (3765, 'http://www.livingreviews.org/lrr-1999-2'), (3766, 'lrr-1999-2Color.pdf'), (3767, 'http://relativity.livingreviews.org/Articles/lrr-1999-2/download/lrr-1999-2Color.pdf'), (3768, '2011-09-14 19:33:44'), (3769, 'http://arxiv.org/abs/1110.3081'), (3770, 'arXiv:1110.3081'), (3771, 'Using the effective-one-body (EOB) formalism and a time-domain Teukolsky code, we generate inspiral, merger, and ringdown waveforms in the small mass-ratio limit. We use EOB inspiral and plunge trajectories to build the Teukolsky equation source term, and compute full coalescence waveforms for a range of black hole spins. By comparing EOB waveforms that were recently developed for comparable mass binary black holes to these Teukolsky waveforms, we improve the EOB model for the (2,2), (2,1), (3,3), and (4,4) modes. Our results can be used to quickly and accurately extract useful information about merger waves for binaries with spin, and should be useful for improving analytic models of such binaries. Although in this analysis we only consider equatorial inspirals (orbital angular momentum parallel to spin), there is no issue of principle preventing us from considering inclined binaries. We will extend this analysis to examine misaligned spin-orbit configurations in future work.'), (3772, '2011-10-17 13:59:30'), (3773, '1110.3081 PDF'), (3774, 84), (3775, '024046'), (3776, '2011-07-29 July 29, 2011'), (3777, 'http://link.aps.org/doi/10.1103/PhysRevD.84.024046'), (3778, '10.1103/PhysRevD.84.024046'), (3779, 'We present a simple method to track the precession of a black-hole-binary system during the inspiral, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitudes of the (ℓ=2, |m|=2) modes are maximized, which we denote the “quadrupole-aligned” frame. We demonstrate the efficacy of this method when applied to waveforms from numerical simulations. In the test case of an equal-mass nonspinning binary, our method locates the direction of the orbital angular momentum to within (Δθ,Δφ)=(0.05°,0.2°). We then apply the method to a q=M2/M1=3 binary that exhibits significant precession. In general, a spinning binary’s orbital angular momentum L is not orthogonal to the orbital plane. Evidence that our method locates the direction of L rather than the normal of the orbital plane is provided by comparison with post-Newtonian results. Also, we observe that it accurately reproduces similar higher-mode amplitudes to a comparable non-precessing binary, and that the frequency of the (ℓ=2, |m|=2) modes is consistent with the “total frequency” of the binary’s motion. The simple form of the quadrupole-aligned waveform may be useful in attempts to analytically model the inspiral-merger-ringdown signal of precessing binaries, and in standardizing the representation of waveforms for studies of accuracy and consistency of source modelling efforts, both numerical and analytical.'), (3780, '2011-09-15 19:34:55'), (3781, 'http://www.arxiv.org/pdf/1110.3081.pdf'), (3782, '2011-10-17 13:59:32'), (3783, 'PhysRevD.84.024046.pdf'), (3784, 'Extracting equation of state parameters from black hole-neutron star mergers. I. Nonspinning black holes'), (3785, '2011-09-15 2011-09-15'), (3786, 'http://arxiv.org/abs/1109.3402'), (3787, 'arXiv:1109.3402'), (3788, 'The late inspiral, merger, and ringdown of a black hole-neutron star (BHNS) system can provide information about the neutron-star equation of state (EOS). Candidate EOSs can be approximated by a parametrized piecewise-polytropic EOS above nuclear density, matched to a fixed low-density EOS; and we report results from a large set of BHNS inspiral simulations that systematically vary two parameters. To within the accuracy of the simulations, we find that, apart from the neutron-star mass, a single physical parameter Lambda, describing its deformability, can be extracted from the late inspiral, merger, and ringdown waveform. This parameter is related to the radius, mass, and l=2 Love number, k_2, of the neutron star by Lambda = 2k_2 R^5/3M_{NS}^5, and it is the same parameter that determines the departure from point-particle dynamics during the early inspiral. Observations of gravitational waves from BHNS inspiral thus restrict the EOS to a surface of constant Lambda in the parameter space, thickened by the measurement error. Using various configurations of a single Advanced LIGO detector, we find that neutron stars are distinguishable from black holes of the same mass and that Lambda^{1/5} or equivalently R can be extracted to 10-40% accuracy from single events for mass ratios of Q=2 and 3 at a distance of 100 Mpc, while with the proposed Einstein Telescope, EOS parameters can be extracted to accuracy an order of magnitude better.'), (3789, '2011-09-16 14:19:39'), (3790, '1109.3402 PDF'), (3791, 'http://www.arxiv.org/pdf/1109.3402.pdf'), (3792, '2011-09-16 14:19:41'), (3793, 'Post-1-Newtonian quadrupole tidal interactions in binary systems'), (3794, '2010-09-24 2010-09-24'), (3795, 'http://arxiv.org/abs/1009.4919'), (3796, 'arXiv:1009.4919'), (3797, "We consider orbital-tidal coupling in a binary stellar system to post-1-Newtonian order. We derive the orbital equations of motion for bodies with spins and mass quadrupole moments and show that they conserve the total linear momentum of the binary. Momentum conservation also allows us to specialize our analysis to the system's center-of-mass-energy frame; we find the binary's relative equation of motion in this frame and also present a generalized Lagrangian from which it can be derived. We then specialize to the case in which the quadrupole moment is adiabatically induced by the tidal field. We show how the adiabatic dynamics for the quadrupole can be incorporated into our action principle and present the simplified orbital equations of motion and conserved energy for the adiabatic case. These results are relevant to the gravitational wave signal of inspiralling binary neutron stars."), (3798, '2011-09-16 17:13:47'), (3799, '1009.4919 PDF'), (3800, 'http://www.arxiv.org/pdf/1009.4919.pdf'), (3801, '2011-09-16 17:13:49'), (3802, 'Accuracy of numerical relativity waveforms from binary neutron star mergers and their comparison with post-Newtonian waveforms'), (3803, '2011-09-16 2011-09-16'), (3804, 'http://arxiv.org/abs/1109.3611'), (3805, 'arXiv:1109.3611'), (3806, 'We present numerical relativity simulations of nine-orbit equal-mass binary neutron star covering the quasi-circular late inspiral and merger. The extracted gravitational waveforms are analyzed for convergence and accuracy. Second order convergence is observed up to contact, i.e. about 3-4 cycles to merger, thus error estimates can be made up to this point. The uncertainties on the phase and the amplitude are dominated by truncation errors and can be minimized to 0.13 rad and less then 1 %, respectively, by using several simulations and extrapolating in resolution. In the latter case finite radius extraction uncertainties become a source of error of the same order and have to be taken into account. The waveforms are tested against accuracy standards for data analysis. The uncertainties on the waveforms are such that accuracy standards are generically not met for signal-to-noise ratios relevant for detection, except for some best cases and optimistic (but rigorous) choice of error bars. A detailed analysis of the errors is thus imperative for the use of numerical relativity waveforms from binary neutron stars in quantitative studies. The waveforms are compared with the post-Newtonian Taylor T4 approximants both for point-particle and including the analytically known tidal corrections. After alignment, the T4 approximants maintain the phasing for three to four cycles, but later they rapidly accumulate about 2.5 rad at contact and about 6 rad at merger.'), (3807, '2011-09-19 13:17:48'), (3808, '1109.3611 PDF'), (3809, 'http://www.arxiv.org/pdf/1109.3611.pdf'), (3810, '2011-09-19 13:17:54'), (3811, 'Gravitational Wave Science in the High School Classroom'), (3812, 'http://arxiv.org/abs/1109.3720'), (3813, 'arXiv:1109.3720'), (3814, 'Gravitational waves have the potential to bring astronomy into the next era by providing an entirely new means of observing astronomical phenomena. By measuring fluctuations down to the sub-attometer scale, scientists are hoping to measure the gravitational effects of extreme cosmic events happening millions of parsecs away. This widely multidisciplinary work encompasses fields ranging from astrophysics to quantum optics. This article discusses the integration of gravitational wave science into a high school astronomy curriculum, where students learn about a variety of topics in the field, with particular focus placed on astrophysical sources, detector technology, and data analysis techniques.'), (3815, '2011-09-20 13:40:33'), (3816, '1109.3720 PDF'), (3817, 'http://www.arxiv.org/pdf/1109.3720.pdf'), (3818, '2011-09-20 13:40:36'), (3819, '1550-7998, 1550-2368'), (3820, '2011-09-00 9/2011'), (3821, '10.1103/PhysRevD.84.064013'), (3822, 'http://link.aps.org/doi/10.1103/PhysRevD.84.064013'), (3823, 'Uncertainty in hybrid gravitational waveforms: Optimizing initial orbital frequencies for binary black-hole simulations'), (3824, '2011-09-21 12:46:48'), (3825, 'Uncertainty in hybrid gravitational waveforms'), (3826, 'An Introduction to Spinors'), (3827, '714-728'), (3828, '1953-07-01 July 01, 1953'), (3829, 'PhysRevD.84.064013.pdf'), (3830, 'A new approach to the Newman-Penrose formalism'), (3831, '2011-09-20 2011-09-20'), (3832, 'http://arxiv.org/abs/1109.4400'), (3833, 'arXiv:1109.4400'), (3834, 'The Newman-Penrose formalism in transverse tetrads, namely those tetrads where \\Psi_1=\\Psi_3=0, is studied. In particular it is shown that the equations governing the dynamics within this formalism can be recast in a particularly compact way, leading to a better understanding of the formalism itself. The particular choice of tetrad allows not only to obtain the expression of Weyl scalars as simple functions of curvature invariants, but also the spin coefficients can be partly determined in an invariant way, by means of a new expression for the Bianchi identities that shows the various degrees of freedom in a more intuitive and direct way. We expect this approach to be very promising for a better understanding of all the equations governing the Newman-Penrose formalism. Such a new insight to the equations can also turn out to be useful for a generalization of the Newman- Penrose formalism to higher dimensions, thus allowing a better analysis of the various degrees of freedom, in view of extending to this case results already known in four dimensions.'), (3835, '2011-09-21 15:22:16'), (3836, '1109.4400 PDF'), (3837, 'http://www.arxiv.org/pdf/1109.4400.pdf'), (3838, '2011-09-21 15:22:18'), (3839, 'Efficient asymptotic frame selection for binary black hole spacetimes using asymptotic radiation'), (3840, '2011-09-23 2011-09-23'), (3841, 'http://arxiv.org/abs/1109.5224'), (3842, 'arXiv:1109.5224'), (3843, 'Previous studies have demonstrated that gravitational radiation reliably encodes information about the natural emission direction of the source (e.g., the orbital plane). In this paper, we demonstrate that these orientations can be efficiently estimated by the principal axes of <L_a L_b>, an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. Evaluating this average at each time provides the instantaneous emission direction. Further averaging across the entire signal yields an average orientation, closely connected to the angular components of the Fisher matrix. The latter direction is well-suited to data analysis and parameter estimation when the instantaneous emission direction evolves significantly. Finally, in the time domain, the average <L_a L_b> provides fast, invariant diagnostics of waveform quality.'), (3844, '2011-09-27 13:45:15'), (3845, '1109.5224 PDF'), (3846, 'http://www.arxiv.org/pdf/1109.5224.pdf'), (3847, '2011-09-27 13:45:20'), (3848, 'Multipole expansions for energy and momenta carried by gravitational waves'), (3849, '2007-07-31 2007-07-31'), (3850, 'http://arxiv.org/abs/0707.4654'), (3851, 'Gen.Rel.Grav.40:2467,2008'), (3852, '10.1007/s10714-007-0570-8'), (3853, 'arXiv:0707.4654'), (3854, 'We present expressions for the energy, linear momentum and angular momentum carried away from an isolated system by gravitational radiation based on spin-weighted spherical harmonics decomposition of the Weyl scalar $\\Psi_4$. We also show that the expressions derived are equivalent to the common expressions obtained when using a framework based on perturbations of a Schwazschild background. The main idea is to collect together all the different expressions in a uniform and consistent way. The formulae presented here are directly applicable to the calculation of the radiated energy, linear momentum and angular momentum starting from the gravitational waveforms which are typically extracted from numerical simulations.'), (3855, '2011-09-27 14:52:52'), (3856, '0707.4654 PDF'), (3857, 'http://www.arxiv.org/pdf/0707.4654.pdf'), (3858, '2011-09-27 14:52:56'), (3859, 'Reduced Basis representations of multi-mode black hole ringdown gravitational waves'), (3860, '2011-09-26 2011-09-26'), (3861, 'http://arxiv.org/abs/1109.5642'), (3862, 'arXiv:1109.5642'), (3863, 'We construct compact and high accuracy Reduced Basis (RB) representations of single and multiple quasinormal modes (QNMs). The RB method determines a hierarchical and relatively small set of the most relevant waveforms. We find that the exponential convergence of the method allows for a dramatic compression of template banks used for ringdown searches. Compressing a catalog with a minimal match $\\MMm=0.99$, we find that the selected RB waveforms are able to represent {\\em any} QNM, including those not in the original bank, with extremely high accuracy, typically less than $10^{-13}$. We then extend our studies to two-mode QNMs. Inclusion of a second mode is expected to help with detection, and might make it possible to infer details of the progenitor of the final black hole. We find that the number of RB waveforms needed to represent any two-mode ringdown waveform with the above high accuracy is {\\em smaller} than the number of metric-based, one-mode templates with $\\MMm=0.99$. For unconstrained two-modes, which would allow for consistency tests of General Relativity, our high accuracy RB has around $10^4$ {\\em fewer} waveforms than the number of metric-based templates for $\\MMm=0.99$. The number of RB elements grows only linearly with the number of multipole modes versus exponentially with the standard approach, resulting in very compact representations even for multiple modes. The results of this paper open the possibility of searches of multi-mode ringdown gravitational waves.'), (3864, '2011-09-27 16:03:23'), (3865, '1109.5642 PDF'), (3866, 'http://www.arxiv.org/pdf/1109.5642.pdf'), (3867, '2011-09-27 16:03:51'), (3868, 'Spin-induced orbital precession and its modulation of the gravitational waveforms from merging binaries'), (3869, 6274), (3870, '1994-06-15 June 15, 1994'), (3871, 'http://link.aps.org/doi/10.1103/PhysRevD.49.6274'), (3872, '10.1103/PhysRevD.49.6274'), (3873, 'Merging compact binaries are currently regarded as the most promising source of gravitational waves for the planned Earth-based LIGO/VIRGO laser-interferometer detector system, and will be an important source also for similar, lower-frequency detectors that might be flown in space (e.g., the proposed LISA mission). During the orbital inspiral, if one or both bodies are rapidly rotating, the general relativistic spin-orbit and spin-spin coupling (i.e., the "dragging of inertial frames" by the bodies\' spins) cause the binary\'s orbital plane to precess. In this paper we analyze the resulting modulation of the inspiral gravitational waveform, using post2-Newtonian equations to describe the precession of the orbital plane, but only the leading-order (Newtonian, quadrupole-moment approximation) equations to describe the orbit, the radiation reaction, the inspiral, and the wave generation. We derive all the formulas one needs to readily compute the spin-modulated gravitational waveform (within the post-Newtonian approximation and the approximation that the precession frequency is much smaller than the orbital frequency). We also develop intuition into what the modulated signals "look like," by a variety of means. We provide approximate, analytical solutions for the precessional motion and the modulated waveforms for two important special cases: the case where the bodies have nearly equal masses and the case where one of the bodies has negligible spin. For these cases, for almost all choices of binary parameters, the motion is a simple precession of the orbital angular momentum around the nearly fixed direction of the total angular momentum, with a few tens of precession periods as the waves sweep through the LIGO/VIRGO observational band. However, when the spin and orbital angular momenta are approximately anti-aligned, there is a transitional-precession epoch during which their near cancellation causes the binary to "lose its gyroscopic bearings" and tumble in space, with a corresponding peculiar sweep of the waveform modulation. We also explore numerically the precessional behaviors that occur for general masses and spins; these typically appear quite similar to our special-case, simple-precession, and transitional-precession solutions. An Appendix develops several diagrammatic aids for understanding intuitively the relation between the precessing orbit and the modulated waveform.'), (3874, '2011-10-01 23:51:45'), (3875, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v49/i12/p6274_1'), (3876, '2011-10-01 23:51:47'), (3877, '2011-10-02 02:40:48'), (3878, '2011-10-02 02:40:50'), (3879, 'Perturbative, Post-Newtonian, and General Relativistic Dynamics of Black Hole Binaries'), (3880, '2011-09-30 2011-09-30'), (3881, 'http://arxiv.org/abs/1109.6848'), (3882, 'arXiv:1109.6848'), (3883, 'The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory, numerical relativity, and the effective-one-body formalism. We review two recent comparisons of the predictions from these various techniques. Both comparisons rely on the calculation of a coordinate invariant relation, in the case of non-spinning binary black holes on quasi-circular orbits. All methods are shown to agree very well in their common domain of validity.'), (3884, '2011-10-03 13:37:36'), (3885, '1109.6848 PDF'), (3886, 'http://www.arxiv.org/pdf/1109.6848.pdf'), (3887, '2011-10-03 13:37:38'), (3888, 'http://link.aps.org/doi/10.1103/PhysRevD.84.064029'), (3889, '10.1103/PhysRevD.84.064029'), (3890, 'Accurate knowledge of the gravitational-wave (GW) signal from inspiraling compact binaries is essential to detect these signatures in the data from GW interferometers. With recent advances in post-Newtonian (PN) theory and numerical relativity (NR) it has become possible to construct inspiral-merger-ringdown waveforms by combining both descriptions into one complete hybrid signal. While addressing the reliability of such waveforms in different points of the physical parameter space, previous studies have identified the PN contribution as the dominant source of error, which can be reduced by incorporating longer NR simulations. In this paper we overcome the two outstanding issues that make it difficult to determine the minimum simulation length necessary to produce suitably accurate hybrids for GW astronomy applications: (1) the relevant criteria for a GW search is the mismatch between the true waveform and a set of model waveforms, optimized over all waveforms in the model, but for discrete hybrids this optimization was not yet possible. (2) these calculations typically require that numerical waveforms already exist, while we develop an algorithm to estimate hybrid mismatch errors without numerical data, which enables us to estimate the necessary NR waveform length before performing the simulation. Our procedure relies on combining supposedly equivalent PN models at highest available order with common data in the NR regime, and their difference serves as a measure of the uncertainty assumed in each waveform. Contrary to some earlier studies, we estimate that ∼10 NR orbits before merger should allow for the construction of waveform families that are accurate enough for detection in a broad range of parameters, only excluding highly spinning, unequal-mass systems. Nonspinning systems, even with high mass-ratio (q≳20) are well modeled for astrophysically reasonable component masses. In addition, the parameter bias is only of the order of 1% for total mass and symmetric mass-ratio and less than 0.1 for the dimensionless spin magnitude. We take the view that similar NR waveform lengths will remain the state of the art in the advanced detector era, and begin to assess the limits of the science that can be done with them.'), (3891, '245-254'), (3892, '2011-11-09 18:26:31'), (3893, 'OPERA and the GPS'), (3894, 'Animating rotation with quaternion curves'), (3895, '2011-10-03 20:19:30'), (3896, 'ACM SIGGRAPH Computer Graphics'), (3897, '00978930'), (3898, '1985-07-01 1985-07-01'), (3899, '10.1145/325165.325242'), (3900, 'http://portal.acm.org/citation.cfm?doid=325165.325242'), (3901, 'p245-shoemake.pdf'), (3902, 'http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.20'), (3903, 'Practical parameterization of rotations using the exponential map'), (3904, 'JOURNAL OF GRAPHICS TOOLS'), (3905, '1998-00-00 1998'), (3906, '29--48'), (3907, '0264-9381, 1361-6382'), (3908, '2010-04-21 2010-04-21'), (3909, '084034'), (3910, '10.1088/0264-9381/27/8/084034'), (3911, 'http://iopscience.iop.org/0264-9381/27/8/084034'), (3912, 'Advances in simulations of generic black-hole binaries'), (3913, 'Intitute of Physics'), (3914, '2011-10-06 15:27:00'), (3915, '0264-9381_26_15_153001.pdf'), (3916, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/26/15/153001/pdf/0264-9381_26_15_153001.pdf'), (3917, '0264-9381_27_8_084034.pdf'), (3918, 'Comparison of Post-Newtonian and Numerical Evolutions of Black-Hole Binaries'), (3919, '2009-01-24 2009-01-24'), (3920, 'http://arxiv.org/abs/0901.3861'), (3921, 'arXiv:0901.3861'), (3922, 'In this paper, we compare the waveforms from the post-Newtonian (PN) approach with the numerical simulations of generic black-hole binaries which have mass ratio $q\\sim0.8$, arbitrarily oriented spins with magnitudes $S_1/m_1^2\\sim0.6$ and $S_2/m_2^2\\sim0.4$, and orbit 9 times from an initial orbital separation of $r\\approx11M$ prior to merger. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of over 98% for the first six cycles of the $(\\ell=2,m=\\pm2)$ mode and over 90% for the $(\\ell=2,m=1)$ and $(\\ell=3,m=3)$ modes.'), (3923, '2011-10-06 15:38:18'), (3924, '0901.3861 PDF'), (3925, 'http://www.arxiv.org/pdf/0901.3861.pdf'), (3926, '2011-10-06 15:38:20'), (3927, 'Modeling gravitational recoil from precessing highly spinning unequal-mass black-hole binaries'), (3928, '064018'), (3929, '2009-03-18 March 18, 2009'), (3930, 'http://link.aps.org/doi/10.1103/PhysRevD.79.064018'), (3931, '10.1103/PhysRevD.79.064018'), (3932, 'We measure the gravitational recoil for unequal-mass black-hole binary mergers, with the larger black hole having intrinsic spin a/mH=0.8, and the smaller black hole nonspinning. We choose our configurations such that, initially, the spins lie on the orbital plane. The spin and orbital plane precess significantly (we introduce a technique to identify the orbital plane at merger), and we find that the out-of plane recoil (i.e. the recoil perpendicular to the orbital plane around merger) varies as η2/(1+q), in agreement with our previous prediction, based on the post-Newtonian scaling.'), (3933, '2011-10-06 15:38:26'), (3934, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i6/e064018'), (3935, '2011-10-06 15:38:28'), (3936, '2011-10-11 21:22:57'), (3937, 134001), (3938, '10.1088/0264-9381/28/13/134001'), (3939, 'http://iopscience.iop.org/0264-9381/28/13/134001'), (3940, 'The status of black-hole binary merger simulations with numerical relativity'), (3941, '2011-10-11 21:39:28'), (3942, 'http://iopscience.iop.org/0264-9381/28/13/134001/pdf/0264-9381_28_13_134001.pdf'), (3943, '2011-10-11 21:39:30'), (3944, 'http://arxiv.org/abs/1110.0467'), (3945, 'arXiv:1110.0467'), (3946, 'The resonant excitation of neutron star (NS) modes by tides is investigated as a source of short gamma-ray burst (sGRB) precursors. We find that the driving of a crust-core interface mode can lead to shattering of the NS crust, liberating ~10^46-10^47 erg of energy seconds before the merger of a NS-NS or NS-black hole binary. Such properties are consistent with Swift/BAT detections of sGRB precursors, and we use the timing of the observed precursors to place weak constraints on the crust equation of state. We describe how a larger sample of precursor detections could be used alongside coincident gravitational wave detections of the inspiral by Advanced LIGO class detectors to probe the NS structure. These two types of observations nicely complement one another, since the former constrains the equation of state and structure near the crust-core boundary, while the latter is more sensitive to the core equation of state.'), (3947, '2011-10-12 20:52:49'), (3948, '1110.0467 PDF'), (3949, 'http://www.arxiv.org/pdf/1110.0467.pdf'), (3950, '2011-10-12 20:52:51'), (3951, 'Comparison of numerical and post-Newtonian waveforms for generic precessing black-hole binaries'), (3952, '084010'), (3953, '2009-04-06 April 06, 2009'), (3954, 'http://link.aps.org/doi/10.1103/PhysRevD.79.084010'), (3955, '10.1103/PhysRevD.79.084010'), (3956, 'We compare waveforms and orbital dynamics from the first long-term, fully nonlinear, numerical simulations of a generic black-hole binary configuration with post-Newtonian (PN) predictions. The binary has mass ratio q∼0.8 with arbitrarily oriented spins of magnitude S1/m12∼0.6 and S2/m22∼0.4 and orbits 9 times prior to merger. The numerical simulation starts with an initial separation of r≈11M and orbital parameters determined by 2.5 PN and 3.5 PN evolutions of a quasi-circular binary starting from r=50M. The resulting binaries have very little eccentricity according to the 2.5 PN and 3.5 PN systems, but show eccentricities of e∼0.01–0.02 and e∼0.002–0.005 in the respective numerical simulations, thus demonstrating that 3.5 PN significantly reduces the eccentricity of the binary compared to 2.5 PN. We perform three numerical evolutions from r≈11M with maximum resolutions of h=M/48, M/53.3, M/59.3, to verify numerical convergence. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of nearly 99% for the first six cycles of the (ℓ=2, m=±2) modes, 91% for the (ℓ=2, m=±1) modes, and nearly 91% for the (ℓ=3, m=±3) modes. The phase differences between numerical and post-Newtonian approximations appear to be independent of the (ℓ,m) modes considered and relatively small for the first 3–4 orbits. An advantage of the 3.5 PN model over the 2.5 PN one seems to be observed, which indicates that still higher PN order (perhaps even 4.0 PN) may yield significantly better waveforms. In addition, we identify features in the waveforms likely related to precession and precession-induced eccentricity.'), (3957, '2011-10-13 14:29:31'), (3958, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i8/e084010'), (3959, '2011-10-13 14:29:33'), (3960, 'Recent progress on the accurate determination of the equation of state of neutron and nuclear matter'), (3961, '2011-10-05 2011-10-05'), (3962, 'http://arxiv.org/abs/1110.0993'), (3963, 'arXiv:1110.0993'), (3964, 'The problem of accurately determining the equation of state of nuclear and neutron matter at density near and beyond saturation is still an open challenge. In this paper we will review the most recent progress made by means of Quantum Monte Carlo calculations, which are at present the only ab-inito method capable to treat a sufficiently large number of particles to give meaningful estimates depending only on the choice of the nucleon-nucleon interaction. In particular, we will discuss the introduction of density-dependent interactions, the study of the temperature dependence of the equation of state, and the possibility of accurately studying the effect of the onset of hyperons by developing an accurate hyperon-nucleon and hyperon-nucleon-nucleon interaction.'), (3965, '2011-10-14 14:33:40'), (3966, '1110.0993 PDF'), (3967, 'http://www.arxiv.org/pdf/1110.0993.pdf'), (3968, '2011-10-14 14:33:42'), (3969, '2010-06-07 2010-06-07'), (3970, 114002), (3971, '10.1088/0264-9381/27/11/114002'), (3972, 'http://iopscience.iop.org/0264-9381/27/11/114002'), (3973, 'Numerical relativity confronts compact neutron star binaries: a review and status report'), (3974, '2011-10-14 14:45:03'), (3975, 'Numerical relativity confronts compact neutron star binaries'), (3976, 'http://iopscience.iop.org/0264-9381/27/11/114002/pdf/0264-9381_27_11_114002.pdf'), (3977, '2011-10-14 14:45:05'), (3978, 'The Evolution of Compact Binary Star Systems'), (3979, '2011-11-18 18:41:47'), (3980, 'Beyond LISA'), (3981, 'lrr-2006-6Color.pdf'), (3982, 'http://relativity.livingreviews.org/Articles/lrr-2006-6/download/lrr-2006-6Color.pdf'), (3983, 'Self-consistent orbital evolution of a particle around a Schwarzschild black hole'), (3984, 'Rotating Stars in Relativity'), (3985, '2003-00-00 2003'), (3986, 'http://www.livingreviews.org/lrr-2003-3'), (3987, 'lrr-2003-3Color.pdf'), (3988, 'http://relativity.livingreviews.org/Articles/lrr-2003-3/download/lrr-2003-3Color.pdf'), (3989, '2011-10-14 21:34:27'), (3990, 'http://www.livingreviews.org/lrr-2006-6'), (3991, '2011-10-14 21:35:10'), (3992, 'Measurement of the neutrino velocity with the OPERA detector in the CNGS beam'), (3993, '2011-09-22 2011-09-22'), (3994, 'http://arxiv.org/abs/1109.4897'), (3995, 'arXiv:1109.4897'), (3996, 'The OPERA neutrino experiment at the underground Gran Sasso Laboratory has measured the velocity of neutrinos from the CERN CNGS beam over a baseline of about 730 km with much higher accuracy than previous studies conducted with accelerator neutrinos. The measurement is based on high-statistics data taken by OPERA in the years 2009, 2010 and 2011. Dedicated upgrades of the CNGS timing system and of the OPERA detector, as well as a high precision geodesy campaign for the measurement of the neutrino baseline, allowed reaching comparable systematic and statistical accuracies. An early arrival time of CNGS muon neutrinos with respect to the one computed assuming the speed of light in vacuum of (60.7 \\pm 6.9 (stat.) \\pm 7.4 (sys.)) ns was measured. This anomaly corresponds to a relative difference of the muon neutrino velocity with respect to the speed of light (v-c)/c = (2.48 \\pm 0.28 (stat.) \\pm 0.30 (sys.)) \\times 10-5.'), (3997, '2011-10-15 22:29:07'), (3998, '1109.4897 PDF'), (3999, 'http://www.arxiv.org/pdf/1109.4897.pdf'), (4000, '2011-10-15 22:29:34'), (4001, '2011-10-17 18:04:39'), (4002, 'http://prd.aps.org/pdf/PRD/v58/i12/e124031'), (4003, '2011-10-17 18:04:41'), (4004, 38), (4005, '0001-7701, 1572-9532'), (4006, '2006-06-28 2006-6-28'), (4007, '1173-1208'), (4008, '10.1007/s10714-006-0311-4'), (4009, 'http://www.springerlink.com/content/e59757r3m6733585/'), (4010, 'Dynamical Evolution and Leading Order Gravitational Wave Emission of Riemann-S Binaries'), (4011, '2011-10-17 18:06:24'), (4012, 406), (4013, '0004-637X, 1538-4357'), (4014, '1993-04-00 04/1993'), (4015, 'L63'), (4016, '10.1086/186787'), (4017, 'http://adsabs.harvard.edu/doi/10.1086/186787'), (4018, 'Hydrodynamic instability and coalescence of close binary systems'), (4019, '2011-10-17 18:09:26'), (4020, '1993ApJ___406L__63L.pdf'), (4021, 'http://www.springerlink.com/content/e59757r3m6733585/fulltext.pdf'), (4022, '2011-10-17 18:12:58'), (4023, 'Resonant Oscillations and Tidal Heating in Coalescing Binary Neutron Stars'), (4024, 270), (4025, '1994-10-01 October 1, 1994'), (4026, 611), (4027, 'http://adsabs.harvard.edu/abs/1994MNRAS.270..611L'), (4028, 'Tidal interaction in a coalescing neutron star binary can resonantly \nexcite the g-mode oscillations of the neutron star when the frequency of \nthe tidal driving force equals the intrinsic g-mode frequencies. We \nstudy the g-mode oscillations of cold neutron stars using recent \nmicroscopic nuclear equations of state, where we determine \nselfconsistently the sound speed and Brunt -Va frequency in the nuclear \nliquid core. The properties of the g-modes associated with the stable \nstratification of the core depend sensitively on the pressure-density \nrelation, as well as on the symmetry energy of the dense nuclear matter. \nThe frequencies of the first ten g-modes lie approximately in the range \n10-100 Hz. Resonant excitations of these g-modes during the last few \nminutes of the binary coalescence result in energy transfer and angular \nmomentum transfer from the binary orbit to the neutron star. The angular \nmomentum transfer is possible because a dynamical tidal lag develops \neven in the absence of fluid viscosity. Since the coupling between the \ng-mode and the tidal potential is weak, however, the amount of energy \ntransfer during a resonance and the induced orbital phase error are very \nsmall. Resonant excitations of the g-modes play an important role in the \ntidal heating of binary neutron stars. Without the resonances, viscous \ndissipation is effective only when the stars are close to contact. The \nresonant oscillations result in dissipation at much larger orbital \nseparation. The actual amount of tidal heating depends on the viscosity \nof the neutron star. Using the microscopic viscosity, we find that the \nbinary neutron stars are heated to a temperature of 108 K before they \ncome into contact. Key words: dense matter - hydrodynamics - binaries: \nclose - stars: neutron - stars: osclllations.'), (4029, '2011-10-17 18:16:37'), (4030, '2011-12-20 2011-12-20'), (4031, '1994MNRAS_270__611L.pdf'), (4032, 'Prospects for Gravitational-Wave Observations of Neutron-Star Tidal Disruption in Neutron-Star–Black-Hole Binaries'), (4033, 3519), (4034, '2000-04-17 April 17, 2000'), (4035, 'http://link.aps.org/doi/10.1103/PhysRevLett.84.3519'), (4036, '10.1103/PhysRevLett.84.3519'), (4037, 'For an inspiraling neutron-star–black-hole (NS-BH) binary, we estimate the gravity-wave frequency ftd at the onset of NS tidal disruption. We model the NS as a tidally distorted, homogeneous, Newtonian ellipsoid on a circular, equatorial geodesic around a Kerr BH. We find that ftd depends strongly on the NS radius R, and estimate that LIGO-II (ca. 2006–2008) might measure R to 15% precision at 140 Mpc ( ∼1event/yr under current estimates). This suggests that LIGO-II might extract valuable information about the NS equation of state from tidal-disruption waves.'), (4038, '2011-10-17 19:05:29'), (4039, 'http://prl.aps.org/pdf/PRL/v84/i16/p3519_1'), (4040, '2011-10-17 19:05:31'), (4041, '2011-10-17 19:55:17'), (4042, '2011-10-17 19:55:19'), (4043, 'A geometric approach to the precession of compact binaries'), (4044, 'http://arxiv.org/abs/1110.2965'), (4045, 'arXiv:1110.2965'), (4046, 'We discuss a geometrical method to define a preferred reference frame for precessing binary systems and the gravitational waves they emit. This minimal-rotation frame is aligned with the angular-momentum axis and fixes the rotation about that axis up to a constant angle, resulting in an essentially invariant frame. Gravitational waveforms decomposed in this frame are similarly invariant under rotations of the inertial frame and exhibit relatively smoothly varying phase. By contrast, earlier prescriptions for radiation-aligned frames induce extraneous features in the gravitational-wave phase which depend on the orientation of the inertial frame, leading to fluctuations in the frequency that may compound to many gravitational-wave cycles. We explore a simplified description of post-Newtonian approximations for precessing systems using the minimal-rotation frame, and describe the construction of analytical/numerical hybrid waveforms for such systems.'), (4047, '2011-10-18 03:06:07'), (4048, '1110.2965 PDF'), (4049, 'http://www.arxiv.org/pdf/1110.2965.pdf'), (4050, '2011-10-18 03:06:14'), (4051, 'Neutron star equation of state via gravitational wave observations'), (4052, '2011-10-17 2011-10-17'), (4053, 'http://arxiv.org/abs/1110.3759'), (4054, 'J. Phys.: Conf. Ser. 189 012024, 2009'), (4055, '10.1088/1742-6596/189/1/012024'), (4056, 'arXiv:1110.3759'), (4057, 'Gravitational wave observations can potentially measure properties of neutron star equations of state by measuring departures from the point-particle limit of the gravitational waveform produced in the late inspiral of a neutron star binary. Numerical simulations of inspiraling neutron star binaries computed for equations of state with varying stiffness are compared. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly if the neutron stars are more compact. This suggests that gravitational wave observations at frequencies around 1 kHz will be able to measure a compactness parameter and place stringent bounds on possible neutron star equations of state. Advanced laser interferometric gravitational wave observatories will be able to tune their frequency band to optimize sensitivity in the required frequency range to make sensitive measures of the late-inspiral phase of the coalescence.'), (4058, '2011-10-18 14:36:19'), (4059, '1110.3759 PDF'), (4060, 'http://www.arxiv.org/pdf/1110.3759.pdf'), (4061, '2011-10-18 14:36:33'), (4062, 321), (4063, '0028-0836'), (4064, '1986-05-01 1986-5-1'), (4065, '17-17'), (4066, '10.1038/321017a0'), (4067, 'http://adsabs.harvard.edu/abs/1986Natur.321...17S'), (4068, 'Mathematics: Hermann Grassmann was right'), (4069, '2011-10-18 15:44:54'), (4070, 'Mathematics'), (4071, '321017a0.pdf'), (4072, 'Hamiltonian Mechanics with Geometric Calculus'), (4073, 'Spinors, Twistors, Clifford Algebras and Quantum Deformations'), (4074, 'Boston'), (4075, '1993-00-00 1993'), (4076, '203--214'), (4077, 'Hamilton.pdf'), (4078, 'Singular disk of matter in the Cooperstock-Tieu galaxy model'), (4079, '1987-00-00 1987'), (4080, 'Norwell, MA'), (4081, '14808_9027725616.djvu'), (4082, 'Clifford algebra to geometric calculus'), (4083, 'New foundations for classical mechanics'), (4084, 'Second'), (4085, 'Boston, MA'), (4086, '2002-00-00 2002'), (4087, 'http://arxiv.org/abs/1411.0674'), (4088, 'Geometric Algebra for Physicists'), (4089, 'Cambridge University Press'), (4090, 'New York, NY'), (4091, 544), (4092, 9780792316237), (4093, 'Springer'), (4094, 'Clifford algebras and their applications in mathematical physics: proceedings of second workshop held at Montpellier, France, 1989'), (4095, 'This volume contains selected papers presented at the Second Workshop on Clifford Algebras and their Applications in Mathematical Physics. These papers range from various algebraic and analytic aspects of Clifford algebras to applications in, for example, gauge fields, relativity theory, supersymmetry and supergravity, and condensed phase physics. Included is a biography and list of publications of Màrio Schenberg, who, next to Marcel Riesz, has made valuable contributions to these topics. This volume will be of interest to mathematicians working in the fields of algebra, geometry or special functions, to physicists working on quantum mechanics or supersymmetry, and to historians of mathematical physics.'), (4096, '1992-03-31 1992-03-31'), (4097, 'Google Books'), (4098, 'Clifford algebras and their applications in mathematical physics'), (4099, 'Google Books Link'), (4100, 'http://books.google.com/books?id=FhU9QpPIscoC'), (4101, '2011-10-18 16:08:58'), (4102, 'New form of the Kerr solution'), (4103, '067503'), (4104, '2000-02-25 February 25, 2000'), (4105, 'http://link.aps.org/doi/10.1103/PhysRevD.61.067503'), (4106, '10.1103/PhysRevD.61.067503'), (4107, 'A new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physical phenomena are particularly clear when related to this time coordinate. The chosen coordinates also ensure that the solution is well behaved at the horizon. The solution is well suited to the tetrad formalism and a convenient null tetrad is presented. The Dirac Hamiltonian in a Kerr background is also given and, for one choice of tetrad, it takes on a simple, Hermitian form.'), (4108, '2011-10-18 19:54:46'), (4109, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v61/i6/e067503'), (4110, '2011-10-18 19:54:48'), (4111, 'Applications of Geometric Algebra in Electromagnetism, Quantum Mechanics and Gravity'), (4112, 'Sixth International Conference on Clifford Algebras and their Applications, Tennessee 2002'), (4113, 467), (4114, 'Birkhauser'), (4115, 'lda_tenn.pdf'), (4116, 20), (4117, '2003-03-21 2003-03-21'), (4118, '1077-1101'), (4119, '10.1088/0264-9381/20/6/304'), (4120, 'http://iopscience.iop.org/0264-9381/20/6/304'), (4121, 'New techniques for analysing axisymmetric gravitational systems: 1. Vacuum fields'), (4122, '2011-10-18 20:07:18'), (4123, 'New techniques for analysing axisymmetric gravitational systems'), (4124, '2005-08-17 2005-08-17'), (4125, 'http://arxiv.org/abs/astro-ph/0508377'), (4126, '0264-9381_20_6_304.pdf'), (4127, 'Gravity, gauge theories and geometric algebra'), (4128, '1998-03-15 March 15 , 1998'), (4129, 'Philosophical Transactions of the Royal Society of London. Series A: \t\t\t\tMathematical, Physical and Engineering Sciences'), (4130, '487 -582'), (4131, 356), (4132, 1737), (4133, 'http://rsta.royalsocietypublishing.org/content/356/1737/487.abstract'), (4134, 'A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the position and orientation of the matter fields. In this manner all properties of the background spacetime are removed from physics and what remains are a set of ‘intrinsic’ relations between physical fields. For a wide range of phenomena, including all present experimental tests, the theory reproduces the predictions of general relativity. Differences do emerge, however, through the first–order nature of the equations and the global properties of the gauge fields and through the relationship with quantum theory. The properties of the gravitational gauge fields are derived from both classical and quantum viewpoints. Field equations are then derived from an action principle and consistency with the minimal coupling procedure selects an action which is unique up to the possible inclusion of a cosmological constant. This in turn singles out a unique form of spin–torsion interaction. A new method for solving the field equations is outlined and applied to the case of a time–dependent, spherically symmetric perfect fluid. A gauge is found which reduces the physics to a set of essentially Newtonian equations. These equations are then applied to the study of cosmology and to the formation and properties of black holes. Insistence on finding global solutions, together with the first–order nature of the equations, leads to a new understanding of the role played by time reversal. This alters the physical picture of the properties of a horizon around a black hole. The existence of global solutions enables one to discuss the properties of field lines inside the horizon due to a point charge held outside it. The Dirac equation is studied in a black hole background and provides a quick (though ultimately unsound) derivation of the Hawking temperature. Some applications to cosmology are also discussed and a study of the Dirac equation in a cosmological background reveals that the only models consistent with homogeneity are spatially flat. It is emphasized throughout that the description of gravity in terms of gauge fields, rather than spacetime geometry, leads to many simple and powerful physical insights. The language of ‘geometric algebra’ best expresses the physical and mathematical content of the theory and is employed throughout. Methods for translating the equations into other languages (tensor and spinor calculus) are given in appendices.'), (4135, '10.1098/rsta.1998.0178'), (4136, '2011-10-18 21:31:01'), (4137, 'arXiv:astro-ph/0508377'), (4138, 'Recently a new model of galactic gravitational field, based on ordinary General Relativity, has been proposed by Cooperstock and Tieu in which no exotic dark matter is needed to fit the observed rotation curve to a reasonable ordinary matter distribution. We argue that in this model the gravitational field is generated not only by the galaxy matter, but by a thin, singular disk as well. The model should therefore be considered unphysical.'), (4139, 'Phil. Trans. R. Soc. Lond. A-1998-Lasenby-487-582.pdf'), (4140, 'Geometric Algebra and Physics'), (4141, '2008-04-14 14 April 2008'), (4142, 'Oxford Undergraduate Physics Conference'), (4143, 'Oxford University'), (4144, 'http://www.mrao.cam.ac.uk/~anthony/oxford_undergrad_physics_conf_april_2008.pdf'), (4145, 'oxford_undergrad_physics_conf_april_2008.pdf'), (4146, 'Fermion scattering by a Schwarzschild black hole'), (4147, '064005'), (4148, 'http://link.aps.org/doi/10.1103/PhysRevD.74.064005'), (4149, '10.1103/PhysRevD.74.064005'), (4150, 'We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. We begin by extending a recent perturbation-theory calculation to next order to obtain Born series for the differential cross section and Mott polarization, valid at small couplings. We continue by deriving an approximation for glory scattering of massive spinor particles by considering classical timelike geodesics and spin precession. Next, we formulate the Dirac equation on a black hole background, and outline a simple numerical method for finding partial wave series solutions. Finally, we present our numerical calculations of absorption and scattering cross sections and polarization, and compare with theoretical expectations.'), (4151, '2011-10-18 22:43:44'), (4152, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i6/e064005'), (4153, '2011-10-18 22:43:46'), (4154, 'http://link.aps.org/doi/10.1103/RevModPhys.25.714'), (4155, 'http://today.msnbc.msn.com/id/44950397/ns/today-food/t/home-chef-challenge-winner-grilled-eggplant-rollatini/#slice-2'), (4156, '2011-10-19 15:37:10'), (4157, 'Grilled eggplant rollatini'), (4158, '2011-10-21 15:29:10'), (4159, 'astro-ph/0508377 PDF'), (4160, 'http://www.arxiv.org/pdf/astro-ph/0508377.pdf'), (4161, '2011-10-21 15:29:12'), (4162, 'On cosmic acceleration without dark energy'), (4163, '2005-06-22 2005-06-22'), (4164, 'http://arxiv.org/abs/astro-ph/0506534'), (4165, 'NewJ.Phys.8:322,2006'), (4166, '10.1088/1367-2630/8/12/322'), (4167, 'arXiv:astro-ph/0506534'), (4168, 'We elaborate on the proposal that the observed acceleration of the Universe is the result of the backreaction of cosmological perturbations, rather than the effect of a negative-pressure dark-energy fluid or a modification of general relativity. Through the effective Friedmann equations describing an inhomogeneous Universe after smoothing, we demonstrate that acceleration in our local Hubble patch is possible even if fluid elements do not individually undergo accelerated expansion. This invalidates the no-go theorem that there can be no acceleration in our local Hubble patch if the Universe only contains irrotational dust. We then study perturbatively the time behavior of general-relativistic cosmological perturbations, applying, where possible, the renormalization group to regularize the dynamics. We show that an instability occurs in the perturbative expansion involving sub-Hubble modes. Whether this is an indication that acceleration in our Hubble patch originates from the backreaction of cosmological perturbations on observable scales requires a fully non-perturbative approach.'), (4169, '2011-10-21 15:29:18'), (4170, 'astro-ph/0506534 PDF'), (4171, 'http://www.arxiv.org/pdf/astro-ph/0506534.pdf'), (4172, '2011-10-21 15:29:23'), (4173, 'Primordial inflation explains why the universe is accelerating today'), (4174, '2005-03-14 2005-03-14'), (4175, 'http://arxiv.org/abs/hep-th/0503117'), (4176, 'arXiv:hep-th/0503117'), (4177, 'We propose an explanation for the present accelerated expansion of the universe that does not invoke dark energy or a modification of gravity and is firmly rooted in inflationary cosmology.'), (4178, '2011-10-21 15:29:25'), (4179, 'hep-th/0503117 PDF'), (4180, 'http://www.arxiv.org/pdf/hep-th/0503117.pdf'), (4181, '2011-10-21 15:29:28'), (4182, 'General Relativity Resolves Galactic Rotation Without Exotic Dark Matter'), (4183, '2005-07-26 2005-07-26'), (4184, 'http://arxiv.org/abs/astro-ph/0507619'), (4185, 'arXiv:astro-ph/0507619'), (4186, 'A galaxy is modeled as a stationary axially symmetric pressure-free fluid in general relativity. For the weak gravitational fields under consideration, the field equations and the equations of motion ultimately lead to one linear and one nonlinear equation relating the angular velocity to the fluid density. It is shown that the rotation curves for the Milky Way, NGC 3031, NGC 3198 and NGC 7331 are consistent with the mass density distributions of the visible matter concentrated in flattened disks. Thus the need for a massive halo of exotic dark matter is removed. For these galaxies we determine the mass density for the luminous threshold as 10^{-21.75} kg.m$^{-3}.'), (4187, '2011-10-21 15:29:34'), (4188, 'astro-ph/0507619 PDF'), (4189, 'http://www.arxiv.org/pdf/astro-ph/0507619.pdf'), (4190, '2011-10-21 15:29:38'), (4191, 'Escape from the clutches of the dark sector? | Cosmic Variance | Discover Magazine'), (4192, 'http://blogs.discovermagazine.com/cosmicvariance/2005/10/17/escape-from-the-clutches-of-the-dark-sector/'), (4193, '2011-10-21 15:29:47'), (4194, '1216-1220'), (4195, '10.1086/533487'), (4196, 'http://iopscience.iop.org/0004-637X/677/2/1216/'), (4197, 'Tidal Love Numbers of Neutron Stars'), (4198, '10.1086/508162'), (4199, '2011-11-30 18:18:13'), (4200, '0004-637X_677_2_1216.pdf'), (4201, 'Relativistic theory of tidal Love numbers'), (4202, '084018'), (4203, '2009-10-14 October 14, 2009'), (4204, 'http://link.aps.org/doi/10.1103/PhysRevD.80.084018'), (4205, 648), (4206, '2006-09-10 2006-09-10'), (4207, 'L109-L113'), (4208, 'http://iopscience.iop.org/508162'), (4209, 'A Direct Empirical Proof of the Existence of Dark Matter'), (4210, '2011-10-21 15:37:48'), (4211, '10.1103/RevModPhys.25.714'), (4212, '2011-10-24 01:06:03'), (4213, 606), (4214, '2004-05-10 2004-05-10'), (4215, '819-824'), (4216, '10.1086/383178'), (4217, 'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/606/2/819/'), (4218, 'Direct Constraints on the Dark Matter Self‐Interaction Cross Section from the Merging Galaxy Cluster 1E 0657−56'), (4219, '2011-10-21 15:38:13'), (4220, '1538-4357_648_2_L109.pdf'), (4221, '0004-637X_606_2_819.pdf'), (4222, 668), (4223, '2007-10-20 2007-10-20'), (4224, '806-814'), (4225, '10.1086/521383'), (4226, 'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/668/2/806'), (4227, 'A Dark Core in Abell 520'), (4228, '2011-10-21 17:30:53'), (4229, '0004-637X_668_2_806.pdf'), (4230, 'Can superhorizon cosmological perturbations explain the acceleration of the universe?'), (4231, 72), (4232, '083501'), (4233, '2005-10-03 October 03, 2005'), (4234, 'http://link.aps.org/doi/10.1103/PhysRevD.72.083501'), (4235, '10.1103/PhysRevD.72.083501'), (4236, 'We investigate the recent suggestions by Barausse et al. and Kolb et al. that the acceleration of the universe could be explained by large superhorizon fluctuations generated by inflation. We show that no acceleration can be produced by this mechanism. We begin by showing how the application of Raychaudhuri equation to inhomogeneous cosmologies results in several “no go” theorems for accelerated expansion. Next we derive an exact solution for a specific case of initial perturbations, for which application of the Kolb et al. expressions leads to an acceleration, while the exact solution reveals that no acceleration is present. We show that the discrepancy can be traced to higher-order terms that were dropped in the Kolb et al. analysis. We proceed with the analysis of initial value formulation of general relativity to argue that causality severely limits what observable effects can be derived from superhorizon perturbations. By constructing a Riemann normal coordinate system on initial slice we show that no infrared divergence terms arise in this coordinate system. Thus any divergences found previously can be eliminated by a local rescaling of coordinates and are unobservable. We perform an explicit analysis of the variance of the deceleration parameter for the case of single-field inflation using usual coordinates and show that the infrared-divergent terms found by Barausse et al. and Kolb et al. cancel against several additional terms not considered in their analysis. Finally, we argue that introducing isocurvature perturbations does not alter our conclusion that the accelerating expansion of the universe cannot be explained by superhorizon modes.'), (4237, '2011-10-21 17:47:23'), (4238, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i8/e083501'), (4239, '2011-10-21 17:47:25'), (4240, 'Do large-scale inhomogeneities explain away dark energy?'), (4241, '023517'), (4242, '2005-07-26 July 26, 2005'), (4243, 'http://link.aps.org/doi/10.1103/PhysRevD.72.023517'), (4244, '10.1103/PhysRevD.72.023517'), (4245, 'Recently, new arguments [ E. Barausse, S. Matarrese and A. Riotto Phys. Rev. D 71 063537 (2005)][E. W. Kolb, S. Matarrese, A. Notari, and A. Riotto, hep-th/0503117 [Phys. Rev. Lett. (to be published)].] for how corrections from super-Hubble modes can explain the present-day acceleration of the universe have appeared in the literature. However, in this paper, we argue that, to second order in spatial gradients, these corrections only amount to a renormalization of local spatial curvature, and thus cannot account for the negative deceleration. Moreover, cosmological observations already put severe bounds on such corrections, at the level of a few percent, while in the context of inflationary models, these corrections are typically limited to ∼10-5. Currently there is no general constraint on the possible correction from higher order gradient terms, but we argue that such corrections are even more constrained in the context of inflationary models.'), (4246, '2011-10-21 17:47:38'), (4247, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i2/e023517'), (4248, '2011-10-21 17:47:40'), (4249, 'Can superhorizon perturbations drive the acceleration of the Universe?'), (4250, 103521), (4251, '2005-05-27 May 27, 2005'), (4252, 'http://link.aps.org/doi/10.1103/PhysRevD.71.103521'), (4253, '10.1103/PhysRevD.71.103521'), (4254, 'It has recently been suggested that the acceleration of the Universe can be explained as the backreaction effect of superhorizon perturbations using second order perturbation theory. If this mechanism is correct, it should also apply to a hypothetical, gedanken universe in which the subhorizon perturbations are absent. In such a gedanken universe it is possible to compute the deceleration parameter q0 measured by comoving observers using local covariant Taylor expansions rather than using second order perturbation theory. The result indicates that second order corrections to q0 are present, but shows that if q0 is negative then its magnitude is constrained to be less than or of the order of the square of the peculiar velocity on Hubble scales today. We argue that, since this quantity is constrained by observations to be small compared to unity, superhorizon perturbations cannot be responsible for the acceleration of the Universe.'), (4255, '2011-10-21 17:51:44'), (4256, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v71/i10/e103521'), (4257, '2011-10-21 17:51:46'), (4258, 'Effects of hyperons in binary neutron star mergers'), (4259, '2011-10-20 2011-10-20'), (4260, 'http://arxiv.org/abs/1110.4442'), (4261, 'arXiv:1110.4442'), (4262, 'Numerical simulations for the merger of binary neutron stars are performed in full general relativity incorporating both nucleonic and hyperonic finite-temperature equations of state (EOS) and neutrino cooling for the first time. It is found that even for the hyperonic EOS, a hypermassive neutron star is first formed after the merger for the typical total mass $\\approx$ 2.7M\\bigodot, and subsequently collapses to a black hole (BH). It is shown that hyperons play a substantial role in the post-merger dynamics, torus formation around the BH, and emission of gravitational waves (GWs). In particular, the existence of hyperons is imprinted in GWs. Therefore, GW observations will provide a potential opportunity to explore the composition of the neutron star matter.'), (4263, '2011-10-21 18:39:18'), (4264, '1110.4442 PDF'), (4265, 'http://www.arxiv.org/pdf/1110.4442.pdf'), (4266, '2011-10-21 18:39:24'), (4267, 'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v25/i3/p714_1'), (4268, '2011-10-24 01:06:05'), (4269, 'Gauge-invariant treatment of gravitational radiation near the source: Analysis and numerical simulations'), (4270, '2585-2594'), (4271, '1990-10-15 October 15, 1990'), (4272, 'http://link.aps.org/doi/10.1103/PhysRevD.42.2585'), (4273, '10.1103/PhysRevD.42.2585'), (4274, 'We discuss a procedure based on the use of multipole-moment expansions for matching numerical solutions for the gravitational-radiation field around a compact source to linear analytic solutions. Gauge-invariant perturbation theory is used to generate even- and odd-parity matching equations for each spherical harmonic order l, m. This technique determines asymptotic wave forms, valid in the local wave zone, from the numerically evolved fields in a weak-field annular region surrounding the isolated source. The separation of the wave form from near-zone and residual gauge effects is demonstrated using fully general-relativistic simulations of relativistic stars undergoing nonradial pulsation.'), (4275, '2011-10-24 01:28:07'), (4276, 'Gauge-invariant treatment of gravitational radiation near the source'), (4277, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v42/i8/p2585_1'), (4278, '2011-10-24 01:28:09'), (4279, 'RevModPhys.52.299.pdf'), (4280, 693), (4281, '2009-03-01 2009-03-01'), (4282, '383-387'), (4283, '10.1088/0004-637X/693/1/383'), (4284, 'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/693/1/383'), (4285, 'Peculiar anisotropic stationary spherically symmetric solution of Einstein equations'), (4286, '2011-10-24 02:24:16'), (4287, '2011-11-01 2011-11-01'), (4288, 'The Contribution of Halo White Dwarf Binaries to the Laser Interferometer Space Antenna Signal'), (4289, '0004-637X_693_1_383.pdf'), (4290, 'Falloff of radiated energy in black hole spacetimes'), (4291, 104029), (4292, '2010-11-12 November 12, 2010'), (4293, 'http://link.aps.org/doi/10.1103/PhysRevD.82.104029'), (4294, '10.1103/PhysRevD.82.104029'), (4295, 'The goal of much research in relativity is to understand gravitational waves generated by a strong-field dynamical spacetime. Quantities of particular interest for many calculations are the Weyl scalar ψ4, which is simply related to the flux of gravitational waves far from the source, and the flux of energy carried to distant observers, E˙. Conservation laws guarantee that, in asympotically flat spacetimes, ψ4∝1/r and E˙∝1/r2 as r→∞. Most calculations extract these quantities at some finite extraction radius. An understanding of finite radius corrections to ψ4 and E˙ allows us to more accurately infer their asymptotic values from a computation. In this paper, we show that, if the final state of the system is a black hole, then the leading correction to ψ4 is O(1/r3), and that to the energy flux is O(1/r4)—not O(1/r2) and O(1/r3), as one might naively guess. Our argument only relies on the behavior of the curvature scalars for black hole spacetimes. Using black hole perturbation theory, we calculate the corrections to the leading falloff, showing that it is quite easy to correct for finite extraction radius effects.'), (4296, '2011-10-24 03:01:22'), (4297, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v82/i10/e104029'), (4298, '2011-10-24 03:01:24'), (4299, 'Reading off gravitational radiation waveforms in numerical relativity calculations: Matching to linearized gravity'), (4300, 37), (4301, '318-332'), (4302, '1988-01-15 January 15, 1988'), (4303, 'http://link.aps.org/doi/10.1103/PhysRevD.37.318'), (4304, '10.1103/PhysRevD.37.318'), (4305, 'Two methods are described, both based on the use of multipole moments in linearized gravity, to read off gravitational radiation waveforms during numerical relativity simulations. In the first, matching is made at a finite radius in the weak-field exterior of a strong-field source to an analytic template developed via an infinitesimal gauge transformation from a general solution to the vacuum weak-field equations. The matching procedure allows the asymptotic waveforms to be separated from the confusing influences of the source’s (e.g., black hole, neutron star, collapsing stellar core) stationary moments, the wave’s near-zone field, and gauge dependencies in the metric. This is achieved by computing the multipole-moment amplitudes of the gravitational field with a set of surface integrals of the metric over one (or more) coordinate two-sphere(s). The two-surface(s) need not be placed far out in the local wave zone, nor does the method require the existence of a deep near zone (i.e., the source need not be slow motion). The procedure is demonstrated through its application to two standard axisymmetric numerical relativity gauges (quasi-isotropic and radial). The second matching approach uses a surface integral over components of the Riemann tensor to eliminate gauge effects. The near-zone field is separated off as in the previous method. This latter technique may be applicable to problems in any gauge.'), (4306, '2011-10-24 16:12:35'), (4307, 'Reading off gravitational radiation waveforms in numerical relativity calculations'), (4308, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v37/i2/p318_1'), (4309, '2011-10-24 16:12:37'), (4310, 401), (4311, '10.1063/1.1665603'), (4312, 'http://link.aip.org/link/?JMP/12/401/1&Agg=doi'), (4313, 'Gravitational Radiation Damping of Slowly Moving Systems Calculated Using Matched Asymptotic Expansions'), (4314, '2011-10-24 16:15:29'), (4315, 'JMathPhys_12_401.pdf'), (4316, '2011-10-01 2011-10-01'), (4317, 195015), (4318, '10.1088/0264-9381/28/19/195015'), (4319, 'http://iopscience.iop.org/0264-9381/28/19/195015'), (4320, 'Notes on the integration of numerical relativity waveforms'), (4321, '2011-10-24 22:39:33'), (4322, 'http://arxiv.org/abs/1111.0327'), (4323, 'arXiv:1111.0327'), (4324, '0264-9381_28_19_195015.pdf'), (4325, 'Characteristic extraction tool for gravitational waveforms'), (4326, '044057'), (4327, '2011-00-00 2011'), (4328, 'http://link.aps.org/doi/10.1103/PhysRevD.84.044057'), (4329, '10.1103/PhysRevD.84.044057'), (4330, 'We develop and calibrate a characteristic waveform extraction tool whose major improvements and corrections of prior versions allow satisfaction of the accuracy standards required for advanced LIGO data analysis. The extraction tool uses a characteristic evolution code to propagate numerical data on an inner worldtube supplied by a 3+1 Cauchy evolution to obtain the gravitational waveform at null infinity. With the new extraction tool, high accuracy and convergence of the numerical error can be demonstrated for an inspiral and merger of mass M binary black holes even for an extraction worldtube radius as small as R=20M. The tool provides a means for unambiguous comparison between waveforms generated by evolution codes based upon different formulations of the Einstein equations and based upon different numerical approximations.'), (4331, '2011-10-24 22:44:45'), (4332, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i4/e044057'), (4333, '2011-10-24 22:44:46'), (4334, 'Notes on Gravitational Waveform Fitting'), (4335, 'fittingnotes.pdf'), (4336, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2010.17913.x/abstract'), (4337, '10.1111/j.1365-2966.2010.17913.x'), (4338, 414), (4339, '1365-2966'), (4340, 'Pulsar timing array observations of gravitational wave source timing parallax'), (4341, '2011-06-11 2011/06/11'), (4342, '50-58'), (4343, 'Pulsar timing arrays (PTAs) act to detect gravitational waves by observing the small, correlated effect the waves have on pulse arrival times at the Earth. This effect has conventionally been evaluated assuming the gravitational wave phase fronts are planar across the array, an assumption that is valid only for sources at distances R≫ 2πL2/λ, where L is physical extent of the array and λ is the radiation wavelength. In the case of PTAs, the array size is of the order of the pulsar–Earth distance (kpc) and λ is of the order of parsec. Correspondingly, for point gravitational wave sources closer than ∼100\xa0Mpc, the PTA response is sensitive to the source parallax across the pulsar–Earth baseline. Here, we evaluate the PTA response to gravitational wave point sources including the important wavefront curvature effects. Taking the wavefront curvature into account, the relative amplitude and phase of the timing residuals associated with a collection of pulsars allow us to measure the distance to, and the sky position of, the source.'), (4344, '2011-10-25 16:54:30'), (4345, 'Wiley Full Text PDF'), (4346, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1111/j.1365-2966.2010.17913.x/asset/j.1365-2966.2010.17913.x.pdf?v=1&t=gu74y41g&s=3605a70584189e906e7df58ad56a14ad11a16cdb'), (4347, '2011-10-25 16:54:32'), (4348, 'Caltech'), (4349, 'Geometric algebra techniques for general relativity'), (4350, 311), (4351, '459-502'), (4352, '2004-06-00 June 2004'), (4353, '10.1016/j.aop.2003.12.009'), (4354, 'http://www.sciencedirect.com/science/article/pii/S0003491604000053'), (4355, 'Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the straightforwardness of coordinate methods. We focus our attention on orthonormal frames and the associated connection bivector, using them to find the Schwarzschild and Kerr solutions, along with a detailed exposition of the Petrov types for the Weyl tensor.'), (4356, '2011-10-27 02:25:12'), (4357, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272507&_user=492137&_pii=S0003491604000053&_check=y&_origin=&_coverDate=30-Jun-2004&view=c&wchp=dGLbVBA-zSkzS&md5=ce6ca86c96435434b5dbeb5d6875455d/1-s2.0-S0003491604000053-main.pdf'), (4358, '2011-10-27 02:25:14'), (4359, 'Clifford algebra, geometric algebra, and applications'), (4360, '2009-07-30 2009-07-30'), (4361, 'http://arxiv.org/abs/0907.5356'), (4362, 'arXiv:0907.5356'), (4363, 'These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction (then called geometric algebra) with geometric applications in mind, as well as in an algebraically more general form which is well suited for combinatorics, and for defining and understanding the numerous products and operations of the algebra. The various applications presented include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.'), (4364, '2011-10-27 02:28:59'), (4365, '0907.5356 PDF'), (4366, 'http://www.arxiv.org/pdf/0907.5356.pdf'), (4367, '2011-10-27 02:29:08'), (4368, 'Accurate gravitational waveforms for binary-black-hole mergers with nearly extremal spins'), (4369, '2011-10-10 2011-10-10'), (4370, 'http://arxiv.org/abs/1110.2229'), (4371, 'arXiv:1110.2229'), (4372, "Motivated by the possibility of observing gravitational waves from merging black holes whose spins are nearly extremal (i.e., 1 in dimensionless units), we present numerical waveforms from simulations of merging black holes with the highest spins simulated to date: (1) a 25.5-orbit inspiral, merger, and ringdown of two holes with equal masses and spins of magnitude 0.97 aligned with the orbital angular momentum; and (2) a previously reported 12.5-orbit inspiral, merger, and ringdown of two holes with equal masses and spins of magnitude 0.95 anti-aligned with the orbital angular momentum. First, we consider the horizon mass and spin evolution of the new aligned-spin simulation. During the inspiral, the horizon area and spin evolve in remarkably close agreement with Alvi's analytic predictions, and the remnant hole's final spin agrees reasonably well with several analytic predictions. We also find that the total energy emitted by a real astrophysical system with these parameters---almost all of which is radiated during the time included in this simulation---would be 10.952% of the initial mass at infinite separation. Second, we consider the gravitational waveforms for both simulations. After estimating their uncertainties, we compare the waveforms to several post-Newtonian approximants, finding significant disagreement well before merger, although the phase of the TaylorT4 approximant happens to agree remarkably well with the numerical prediction in the aligned-spin case. We find that the post-Newtonian waveforms have sufficient uncertainty that hybridized waveforms will require far longer numerical simulations (in the absence of improved post-Newtonian waveforms) for accurate parameter estimation of low-mass binary systems."), (4373, '2011-10-27 13:07:03'), (4374, '1110.2229 PDF'), (4375, 'http://www.arxiv.org/pdf/1110.2229.pdf'), (4376, '2011-10-27 13:07:10'), (4377, 'Post-Newtonian, Quasi-Circular Binary Inspirals in Quadratic Modified Gravity'), (4378, '2011-10-26 2011-10-26'), (4379, 'http://arxiv.org/abs/1110.5950'), (4380, 'arXiv:1110.5950'), (4381, 'We consider a general class of quantum gravity-inspired, modified gravity theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to scalar fields with standard kinetic energy. This class of theories includes Einstein-Dilaton-Gauss-Bonnet and Chern-Simons modified gravity as special cases. We analytically derive and solve the coupled field equations in the post-Newtonian approximation, assuming a comparable-mass, spinning black hole binary source in a quasi-circular, weak-field/slow-motion orbit. We find that a naive subtraction of divergent piece associated with the point-particle approximation is ill-suited to represent compact objects in these theories. Instead, we model them by appropriate effective sources built so that known strong-field solutions are reproduced in the far-field limit. In doing so, we prove that black holes in Einstein-Dilaton-Gauss-Bonnet and Chern-Simons theory can have hair, while neutron stars have no scalar monopole charge, in diametrical opposition to results in scalar-tensor theories. We then employ techniques similar to the direct integration of the relaxed Einstein equations to obtain analytic expressions for the scalar field, metric perturbation, and the associated gravitational wave luminosity measured at infinity. We find that scalar field emission mainly dominates the energy flux budget, sourcing electric-type (even-parity) dipole scalar radiation and magnetic-type (odd-parity) quadrupole scalar radiation, correcting the General Relativistic prediction at relative -1PN and 2PN orders. Such modifications lead to corrections in the emitted gravitational waves that can be mapped to the parameterized post-Einsteinian framework. Such modifications could be strongly constrained with gravitational wave observations.'), (4382, '2011-10-28 20:10:49'), (4383, '1110.5950 PDF'), (4384, 'http://www.arxiv.org/pdf/1110.5950.pdf'), (4385, '2011-10-28 20:10:51'), (4386, 'Overview of Geometric Algebra in Physics'), (4387, 'http://geocalc.clas.asu.edu/html/Overview.html'), (4388, '2011-10-29 18:44:13'), (4389, '00029505'), (4390, 104), (4391, '10.1119/1.1522700'), (4392, 'http://link.aip.org/link/AJPIAS/v71/i2/p104/s1&Agg=doi'), (4393, 'Oersted Medal Lecture 2002: Reforming the mathematical language of physics'), (4394, '2011-10-29 18:46:51'), (4395, 'Oersted Medal Lecture 2002'), (4396, 'AJP000104.pdf'), (4397, 691), (4398, '10.1119/1.1571836'), (4399, 'http://link.aip.org/link/AJPIAS/v71/i7/p691/s1&Agg=doi'), (4400, 'Spacetime physics with geometric algebra'), (4401, '2011-10-29 18:48:03'), (4402, 'AJP000691.pdf'), (4403, 'Foundations of Physics'), (4404, 35), (4405, '0015-9018, 1572-9516'), (4406, '2005-06-00 06/2005'), (4407, '903-970'), (4408, '10.1007/s10701-005-5828-y'), (4409, 'http://www.springerlink.com.proxy.library.cornell.edu/content/jt63m68488j71814/'), (4410, 'Gauge Theory Gravity with Geometric Calculus'), (4411, '2011-10-29 18:59:43'), (4412, 'fulltext-5.pdf'), (4413, 'Electromagnetic extraction of energy from Kerr black holes'), (4414, 179), (4415, '1977-05-01 May 1, 1977'), (4416, '433-456'), (4417, 'http://adsabs.harvard.edu/abs/1977MNRAS.179..433B'), (4418, 'It is shown that if the magnetic field and angular momentum of a Kerr \nblack hole are large enough, the vacuum surrounding the hole is unstable \nbecause any stray charged particles will be electrostatically \naccelerated and will radiate, with the radiation producing \nelectron-positron pairs so freely that the electromagnetic field in the \nvicinity of the event horizon will become approximately force-free. \nEquations governing stationary force-free electromagnetic fields in Kerr \nspacetime are derived, and it is found that energy and angular momentum \ncan be extracted from a rotating black hole by a purely electromagnetic \nmechanism. A perturbation technique is outlined for calculating \napproximate solutions under certain circumstances, and solutions are \nobtained for a split monopole magnetic field as well as for a \nparaboloidal magnetic field. The present concepts are applied to a model \nof an active galactic nucleus containing a massive black hole surrounded \nby an accretion disk.'), (4419, '2011-10-29 19:14:14'), (4420, '2011-10-29 19:14:16'), (4421, '1977MNRAS_179__433B.pdf'), (4422, 'Relativistic Binary Pulsar B1913+16: Thirty Years of Observations and Analysis'), (4423, '2004-07-07 2004-07-07'), (4424, 'http://arxiv.org/abs/astro-ph/0407149'), (4425, 'arXiv:astro-ph/0407149'), (4426, 'We describe results derived from thirty years of observations of PSR B1913+16. Together with the Keplerian orbital parameters, measurements of the relativistic periastron advance and a combination of gravitational redshift and time dilation yield the stellar masses with high accuracy. The measured rate of change of orbital period agrees with that expected from the emission of gravitational radiation, according to general relativity, to within about 0.2 percent. Systematic effects depending on the pulsar distance and on poorly known galactic constants now dominate the error budget, so tighter bounds will be difficult to obtain. Geodetic precession of the pulsar spin axis leads to secular changes in pulse shape as the pulsar-observer geometry changes. This effect makes it possible to model the two-dimensional structure of the beam. We find that the beam is elongated in the latitude direction and appears to be pinched in longitude near its center.'), (4427, '2011-10-30 16:04:02'), (4428, 'Relativistic Binary Pulsar B1913+16'), (4429, 'astro-ph/0407149 PDF'), (4430, 'http://www.arxiv.org/pdf/astro-ph/0407149.pdf'), (4431, '2011-10-30 16:04:07'), (4432, 'Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16'), (4433, '2010-11-02 2010-11-02'), (4434, 'http://arxiv.org/abs/1011.0718'), (4435, 'Astrophys.J.722:1030-1034,2010'), (4436, '10.1088/0004-637X/722/2/1030'), (4437, 'arXiv:1011.0718'), (4438, "We present results of more than three decades of timing measurements of the first known binary pulsar, PSR B1913+16. Like most other pulsars, its rotational behavior over such long time scales is significantly affected by small-scale irregularities not explicitly accounted for in a deterministic model. Nevertheless, the physically important astrometric, spin, and orbital parameters are well determined and well decoupled from the timing noise. We have determined a significant result for proper motion, $\\mu_{\\alpha} = -1.43\\pm0.13$, $\\mu_{\\delta}=-0.70\\pm0.13$ mas yr$^{-1}$. The pulsar exhibited a small timing glitch in May 2003, with ${\\Delta f}/f=3.7\\times10^{-11}$, and a smaller timing peculiarity in mid-1992. A relativistic solution for orbital parameters yields improved mass estimates for the pulsar and its companion, $m_1=1.4398\\pm0.0002 \\ M_{\\sun}$ and $m_2=1.3886\\pm0.0002 \\ M_{\\sun}$. The system's orbital period has been decreasing at a rate $0.997\\pm0.002$ times that predicted as a result of gravitational radiation damping in general relativity. As we have shown before, this result provides conclusive evidence for the existence of gravitational radiation as predicted by Einstein's theory."), (4439, '2011-10-30 16:11:08'), (4440, '1011.0718 PDF'), (4441, 'http://www.arxiv.org/pdf/1011.0718.pdf'), (4442, '2011-10-30 16:11:12'), (4443, 'Linear Stability Analysis and the Speed of Gravitational Waves in Dynamical Chern-Simons Modified Gravity'), (4444, '2010-07-14 2010-07-14'), (4445, 'http://arxiv.org/abs/1007.2429'), (4446, 'arXiv:1007.2429'), (4447, 'We perform a linear stability analysis of dynamical Chern-Simons modified gravity in the geometric optics approximation and find that it is linearly stable on the backgrounds considered. Our analysis also reveals that gravitational waves in the modified theory travel at the speed of light in Minkowski spacetime. However, on a Schwarzschild background the characteristic speed of propagation along a given direction splits into two modes, one subluminal and one superluminal. The width of the splitting depends on the azimuthal components of the propagation vector, is linearly proportional to the mass of the black hole, and decreases with the third inverse power of the distance from the black hole. Radial propagation is unaffected, implying that as probed by gravitational waves the location of the event horizon of the spacetime is unaltered. The analysis further reveals that when a high frequency, pure gravitational wave is scattered from a black hole, a scalar wave of comparable amplitude is excited, and vice-versa.'), (4448, '2011-10-31 00:02:04'), (4449, '1007.2429 PDF'), (4450, 'http://www.arxiv.org/pdf/1007.2429.pdf'), (4451, '2011-10-31 00:02:06'), (4452, 'Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order'), (4453, 124002), (4454, '1998-10-29 October 29, 1998'), (4455, 'http://link.aps.org/doi/10.1103/PhysRevD.58.124002'), (4456, '10.1103/PhysRevD.58.124002'), (4457, 'We derive the gravitational field and equations of motion of compact binary systems up to the 5/2 post-Newtonian approximation of general relativity (where radiation-reaction effects first appear). The approximate post-Newtonian gravitational field might be used in the problem of initial conditions for the numerical evolution of binary black-hole space-times. On the other hand, we recover the Damour-Deruelle 2.5PN equations of motion of compact binary systems. Our method is based on an expression of the post-Newtonian metric valid for general (continuous) fluids. We substitute into the fluid metric the standard stress-energy tensor appropriate for a system of two pointlike particles. We remove systematically the infinite self-field of each particle by means of the Hadamard finite part regularization.'), (4458, '2011-10-31 01:42:09'), (4459, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i12/e124002'), (4460, '2011-10-31 01:42:11'), (4461, 'No hair theorems for positive \\Lambda'), (4462, '2007-02-01 2007-02-01'), (4463, 'http://arxiv.org/abs/gr-qc/0702006'), (4464, 'Phys.Rev.Lett.99:201101,2007'), (4465, '10.1103/PhysRevLett.99.201101'), (4466, 'arXiv:gr-qc/0702006'), (4467, 'We extend all known black hole no-hair theorems to space-times endowed with a positive cosmological constant $\\Lambda.$ Specifically, we prove that static spherical black holes with $\\Lambda>0$ cannot support scalar fields in convex potentials and Proca-massive vector fields in the region between black hole and cosmic horizons. We also demonstrate the existence of at least one type of quantum hair, and of exactly one charged solution for the Abelian Higgs model. Our method of proof can be applied to investigate other types of quantum or topological hair on black holes in the presence of a positive $\\Lambda.$'), (4468, '2011-10-31 16:44:24'), (4469, 'gr-qc/0702006 PDF'), (4470, 'http://www.arxiv.org/pdf/gr-qc/0702006.pdf'), (4471, '2011-10-31 16:44:26'), (4472, 'Chern-Simons Modified General Relativity'), (4473, '2009-07-15 2009-07-15'), (4474, 'http://arxiv.org/abs/0907.2562'), (4475, 'arXiv:0907.2562'), (4476, 'Chern-Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation in particle physics and string theory. In this review, we begin by providing a pedagogical derivation of the three distinct ways such an extension arises: (1) in particle physics, (2) from string theory and (3) geometrically. We then review many exact and approximate, vacuum solutions of the modified theory, and discuss possible matter couplings. Following this, we review the myriad astrophysical, solar system, gravitational wave and cosmological probes that bound Chern-Simons modified gravity, including discussions of cosmic baryon asymmetry and inflation. The review closes with a discussion of possible future directions in which to test and study gravitational parity violation.'), (4477, '2011-10-31 18:18:24'), (4478, '0907.2562 PDF'), (4479, 'http://www.arxiv.org/pdf/0907.2562.pdf'), (4480, '2011-10-31 18:18:33'), (4481, 'LISA: Probing the Universe with Gravitational Waves'), (4482, 'Bulletin of the American Astronomical Society'), (4483, 209), (4484, '2006-12-01 December 1, 2006'), (4485, 990), (4486, 'http://adsabs.harvard.edu/abs/2006AAS...209.7401P'), (4487, 'LISA is a joint NASA/ESA space mission for detection and study of \nlow-frequency gravitational waves in the band from 0.1 mHz to 0.1 Hz. \nThe mission consists of three satellites separated by a nominal distance \nof 5 million kilometers, with precision metrology provided by laser \nranging. LISA will detect many new sources of gravitational waves \nincluding: the inspiral and merger of supermassive black holes resulting \nfrom galaxy mergers anywhere in the observable universe, emission from \nthousands of individual ultra-compact binaries in our galaxy, and \nnumerous cases of inspiral of small black holes, neutrons stars, and \nwhite dwarfs into the supermassive black holes that reside in the nuclei \nof most galaxies. These sources not only provide unique astrophysical \ninformation about the evolution of galaxies and stars, but the systems \ncan also be used as “laboratories” for making precision \nmeasurements of physical phenomena that will lead to new insights into \nfundamental physics and cosmology. In addition to radiation from \nwell-known astrophysical sources, some of the most exciting science may \ncome from LISA searches for gravitational waves from the very early \nuniverse, such as waves from fundamental phase transitions or from the \ndynamics of cosmic superstrings. We survey the science goals of LISA and \ntheir impact on physics and astrophysics.'), (4488, '2011-11-01 02:29:37'), (4489, 'LISA'), (4490, 'Astronomy and astrophysics with gravitational waves in the Advanced Detector Era'), (4491, 'LISA-LIST-RP-436_v1.2.pdf'), (4492, 'A practical guide to the massive black hole cosmic history'), (4493, '2011-10-28 2011-10-28'), (4494, 'http://arxiv.org/abs/1110.6445'), (4495, 'arXiv:1110.6445'), (4496, 'I review our current understanding of massive black hole (MBH) formation and evolution along the cosmic history. After a brief introductory overview of the relevance of MBHs in the hierarchical structure formation paradigm, I discuss the main viable channels for seed BH formation at high redshift and for their subsequent mass growth and spin evolution. The emerging hierarchical picture, where MBHs grow through merger triggered accretion episodes, acquiring their mass while shining as quasars, is overall robust, but too simplistic to explain the diversity observed in MBH phenomenology. I briefly discuss which future observations will help to shed light on the MBH cosmic history in the near future, paying particular attention to the upcoming gravitational wave window.'), (4497, '2011-11-01 13:08:03'), (4498, '1110.6445 PDF'), (4499, 'http://www.arxiv.org/pdf/1110.6445.pdf'), (4500, '2011-11-01 13:08:08'), (4501, '10.1063/PT.3.1332'), (4502, 'http://physicstoday.org.proxy.library.cornell.edu/resource/1/phtoad/v64/i11/p49_s1#figref_f1'), (4503, 'Problems with problem sets'), (4504, '2011-11-01 20:46:38'), (4505, 'PTO000049.pdf'), (4506, 'Towards improving the prospects for coordinated gravitational-wave and electromagnetic observations'), (4507, '2011-10-31 2011-10-31'), (4508, 'http://arxiv.org/abs/1111.0005'), (4509, 'arXiv:1111.0005'), (4510, 'We discuss two approaches to searches for gravitational-wave (GW) and electromagnetic (EM) counterparts of binary neutron star mergers. The first approach relies on triggering archival searches of GW detector data based on detections of EM transients. We introduce a quantitative approach to evaluate the improvement to GW detector reach due to the extra information gained from the EM transient and the increased confidence in the presence of a signal from a binary merger. We also advocate utilizing other transients in addition to short gamma ray bursts. The second approach involves following up GW candidates with targeted EM observations. We argue for the use of slower but optimal parameter-estimation techniques to localize the source on the sky, and for a more sophisticated use of astrophysical prior information, including galaxy catalogs, to find preferred followup locations.'), (4511, '2011-11-02 18:57:09'), (4512, '1111.0005 PDF'), (4513, 'http://www.arxiv.org/pdf/1111.0005.pdf'), (4514, '2011-11-02 18:57:11'), (4515, 'The Constancy of the Constants of Nature: Updates'), (4516, 'http://arxiv.org/abs/1111.0092'), (4517, 'arXiv:1111.0092'), (4518, 'The current observational and experimental bounds on time variation of the constants of nature (the fine structure constant $\\alpha$, the gravitational constant $G$ and the proton-electron mass ratio $\\mu=m_p/m_e$) are reviewed.'), (4519, '2011-11-02 18:59:32'), (4520, 'The Constancy of the Constants of Nature'), (4521, '1111.0092 PDF'), (4522, 'http://www.arxiv.org/pdf/1111.0092.pdf'), (4523, '2011-11-02 18:59:34'), (4524, 'Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a non-vanishing spacelike components of the stress-energy-momentum tensor. In spite of its strange nature, this solution provides with non-trivial descriptions of gravitational effects. We show that the main aspects found in the \\emph{dark matter phenomena} can be satisfactorily described by this geometry. We comment on the relevance it could have to consider non-vanishing spacelike components of the stress-energy-momentum tensor ascribed to dark matter.'), (4525, '2011-11-03 13:47:37'), (4526, '1111.0327 PDF'), (4527, 'http://www.arxiv.org/pdf/1111.0327.pdf'), (4528, '2011-11-03 13:47:41'), (4529, 'On Lorentzian causality with continuous metrics'), (4530, '2011-11-02 2011-11-02'), (4531, 'http://arxiv.org/abs/1111.0400'), (4532, 'arXiv:1111.0400'), (4533, 'We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when metrics which are merely continuous are considered. We show that existence of time functions remains true on domains of dependence with continuous metrics, and that $C^{1,1}$ differentiability of the metric suffices for many key results of the smooth causality theory.'), (4534, '2011-11-03 15:51:16'), (4535, '1111.0400 PDF'), (4536, 'http://www.arxiv.org/pdf/1111.0400.pdf'), (4537, '2011-11-03 15:51:24'), (4538, 134004), (4539, '10.1088/0264-9381/28/13/134004'), (4540, 'http://iopscience.iop.org/0264-9381/28/13/134004'), (4541, '11-orbit inspiral of a mass ratio 4:1 black-hole binary'), (4542, '2011-11-07 23:32:46'), (4543, '11-orbit inspiral of a mass ratio 4'), (4544, 'http://iopscience.iop.org/0264-9381/28/13/134004/pdf/0264-9381_28_13_134004.pdf'), (4545, '2011-11-07 23:32:48'), (4546, 'http://arxiv.org/abs/1112.2202'), (4547, 'Black Holes: The Membrane Paradigm'), (4548, 'Yale University Press'), (4549, 'New Haven, CT'), (4550, 'BHMP_preface_chap1.pdf'), (4551, 'scientificamerican0488-69.pdf'), (4552, 'Gravitational Waves and Time Domain Astronomy'), (4553, '2011-11-07 2011-11-07'), (4554, 'http://arxiv.org/abs/1111.1701'), (4555, 'arXiv:1111.1701'), (4556, 'The gravitational wave window onto the universe will open in roughly five years, when Advanced LIGO and Virgo achieve the first detections of high frequency gravitational waves, most likely coming from compact binary mergers. Electromagnetic follow-up of these triggers, using radio, optical, and high energy telescopes, promises exciting opportunities in multi-messenger time domain astronomy. In the next decade, space-based observations of low frequency gravitational waves from massive black hole mergers, and their electromagnetic counterparts, will open up further vistas for discovery. This two-part workshop at featured brief presentations and stimulating discussions on the challenges and opportunities presented by gravitational wave astronomy. Highlights from the workshop, with the emphasis on strategies for electromagnetic follow-up, are presented in this report.'), (4557, '2011-11-08 17:04:41'), (4558, '1111.1701 PDF'), (4559, 'http://www.arxiv.org/pdf/1111.1701.pdf'), (4560, '2011-11-08 17:04:46'), (4561, 'Black hole-neutron star mergers for 10 solar mass black holes'), (4562, 'http://arxiv.org/abs/1111.1677'), (4563, 'arXiv:1111.1677'), (4564, 'General relativistic simulations of black hole-neutron star mergers have currently been limited to low-mass black holes (less than 7 solar mass), even though population synthesis models indicate that a majority of mergers might involve more massive black holes (10 solar mass or more). We present the first general relativistic simulations of black hole-neutron star mergers with 10 solar mass black holes. For massive black holes, the tidal forces acting on the neutron star are usually too weak to disrupt the star before it reaches the innermost stable circular orbit of the black hole. Varying the spin of the black hole in the range a/M = 0.5-0.9, we find that mergers result in the disruption of the star and the formation of a massive accretion disk only for large spins a/M>0.7-0.9. From these results, we obtain updated constraints on the ability of BHNS mergers to be the progenitors of short gamma-ray bursts as a function of the mass and spin of the black hole. We also discuss the dependence of the gravitational wave signal on the black hole parameters, and provide waveforms and spectra from simulations beginning 7-8 orbits before merger.'), (4565, '2011-11-08 17:04:53'), (4566, '1111.1677 PDF'), (4567, 'http://www.arxiv.org/pdf/1111.1677.pdf'), (4568, '2011-11-08 17:04:56'), (4569, 'Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes'), (4570, '2005-02-14 2005-02-14'), (4571, 'http://arxiv.org/abs/gr-qc/0502064'), (4572, 'Class.Quant.Grav.22:R167,2005; Erratum-ibid.23:4297,2006'), (4573, '10.1088/0264-9381/23/12/C01'), (4574, 'arXiv:gr-qc/0502064'), (4575, 'The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this paper is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of Schwarzschild black hole spacetimes driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes.'), (4576, '2011-11-08 17:15:48'), (4577, 'gr-qc/0502064 PDF'), (4578, 'http://www.arxiv.org/pdf/gr-qc/0502064.pdf'), (4579, '2011-11-08 17:15:51'), (4580, 'Stability of a Schwarzschild Singularity'), (4581, 'Physical Review'), (4582, 'Phys. Rev.'), (4583, 108), (4584, '1063-1069'), (4585, '1957-11-15 November 15, 1957'), (4586, 'http://link.aps.org/doi/10.1103/PhysRev.108.1063'), (4587, '10.1103/PhysRev.108.1063'), (4588, 'It is shown that a Schwarzschild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and will therefore remain stable if subjected to a small nonspherical perturbation.'), (4589, '2011-11-08 17:23:18'), (4590, 'http://prola.aps.org.proxy.library.cornell.edu/pdf/PR/v108/i4/p1063_1'), (4591, '2011-11-08 17:23:20'), (4592, 'Effective Potential for Even-Parity Regge-Wheeler Gravitational Perturbation Equations'), (4593, '737-738'), (4594, '1970-03-30 March 30, 1970'), (4595, 'http://link.aps.org/doi/10.1103/PhysRevLett.24.737'), (4596, '10.1103/PhysRevLett.24.737'), (4597, 'The Schrödinger-type equation for odd-parity perturbations on a background geometry has been extended to the even-parity perturbations. This should greatly simplify the analysis for calculations of gravitational radiation from stars and from objects falling into black holes.'), (4598, '2011-11-08 17:23:28'), (4599, 'PhysRevD.84.064029.pdf'), (4600, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1046/j.1365-8711.1999.02703.x/abstract'), (4601, 'PhysRevLett.24.737.pdf'), (4602, '2009-04-07 2009-04-07'), (4603, '075009'), (4604, '10.1088/0264-9381/26/7/075009'), (4605, 'http://iopscience.iop.org/0264-9381/26/7/075009'), (4606, 'Implementation of higher-order absorbing boundary conditions for the Einstein equations'), (4607, '2011-11-08 17:26:58'), (4608, '10.1046/j.1365-8711.1999.02703.x'), (4609, 308), (4610, '0264-9381_26_7_075009.pdf'), (4611, 'Resonant tidal excitations of rotating neutron stars in coalescing binaries'), (4612, '1999-09-01 1999/09/01'), (4613, '153-166'), (4614, 'In a coalescing neutron star–neutron star or neutron star–black hole binary, oscillation modes of the neutron star can be resonantly excited by the companion during the final minutes of the binary inspiral, when the orbital frequency sweeps up from a few Hz to a few thousand Hz. The resulting resonant energy transfer between the orbit and the neutron star speeds up or slows down the inspiral, depending on whether the resonant mode has positive or negative energy, and induces a phase change in the emitted gravitational waves from the binary. While only g-modes can be excited for a non-rotating neutron star, f-modes and r-modes can also be excited when the neutron star is spinning. A tidal resonance, designated by the index (\xa0jk, m) ({\xa0jk} specifies the angular order of the mode, as in the spherical harmonic Yjk), occurs when the mode frequency equals m times the orbital frequency. For the f-mode resonance to occur before coalescence, the neutron star must have rapid rotation, with spin frequency νs≳710\xa0Hz for the (22,2)-resonance and νs≳570\xa0Hz for the (33,3)-resonance (assuming canonical neutron star mass, M=1.4\xa0M⊙, and radius, R=10\xa0km; however, for R=15\xa0km, these critical spin frequencies become 330 and 260\xa0Hz, respectively). Although current observations suggest that such high rotation rates may be unlikely for coalescing binary neutron stars, these rates are physically allowed. Because of their strong tidal coupling, the f-mode resonances induce a large change in the number of orbital cycles of coalescence, ΔNorb, with the maximum ΔNorb∼10–1000 for the (22,2)-resonance and ΔNorb∼1 for the (33,3)-resonance. Such f-mode resonant effects, if present, must be included in constructing the templates of waveforms used in searching for gravitational wave signals. Higher order f-mode resonances can occur at slower rotation rates, but the induced orbital change is much smaller (ΔNorb≲0.1). For the dominant g-mode (22,2)-resonance, even modest rotation (νs≲100\xa0Hz) can enhance the resonant effect on the orbit by shifting the resonance to a smaller orbital frequency. However, because of the weak coupling between the g-mode and the tidal potential, ΔNorb lies in the range 10−3–10−2 (depending strongly on the neutron star equation of state) and is probably negligible for the purpose of detecting gravitational waves. Resonant excitations of r-modes require misaligned spin–orbit inclinations, and the dominant resonances correspond to octopolar excitations of the jk=2 mode, with (jk, m)=(22,3) and (22,1). Since the tidal coupling of the r-mode depends strongly on rotation rate, ΔNorb≲10−2(R/10\xa0km)10(M/1.4\xa0M⊙)−20/3 is negligible for canonical neutron star parameters, but can be appreciable if the neutron star radius is larger.'), (4615, '2011-11-13 20:33:19'), (4616, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1046/j.1365-8711.1999.02703.x/asset/j.1365-8711.1999.02703.x.pdf?v=1&t=guyi4qk8&s=6f5e152f902d8a3150bb29a1b78d65af7f5ef11d'), (4617, '2011-11-13 20:33:21'), (4618, 'Cosmological distance indicators by coalescing binaries'), (4619, '2011-11-11 2011-11-11'), (4620, 'http://arxiv.org/abs/1111.2816'), (4621, 'arXiv:1111.2816'), (4622, 'Gravitational waves detected from well-localized inspiraling binaries would allow to determine, directly and independently, both binary luminosity and redshift. In this case, such systems could behave as "standard candles" providing an excellent probe of cosmic distances up to z < 0.1 and thus complementing other indicators of cosmological distance ladder.'), (4623, '2011-11-14 13:59:29'), (4624, '1111.2816 PDF'), (4625, 'http://www.arxiv.org/pdf/1111.2816.pdf'), (4626, '2011-11-14 13:59:33'), (4627, 'The 2.5PN linear momentum flux and associated recoil from inspiralling compact binaries in quasi-circular orbits: Nonspinning case'), (4628, 'http://arxiv.org/abs/1111.2701'), (4629, 'arXiv:1111.2701'), (4630, 'Anisotropic emission of gravitational-waves (GWs) from inspiralling compact binaries leads to the loss of linear momentum and hence gravitational recoil of the system. The loss rate of linear momentum in the far-zone of the source (a nonspinning binary system of black holes in quasi-circular orbit) is investigated at the 2.5 post-Newtonian (PN) order and used to provide an analytical expression in harmonic coordinates for the 2.5PN accurate recoil velocity of the binary accumulated in the inspiral phase. The maximum recoil velocity of the binary system at the end of its inspiral phase (i.e at the innermost stable circular orbit (ISCO)) estimated by the 2.5PN formula is of the order of 4 km/s which is smaller than the 2PN estimate of 22 km/s and indicates the importance of higher order post-Newtonian (PN) corrections. Going beyond inspiral, we also provide an estimate of the more important contribution to the recoil velocity from the plunge phase. The maximum recoil velocity at the end of the plunge, involving contributions both from inspiral and plunge phase, for a binary with symmetric mass ratio $\\nu=0.2$ is of the order of 182 km/s.'), (4631, '2011-11-14 14:13:23'), (4632, 'The 2.5PN linear momentum flux and associated recoil from inspiralling compact binaries in quasi-circular orbits'), (4633, '1111.2701 PDF'), (4634, 'http://www.arxiv.org/pdf/1111.2701.pdf'), (4635, '2011-11-14 14:13:26'), (4636, 'Superconducting Antenna Concept for Gravitational Wave Radiation'), (4637, '2011-11-10 2011-11-10'), (4638, 'http://arxiv.org/abs/1111.2655'), (4639, 'arXiv:1111.2655'), (4640, 'A new concept for detectors of gravitational wave radiation is discussed. Estimates of its sensitivity suggest that these devices will be able to detect gravitational waves with amplitudes as low as h0~10-26. Such sensitivity could be obtained at spatial scales as small as 10 meters. Devices based on this concept require operational temperatures below the critical temperatures of their superconducting components.'), (4641, '2011-11-14 14:15:02'), (4642, '1111.2655 PDF'), (4643, 'http://www.arxiv.org/pdf/1111.2655.pdf'), (4644, '2011-11-14 14:15:06'), (4645, 'Lagrangian perturbation theory of nonrelativistic fluids'), (4646, 221), (4647, '1978-05-01 May 1, 1978'), (4648, '937-957'), (4649, 'http://adsabs.harvard.edu/abs/1978ApJ...221..937F'), (4650, 'The reported investigation is concerned with fluid perturbation theory \nand with the secular instability of rotating Newtonian stars. A \nformalism is developed for perturbations of a stationary Newtonian \nfluid, and a description is introduced of fluid perturbations in terms \nof a Lagrangian displacement. The class of trivial displacements is \nidentified, and an explicit form is obtained for the generic trivial. \nThe formal structure of the perturbation equations is considered. The \ncanonical energy and angular momentum are introduced, together with two \nrelated dynamically conserved inner products. It is found that the \ncanonical energy and angular momentum do not vanish on trivial \ndisplacements. An explicit relation is obtained between the canonical \nand physical conserved quantities. The inner products are used to \ncharacterize a dynamically invariant class of canonical displacements \northogonal to the trivials.'), (4651, '2011-11-14 16:22:25'), (4652, 'http://arxiv.org/abs/1112.4821'), (4653, '1978ApJ___221__937F.pdf'), (4654, 'Secular instability of rotating Newtonian stars'), (4655, 222), (4656, '281-296'), (4657, 'http://adsabs.harvard.edu/abs/1978ApJ...222..281F'), (4658, 'The effect of gravitational radiation and of viscosity on the stability \nof rotating self-gravitating fluids is analyzed. It is found that all \nrotating stars are unstable or marginally unstable to gravitational \nradiation. The stability criterion for stability against viscosity is \nshown to involve the canonical energy in a rotating frame, a functional \ninvariant under gauge transformations associated with the trivial \ndisplacements. A star is locally stable against viscosity if and only if \nthe specific entropy increases outward (in the sense of decreasing \npressure). The behavior of normal modes is considered and applied to \nelucidate the generic radiation-induced instability.'), (4659, '2011-11-14 16:23:15'), (4660, 'arXiv:1112.4821'), (4661, '1978ApJ___222__281F.pdf'), (4662, 'Courses of Study 2010-2011'), (4663, 'http://registrar.sas.cornell.edu/CoSArchive/Courses10/CoSdetail.php?college=AS&number=1112&prefix=PHYS&title=Physics+I%3A+Mechanics+%28PBS%29'), (4664, '2011-11-17 18:45:18'), (4665, 'PhysRevD.72.083005.pdf'), (4666, 'Le Voyage dans la Lune (Uni Music) - 1902 HQ restored - A Trip to the Moon'), (4667, '2011-08-14 2011-08-14'), (4668, 'http://www.youtube.com/watch?v=uMBkDT_eG5g&feature=youtube_gdata_player'), (4669, '763 seconds'), (4670, "Путешествие на Луну - 月球旅行记 - Viaje a la Luna - 달세계 여행 - Die Reise zum Mond - מסע אל הירח - Viaggio nella Luna - Resan till månen - رحلة إلى القمر - Viagem à Lua - Georges Méliès - Ένα ταξίδι στο φεγγάρι - Жорж Мельес - చంద్రుడు, ఒక ట్రిప్ - Journey to the Moon - चंद्रमा के लिए एक यात्रा - Le Voyage dans la Lune - การเดินทางไปดวงจันทร์ - A Trip to the Moon - Tá Turas go dtí an Ghealach\n\nРеставрация: Красный кофе\n\nФильм считается одним из безусловных шедевров раннего кинематографа благодаря постановочной изобретательности Мельеса: он блистательно выдержал ироническую интонацию и наполнил картину спецэффектами, большинство которых изобрёл сам.\nХрестоматийную известность приобрёл кадр, где снаряд попадает Луне прямо в глаз.\n\nA Trip to the Moon is the first science fiction film, and uses innovative animation and special effects, including the well-known image of the spaceship landing in the moon's eye.\n\nL'art muet franchit un cap et ouvre de nouvelles perspectives à la production cinématographique de ce début de siècle. Le Voyage dans la Lune a été projeté dans le monde entier avec un égal succès. Il fut même abondamment plagié. Néanmoins, c'est encore le réalisateur lui-même qui s'y illustra le mieux jusqu'à ce que le genre féerique qu'il a créé tombe en désuétude.\n\n《月球旅行记》是一部1902年拍摄的法国黑白无声科幻电影，英文名为A Trip to the Moon。这部电影大致上基于儒勒·凡尔纳的小说《从地球到月球》以及赫伯特·乔治·威尔斯的小说《最早登上月球的人》。乔治·梅里爱 担任了这部电影的编剧和导演.\n\nThis movie use for nonprofit educational purposes."), (4671, 'YouTube'), (4672, '2011-11-19 04:01:05'), (4673, 'The OPERA neutrino experiment at the underground Gran Sasso Laboratory has measured the velocity of neutrinos from the CERN CNGS beam over a baseline of about 730 km with much higher accuracy than previous studies conducted with accelerator neutrinos. The measurement is based on high-statistics data taken by OPERA in the years 2009, 2010 and 2011. Dedicated upgrades of the CNGS timing system and of the OPERA detector, as well as a high precision geodesy campaign for the measurement of the neutrino baseline, allowed reaching comparable systematic and statistical accuracies. An early arrival time of CNGS muon neutrinos with respect to the one computed assuming the speed of light in vacuum of (57.8 \\pm 7.8 (stat.)+8.3-5.9 (sys.)) ns was measured. This anomaly corresponds to a relative difference of the muon neutrino velocity with respect to the speed of light (v-c)/c = (2.37 \\pm 0.32 (stat.) (sys.)) \\times10-5. The above result, obtained by comparing the time distributions of neutrino interactions and of protons hitting the CNGS target in 10.5 {\\mu}s long extractions, was confirmed by a test performed using a beam with a short-bunch time-structure allowing to measure the neutrino time of flight at the single interaction level.'), (4674, '2011-11-19 15:29:14'), (4675, '2011-11-19 15:30:24'), (4676, 'Geometric (Clifford) algebra and its applications'), (4677, '2006-05-10 2006-05-10'), (4678, 'http://arxiv.org/abs/math/0605280'), (4679, 'Trita-MAT. MA, ISSN 1401-2278; 2006:01'), (4680, 'arXiv:math/0605280'), (4681, 'In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to define Clifford algebras with scalars in arbitrary rings and provides new suggestions for an infinite-dimensional approach. Furthermore, I give a quick review of classic results regarding geometric algebras, such as their classification in terms of matrix algebras, the connection to orthogonal and Spin groups, and their representation theory. A number of lower-dimensional examples are worked out in a systematic way using so called norm functions, while general applications of representation theory include normed division algebras and vector fields on spheres. I also consider examples in relativistic physics, where reformulations in terms of geometric algebra give rise to both computational and conceptual simplifications.'), (4682, '2011-11-22 15:24:34'), (4683, 'math/0605280 PDF'), (4684, 'http://www.arxiv.org/pdf/math/0605280.pdf'), (4685, '2011-11-22 15:24:40'), (4686, 'Clifford v. Timms ; Clifford v. Phillips ; Hill v. Clifford.'), (4687, 'The Lancet'), (4688, 169), (4689, 4373), (4690, '1721-1722'), (4691, '1907-06-22 June 22, 1907'), (4692, '0140-6736'), (4693, '10.1016/S0140-6736(01)48193-1'), (4694, 'http://www.sciencedirect.com/science/article/pii/S0140673601481931'), (4695, '2011-11-22 15:29:32'), (4696, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271074&_user=492137&_pii=S0140673601481931&_check=y&_origin=&_coverDate=22-Jun-1907&view=c&wchp=dGLzVlt-zSkzS&md5=197ceaa203d791ad76809cba3d27252a/1-s2.0-S0140673601481931-main.pdf'), (4697, '2011-11-22 15:29:34'), (4698, 'Reconstructing the Neutron-Star Equation of State from Astrophysical Measurements'), (4699, '2009-05-12 2009-05-12'), (4700, 'http://arxiv.org/abs/0905.1959'), (4701, 'Phys.Rev.D80:103003,2009'), (4702, '10.1103/PhysRevD.80.103003'), (4703, 'arXiv:0905.1959'), (4704, 'The properties of matter at ultra-high densities, low temperatures, and with a significant asymmetry between protons and neutrons can be studied exclusively through astrophysical observations of neutron stars. We show that measurements of the masses and radii of neutron stars can lead to tight constraints on the pressure of matter at three fiducial densities, from 1.85 to 7.4 times the density of nuclear saturation, in a manner that is largely model-independent and that captures the key characteristics of the equation of state. We demonstrate that observations with 10% uncertainties of at least three neutron stars can lead to measurements of the pressure at these fiducial densities with an accuracy of 0.11 dex or ~ 30%. Observations of three neutron stars with 5% uncertainties are sufficient to distinguish at a better than 3-sigma confidence level between currently proposed equations of state. In the electromagnetic spectrum, such accurate measurements will become possible for weakly-magnetic neutron stars during thermonuclear flashes and in quiescence with future missions such as the International X-ray Observatory (IXO).'), (4705, '2011-11-23 05:04:22'), (4706, '0905.1959 PDF'), (4707, 'http://www.arxiv.org/pdf/0905.1959.pdf'), (4708, '2011-11-23 05:04:24'), (4709, 'Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence: Further investigations'), (4710, '2011-11-22 2011-11-22'), (4711, 'http://arxiv.org/abs/1111.5274'), (4712, 'arXiv:1111.5274'), (4713, 'Coalescences of binary neutron stars and/or black holes are candidate sources for the first direct detection of gravitational waves. These events will also provide us with the very first empirical access to the genuinely strong-field dynamics of General Relativity (GR). We elaborate on a framework based on Bayesian model selection aimed at detecting deviations from GR, subject to the constraints of Advanced Virgo and LIGO detectors, first introduced by Li et al. (2011). The key aspect of the framework is testing the consistency of the post-Newtonian gravitational-wave phase coefficients in the inspiral regime with the predictions made by GR, without relying on any specific alternative theory of gravity. The framework is suitable for low signal-to-noise events through construction of multiple subtests, most of which involving only a limited number of phase coefficients. The framework also naturally allows for the combination of multiple sources to increase the information extracted for GR testing. In our previous work, we conjectured that this framework can detect generic deviations from GR that can in principle not be accomodated by our model waveforms, on condition that the change in phase near frequencies where the detectors are the most sensitive is comparable to that induced by simple shifts in the lower-order phase coefficients of more than a few percent. To further support this claim, we perform additional numerical experiments in Gaussian and stationary noise according to the expected Advanced LIGO/Virgo noise curves, and injecting signals whose phasing differs structurally from the predictions of GR, but with the magnitude of the deviation still being small. We find that even then, a violation of GR can be established with good confidence.'), (4714, '2011-11-23 14:37:13'), (4715, 'Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence'), (4716, '1111.5274 PDF'), (4717, 'http://www.arxiv.org/pdf/1111.5274.pdf'), (4718, '2011-11-23 14:37:22'), (4719, 'The Gravitational Wave International Committee Roadmap: The future of gravitational wave astronomy'), (4720, '2011-11-24 2011-11-24'), (4721, 'http://arxiv.org/abs/1111.5825'), (4722, 'arXiv:1111.5825'), (4723, "Gravitational wave science is on the verge of direct observation of the waves predicted by Einstein's General Theory of Relativity and opening the exciting new field of gravitational wave astronomy. In the coming decades, ultra-sensitive arrays of ground-based instruments and complementary spaced-based instruments will observe the gravitational wave sky, inevitably discovering entirely unexpected phenomena while providing new insight into many of the most profound astrophysical phenomena known. in July 2007 the Gravitational Wave International Committee (GWIC) initiated the development of a strategic roadmap for the field of gravitational wave science with a 30-year horizon. The goal of this roadmap is to serve the international gravitational wave community and its stakeholders as a tool for the development of capabilities and facilities needed to address the exciting scientific opportunities on the intermediate and long-term horizons."), (4724, '2011-11-28 13:20:40'), (4725, 'The Gravitational Wave International Committee Roadmap'), (4726, '1111.5825 PDF'), (4727, 'http://www.arxiv.org/pdf/1111.5825.pdf'), (4728, '2011-11-28 13:21:18'), (4729, '2011-11-28 16:05:17'), (4730, '2011-11-28 16:05:35'), (4731, 'Reduced basis catalogs for gravitational wave templates'), (4732, '2011-01-19 2011-01-19'), (4733, 'http://arxiv.org/abs/1101.3765'), (4734, 'Phys.Rev.Lett.106:221102,2011'), (4735, '10.1103/PhysRevLett.106.221102'), (4736, 'arXiv:1101.3765'), (4737, 'We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for non-spinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about $10-10^5$ fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.'), (4738, '2011-11-28 19:55:26'), (4739, '1101.3765 PDF'), (4740, 'http://www.arxiv.org/pdf/1101.3765.pdf'), (4741, '2011-11-28 19:55:33'), (4742, 'Imprint of the merger and ring-down on the gravitational wave background from black hole binaries coalescence'), (4743, '2011-11-25 2011-11-25'), (4744, 'http://arxiv.org/abs/1111.6125'), (4745, 'arXiv:1111.6125'), (4746, 'We compute the gravitational wave background (GWB) generated by a cosmological population of (BH-BH) binaries using hybrid waveforms recently produced by numerical simulations of (BH-BH) coalescence, which include the inspiral, merger and ring-down contributions. A large sample of binary systems is simulated using the population synthesis code SeBa, and we extract fundamental statistical information on (BH-BH) physical parameters (primary and secondary BH masses, orbital separations and eccentricities, formation and merger timescales). We then derive the binary birth and merger rates using the theoretical cosmic star formation history obtained from a numerical study which reproduces the available observational data at redshifts $z < 8$. We evaluate the contributions of the inspiral, merger and ring-down signals to the GWB, and discuss how these depend on the parameters which critically affect the number of coalescing (BH-BH) systems. We find that Advanced LIGO/Virgo have a chance to detect the GWB signal from the inspiral phase with a $(S/N)=10$ only for the most optimistic model, which predicts the highest local merger rate of 0.85 Mpc$^{-3}$ Myr$^{-1}$. Third generation detectors, such as ET, could reveal the GWB from the inspiral phase predicted by any of the considered models. In addition, ET could sample the merger phase of the evolution at least for models which predict local merger rates between $[0.053 - 0.85]$ Mpc$^{-3}$ Myr$^{-1}$, which are more than a factor 2 lower the the upper limit inferred from the analysis of the LIGO S5 run\\cite{Abadieetal2011}.'), (4747, '2011-11-29 15:49:10'), (4748, '1111.6125 PDF'), (4749, 'http://www.arxiv.org/pdf/1111.6125.pdf'), (4750, '2011-11-29 15:49:41'), (4751, 'Tidal interaction in compact binaries: a post-Newtonian affine framework'), (4752, '2011-11-28 2011-11-28'), (4753, 'http://arxiv.org/abs/1111.6607'), (4754, 'arXiv:1111.6607'), (4755, 'We develop a semi-analytical approach, based on the post-Newtonian expansion and on the affine approximation, to model the tidal deformation of neutron stars in the coalescence of black hole-neutron star or neutron star-neutron star binaries. Our equations describe, in a unified framework, both the system orbital evolution, and the neutron star deformations. These are driven by the tidal tensor, which we expand at 1/c^3 post-Newtonian order, including spin terms. We test the theoretical framework by simulating black hole-neutron star coalescence up to the onset of mass shedding, which we determine by comparing the shape of the star with the Roche lobe. We validate our approach by comparing our results with those of fully relativistic, numerical simulations.'), (4756, '2011-11-30 14:54:23'), (4757, 'Tidal interaction in compact binaries'), (4758, '1111.6607 PDF'), (4759, 'http://www.arxiv.org/pdf/1111.6607.pdf'), (4760, '2011-11-30 14:54:25'), (4761, '10.1103/PhysRevD.80.084018'), (4762, 'In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body’s internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.'), (4763, 'Toward Early-Warning Detection of Gravitational Waves from Compact Binary Coalescence'), (4764, 'http://prd.aps.org/pdf/PRD/v80/i8/e084018'), (4765, '2011-07-13 2011-07-13'), (4766, '2011-11-30 18:22:42'), (4767, '2011-11-30 18:22:44'), (4768, 'Relativistic tidal properties of neutron stars'), (4769, '084035'), (4770, '2009-10-23 October 23, 2009'), (4771, 'http://link.aps.org/doi/10.1103/PhysRevD.80.084035'), (4772, '10.1103/PhysRevD.80.084035'), (4773, 'We study the various linear responses of neutron stars to external relativistic tidal fields. We focus on three different tidal responses, associated to three different tidal coefficients: (i) a gravito-electric-type coefficient Gμℓ=[length]2ℓ+1 measuring the ℓth-order mass multipolar moment GMa1…aℓ induced in a star by an external ℓth-order gravito-electric tidal field Ga1…aℓ; (ii) a gravito-magnetic-type coefficient Gσℓ=[length]2ℓ+1 measuring the ℓth spin multipole moment GSa1…aℓ induced in a star by an external ℓth-order gravito-magnetic tidal field Ha1…aℓ; and (iii) a dimensionless “shape” Love number hℓ measuring the distortion of the shape of the surface of a star by an external ℓth-order gravito-electric tidal field. All the dimensionless tidal coefficients Gμℓ/R2ℓ+1, Gσℓ/R2ℓ+1, and hℓ (where R is the radius of the star) are found to have a strong sensitivity to the value of the star’s “compactness” c≡GM/(c02R) (where we indicate by c0 the speed of light). In particular, Gμℓ/R2ℓ+1∼kℓ is found to strongly decrease, as c increases, down to a zero value as c is formally extended to the “black hole (BH) limit” cBH=1/2. The shape Love number hℓ is also found to significantly decrease as c increases, though it does not vanish in the formal limit c→cBH, but is rather found to agree with the recently determined shape Love numbers of black holes. The formal vanishing of μℓ and σℓ as c→cBH is a consequence of the no-hair properties of black holes. This vanishing suggests, but in no way proves, that the effective action describing the gravitational interactions of black holes may not need to be augmented by nonminimal worldline couplings.'), (4774, '2011-11-30 18:23:24'), (4775, 'http://prd.aps.org/pdf/PRD/v80/i8/e084035'), (4776, '2011-11-30 18:23:26'), (4777, '2011-12-05 2011-12-05'), (4778, 'http://arxiv.org/abs/1112.1057'), (4779, 'arXiv:1112.1057'), (4780, 'With the advanced gravitational wave detectors coming on line in the next 5 years, we expect to make the first detections of gravitational waves from astrophysical sources, and study the properties of the waves themselves as tests of General Relativity. In addition, these gravitational waves will be powerful tools for the study of their astrophysical sources and source populations. They carry information that is quite complementary to what can be learned from electromagnetic or neutrino observations, probing the central gravitational engines that power the electromagnetic emissions. Preparations are being made to enable near-simultaneous observations of both gravitational wave and electromagnetic observations of transient sources, using low-latency search pipelines and rapid sky localization. We will review the many opportunities for multi-messenger astronomy and astrophysics with gravitational waves enabled by the advanced detectors, and the preparations that are being made to quickly and fully exploit them.'), (4781, '2011-12-06 16:15:33'), (4782, '1112.1057 PDF'), (4783, 'http://www.arxiv.org/pdf/1112.1057.pdf'), (4784, '2011-12-06 16:15:35'), (4785, 'The Angular Momenta of Neutron Stars and Black Holes as a Window on Supernovae'), (4786, '2011-02-07 2011-02-07'), (4787, 'http://arxiv.org/abs/1102.1500'), (4788, 'arXiv:1102.1500'), (4789, 'It is now clear that a subset of supernovae display evidence for jets and are observed as gamma-ray bursts. The angular momentum distribution of massive stellar endpoints provides a rare means of constraining the nature of the central engine in core-collapse explosions. Unlike supermassive black holes, the spin of stellar-mass black holes in X-ray binary systems is little affected by accretion, and accurately reflects the spin set at birth. A modest number of stellar-mass black hole angular momenta have now been measured using two independent X-ray spectroscopic techniques. In contrast, rotation-powered pulsars spin-down over time, via magnetic braking, but a modest number of natal spin periods have now been estimated. For both canonical and extreme neutron star parameters, statistical tests strongly suggest that the angular momentum distributions of black holes and neutron stars are markedly different. Within the context of prevalent models for core-collapse supernovae, the angular momentum distributions are consistent with black holes typically being produced in GRB-like supernovae with jets, and with neutron stars typically being produced in supernovae with too little angular momentum to produce jets via magnetohydrodynamic processes. It is possible that neutron stars are imbued with high spin initially, and rapidly spun-down shortly after the supernova event, but the available mechanisms may be inconsistent with some observed pulsar properties.'), (4790, '2011-12-07 20:47:50'), (4791, '1102.1500 PDF'), (4792, 'http://www.arxiv.org/pdf/1102.1500.pdf'), (4793, '2011-12-07 20:47:57'), (4794, 'Singular value decomposition applied to compact binary coalescence gravitational-wave signals'), (4795, '044025'), (4796, 'http://link.aps.org/doi/10.1103/PhysRevD.82.044025'), (4797, '10.1103/PhysRevD.82.044025'), (4798, 'We investigate the application of the singular value decomposition to compact-binary, gravitational-wave data-analysis. We find that the truncated singular value decomposition reduces the number of filters required to analyze a given region of parameter space of compact-binary coalescence waveforms by an order of magnitude with high reconstruction accuracy. We also compute an analytic expression for the expected signal loss due to the singular value decomposition truncation.'), (4799, '2011-12-08 01:33:30'), (4800, 'http://prd.aps.org/pdf/PRD/v82/i4/e044025'), (4801, '2011-12-08 01:33:32'), (4802, '2011-12-08 01:34:17'), (4803, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v82/i4/e044025'), (4804, '2011-12-08 01:34:19'), (4805, 'Accessibility of the Gravitational-Wave Background due to Binary Coalescences to Second and Third Generation Gravitational-Wave Detectors'), (4806, '2011-12-08 2011-12-08'), (4807, 'http://arxiv.org/abs/1112.1898'), (4808, 'arXiv:1112.1898'), (4809, "Compact binary coalescences, such as binary neutron stars or black holes, are among the most promising candidate sources for the current and future terrestrial gravitational-wave detectors. While such sources are best searched using matched template techniques and chirp template banks, integrating chirp signals from binaries over the entire Universe also leads to a gravitational-wave background (GWB). In this paper we systematically scan the parameter space for the binary coalescence GWB models, taking into account uncertainties in the star formation rate and in the delay time between the formation and coalescence of the binary, and we compare the computed GWB to the sensitivities of the second and third generation gravitational-wave detector networks. We find that second generation detectors are likely to detect the binary coalescence GWB, while the third generation detectors will probe most of the available parameter space. The binary coalescence GWB will, in fact, be a foreground for the third-generation detectors, potentially masking the GWB background due to cosmological sources. Accessing the cosmological GWB with third generation detectors will therefore require identification and subtraction of all inspiral signals from all binaries in the detectors' frequency band."), (4810, '2011-12-09 15:40:31'), (4811, '1112.1898 PDF'), (4812, 'http://www.arxiv.org/pdf/1112.1898.pdf'), (4813, '2011-12-09 15:40:33'), (4814, 'arXiv:1112.2202'), (4815, 'I comment about the adequacy of the GPS to model a particularly defined synchronization in a rotating frame of reference described in a general relativistic framework.'), (4816, '2011-12-12 16:28:19'), (4817, '1112.2202 PDF'), (4818, 'http://www.arxiv.org/pdf/1112.2202.pdf'), (4819, '2011-12-12 16:28:21'), (4820, 'What if ... General Relativity is not the theory?'), (4821, '2011-12-09 2011-12-09'), (4822, 'http://arxiv.org/abs/1112.2048'), (4823, 'arXiv:1112.2048'), (4824, "The nature of gravity is fundamental to understand the scaffolding of the Universe and its evolution. Einstein's general theory of relativity has been scrutinized for over ninety five years and shown to describe accurately all phenomena from the solar system to the Universe. However, this success is achieved in the case of the largest scales provided one admits contributions to energy-momentum tensor involving dark components such as dark energy and dark matter. Moreover, the theory has well known shortcomings, such as the problem of singularities, the cosmological constant problem and the well known initial conditions problems for the cosmological description. Furthermore, general relativity also does not fit the well known procedures that allow for the quantization of the other fundamental interactions. In this discussion we briefly review the experimental bounds on the foundational principles of general relativity, and present three recent proposals to extend general relativity or, at least, to regard it under different perspectives."), (4825, '2011-12-12 16:47:07'), (4826, '1112.2048 PDF'), (4827, 'http://www.arxiv.org/pdf/1112.2048.pdf'), (4828, '2011-12-12 16:47:11'), (4829, 'Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries and its effective-one-body representation'), (4830, '2011-12-13 2011-12-13'), (4831, 'http://arxiv.org/abs/1112.2840'), (4832, 'arXiv:1112.2840'), (4833, 'We propose, within the effective one body (EOB) approach, a new, resummed, analytical representation of the gravitational wave energy flux absorbed by a system of two circularized (nonspinning) black holes. This expression is such to be well-behaved in the strong-field, fast motion regime, notably up to the EOB-defined last unstable orbit. Building conceptually upon the procedure adopted to resum the multipolar asymptotic energy flux, we introduce a {\\it multiplicative} decomposition of the multipolar absorbed flux made by three factors: (i) the leading-order contribution, (ii) an "effective source" and (iii) a new residual amplitude correction $(\\tilde{\\rho}_\\lm^H)^{2\\ell}$. In the test-mass limit, we use a frequency-domain perturbative approach to accurately compute numerically the horizon-absorbed fluxes along a sequence of stable and unstable circular orbits and we extract from them the functions $\\tilde{\\rho}_\\lm^H$. These quantities are then fitted via rational functions. The resulting analytically represented test-mass knowledge is then suitably {\\it hybridized} with lower-order analytical information that is valid for any mass ratio. This yields a resummed representation of the absorbed flux for a generic, circularized, nonspinning black-hole binary. Our result adds new information to the state-of-the-art calculation of the absorbed flux at fractional 5 post-Newtonian order [S. Taylor and E. Poisson, Phys. Rev. D {\\bf 78} 084016 (2008)], that is recovered in the weak-field limit approximation by construction.'), (4834, '2011-12-14 15:17:13'), (4835, '1112.2840 PDF'), (4836, 'http://www.arxiv.org/pdf/1112.2840.pdf'), (4837, '2011-12-14 15:17:17'), (4838, 'Nonrotating black hole in a post-Newtonian tidal environment'), (4839, '2008-10-09 October 09, 2008'), (4840, 'http://link.aps.org/doi/10.1103/PhysRevD.78.084016'), (4841, '10.1103/PhysRevD.78.084016'), (4842, 'We examine the motion and tidal dynamics of a nonrotating black hole placed within a post-Newtonian external spacetime. The black hole’s gravity is described accurately to all orders in Gm/c2r, where m is the black-hole mass and r is the distance to the black hole. The tidal perturbation created by the external environment is treated as a small perturbation. At a large distance from the black hole, the gravitational field of the external distribution of matter is assumed to be sufficiently weak to be adequately described by the (first) post-Newtonian approximation to general relativity. There, the black hole is treated as a monopole contribution to the total gravitational field. There exists an overlap in the domains of validity of each description, and the black-hole and post-Newtonian metrics are matched in the overlap. The matching procedure produces (i) a justification of the statement that a nonrotating black hole is a post-Newtonian monopole; (ii) a complete characterization of the coordinate transformation between the inertial, barycentric frame and the accelerated, black-hole frame; (iii) the equations of motion for the black hole; and (iv) the gravito-electric and gravito-magnetic tidal fields acting on the black hole. We first calculate the equations of motion and tidal fields by making no assumptions regarding the nature of the post-Newtonian environment; this could contain a continuous distribution of matter (so as to model a galactic core) or any number of condensed bodies. We next specialize our discussion to a situation in which the black hole is a member of a post-Newtonian two-body system. As an application of our results, we examine the geometry of the deformed event horizon and calculate the tidal heating of the black hole, the rate at which it acquires mass as a result of its tidal interaction with the companion body.'), (4843, '2011-12-14 15:20:07'), (4844, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i8/e084016'), (4845, '2011-12-14 15:20:09'), (4846, 'Quantum mechanics from a universal action reservoir'), (4847, '2006-05-08 2006-05-08'), (4848, 'http://arxiv.org/abs/physics/0605068'), (4849, 'arXiv:physics/0605068'), (4850, 'A heuristic derivation of quantum mechanics using information theory requires a foundational physical principle: the existence of a universal action reservoir, analogous to the energy reservoir of a canonical ensemble.'), (4851, '2011-12-14 18:36:03'), (4852, 'physics/0605068 PDF'), (4853, 'http://www.arxiv.org/pdf/physics/0605068.pdf'), (4854, '2011-12-14 18:36:05'), (4855, 'Can binary mergers produce maximally spinning black holes?'), (4856, '084030'), (4857, '2008-10-23 October 23, 2008'), (4858, 'http://link.aps.org/doi/10.1103/PhysRevD.78.084030'), (4859, '10.1103/PhysRevD.78.084030'), (4860, 'Gravitational waves carry away both energy and angular momentum as binary black holes inspiral and merge. The relative efficiency with which they are radiated determines whether the final black hole of mass Mf and spin Sf saturates the Kerr limit (χf≡Sf/Mf2≤1). Extrapolating from the test-particle limit, we propose expressions for Sf and Mf for mergers with initial spins aligned or anti-aligned with the orbital angular momentum. We predict the the final spin at plunge for equal-mass nonspinning binaries to better than 1%, and that equal-mass maximally spinning aligned mergers lead to nearly maximally spinning final black holes (χf≃0.9988). We also find black holes can always be spun up by aligned mergers provided the mass ratio is small enough.'), (4861, '2011-12-16 15:31:21'), (4862, 'http://prd.aps.org/pdf/PRD/v78/i8/e084030'), (4863, '2011-12-16 15:31:23'), (4864, "The motion of a charged particle is influenced by the self-force arising from the particle's interaction with its own field. In a curved spacetime, this self-force depends on the entire past history of the particle and is difficult to evaluate. As a result, all existing self-force evaluations in curved spacetime are for particles moving along a fixed trajectory. Here, for the first time, we overcome this longstanding limitation and present fully self-consistent orbits and waveforms of a scalar charged particle around a Schwarzschild black hole."), (4865, '2011-12-21 21:58:02'), (4866, '1112.4821 PDF'), (4867, 'http://www.arxiv.org/pdf/1112.4821.pdf'), (4868, '2011-12-21 21:58:10'), (4869, 'http://arxiv.org/abs/1107.2665'), (4870, 'arXiv:1107.2665'), (4871, 'Rapid detection of compact binary coalescence with a network of advanced gravitational-wave detectors will offer a unique opportunity for multi-messenger astronomy. Prompt detection alerts for the astronomical community might make it possible to observe the onset of electromagnetic emission from compact binary coalescence. We demonstrate a computationally practical filtering strategy that could produce early-warning triggers before gravitational radiation from the final merger has arrived at the detectors.'), (4872, '2012-01-20 09:58:43'), (4873, '1107.2665 PDF'), (4874, 'http://www.arxiv.org/pdf/1107.2665.pdf'), (4875, '2012-01-20 09:58:51'), (4876, 'Is J enough? Comparison of gravitational waves emitted along the total angular momentum direction with other preferred orientations'), (4877, '2012-01-10 2012-01-10'), (4878, 'http://arxiv.org/abs/1201.2113'), (4879, 'arXiv:1201.2113'), (4880, 'The gravitational wave signature emitted from a merging binary depends on the orientation of an observer relative to the binary. Previous studies suggest that emission along the total initial or total final angular momenta leads to both the strongest and simplest signal from a precessing compact binary. In this paper we describe a concrete counterexample: a binary with $m_1/m_2=4$, $a_1=0.6 \\hat{x} = -a_2$, placed in orbit in the x,y plane. We extract the gravitational wave emission along several proposed emission directions, including the initial (Newtonian) orbital angular momentum; the final (~ initial) total angular momentum; and the dominant principal axis of $<L_a L_b>_M$. Using several diagnostics, we show that the suggested preferred directions are not representative. For example, only for a handful of other directions (< 15%) will the gravitational wave signal have comparable shape to the one extracted along each of these fiducial directions, as measured by a generalized overlap (>0.95). We conclude that the information available in just one direction (or mode) does not adequately encode the complexity of orientation-dependent emission for even short signals from merging black hole binaries. Future investigations of precessing, unequal-mass binaries should carefully explore and model their orientation-dependent emission.'), (4881, '2012-01-20 10:28:15'), (4882, 'Is J enough?'), (4883, '1201.2113 PDF'), (4884, 'http://www.arxiv.org/pdf/1201.2113.pdf'), (4885, '2012-01-20 10:28:26'), (4886, 'Direct Measurement of the Positive Acceleration of the Universe and Testing Inhomogeneous Models under Gravitational Wave Cosmology'), (4887, '2011-12-27 2011-12-27'), (4888, 'http://arxiv.org/abs/1112.6040'), (4889, 'arXiv:1112.6040'), (4890, 'One possibility for explaining the apparent accelerating expansion of the universe is that we live in the center of a spherically inhomogeneous universe. Although current observations cannot fully distinguish $\\Lambda$CDM and these inhomogeneous models, direct measurement of the acceleration of the universe can be a powerful tool in probing them. We have shown that, if $\\Lambda$CDM is the correct model, DECIGO/BBO would be able to detect the positive redshift drift (which is the time evolution of the source redshift $z$) in 3--5 year gravitational wave (GW) observations from neutron-star binaries, which enables us to rule out any Lema\\^itre-Tolman-Bondi (LTB) void model with monotonically increasing density profile. We may even be able to rule out any LTB model unless we allow unrealistically steep density profile at $z\\sim 0$. This test can be performed with GW observations alone, without any reference to electromagnetic observations, and is more powerful than the redshift drift measurement using Lyman $\\alpha$ forest.'), (4891, '2012-01-20 10:36:11'), (4892, '1112.6040 PDF'), (4893, 'http://www.arxiv.org/pdf/1112.6040.pdf'), (4894, '2012-01-20 10:36:15'), (4895, 'Non-sky-averaged sensitivity curves for space-based gravitational-wave observatories'), (4896, '2012-01-17 2012-01-17'), (4897, 'http://arxiv.org/abs/1201.3684'), (4898, 'arXiv:1201.3684'), (4899, 'The signal-to-noise ratio (SNR) is used in gravitational-wave observations as the basic figure of merit for detection confidence and, together with the Fisher matrix, for the amount of physical information that can be extracted from a detected signal. SNRs are usually computed from a sensitivity curve, which describes the gravitational-wave amplitude needed by a monochromatic source of given frequency to achieve a threshold SNR. For interferometric space-based detectors similar to LISA, which are sensitive to long-lived signals and have constantly changing position and orientation, exact SNRs need to be computed on a source-by-source basis. For convenience, most authors prefer to work with sky-averaged sensitivities, accepting inaccurate SNRs for individual sources and giving up control over the statistical distribution of SNRs for source populations. In this paper, we describe a straightforward end-to-end recipe to compute the non-sky-averaged sensitivity of interferometric space-based detectors of any geometry, and we use it to generate a sampling distribution of sensitivities for a given source population. In effect, we derive error bars for the sky-averaged sensitivity curve. As a worked-out example, we consider isotropic and Galactic-disk populations of monochromatic sources, as observed with the "classic LISA" configuration. We confirm that the (standard) inverse-rms average sensitivity for the isotropic population remains the same whether or not the LISA orbits are included in the computation. However, detector motion tightens the distribution of sensitivities, so for 50% of sources the sensitivity is within 30% of its average. For the Galactic-disk population, the average and distribution of the sensitivity for a moving detector turn out to be similar to the isotropic case.'), (4900, '2012-01-20 10:36:59'), (4901, '1201.3684 PDF'), (4902, 'http://www.arxiv.org/pdf/1201.3684.pdf'), (4903, '2012-01-20 10:37:18'), (4904, 'Gravitational radiation from compact binary systems in the massive Brans-Dicke theory of gravity'), (4905, 'http://arxiv.org/abs/1112.4903'), (4906, 'arXiv:1112.4903'), (4907, 'We derive the equations of motion, the periastron shift, and the gravitational radiation damping for quasicircular compact binaries in a massive variant of the Brans-Dicke theory of gravity. We also study the Shapiro time delay and the Nordtvedt effect in this theory. By comparing with recent observational data, we put bounds on the two parameters of the theory: the Brans-Dicke coupling parameter \\omega_{BD} and the scalar mass m_s. We find that the most stringent bounds come from Cassini measurements of the Shapiro time delay in the Solar System, that yield a lower bound \\omega_{BD}>40000 for scalar masses m_s<2.5x10^{-20} eV, to 95% confidence. In comparison, observations of the Nordtvedt effect using Lunar Laser Ranging (LLR) experiments yield \\omega_{BD}>1000 for m_s<2.5x10^{-20} eV. Observations of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012+5307 yield \\omega_{BD}>1250 for m_s<10^{-20} eV. A first estimate suggests that bounds comparable to the Shapiro time delay may come from observations of radiation damping in the eccentric white dwarf-neutron star binary PSR J1141-6545, but a quantitative prediction requires the extension of our work to eccentric orbits.'), (4908, '2012-01-20 10:38:25'), (4909, '1112.4903 PDF'), (4910, 'http://www.arxiv.org/pdf/1112.4903.pdf'), (4911, '2012-01-20 10:38:33'), (4912, 'Gravitational Waves from Compact Binaries as Probes of the Universe'), (4913, '2011-12-15 2011-12-15'), (4914, 'http://arxiv.org/abs/1112.3694'), (4915, 'arXiv:1112.3694'), (4916, 'The future detection of gravitational wave forces us to consider the many ways in which astrophysics, gravitational wave theory and fundamental theory will interact. In this paper, I summarize some recent work done to develop such an interface. In particular, I concentrate on how non-vacuum astrophysical environments can modify the gravitational wave signal emitted by compact binary inspirals, and whether signatures from the former are detectable by current and future gravitational wave detectors. I also describe the interface between gravitational wave modeling and fundamental theory, focusing on the status of the parameterized post-Einsteinian framework (a general framework to detect deviations away from General Relativity in future gravitational wave data) and its current data analysis implementation.'), (4917, '2012-01-20 10:39:35'), (4918, '1112.3694 PDF'), (4919, 'http://www.arxiv.org/pdf/1112.3694.pdf'), (4920, '2012-01-20 10:39:47'), (4921, 'Late Inspiral and Merger of Binary Black Holes in Scalar-Tensor Theories of Gravity'), (4922, '2011-12-16 2011-12-16'), (4923, 'http://arxiv.org/abs/1112.3928'), (4924, 'arXiv:1112.3928'), (4925, "Gravitational wave observations will probe non-linear gravitational interactions and thus enable strong tests of Einstein's theory of general relativity. We present a numerical relativity study of the late inspiral and merger of binary black holes in scalar-tensor theories of gravity. We consider black hole binaries in an inhomogeneous scalar field, specifically binaries inside a scalar field bubble, in some cases with a potential. We calculate the emission of dipole radiation. We also show how these configurations trigger detectable differences between gravitational waves in scalar-tensor gravity and the corresponding waves in general relativity. We conclude that, barring an external mechanism to induce dynamics in the scalar field, scalar-tensor gravity binary black holes alone are not capable of awaking a dormant scalar field, and are thus observationally indistinguishable from their general relativistic counterparts."), (4926, '2012-01-20 10:40:19'), (4927, '1112.3928 PDF'), (4928, 'http://www.arxiv.org/pdf/1112.3928.pdf'), (4929, '2012-01-20 10:40:29'), (4930, 'Geometric algebra for physicists'), (4931, 'Efficient and accurate rotation of finite spherical harmonics expansions'), (4932, 231), (4933, 'Cambridge Univ. Press'), (4934, 'elearning.unifr.ch'), (4935, 'Physical template family for gravitational waves from precessing binaries of spinning compact objects: Application to single-spin binaries'), (4936, 9780521539272), (4937, '2. ed.'), (4938, 'The geometry of physics'), (4939, 'Gravitation'), (4940, 9780716703440), (4941, 'http://arxiv.org/abs/1410.2130'), (4942, 'W. H. Freeman'), (4943, '1973-00-00 1973'), (4944, 104017), (4945, 9780521829601), (4946, '3. pr.'), (4947, 'A course in modern mathematical physics'), (4948, 'Measuring cosmological distances by coalescing binaries'), (4949, '2012-01-24 2012-01-24'), (4950, 'http://arxiv.org/abs/1201.5087'), (4951, 'arXiv:1201.5087'), (4952, 'Gravitational waves detected from well-localized inspiraling binaries would allow us to determine, directly and independently, binary luminosity and redshift. In this case, such systems could behave as "standard candles" providing an excellent probe of cosmic distances up to z <0.1 and complementing other indicators of cosmological distance ladder.'), (4953, '2012-01-25 15:48:32'), (4954, '1201.5087 PDF'), (4955, 'http://www.arxiv.org/pdf/1201.5087.pdf'), (4956, '2012-01-25 15:48:34'), (4957, 'The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries'), (4958, '2012-01-25 2012-01-25'), (4959, 'http://arxiv.org/abs/1201.5319'), (4960, 'arXiv:1201.5319'), (4961, 'The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations.'), (4962, '2012-01-26 13:28:34'), (4963, '1201.5319 PDF'), (4964, 'http://www.arxiv.org/pdf/1201.5319.pdf'), (4965, '2012-01-26 13:29:04'), (4966, '2012-02-21 2012-02-21'), (4967, '045003'), (4968, '10.1088/0264-9381/29/4/045003'), (4969, 'http://iopscience.iop.org/0264-9381/29/4/045003'), (4970, 'High-accuracy gravitational waveforms for binary black hole mergers with nearly extremal spins'), (4971, '2012-01-27 17:51:11'), (4972, 'http://iopscience.iop.org/0264-9381/29/4/045003/pdf/0264-9381_29_4_045003.pdf'), (4973, '2012-01-27 17:51:13'), (4974, 'Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description'), (4975, '2012-02-16 2012-02-16'), (4976, 'http://arxiv.org/abs/1202.3565'), (4977, 'arXiv:1202.3565'), (4978, "The gravitational-wave signal from inspiralling neutron-star--neutron-star (or black-hole--neutron-star) binaries will be influenced by tidal coupling in the system. An important science goal in the gravitational-wave detection of these systems is to obtain information about the equation of state of neutron star matter via the measurement of the tidal polarizability parameters of neutron stars. To extract this piece of information will require to have accurate analytical descriptions of both the motion and the radiation of tidally interacting binaries. We improve the analytical description of the late inspiral dynamics by computing the next-to-next-to-leading order relativistic correction to the tidal interaction energy. Our calculation is based on an effective-action approach to tidal interactions, and on its transcription within the effective-one-body formalism. We find that second-order relativistic effects (quadratic in the relativistic gravitational potential $u=G(m_1 +m_2)/(c^2 r)$) significantly increase the effective tidal polarizability of neutron stars by a distance-dependent amplification factor of the form $1 + \\alpha_1 \\, u + \\alpha_2 \\, u^2 +...$ where, say for an equal-mass binary, $\\alpha_1=5/4=1.25$ (as previously known) and $\\alpha_2=85/14\\simeq6.07143$ (as determined here for the first time). We argue that higher-order relativistic effects will lead to further amplification, and we suggest a Pad\\'e-type way of resumming them. We recommend to test our results by comparing resolution-extrapolated numerical simulations of inspiralling-binary neutron stars to their effective one body description."), (4979, '2012-02-17 14:58:40'), (4980, '1202.3565 PDF'), (4981, 'http://www.arxiv.org/pdf/1202.3565.pdf'), (4982, 'The influence of gravitational wave momentum losses on the centre of mass motion of a Newtonian binary system'), (4983, 203), (4984, '1983-06-01 June 1, 1983'), (4985, '1049-1062'), (4986, 'http://adsabs.harvard.edu/abs/1983MNRAS.203.1049F'), (4987, "Following Bekenstein's (1973) work on recoiling black holes, the \ngravitational wave linear momentum flux from a binary system of two \npoint masses in Keplerian orbit is calculated. The quasi-Newtonian \napproach is adopted, and the resulting motion of the center of mass is \ncalculated. As such a system decays via gravitational wave energy \nlosses, the size of the orbit decreases until the components merge or \nbecome tidally disrupted. Thereafter, the center of mass moves with the \nlinear momentum necessary to balance that carried off by the \ngravitational waves. In the case of a binary black hole system, the \nvelocity of the center of mass could be of astrophysical significance, \nalthough numerical studies would be necessary to check this claim."), (4988, '2012-02-20 19:11:56'), (4989, 'Spinors and Space-time Vol. 2: Spinor and twistor methods in space-time geometry'), (4990, 'Spinors and Space-Time Vol. 1: Two-Spinor Calculus and Relativistic Fields'), (4991, '1983MNRAS_203_1049F.pdf'), (4992, "Representing Rotations In Quaternion Arithmetic at Simon's Graphics Blog"), (4993, 'http://www.sjbrown.co.uk/2002/05/01/quaternions/'), (4994, '2012-02-27 14:25:19'), (4995, 'The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries'), (4996, '2012-04-04 2012-04-04'), (4997, 'http://arxiv.org/abs/1204.1043'), (4998, '2012-02-27 14:27:14'), (4999, 652), (5000, 9781584500490), (5001, 'Cengage Learning'), (5002, 'Game programming gems'), (5003, 'For the countless tasks involved in creating a game engine there are an equal number of possible solutions. But instead of spending hours and hours trying to develop your own answers, now you can find out how the pros do it! Game Programming Gems is a hands-on, comprehensive resource packed with a variety of game programming algorithms written by experts from the game industry and edited by Mark DeLoura, former software engineering lead for Nintendo of America, Inc. and now the newly appointed editor-in-chief of Game Developer magazine. From animation and artificial intelligence to Z-buffering, lighting calculations, weather effects, curved surfaces, mutliple layer Internet gaming, to music and sound effects, all of the major techniques needed to develop a competitive game engine are covered. Game Programming Gems is written in a style accessible to individuals with a range of expertise levels. All of the source code for each algorithm is included and can be used by advanced programmers immediately. For aspiring programmers, there is a detailed tutorial to work through before attempting the code, and suggestions for possible modifications and optimizations are included as well.'), (5004, 'http://books.google.com/books?id=hiBFUv_FT0wC'), (5005, '2012-02-29 16:46:11'), (5006, 'Effects of post-Newtonian Spin Alignment on the Distribution of Black-Hole Recoils'), (5007, '2012-03-13 2012-03-13'), (5008, 'http://arxiv.org/abs/1203.2920'), (5009, 'arXiv:1203.2920'), (5010, 'Recent numerical relativity simulations have shown that the final black hole produced in a binary merger can recoil with a velocity as large as 5,000 km/s. Because of enhanced gravitational-wave emission in the so-called "hang-up" configurations, this maximum recoil occurs when the black-hole spins are partially aligned with the orbital angular momentum. We revisit our previous statistical analysis of post-Newtonian evolutions of black-hole binaries in the light of these new findings. We demonstrate that despite these new configurations with enhanced recoil velocities, spin alignment during the post-Newtonian stage of the inspiral will still significantly suppress (or enhance) kick magnitudes when the initial spin of the more massive black hole is more (or less) closely aligned with the orbital angular momentum than that of the smaller hole. We present a preliminary study of how this post-Newtonian spin alignment affects the ejection probabilities of supermassive black holes from their host galaxies with astrophysically motivated mass ratio and initial spin distributions. We find that spin alignment suppresses (enhances) ejection probabilities by ~ 40% (20%) for an observationally motivated mass-dependent galactic escape velocity, and by an even greater amount for a constant escape velocity of 1,000 km/s. Kick suppression is thus at least a factor two more efficient than enhancement.'), (5011, '2012-03-15 13:24:07'), (5012, '1203.2920 PDF'), (5013, 'http://www.arxiv.org/pdf/1203.2920.pdf'), (5014, 'Geometric approach to the precession of compact binaries'), (5015, 124011), (5016, '2011-12-02 December 02, 2011'), (5017, 'http://link.aps.org/doi/10.1103/PhysRevD.84.124011'), (5018, '10.1103/PhysRevD.84.124011'), (5019, '2012-03-15 20:49:55'), (5020, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i12/e124011'), (5021, 'Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis'), (5022, 'Journal of Computational Physics'), (5023, 227), (5024, '1094-1125'), (5025, '2007-12-10 December 10, 2007'), (5026, '0021-9991'), (5027, '10.1016/j.jcp.2007.08.029'), (5028, 'http://www.sciencedirect.com/science/article/pii/S0021999107003816'), (5029, 'We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch – which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The “continuation functions” arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.'), (5030, '2012-03-15 22:23:19'), (5031, 'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272570&_user=492137&_pii=S0021999107003816&_check=y&_origin=article&_zone=toolbar&_coverDate=10-Dec-2007&view=c&originContentFamily=serial&wchp=dGLzVlB-zSkzS&md5=ff78787591d337e95d27ffcb70811224/1-s2.0-S0021999107003816-main.pdf'), (5032, 'Gravitational wave spectrum of anisotropic neutron stars in Cowling approximation'), (5033, '2012-03-18 2012-03-18'), (5034, 'http://arxiv.org/abs/1203.3963'), (5035, 'arXiv:1203.3963'), (5036, 'One of the most common assumption in the studies of neutron star models and their oscillations is that the pressure is isotopic but there are arguments that this may not be correct. Thus in the present paper we make a first step towards studying the nonradial oscillations of neutron stars with anisotropic pressure. We adopt the so-called Cowling approximation where the spacetime metric is kept fixed and the oscillation spectrum for the first few fluid modes is obtained. The effect of the anisotropy on the frequencies is apparent, although with the present results it might be hard to distinguish it from the changes in the frequencies caused by different equations of state.'), (5037, '2012-03-20 15:11:09'), (5038, '1203.3963 PDF'), (5039, 'http://www.arxiv.org/pdf/1203.3963.pdf'), (5040, 'Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals'), (5041, '2012-03-20 2012-03-20'), (5042, 'http://arxiv.org/abs/1203.4352'), (5043, 'arXiv:1203.4352'), (5044, 'The gravitational wave signal from a binary neutron star inspiral contains information on the nuclear equation of state. This information is contained in a combination of the tidal polarizability parameters of the two neutron stars and is clearest in the late inspiral, just before merger. We use the recently defined tidal extension of the effective one-body formalism to construct a controlled analytical description of the frequency-domain phasing of neutron star inspirals up to merger. Exploiting this analytical description we find that the tidal polarizability parameters of neutron stars can be measured by the advanced LIGO-Virgo detector network from gravitational wave signals having a reasonable signal-to-noise ratio of $\\rho=16$. This measurability result seems to hold for all the nuclear equations of state leading to a maximum mass larger than $1.97M_\\odot$. We also propose a promising new way of extracting information on the nuclear equation of state from a coherent analysis of an ensemble of gravitational wave observations of separate binary merger events.'), (5045, '2012-03-21 18:51:03'), (5046, '1203.4352 PDF'), (5047, 'http://www.arxiv.org/pdf/1203.4352.pdf'), (5048, 'http://arxiv.org/abs/1402.0035'), (5049, 'arXiv:1402.0035 [astro-ph]'), (5050, '2014-01-31 2014-01-31'), (5051, 'AIP Conference Proceedings 1577, 153 (2014)'), (5052, '2014-02-05 21:59:50'), (5053, "The observable macroscopic properties of relativistic stars (whose equations of state are known) can be predicted by solving the stellar structure equations that follow from Einstein's equation. For neutron stars, however, our knowledge of the equation of state is poor, so the direct stellar structure problem can not be solved without modeling the highest density part of the equation of state in some way. This talk will describe recent work on developing a model independent approach to determining the high-density neutron-star equation of state by solving an inverse stellar structure problem. This method uses the fact that Einstein's equation provides a deterministic relationship between the equation of state and the macroscopic observables of the stars which are composed of that material. This talk illustrates how this method will be able to determine the high-density part of the neutron-star equation of state with few percent accuracy when high quality measurements of the masses and radii of just two or three neutron stars become available. This talk will also show that this method can be used with measurements of other macroscopic observables, like the masses and tidal deformabilities, which can (in principle) be measured by gravitational wave observations of binary neutron-star mergers."), (5054, 'The Relativistic Inverse Stellar Structure Problem'), (5055, 'http://www.arxiv.org/pdf/1402.0035.pdf'), (5056, '1402.0035 PDF'), (5057, 'http://arxiv.org/abs/1402.0053'), (5058, 'arXiv:1402.0053 [astro-ph, physics:gr-qc]'), (5059, '2014-02-01 2014-02-01'), (5060, '2014-02-05 22:00:24'), (5061, 'CargoCult.pdf'), (5062, 'Cargo Cult Science'), (5063, "Caltech's E&S"), (5064, 'Geometric Tools'), (5065, 'arXiv:1204.1043'), (5066, 'www.geometrictools.com/Documentation/Documentation.html'), (5067, 'RotationIssues.pdf'), (5068, 'Quaternions.pdf'), (5069, 'LinearAlgebraicQuaternions.pdf'), (5070, 'Efficient parameter estimation is critical for Gravitational-Wave astronomy. In the case of compact binary coalescence, the high dimensional parameter space demands efficient sampling techniques - such as Markov chain Monte Carlo (MCMC). A number of degeneracies effectively reduce the dimensionality of the parameter space and, when known, can render sampling algorithms more efficient with problem-specific improvements. We present in this paper an analytical description of a degeneracy involving the extrinsic parameters of a compact binary coalescence gravitational-wave signal, when data from a three detector network (such as Advanced LIGO/Virgo) is available. We use this new formula to construct a jump proposal, a framework for a generic sampler to take advantage of the degeneracy. We show the gain in efficiency for a MCMC sampler in the analysis of the gravitational-wave signal from a compact binary coalescence.'), (5071, 'Physically motivated exploration of the extrinsic parameter space in ground-based gravitational-wave astronomy'), (5072, 'http://www.arxiv.org/pdf/1402.0053.pdf'), (5073, 'Compact binaries detection rates from gravitational wave interferometers: comparison of different procedures'), (5074, '2012-03-22 2012-03-22'), (5075, 'http://arxiv.org/abs/1203.5110'), (5076, 'arXiv:1203.5110'), (5077, 'In this paper we perform a detailed analysis of the effect of various approximations that have been adopted in the literature to compute the detection rates of compact binary coalescences for first, second and third generation gravitational wave detectors. In particular, we compute the detection rates for the coalescence of BH-BH, NS-NS, and BH-NS systems taking into account their specific statistical properties obtained from population synthesis models (distributions of masses and delay times), the cosmic star formation rate history and the effects of redshift on the emitted gravitational wave signals. We then compare our findings with procedures adopted in the literature that are based on different levels of approximations, such as using averaged values for the total mass and symmetric mass ratio for all the systems of a binary population, using these to compute the horizon distance for individual detectors, or estimating the coalescence rate density within this distance by its local value. We find that most of these approximations are adequate to estimate the detection rates of first generation interferometers, because these are sensitive only to very low redshifts (even for BH-BH systems, the maximum detectable redshift for LIGO/VIRGO is $z \\le 0.02$). However, for second generation interferometers, such as Advanced LIGO/VIRGO, the adopted approximations can lead to a factor $\\gtrsim3$ error in the estimated detection rates, and can not be applied to third generation detectors, such as the Einstein Telescope for which we give the estimated detection rate using no approximations.'), (5078, '2012-03-27 15:21:48'), (5079, 'Compact binaries detection rates from gravitational wave interferometers'), (5080, '1203.5110 PDF'), (5081, 'http://www.arxiv.org/pdf/1203.5110.pdf'), (5082, 'Nonspinning searches for spinning binaries in ground-based detector data: Amplitude and mismatch predictions in the constant precession cone approximation'), (5083, '2012-03-27 2012-03-27'), (5084, 'http://arxiv.org/abs/1203.6060'), (5085, 'arXiv:1203.6060'), (5086, "Current searches for compact binary mergers by ground-based gravitational-wave detectors assume for simplicity the two bodies are not spinning. If the binary contains compact objects with significant spin, then this can reduce the sensitivity of these searches, particularly for black hole--neutron star binaries. In this paper we investigate the effect of neglecting precession on the sensitivity of searches for spinning binaries using non-spinning waveform models. We demonstrate that in the sensitive band of Advanced LIGO, the angle between the binary's orbital angular momentum and its total angular momentum is approximately constant. Under this \\emph{constant precession cone} approximation, we show that the gravitational-wave phasing is modulated in two ways: a secular increase of the gravitational-wave phase due to precession and an oscillation around this secular increase. We show that this secular evolution occurs in precisely three ways, corresponding to physically different apparent evolutions of the binary's precession about the line of sight. We estimate the best possible fitting factor between \\emph{any} non-precessing template model and a single precessing signal, in the limit of a constant precession cone. Our closed form estimate of the fitting-factor depends only the geometry of the in-band precession cone; it does not depend explicitly on binary parameters, detector response, or details of either signal model. The precessing black hole--neutron star waveforms least accurately matched by nonspinning waveforms correspond to viewing geometries where the precession cone sweeps the orbital plane repeatedly across the line of sight, in an unfavorable polarization alignment."), (5087, '2012-03-28 14:11:44'), (5088, 'Nonspinning searches for spinning binaries in ground-based detector data'), (5089, '1203.6060 PDF'), (5090, 'http://www.arxiv.org/pdf/1203.6060.pdf'), (5091, 'We compute the quadrupole mode of the gravitational waveform of inspiralling compact binaries at the third and a half post-Newtonian (3.5PN) approximation of general relativity. The computation is performed using the multipolar post-Newtonian formalism, and restricted to binaries without spins moving on quasi-circular orbits. The new inputs mainly include the 3.5PN terms in the mass quadrupole moment of the source, and the control of required subdominant corrections to the contributions of hereditary integrals (tails and non-linear memory effect). The result is given in the form of the quadrupolar mode (2,2) in a spin-weighted spherical harmonic decomposition of the waveform, and will allow a more accurate comparison with the outcome of numerical relativity simulations.'), (5092, '2012-04-05 12:18:14'), (5093, '1204.1043 PDF'), (5094, 'http://www.arxiv.org/pdf/1204.1043.pdf'), (5095, 'http://www.cs.cmu.edu/afs/cs/user/spiff/www/moedit99/'), (5096, '2012-04-05 19:32:28'), (5097, 'Equation-of-state dependence of the gravitational-wave signal from the ring-down phase of neutron-star mergers'), (5098, 'expmap.pdf'), (5099, 'Journal of Graphics Tools'), (5100, '3.3'), (5101, 'Errors and Omissions in Marc Alexa\'s "Linear Combination of Transformations"'), (5102, 'alexa-error-1.pdf'), (5103, '2002-05-01 May 1, 2002'), (5104, '2012-04-06 18:59:54'), (5105, '2012-04-09 2012-04-09'), (5106, 'PhysRevD.79.084010.pdf'), (5107, 'Geometric Algebra Module for Sympy — SymPy 0.7.1-git documentation'), (5108, 'http://docs.sympy.org/dev/modules/galgebra/GA/GAsympy.html'), (5109, '2012-04-06 20:20:51'), (5110, 'http://arxiv.org/abs/1204.1888'), (5111, 'arXiv:1204.1888'), (5112, 'Neutron-star (NS) merger simulations are conducted for 38 representative microphysical descriptions of high-density matter in order to explore the equation-of-state dependence of the postmerger ring-down phase. The formation of a deformed, oscillating, differentially rotating very massive NS is the typical outcome of the coalescence of two stars with 1.35 $M_{\\odot}$ for most candidate EoSs. The oscillations of this object imprint a pronounced peak in the gravitational-wave (GW) spectra, which is used to characterize the emission for a given model. The peak frequency of this postmerger GW signal correlates very well with the radii of nonrotating NSs, and thus allows to constrain the high-density EoS by a GW detection. In the case of 1.35-1.35 $M_{\\odot}$ mergers the peak frequency scales particularly well with the radius of a NS with 1.6 $M_{\\odot}$, where the maximum deviation from this correlation is only 60 meters for fully microphysical EoSs which are compatible with NS observations. Combined with the uncertainty in the determination of the peak frequency it appears likely that a GW detection can measure the radius of a 1.6 $M_{\\odot}$ NS with an accuracy of about 100 to 200 meters. We also uncover relations of the peak frequency with the radii of nonrotating NSs with 1.35 $M_{\\odot}$ or 1.8 $M_{\\odot}$, with the radius or the central energy density of the maximum-mass Tolman-Oppenheimer-Volkoff configuration, and with the pressure or sound speed at a fiducial rest-mass density of about twice nuclear saturation density. Furthermore, it is found that a determination of the dominant postmerger GW frequency can provide an upper limit for the maximum mass of nonrotating NSs. The prospects for a detection of the postmerger GW signal and a determination of the dominant GW frequency are estimated to be in the range of 0.015 to 1.2 events per year with the upcoming Advanced LIGO detector.'), (5113, '2012-04-10 13:28:36'), (5114, '1204.1888 PDF'), (5115, 'http://www.arxiv.org/pdf/1204.1888.pdf'), (5116, 'Probing the Inhomogeneous Universe with Gravitational Wave Cosmology'), (5117, '2012-04-07 2012-04-07'), (5118, 'http://arxiv.org/abs/1204.1670'), (5119, 'arXiv:1204.1670'), (5120, 'If we assume that we live in the center of a spherical inhomogeneous universe, we can explain the apparent accelerating expansion of the universe without introducing the unknown dark energy or modifying gravitational theory. Direct measurement of the cosmic acceleration can be a powerful tool in distinguishing $\\Lambda$CDM and the inhomogeneous models. If $\\Lambda$CDM is the correct model, we have shown that DECIGO/BBO has sufficient ability to detect the positive redshift drift of the source by observing gravitational waves from neutron star binaries for 5-10 years. This enables us to rule out any Lema\\^itre-Tolman-Bondi (LTB) void model with monotonically increasing density profile. Furthermore, by detecting the positive redshift drift at $z\\sim 0$, we can even rule out generic LTB models unless we allow unrealistically steep density gradient at $z\\sim 0$. We also show that the measurement accuracy is slightly improved when we consider the joint search of DECIGO/BBO and the third generation Einstein Telescope. This test can be performed with GW observations alone without any reference to electromagnetic observations.'), (5121, '2012-04-10 13:58:14'), (5122, '1204.1670 PDF'), (5123, 'http://www.arxiv.org/pdf/1204.1670.pdf'), (5124, 'Journal of the Royal Statistical Society. Series C (Applied Statistics)'), (5125, 'Fitting Smooth Paths to Rotation Data'), (5126, 36), (5127, '0035-9254'), (5128, 'http://www.jstor.org/stable/2347791'), (5129, '1987-01-01 January 01, 1987'), (5130, '325-331'), (5131, 'In the study of plate tectonics in geophysics, estimates are available of the cumulative motion of continental plates relative to each other between various geological epochs. For a given pair of plates this relative movement may be summarized at each time by a 3× 3 proper rotation matrix describing the orientation of a plate relative to its initial position. The general problem of point and interval rotation estimation at other times is addressed by using a spline method for fitting smooth paths to such sequences of cumulative rotations. The parameterization of 3× 3 rotations as unsigned four-dimensional directions is particularly convenient. The preferred tangent space projection also makes easy the construction of point and interval estimates of the instantaneous angular velocity vector of the relative motion.'), (5132, 'ArticleType: research-article / Full publication date: 1987 / Copyright © 1987 Royal Statistical Society'), (5133, '10.2307/2347791'), (5134, '2012-04-10 15:13:40'), (5135, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2347791.pdf?acceptTC=true'), (5136, 'Canonical Angles In A Compact Binary Star System With Spinning Components: Approximative Solution Through Next-To-Leading-Order Spin-Orbit Interaction for Circular Orbits'), (5137, 'http://www.jstor.org/stable/2347843'), (5138, '34-46'), (5139, 'Given a set of data points on the sphere at known times, one often wishes to fit a smooth path to the data. In this paper we propose a unified approach to deal with such problems. Our method can be described as "unwrapping" the data onto the plane, where standard curve fitting techniques can then be applied. As an important example of our approach, we define and fit "spherical spline functions".'), (5140, '10.2307/2347843'), (5141, '2012-04-10 15:40:14'), (5142, 'http://www.jstor.org/stable/pdfplus/2347843.pdf?acceptTC=true'), (5143, 532), (5144, 9780120884001), (5145, 'Morgan Kaufmann'), (5146, 'Visualizing quaternions'), (5147, "Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions.* Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing.* Covers both non-mathematical and mathematical approaches to quaternions.* Companion website with an assortment of quaternion utilities and sample code, data sets for the book's illustrations, and Mathematica notebooks with essential algebraic utilities."), (5148, '2005-12-29 2005-12-29'), (5149, 'http://books.google.com/books?id=CoUB09xzme4C'), (5150, '2012-04-10 17:30:53'), (5151, 'A general construction scheme for unit quaternion curves with simple high order derivatives'), (5152, 'Proceedings of the 22nd annual conference on Computer graphics and interactive techniques'), (5153, "SIGGRAPH '95"), (5154, '1995-00-00 1995'), (5155, '0-89791-701-4'), (5156, '369–376'), (5157, 'http://doi.acm.org/10.1145/218380.218486'), (5158, '10.1145/218380.218486'), (5159, 'ACM'), (5160, 'New York, NY, USA'), (5161, 'ACM Digital Library'), (5162, '2012-04-10 19:41:09'), (5163, 'On cubics: A survey'), (5164, 'Computer Graphics and Image Processing'), (5165, '2012-04-10 19:41:32'), (5166, '201-226'), (5167, '1982-07-00 July 1982'), (5168, 'p369-kim.pdf'), (5169, '0146-664X'), (5170, '10.1016/0146-664X(82)90009-0'), (5171, 'http://www.sciencedirect.com/science/article/pii/0146664X82900090'), (5172, "Standard cubics, i.e., nonrational cubics, are the simplest twisted curves—hence their considerable importance for CAGD. Rational cubics allow modification of their fullness even when the end tangents are kept fixed; this is the reason why they are occasionally preferred to standard cubics in CAGD. We shall point out connections between the various representations and their underlying geometric properties. This should serve as an easy and intuitive introduction and help the potential user choose a suitable representation. (This survey was initiated by Forrest's article “The twisted cubic curve” [14] and the subsequent correspondence with A. Ball [4] on some minor misunderstandings.) Some new algorithms can be obtained in a straightforward way."), (5173, '2012-04-11 20:30:30'), (5174, 'On cubics'), (5175, 'http://pdn.sciencedirect.com/science?_ob=MiamiImageURL&_cid=273220&_user=492137&_pii=0146664X82900090&_check=y&_origin=article&_zone=toolbar&_coverDate=31-Jul-1982&view=c&originContentFamily=serial&wchp=dGLzVlS-zSkzk&md5=ecb0e9087396b91f148cf95350857a70/1-s2.0-0146664X82900090-main.pdf'), (5176, 'Angular Momentum in General Relativity: A New Definition'), (5177, '1150-1153'), (5178, 'http://link.aps.org/doi/10.1103/PhysRevLett.81.1150'), (5179, '10.1103/PhysRevLett.81.1150'), (5180, 'Although considerable progress has been made in generalizing the concept of angular momentum to general relativity, until now no satisfactory definition that allows for the exchange of angular momentum has been given. I here give the first such definition. It is a definition at null infinity, the place and time where gravity waves reach in the limit far from all masses. The definition applies to any isolated system of masses including those that change their angular momentum L by emitting gravity waves. L̇ is given solely in terms of parameters in principle measurable directly by Michelson interferometer gravitational wave detectors such as LIGO or LISA.'), (5181, '2012-04-17 22:05:22'), (5182, 'Angular Momentum in General Relativity'), (5183, 'Group Theory and Its Applications to the Quantum Mechanics of Atomic Spectra'), (5184, '2012-04-17 22:05:49'), (5185, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v81/i6/p1150_1'), (5186, '2012-04-18 19:13:32'), (5187, 'Academic Press'), (5188, '1959-00-00 1959'), (5189, 'Wigner E. - Group.Theory.and.Its.Application.to.the.Quantum.Mechanics.of.Atomic.Spectra_1959.djvu'), (5190, 'gaworkbook.pdf'), (5191, 'http://web4.uwindsor.ca/users/b/baylis/main.nsf/9d019077a3c4f6768525698a00593654/e639e0cdf0d162c985256bb2004c8fde/$FILE/gaworkbook.pdf'), (5192, '2012-04-29 15:54:14'), (5193, 'Gravity and strings'), (5194, 'http://web4.uwindsor.ca/users/b/baylis/main.nsf/'), (5195, '2012-04-29 15:58:37'), (5196, "Clifford's Geometric Algebra of Physical Space"), (5197, 'cainphys.pdf'), (5198, 'On the determination of the spin of the black hole in Cyg X-1 from X-ray reflection spectra'), (5199, '2012-04-26 2012-04-26'), (5200, 'http://arxiv.org/abs/1204.5854'), (5201, 'arXiv:1204.5854'), (5202, 'The spin of Cygnus X-1 is measured by fitting reflection models to Suzaku data covering the energy band 0.9-400 keV. The inner radius of the accretion disc is found to lie within 2 gravitational radii (r_g=GM/c^2) and a value for the dimensionless black hole spin is obtained of 0.97^{+0.014}_{-0.02}. This agrees with recent measurements using the continuum fitting method by Gou et al. and of the broad iron line by Duro et al. The disc inclination is measured at 23.7^{+6.7}_{-5.4} deg, which is consistent with the recent optical measurement of the binary system inclination by Orosz et al of 27+/-0.8 deg. We pay special attention to the emissivity profile caused by irradiation of the inner disc by the hard power-law source. The X-ray observations and simulations show that the index q of that profile deviates from the commonly used, Newtonian, value of 3 within 3r_g, steepening considerably within 2r_g, as expected in the strong gravity regime.'), (5203, '2012-04-29 16:23:19'), (5204, '1204.5854 PDF'), (5205, 'http://www.arxiv.org/pdf/1204.5854.pdf'), (5206, '0305-4470, 1361-6447'), (5207, '1996-09-21 1996-09-21'), (5208, '6059-6072'), (5209, '10.1088/0305-4470/29/18/032'), (5210, 'http://iopscience.iop.org/0305-4470/29/18/032'), (5211, '2004-05-19 May 19, 2004'), (5212, '2012-04-30 22:25:41'), (5213, '0521824753'), (5214, "Wigner's D-matrix elements for SU(3) -- a generating-function approach"), (5215, '0305-4470_29_18_032.pdf'), (5216, 'Cosmology with the lights off: standard sirens in the Einstein Telescope era'), (5217, '2012-04-30 2012-04-30'), (5218, 'http://arxiv.org/abs/1204.6739'), (5219, 'arXiv:1204.6739'), (5220, 'We explore the prospects for constraining cosmology using gravitational wave (GW) observations of neutron star binaries by the proposed Einstein Telescope (ET), exploiting the narrowness of the neutron star mass function. Double neutron star (DNS) binaries are expected to be one of the first sources detected after "first-light" of Advanced LIGO and are expected to be detected at a rate of a few tens per year in the advanced era. However the proposed Einstein Telescope (ET) could catalogue tens of thousands per year. Combining the measured source redshift distributions with GW-network distance determinations will permit not only the precision measurement of background cosmological parameters, but will provide an insight into the astrophysical properties of these DNS systems. Of particular interest will be to probe the distribution of delay times between DNS-binary creation and subsequent merger, as well as the evolution of the star-formation rate density within ET\'s detection horizon. Keeping H_0, Omega_{m,0} and Omega_{\\Lambda,0} fixed and investigating the precision with which the dark energy equation-of-state parameters could be recovered, we found that with 10^5 detected DNS binaries we could constrain these parameters to an accuracy similar to forecasted constraints from future CMB+BAO+SNIa measurements. Furthermore, modeling the merger delay-time distribution as a power-law, and the star-formation rate (SFR) density as a parametrised version of the Porciani and Madau SF2 model, we find that the associated astrophysical parameters are constrained to within ~ 10%. All parameter precisions scaled as 1/sqrt(N), where N is the number of catalogued detections. We also investigated how precisions varied with the intrinsic underlying properties of the Universe and with the distance reach of the network (which may be affected by the lower frequency cutoff of the detector).'), (5221, '2012-05-01 13:37:36'), (5222, 'Cosmology with the lights off'), (5223, '1204.6739 PDF'), (5224, 'http://www.arxiv.org/pdf/1204.6739.pdf'), (5225, 'http://link.aps.org/doi/10.1103/PhysRevD.69.104017'), (5226, 'The quantum theory of fields'), (5227, '0521550017'), (5228, 'Reprinted (with corr.)'), (5229, 'The large scale structure of space-time'), (5230, '0521099064'), (5231, 'Rep ed.'), (5232, '1976-00-00 1976'), (5233, 'Functional analysis'), (5234, '0486662896'), (5235, 'Dover ed.'), (5236, 'Dover Publications'), (5237, '1990-00-00 1990'), (5238, 'An introduction to algebraic topology'), (5239, 9780387966), (5240, 'corr. 2. print.'), (5241, 'Springer-Verlag'), (5242, '1988-00-00 1988'), (5243, 1558), (5244, 'AIP Publishing'), (5245, '525-528'), (5246, '2013-10-17 2013/10/17'), (5247, 'Topology'), (5248, 9780131816), (5249, 'Prentice Hall'), (5250, 'Thinking physics is Gedanken physics'), (5251, 9780935218), (5252, '10.1103/PhysRevD.69.104017'), (5253, 'Insight Press'), (5254, 'A first course in general relativity'), (5255, 9780521277), (5256, 'Reprinted.'), (5257, 'Geometry of differential forms'), (5258, '0821810456'), (5259, '[Reprint.].'), (5260, 'American Math. Soc.'), (5261, 'Differential topology'), (5262, 9780132126), (5263, 'Prentice-Hall'), (5264, 'Abstract algebra'), (5265, 9780135693), (5266, 'Group theory'), (5267, '0486653773'), (5268, 'Reprint.'), (5269, 'Dover'), (5270, 'Cosmological physics'), (5271, 9780521422), (5272, '8. print. with corr.'), (5273, 'Quantum field theory in curved spacetime and black holes thermodynamics'), (5274, 9780226870), (5275, '[Nachdr.]'), (5276, 'The University of Chicago Press'), (5277, '1994-00-00 1994'), (5278, 'Classical mechanics'), (5279, 9788178085), (5280, 'Pearson Education'), (5281, 'Mathematical methods of classical mechanics'), (5282, 9780387968), (5283, 'The detection of the gravitational waves (GWs) emitted by precessing binaries of spinning compact objects is complicated by the large number of parameters (such as the magnitudes and initial directions of the spins, and the position and orientation of the binary with respect to the detector) that are required to model accurately the precession-induced modulations of the GW signal. In this paper we describe a fast matched-filtering search scheme for precessing binaries, and we adopt the physical template family proposed by Buonanno, Chen, and Vallisneri [Phys. Rev. D 67, 104025 (2003)] for ground-based interferometers. This family provides essentially exact waveforms, written directly in terms of the physical parameters, for binaries with a single significant spin, and for which the observed GW signal is emitted during the phase of adiabatic inspiral (for LIGO-I and VIRGO, this corresponds to a total mass M≲15M⊙). We show how the detection statistic can be maximized automatically over all the parameters (including the position and orientation of the binary with respect to the detector), except four (the two masses, the magnitude of the single spin, and the opening angle between the spin and the orbital angular momentum), so the template bank used in the search is only four-dimensional; this technique is relevant also to the searches for GW from extreme-mass-ratio inspirals and supermassive black hole inspirals to be performed using the space-borne detector LISA. Using the LIGO-I design sensitivity, we compute the detection threshold (∼10) required for a false-alarm probability of 10-3/yr and the number of templates (∼76000) required for a minimum match of 0.97 for the mass range (m1,m2)=[7,12]M⊙×[1,3]M⊙.'), (5284, 'Group theory and its application to physical problems'), (5285, 9780486661), (5286, 'Unabridged, corr. republ. of the 2. print.'), (5287, '2013-08-14 08:35:42'), (5288, '2000-11-07 2000-11-07'), (5289, 'Wiley'), (5290, '2012-05-23 19:29:12'), (5291, 9780201624), (5292, 'Updated ed.'), (5293, 'Addison-Wesley Pub.'), (5294, 'Modern elementary particle physics'), (5295, 'A first course in string theory'), (5296, 9780521831), (5297, '6. print.'), (5298, 'Modern elementary particle physics: The fundamental particles and forces?'), (5299, 'A course in modern mathematical physics: Groups, Hilbert space and differential geometry'), (5300, 'The geometry of physics: An introduction'), (5301, 'An introduction to modern astrophysics'), (5302, 9780805304), (5303, 'Pearson, Addison-Wesley'), (5304, 'Lie groups'), (5305, 9783540152), (5306, '10 Exact Gravitationally-Conserved Quantities'), (5307, 15), (5308, '231-233'), (5309, '1965-00-00 1965'), (5310, 'http://link.aps.org/doi/10.1103/PhysRevLett.15.231'), (5311, '10.1103/PhysRevLett.15.231'), (5312, '2012-05-05 16:02:05'), (5313, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v15/i6/p231_1'), (5314, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v6/i6/p902_s1?isAuthorized=no'), (5315, 'The purpose of this paper is to propose a definition of multipole structure of gravitational sources in terms of the characteristic initial data for asymptotic solutions of the field equations. This definition is based upon a detailed study of the corresponding data for the linearized equations and upon the close analogy between the Maxwell and the linearized gravitational fields.'), (5316, '1965-06-01 1965-06-01'), (5317, 'doi:10.1063/1.1704349'), (5318, '902-914'), (5319, 'Structure of Gravitational Sources'), (5320, 'SPIE/AIP'), (5321, '2012-05-05 16:10:37'), (5322, 'AIP Journal Snapshot'), (5323, '064041'), (5324, 'http://link.aps.org/doi/10.1103/PhysRevD.84.064041'), (5325, 'AIP Journal PDF'), (5326, 'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/6/902/1/pdf'), (5327, '2012-05-05 16:11:57'), (5328, '2012-05-08 15:33:00'), (5329, '2007-09-10 2007-09-10'), (5330, '0521880688'), (5331, 1256), (5332, 'Numerical Recipes 3rd Edition: The Art of Scientific Computing'), (5333, 'Amazon.com'), (5334, 'Numerical Recipes 3rd Edition'), (5335, 'The apparent shape of a relativistically moving sphere'), (5336, '10.1103/PhysRevD.84.064041'), (5337, 'Gravitational waves contain tail effects which are due to the backscattering of linear waves in the curved space-time geometry around the source. In this paper we improve the knowledge and accuracy of the two-body inspiraling post-Newtonian (PN) dynamics and gravitational-wave signal by computing the spin-orbit terms induced by tail effects. Notably, we derive those terms at 3PN order in the gravitational-wave energy flux, and 2.5PN and 3PN orders in the wave polarizations. This is then used to derive the spin-orbit tail effects in the phasing through 3PN order. Our results can be employed to carry out more accurate comparisons with numerical-relativity simulations and to improve the accuracy of analytical templates aimed at describing the whole process of inspiral, merger, and ringdown.'), (5338, 'NR.pdf'), (5339, 'Mass Measurements of Black Holes in X-Ray Transients: Is There a Mass Gap?'), (5340, '2012-05-08 2012-05-08'), (5341, 'http://arxiv.org/abs/1205.1805'), (5342, 'arXiv:1205.1805'), (5343, 'We explore possible systematic errors in the mass measurements of stellar mass black holes. We find that significant errors can arise from the assumption of zero or constant emission from the accretion flow, which is commonly used when determining orbital inclination by modelling ellipsoidal variations. For A0620-00, the system with the best available data, we show that typical data sets and analysis procedures can lead to systematic underestimates of the inclination by ten degrees or more. A careful examination of the available data for the 15 other X-ray transients with low-mass donors suggests that this effect may significantly reduce the black hole mass estimates in several other cases, most notably that of GRO J0422+32. With these revisions, our analysis of the black hole mass distribution in soft X-ray transients does not suggest any "mass gap" between the low end of the distribution and the maximum theoretical neutron star mass, as has been identified in previous studies. Nevertheless, we find that the mass distribution retains other previously identified characteristics, namely a peak around 8M\\odot, a paucity of sources with masses below 5M\\odot, and a sharp drop-off above 10M\\odot.'), (5344, '2012-05-10 14:14:26'), (5345, 'Mass Measurements of Black Holes in X-Ray Transients'), (5346, '1205.1805 PDF'), (5347, 'http://www.arxiv.org/pdf/1205.1805.pdf'), (5348, 'Asymptotic frame selection for binary black hole spacetimes II: Post-Newtonian limit'), (5349, '2012-05-10 2012-05-10'), (5350, 'http://arxiv.org/abs/1205.2287'), (5351, 'arXiv:1205.2287'), (5352, 'One way to select a preferred frame from gravitational radiation is via the principal axes of < L L>, an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. In this paper we evaluate this time-domain average for a quasicircular binary using approximate (post-Newtonian) waveforms. For nonprecessing unequal-mass binaries, we show the dominant eigenvector of this tensor lies along the orbital angular momentum. For precessing binaries, this frame is not generally aligned with either the orbital or total angular momentum, working to leading order in the spins. The difference between these two quantities grows with time, as the binary approaches the end of the inspiral and both precession and higher harmonics become more significant.'), (5353, '2012-05-11 12:29:29'), (5354, 'Asymptotic frame selection for binary black hole spacetimes II'), (5355, '1205.2287 PDF'), (5356, 'http://www.arxiv.org/pdf/1205.2287.pdf'), (5357, '2012-06-12 03:09:31'), (5358, 'Tidal effects in binary neutron star coalescence'), (5359, '2012-05-15 2012-05-15'), (5360, 'http://arxiv.org/abs/1205.3403'), (5361, 'arXiv:1205.3403'), (5362, 'We compare dynamics and waveforms from binary neutron star coalescence as computed by new long-term ($\\sim 10 $ orbits) numerical relativity simulations and by the tidal effective-one-body (EOB) model including analytical tidal corrections up to second post-Newtonian order (2PN). The current analytical knowledge encoded in the tidal EOB model is found to be sufficient to reproduce the numerical data up to contact and within their uncertainties. Remarkably, no calibration of any tidal EOB free parameters is required, beside those already fitted to binary black holes data. The inclusion of 2PN tidal corrections minimizes the differences with the numerical data, but it is not possible to significantly distinguish them from the leading-order tidal contribution. The presence of a relevant amplification of tidal effects is likely to be excluded, although it can appear as a consequence of numerical inaccuracies. We conclude that the tidally-completed effective-one-body model provides nowadays the most advanced and accurate tool for modelling gravitational waveforms from binary neutron star inspiral up to contact. This work also points out the importance of extensive tests to assess the uncertainties of the numerical data, and the potential need of new numerical strategies to perform accurate simulations.'), (5363, '2012-05-16 14:24:18'), (5364, '1205.3403 PDF'), (5365, 'http://www.arxiv.org/pdf/1205.3403.pdf'), (5366, 'Principles of Quantum Mechanics'), (5367, 'Physical template family for gravitational waves from precessing binaries of spinning compact objects'), (5368, 'second'), (5369, 'New York'), (5370, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v69/i10/e104017'), (5371, 'Plenum Press'), (5372, 'Shankar R. Principles of quantum mechanics (2ed., Plenum, 1994)(no pages 428-654)(T)(453s).djvu'), (5373, 'Addison Wesley'), (5374, '1993-09-10 1993-09-10'), (5375, '0201539292'), (5376, 500), (5377, 'Modern Quantum Mechanics'), (5378, '137-139'), (5379, 55), (5380, 'revised'), (5381, 'Sakurai.Modern Quantum Mechanics(T).djvu'), (5382, 'Introduction to topology'), (5383, 9780821821), (5384, 'American Mathematical Society'), (5385, 'General relativity'), (5386, 'Univ. of Chicago Press'), (5387, 'Spin-orbit resonance and the evolution of compact binary systems'), (5388, '0262020491'), (5389, 'M.I.T. Press'), (5390, '0262020696'), (5391, '0262020483'), (5392, 'MIT Press'), (5393, 124020), (5394, '10.1017/S0305004100033776'), (5395, 'Cambridge Journals PDF'), (5396, 'Fundamentals of mathematics: Geometry'), (5397, 'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?type=1&fid=2117060&jid=PSP&volumeId=55&issueId=01&aid=2049244&bodyId=&membershipNumber=&societyETOCSession='), (5398, 'Fundamentals of mathematics: Analysis'), (5399, 'Translated by S. H. Gould'), (5400, 'Fundamentals of mathematics: Foundations of Mathematics / The Real Number System and Algebra'), (5401, 'Wald R.M. General relativity (1984)(T)(494s).djvu'), (5402, 'Schutz B.F. A first course in general relativity (CUP, 1985)(ISBN 0521277035)(KA)(T)(390s).djvu'), (5403, 'Szekeres, Peter - A Course in Modern Mathematical Physics - Groups, Hilbert Spaces and Differential Geometry (2005) (600p)(T).djvu'), (5404, 'Getting things done : the art of stress-free productivity'), (5405, 9780142000), (5406, '[repr.].'), (5407, 'Penguin Books'), (5408, 'Getting things done'), (5409, 'Brain boot camp : work out your mind with your very own electronic coach'), (5410, 9780811869), (5411, 'Chronicle Books'), (5412, 'Brain boot camp'), (5413, 'Imagine life with a well-behaved dog : a 3-step positive dog-training program'), (5414, 9780312598), (5415, '1st ed.'), (5416, "St. Martin's Griffin"), (5417, 'Imagine life with a well-behaved dog'), (5418, 'Goldstein, Poole, Safko. Classical mechanics (3ed., AW, 2000)(T)(C)(636s)(T).djvu'), (5419, 'third'), (5420, 'first'), (5421, 'Radiation reaction at 3.5 post-Newtonian order in effective field theory'), (5422, '2012-05-16 2012-05-16'), (5423, 'http://arxiv.org/abs/1205.3842'), (5424, 'arXiv:1205.3842'), (5425, "We derive the radiation reaction forces on a compact binary inspiral through 3.5 order in the post-Newtonian expansion using the effective field theory approach. We utilize a recent formulation of Hamilton's variational principle that rigorously extends the usual Lagrangian and Hamiltonian formalisms to dissipative systems, including the inspiral of a compact binary from the emission of gravitational waves. We find agreement with previous results, which thus provides a non-trivial confirmation of the extended variational principle. The results from this work nearly complete the equations of motion for the generic inspiral of a compact binary with spinning constituents through 3.5 post-Newtonian order, as derived entirely with effective field theory, with only the spin-orbit corrections to the potential at 3.5 post-Newtonian remaining."), (5426, '2012-05-18 13:54:29'), (5427, '1205.3842 PDF'), (5428, 'http://www.arxiv.org/pdf/1205.3842.pdf'), (5429, 1072), (5430, 9780486612720), (5431, 'Courier Dover Publications'), (5432, 'Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables'), (5433, 'This book is a compendium of mathematical formulas, tables, and graphs. It contains a table of analytical integrals, differential equations, and numerical series; and includes tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration, and techniques for point interpolation and function approximation. Additionally, it devotes a entire section to mathematical and physical constants as fractions and powers of Pi, e, and prime numbers; and discusses statistics by presenting combinatorial analysis and probability functions.'), (5434, '1964-00-00 1964'), (5435, 'Handbook of Mathematical Functions'), (5436, 'http://books.google.com/books?id=MtU8uP7XMvoC'), (5437, '2012-05-20 15:02:53'), (5438, 'An algorithm for smoothing, differentiation and integration of experimental data using spline functions'), (5439, 'Journal of Computational and Applied Mathematics'), (5440, '165-184'), (5441, '1975-09-00 September 1975'), (5442, '0377-0427'), (5443, '10.1016/0771-050X(75)90034-0'), (5444, 'http://www.sciencedirect.com/science/article/pii/0771050X75900340'), (5445, 'This paper presents an algorithm for fitting a smoothing spline function to a set of experimental or tabulated data. The obtained spline approximation can be used for differentiation and integration of the given discrete function. Because of the ease of computation and the good conditioning properties we use normalised B-splines to represent the smoothing spline. A Fortran implementation of the algorithm is given.'), (5446, '2012-05-21 20:27:34'), (5447, 'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271610&_user=492137&_pii=0771050X75900340&_check=y&_origin=article&_zone=toolbar&_coverDate=30-Sep-1975&view=c&originContentFamily=serial&wchp=dGLbVlB-zSkzk&md5=34d7bc40d7dbe28acc37eec6d7025133/1-s2.0-0771050X75900340-main.pdf'), (5448, 'Gravitational Waves from Merging Compact Binaries'), (5449, 'Annual Review of Astronomy and Astrophysics'), (5450, '107-157'), (5451, '10.1146/annurev-astro-082708-101711'), (5452, 'http://www.annualreviews.org/doi/abs/10.1146/annurev-astro-082708-101711'), (5453, 'Largely motivated by the development of highly sensitive gravitational-wave detectors, our understanding of merging compact binaries and the gravitational waves they generate has improved dramatically in recent years. Breakthroughs in numerical relativity now allow us to model the coalescence of two black holes with no approximations or simplifications. There has also been outstanding progress in our analytical understanding of binaries. We review these developments, examining merging binaries using black hole perturbation theory, post-Newtonian expansions, and direct numerical integration of the field equations. We summarize these approaches and what they have taught us about gravitational waves from compact binaries. We place these results in the context of gravitational-wave generating systems, analyzing the impact gravitational-wave emission has on their sources, as well as what we can learn about them from direct gravitational-wave measurements.'), (5454, 'Annual Reviews'), (5455, '2012-05-22 13:10:17'), (5456, '2004-12-16 December 16, 2004'), (5457, 'annurev-astro-082708-101711.pdf'), (5458, 'Gravitational waves from compact binaries'), (5459, 'http://arxiv.org/abs/1108.1307'), (5460, 'arXiv:1108.1307'), (5461, 'In this review, I give a summary of the history of our understanding of gravitational waves and how compact binaries were used to transform their status from mathematical artefact to physical reality. I also describe the types of compact (stellar) binaries that LISA will observe as soon as it is switched on. Finally, the status and near future of LIGO, Virgo and GEO are discussed, as well as the expected detection rates for the Advanced detectors, and the accuracies with which binary parameters can be determined when BH/NS inspirals are detected.'), (5462, '2012-05-22 13:40:42'), (5463, '1108.1307 PDF'), (5464, 'http://www.arxiv.org/pdf/1108.1307.pdf'), (5465, 'Searching for gravitational waves from the inspiral of precessing binary systems: Problems with current waveforms'), (5466, '042003'), (5467, '2003-02-28 February 28, 2003'), (5468, 'http://link.aps.org/doi/10.1103/PhysRevD.67.042003'), (5469, '10.1103/PhysRevD.67.042003'), (5470, 'We consider the problem of searching for gravitational waves emitted during the inspiral phase of binary systems when the orbital plane precesses due to relativistic spin-orbit coupling. This effect takes place when the spins of the binary members are misaligned with respect to the orbital angular momentum. As a first step we assess the importance of precession specifically for the first generation of Laser Interferometric Gravitational Wave Observatory (LIGO) detectors. We investigate the extent of the signal-to-noise ratio reduction and, hence, detection rate that occurs when precession effects are not accounted for in the template waveforms. We restrict our analysis to binary systems that undergo the so-called simple precession and have a total mass ≲10M⊙. We find that for binary systems with rather high mass ratios (e.g., a 1.4M⊙ neutron star and a 10M⊙ black hole) the detection rate can decrease by almost an order of magnitude. Current astrophysical estimates of the rate of binary inspiral events suggest that LIGO could detect at most a few events per year, and therefore the reduction of the detection rate even by a factor of a few is critical. In the second part of our analysis, we examine whether the effect of precession could be included in the templates by capturing the main features of the phase modulation through a small number of extra parameters. Specifically we examine and tested for the first time the 3-parameter family suggested by Apostolatos. We find that, even though these “mimic” templates improve the detection rate, they are still inadequate in recovering the signal-to-noise ratio at the desired level. We conclude that a more complex template family is needed in the near future, still maintaining the number of additional parameters as small as possible in order to reduce the computational costs.'), (5471, '2012-05-22 14:31:25'), (5472, 'Searching for gravitational waves from the inspiral of precessing binary systems'), (5473, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i4/e042003'), (5474, '2005-10-20 2005-10-20'), (5475, 'http://iopscience.iop.org/444346'), (5476, '2012-05-22 14:35:46'), (5477, 'Searching for gravitational waves from the inspiral of precessing binary systems: Astrophysical expectations and detection efficiency of “spiky” templates'), (5478, 69), (5479, 102002), (5480, '2004-05-14 May 14, 2004'), (5481, 'http://link.aps.org/doi/10.1103/PhysRevD.69.102002'), (5482, '10.1103/PhysRevD.69.102002'), (5483, 'Relativistic spin-orbit and spin-spin couplings have been shown to modify the gravitational wave forms expected from inspiraling binaries with a black hole and a neutron star. As a result inspiral signals may be missed due to significant losses in signal-to-noise ratio, if precession effects are ignored in gravitational-wave searches. We examine the sensitivity of the anticipated loss of signal-to-noise ratio on two factors: the accuracy of the precessing wave forms adopted as the true signals and the expected distributions of spin-orbit tilt angles, given the current understanding of their physical origin. We find that the results obtained using signals generated by approximate techniques are in good agreement with the ones obtained by integrating the 2PN equations. This shows that a complete account of all high-order post-Newtonian effects is usually not necessary for the determination of detection efficiencies. Based on our current astrophysical expectations, large tilt angles are not favored and as a result the decrease in detection rate varies rather slowly with respect to the black hole spin magnitude and is within 20–30 % of the maximum possible values.'), (5484, '2012-05-22 14:40:25'), (5485, 'http://link.aps.org/doi/10.1103/PhysRevD.70.124020'), (5486, 'PhysRevD.69.102002.pdf'), (5487, 'Searching for gravitational waves from the inspiral of precessing binary systems: New hierarchical scheme using “spiky” templates'), (5488, '082002'), (5489, '2003-04-11 April 11, 2003'), (5490, 'http://link.aps.org/doi/10.1103/PhysRevD.67.082002'), (5491, '10.1103/PhysRevD.67.082002'), (5492, 'In a recent investigation of the effects of precession on the anticipated detection of gravitational-wave inspiral signals from compact object binaries with moderate total masses ≲10M⊙, we found that (i) if precession is ignored, the inspiral detection rate can decrease by almost a factor of 10, and (ii) previously proposed “mimic” templates cannot improve the detection rate significantly (by more than a factor of 2). In this paper we propose a new family of templates that can improve the detection rate by a factor of 5 or 6 in cases where precession is most important. Our proposed method for these new “mimic” templates involves a hierarchical scheme of efficient, two-parameter template searches that can account for a sequence of spikes that appear in the residual inspiral phase, after one corrects for any oscillatory modification in the phase. We present our results for two cases of compact object masses (10 and 1.4M⊙ and 7 and 3M⊙) as a function of spin properties. Although further work is needed to fully assess the computational efficiency of this newly proposed template family, we conclude that these “spiky templates” are good candidates for a family of precession templates used in realistic searches that can improve detection rates of inspiral events.'), (5493, '2012-05-22 14:55:15'), (5494, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i8/e082002'), (5495, 'Detecting gravitational waves from precessing binaries of spinning compact objects. II. Search implementation for low-mass binaries'), (5496, '2005-10-26 October 26, 2005'), (5497, 'http://link.aps.org/doi/10.1103/PhysRevD.72.084027'), (5498, '10.1103/PhysRevD.72.084027'), (5499, 'Detection template families (DTFs) are built to capture the essential features of true gravitational waveforms using a small set of phenomenological waveform parameters. Buonanno, Chen, and Vallisneri [ Phys. Rev. D 67 104025 (2003)] proposed the BCV2 DTF to perform computationally efficient searches for signals from precessing binaries of compact stellar objects. Here we test the signal-matching performance of the BCV2 DTF for asymmetric-mass-ratio binaries, and specifically for double-black-hole binaries with component masses (m1,m2)∈[6,12]M⊙×[1,3]M⊙, and for black-hole–neutron-star binaries with component masses (m1,m2)=(10M⊙,1.4M⊙); we take all black holes to be maximally spinning. We find a satisfactory signal-matching performance, with fitting factors averaging between 0.94 and 0.98. We also scope out the region of BCV2 parameters needed for a template-based search, we evaluate the template match metric, we discuss a template-placement strategy, and we estimate the number of templates needed for searches at the LIGO design sensitivity. In addition, after gaining more insight in the dynamics of spin-orbit precession, we propose a modification of the BCV2 DTF that is parametrized by physical (rather than phenomenological) parameters. We test this modified “BCV2P” DTF for the (10M⊙, 1.4M⊙) black-hole–neutron-star system, finding a signal-matching performance comparable to the BCV2 DTF, and a reliable parameter-estimation capability for target-binary quantities such as the chirp mass and the opening angle (the angle between the black-hole spin and the orbital angular momentum).'), (5500, '2012-05-22 15:06:21'), (5501, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i8/e084027'), (5502, 'Expected masses of merging compact object binaries observed in gravitational waves'), (5503, '2004-08-01 2004/08/01'), (5504, 352), (5505, '10.1111/j.1365-2966.2004.08028.x'), (5506, '1372-1380'), (5507, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2004.08028.x/abstract;jsessionid=F0398C0343139ED8366977DB4F5358DA.d01t03?systemMessage=Wiley+Online+Library+will+be+disrupted+on+26+May+from+10%3A00-12%3A00+BST+%2805%3A00-07%3A00+EDT%29+for+essential+maintenance'), (5508, '2012-05-22 15:40:27'), (5509, 'onlinelibrary.wiley.com.proxy.library.cornell.edu'), (5510, 'We use the well-tested StarTrack binary population synthesis code to examine the properties of the population of compact object binaries. We calculate the distribution of masses and mass ratios, taking into account weights introduced by observability in gravitational waves during inspiral. We find that in the observability-weighted distribution of double neutron star binaries there are two peaks: one for nearly equal-mass systems, and one for systems consisting of a low- and a high-mass neutron star, q= 0.6–0.7. The observability-weighted distribution of black hole neutron star binaries is concentrated on systems with mass ratio q= 0.3–0.5, while for double black hole binaries the observability-weighted distribution is dominated by massive, nearly equal-mass binaries with q > 0.7.'), (5511, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1111/j.1365-2966.2004.08028.x/asset/j.1365-2966.2004.08028.x.pdf?v=1&t=h2j4rop7&s=eb918feabcf6216ac3c9a6805ae1d2db408d1909'), (5512, 572), (5513, '2002-06-10 2002-06-10'), (5514, '407-431'), (5515, '10.1086/340304'), (5516, 'http://iopscience.iop.org/340304'), (5517, 'A Comprehensive Study of Binary Compact Objects as Gravitational Wave Sources: Evolutionary Channels, Rates, and Physical Properties'), (5518, '2012-05-22 15:57:21'), (5519, 'A Comprehensive Study of Binary Compact Objects as Gravitational Wave Sources'), (5520, 'http://iopscience.iop.org/0004-637X/572/1/407/pdf/0004-637X_572_1_407.pdf'), (5521, 'Effect of gravitational radiation reaction on circular orbits around a spinning black hole'), (5522, 'R3159-R3162'), (5523, 'http://link.aps.org/doi/10.1103/PhysRevD.52.R3159'), (5524, '10.1103/PhysRevD.52.R3159'), (5525, 'The effect of gravitational radiation reaction on circular orbits around a spinning (Kerr) black hole is computed to leading order in S (the magnitude of the spin angular momentum of the hole) and in the strength of gravity M/r (where M is the mass of the black hole, r is the orbital radius, and G=c=1). The radiation reaction makes the orbit shrink but leaves it circular and drives the orbital plane very slowly toward antialignment with the spin of the hole: tan(ι/2)=tan(ι0/2)[1+(61/72)(S/M2)(M/r)3/2], where ι is the angle between the normal to the orbital plane and the spin direction, and ι0 is the initial value of ι, when r is very large.'), (5526, '2012-05-22 16:59:49'), (5527, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v52/i6/pR3159_1'), (5528, 'Birth kicks as the origin of pulsar rotation'), (5529, '1998-05-14 1998-05-14'), (5530, 393), (5531, 6681), (5532, '10.1038/30168'), (5533, "Radio pulsars are thought to born with spin periods of 0.02–0.5 s and space velocities of 100–1,000 km s-1, and they are inferred to have initial dipole magnetic fields of 1011–1013 G (refs 1–5). The average space velocity of their progenitor stars is less than 15 km s-1, which means that pulsars must receive a substantial 'kick' at birth. Here we propose that the birth characteristics of pulsars have a simple physical connection with each other. Magnetic fields maintained by differential rotation between the core and envelope of the progenitor would keep the whole star in a state of approximately uniform rotation until10 years before the explosion. Such a slowly rotating core has 1,000 times less angular momentum than required to explain the rotation of pulsars. The specific physical process that 'kicks' the neutron star at birth has not been identified, but unless its force is exerted exactly head-on6 it will also cause the neutron star to rotate. We identify this process as the origin of the spin of pulsars. Such kicks may cause a correlation between the velocity and spin vectors of pulsars. We predict that many neutron stars are born with periods longer than 2 s, and never become radio pulsars."), (5534, 139), (5535, 'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v393/n6681/abs/393139a0.html'), (5536, '2012-05-22 18:05:13'), (5537, 'www.nature.com.proxy.library.cornell.edu'), (5538, 'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v393/n6681/pdf/393139a0.pdf'), (5539, '2009-06-07 2009-06-07'), (5540, 114007), (5541, '10.1088/0264-9381/26/11/114007'), (5542, 'http://iopscience.iop.org/0264-9381/26/11/114007'), (5543, 'Degeneracies in sky localization determination from a spinning coalescing binary through gravitational wave observations: a Markov-chain Monte Carlo analysis for two detectors'), (5544, '2012-05-22 18:20:07'), (5545, 'Degeneracies in sky localization determination from a spinning coalescing binary through gravitational wave observations'), (5546, '10.1103/PhysRevD.70.124020'), (5547, '0264-9381_26_11_114007.pdf'), (5548, 549), (5549, '2001-03-10 2001-03-10'), (5550, '1111-1118'), (5551, '10.1086/319455'), (5552, 'http://iopscience.iop.org/319455'), (5553, 'Pulsar Jets: Implications for Neutron Star Kicks and Initial Spins'), (5554, '2012-05-22 18:36:08'), (5555, 'Pulsar Jets'), (5556, 'http://iopscience.iop.org/0004-637X/549/2/1111/pdf/0004-637X_549_2_1111.pdf'), (5557, 656), (5558, '2007-02-10 2007-02-10'), (5559, '399-407'), (5560, '10.1086/510352'), (5561, 'http://iopscience.iop.org/510352'), (5562, 'Spin‐Kick Correlation in Neutron Stars: Alignment Conditions and Implications'), (5563, '2012-05-22 19:25:47'), (5564, 'Spin‐Kick Correlation in Neutron Stars'), (5565, 'http://iopscience.iop.org/0004-637X/656/1/399/pdf/0004-637X_656_1_399.pdf'), (5566, 'Starting with a post-Newtonian description of compact binary systems, we derive a set of equations that describes the evolution of the orbital angular momentum and both spin vectors during inspiral. We find regions of phase space that exhibit resonance behavior, characterized by small librations of the spin vectors around a fixed orientation. Because of the loss of energy and orbital angular momentum through radiation reaction, systems can eventually be captured into these resonance orientations. By investigating the long-term evolution of compact binaries with a variety of initial conditions, we find that the distribution in parameter space can be strongly affected by resonance captures. This has the effect of significantly reducing the size of search space for gravitational wave sources, in turn improving the chances of detecting such sources through methods of template matching. Furthermore, by calculating the expected spin distribution at the end of the inspiral phase, we can predict what are the most likely initial conditions for the plunge phase, a result of great interest for numerical relativity calculations.'), (5567, '2012-05-23 19:29:25'), (5568, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v70/i12/e124020'), (5569, '2001-12-21 2001-12-21'), (5570, '5487-5510'), (5571, '10.1088/0264-9381/18/24/312'), (5572, 'http://iopscience.iop.org/0264-9381/18/24/312'), (5573, 'On certain quasi-local spin-angular momentum expressions for large spheres near the null infinity'), (5574, '2012-05-23 22:21:43'), (5575, 'Mathematics of classical and quantum physics'), (5576, '0264-9381_18_24_312.pdf'), (5577, 'Angular momentum in general relativity: The definition at null infinity includes the spatial definition as a special case'), (5578, 104002), (5579, '2001-04-04 April 04, 2001'), (5580, 'http://link.aps.org/doi/10.1103/PhysRevD.63.104002'), (5581, '10.1103/PhysRevD.63.104002'), (5582, 'I show that the definition of angular momentum at null infinity given by A. Rizzi, Phys. Rev. Lett. 81, 1150 (1998), reduces to the Arnowitt-Deser-Misner definition at spatial infinity in the appropriate limit. This identification reinforces the gauge condition of the null definition as well as the null definition itself. Insight into the place of the null and spatial definitions is also gained. The methods used in this paper are very useful for understanding far-field problems in general relativity; a set of Appendixes gives details of the methods.'), (5583, '2012-05-23 22:25:58'), (5584, 'Angular momentum in general relativity'), (5585, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i10/e104002'), (5586, 21), (5587, '2004-12-07 2004-12-07'), (5588, '5409-5425'), (5589, '10.1088/0264-9381/21/23/008'), (5590, 'http://iopscience.iop.org/0264-9381/21/23/008'), (5591, 'Intrinsic angular momentum and centre of mass in general relativity'), (5592, '2012-05-23 22:26:18'), (5593, '048667164X'), (5594, '0264-9381_21_23_008.pdf'), (5595, 'http://arxiv.org/abs/1306.3901'), (5596, 'A formalism is presented for the treatment of space‐times, which is intermediate between a fully covariant approach and the spin‐coefficient method of Newman and Penrose. With the present formalism, a pair of null directions only, rather than an entire null tetrad, is singled out at each point. The concept of a spin‐ and boost‐weighted quantity is defined, the formalism operating entirely with such quantities. This entails the introduction of modified differentiation operators, one of which represents a natural extension of the definition of the operator which had been introduced earlier by Newman and Penrose. For suitable problems, the present formalism should lead to considerable simplifications over that achieved by the standard spin‐coefficient method.'), (5597, '1973-07-01 1973-07-01'), (5598, 'doi:10.1063/1.1666410'), (5599, '874-881'), (5600, 'A space‐time calculus based on pairs of null directions'), (5601, 14), (5602, '2013-06-17 2013-06-17'), (5603, 'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/14/874/1/pdf'), (5604, '2013-06-18 14:40:32'), (5605, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v14/i7/p874_s1'), (5606, 'We study the ability of the advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem. The cosmic censorship conjecture, which is believed to be true in the theory of general relativity, limits the spin-to-mass-squared ratio of a Kerr black hole. The no-hair theorem, which is also believed to be true in the theory of general relativity, suggests a particular value for the tidal Love number of a non-rotating black hole. Using the Fisher matrix formalism, we examine the measurability of the spin and tidal deformability of compact binary systems involving at least one putative black hole. Using parameter measurement errors and correlations obtained from the Fisher matrix, we determine the smallest detectable violation of bounds implied by the cosmic censorship conjecture and the no-hair theorem. We examine the effect of excluding unphysical areas of parameter space when determining the smallest detectable apparent violations, and we examine the effect of different post-Newtonian corrections to the amplitude of the compact binary coalescence gravitational waveform. In addition, we perform a brief study of how the recently calculated 3.0 pN and 3.5 pN spin-orbit corrections to the phase affect spin and mass parameter measurability. We find that physical priors on the symmetric mass ratio and higher harmonics in the gravitational waveform could significantly affect the ability of aLIGO to investigate cosmic censorship and the no-hair theorem for certain systems.'), (5607, '2012-05-23 23:13:13'), (5608, '10.1103/PhysRevD.87.104006'), (5609, '2012-05-23 23:14:02'), (5610, '[Unabridged and corr. republ. in one vol.].'), (5611, '1992-00-00 1992'), (5612, 'Einstein for beginners'), (5613, 9780679725), (5614, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i6/e064041'), (5615, 'Pantheon Books'), (5616, 'The cartoon guide to physics'), (5617, 9780062731), (5618, '2012-06-13 14:22:46'), (5619, 'HarperPerennial'), (5620, '1991-00-00 1991'), (5621, 'Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems'), (5622, '1962-08-21 08/21/1962'), (5623, '10.1098/rspa.1962.0161'), (5624, 'Proc. R. Soc. Lond. A'), (5625, 269), (5626, 1336), (5627, 'http://rspa.royalsocietypublishing.org/content/269/1336/21'), (5628, '21-52'), (5629, '1364-5021, 1471-2946'), (5630, '2012-06-05 02:58:16'), (5631, 'rspa.royalsocietypublishing.org.proxy.library.cornell.edu'), (5632, "This paper is divided into four parts. In part A, some general considerations about gravitational radiation are followed by a treatment of the scalar wave equation in the manner later to be applied to Einstein's field equations. In part B, a co-ordinate system is specified which is suitable for investigation of outgoing gravitational waves from an isolated axi-symmetric reflexion-symmetric system. The metric is expanded in negative powers of a suitably defined radial co-ordinate r, and the vacuum field equations are investigated in detail. It is shown that the flow of information to infinity is controlled by a single function of two variables called the news function. Together with initial conditions specified on a light cone, this function fully defines the behaviour of the system. No constraints of any kind are encountered. In part C, the transformations leaving the metric in the chosen form are determined. An investigation of the corresponding transformations in Minkowski space suggests that no generality is lost by assuming that the transformations, like the metric, may be expanded in negative powers of r. In part D, the mass of the system is defined in a way which in static metrics agrees with the usual definition. The principal result of the paper is then deduced, namely, that the mass of a system is constant if and only if there is no news; if there is news, the mass decreases monotonically so long as it continues. The linear approximation is next discussed, chiefly for its heuristic value, and employed in the analysis of a receiver for gravitational waves. Sandwich waves are constructed, and certain non-radiative but non-static solutions are discussed. This part concludes with a tentative classification of time-dependent solutions of the types considered."), (5633, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v19/i7/p1542_s1?isAuthorized=no'), (5634, 'Gravitational Waves in General Relativity. VIII. Waves in Asymptotically Flat Space-Time'), (5635, '1962-10-30 10/30/1962'), (5636, '10.1098/rspa.1962.0206'), (5637, 1340), (5638, 'http://rspa.royalsocietypublishing.org/content/270/1340/103'), (5639, '103-126'), (5640, 'Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals'), (5641, 'Gravitational fields containing bounded sources and gravitational radiation are examined by analyzing their properties at spatial infinity. A convenient way of splitting the metric tensor and the Einstein field equations, applicable in any space-time, is first introduced. Then suitable boundary conditions are set. The group of co-ordinate transformations that preserves the boundary conditions is analyzed. Different possible gravitational fields are characterized intrinsically by a combination of (i) characteristic initial data, and (ii) Dirichlet data at spatial infinity. To determine a particular solution one must specify four functions of three variables and three functions of two variables; these functions are not subject to constraints. A method for integrating the field equations is given; the asymptotic behaviour of the metric and Riemann tensors for large spatial distances is analyzed in detail; the dynamical variables of the radiation modes are exhibited; and a superposition principle for the radiation modes of the gravitational field is suggested. Among the results are: (i) the group of allowed co-ordinate transformations contains the inhomogeneous orthochronous Lorentz group as a subgroup; (ii) each of the five leading terms in an asymptotic expansion of the Riemann tensor has the algebraic structure previously predicted from analyzing the Petrov classification; (iii) gravitational waves appear to carry mass away from the interior; (iv) time-dependent periodic solutions of the field equations which obey the stated boundary conditions do not exist. It was found that the general fields studied in the present work are in many ways very similar to the axially symmetric fields recently studied by Bondi, van der Burg & Metzner.'), (5642, '2012-07-12 2012-07-12'), (5643, '2012-06-05 03:00:42'), (5644, 'Proc. R. Soc. Lond. A-1962-Bondi-21-52.pdf'), (5645, 'Proc. R. Soc. Lond. A-1962-Sachs-103-26.pdf'), (5646, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v3/i5/p891_s1?isAuthorized=no'), (5647, 'The asymptotic behavior of the Weyl tensor and metric tensor is investigated for probably all asymptotically flat solutions of the empty space Einstein field equations. The systematic investigation utilizes a set of first order differential equations which are equivalent to the empty space Einstein equations. These are solved asymptotically, subject to a condition imposed on a tetrad component of the Riemann tensor ψ0 which ensures the approach to flatness at spatial infinity of the space‐time. If ψ0 is assumed to be an analytic function of a suitably defined radial coordinate, uniqueness of the solutions can be proved. However, this paper makes considerable progress toward establishing a rigorous proof of uniqueness in the nonanalytic case. A brief discussion of the remaining coordinate freedom, with certain topological aspects, is also included.'), (5648, '1962-09-01 1962-09-01'), (5649, 'doi:10.1063/1.1724303'), (5650, '891-901'), (5651, '2012-06-05 03:08:20'), (5652, 'http://arxiv.org/abs/1207.3088'), (5653, 'arXiv:1207.3088'), (5654, 'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/3/891/1/pdf'), (5655, '2012-06-05 03:09:11'), (5656, 'Asymptotic Symmetries in Gravitational Theory'), (5657, 128), (5658, '2851-2864'), (5659, '1962-12-15 December 15, 1962'), (5660, 'http://link.aps.org/doi/10.1103/PhysRev.128.2851'), (5661, '10.1103/PhysRev.128.2851'), (5662, 'It is pointed out that the definition of the inhomogeneous Lorentz group as a symmetry group breaks down in the presence of gravitational fields even when the dynamical effects of gravitational forces are completely negligible. An attempt is made to rederive the Lorentz group as an "asymptotic symmetry group" which leaves invariant the form of the boundary conditions appropriate for asymptotically flat gravitational fields. By analyzing recent work of Bondi and others on gravitational radiation it is shown that, with apparently reasonable boundary conditions, one obtains not the Lorentz group but a larger group. The name "generalized Bondi-Metzner group" ("GBM group") is suggested for this larger group.'), (5663, '2012-06-05 03:09:26'), (5664, 'http://prola.aps.org.proxy.library.cornell.edu/pdf/PR/v128/i6/p2851_1'), (5665, 'JMathPhys_3_891.pdf'), (5666, 'On the point mass approximation to calculate the gravitational wave signal from white dwarf binaries'), (5667, '2012-06-04 2012-06-04'), (5668, 'http://arxiv.org/abs/1206.0744'), (5669, 'arXiv:1206.0744'), (5670, 'Double white dwarf binaries in the Galaxy dominate the gravitational wave sky and would be detectable for an instrument such as LISA. Most studies have calculated the expected gravitational wave signal under the assumption that the binary white dwarf system can be represented by two point masses in orbit. We discuss the accuracy of this approximation for real astrophysical systems. For non-relativistic binaries in circular orbit the gravitational wave signal can easily be calculated. We show that for these systems the point mass approximation is completely justified when the individual stars are axisymmetric irrespective of their size. We find that the signal obtained from Smoothed-Particle Hydrodynamics simulations of tidally deformed, Roche-lobe filling white dwarfs, including one case when an accretion disc is present, is consistent with the point mass approximation. The difference is typically at the level of one per cent or less in realistic cases, yielding small errors in the inferred parameters of the binaries.'), (5671, '2012-06-06 14:51:10'), (5672, '1206.0744 PDF'), (5673, 'http://www.arxiv.org/pdf/1206.0744.pdf'), (5674, 'A New Method for Gravitational Wave Detection with Atomic Sensors'), (5675, '2012-06-05 2012-06-05'), (5676, 'http://arxiv.org/abs/1206.0818'), (5677, 'arXiv:1206.0818'), (5678, 'Laser frequency noise is a dominant noise background for the detection of gravitational waves using long-baseline optical interferometry. Amelioration of this noise requires near simultaneous strain measurements on more than one interferometer baseline, necessitating, for example, more than two satellites for a space-based detector, or two interferometer arms for a ground-based detector. We describe a new detection strategy based on recent advances in optical atomic clocks and atom interferometry which can operate at long-baselines and which is immune to laser frequency noise. Laser frequency noise is suppressed because the signal arises strictly from the light propagation time between two ensembles of atoms. This new class of sensor allows sensitive gravitational wave detection with only a single baseline. This approach also has practical applications in, for example, the development of ultra-sensitive gravimeters and gravity gradiometers.'), (5679, '2012-06-06 14:58:16'), (5680, '1206.0818 PDF'), (5681, 'http://www.arxiv.org/pdf/1206.0818.pdf'), (5682, '2012-06-21 2012-06-21'), (5683, 124001), (5684, '10.1088/0264-9381/29/12/124001'), (5685, 'http://iopscience.iop.org/0264-9381/29/12/124001'), (5686, '2012-06-06 15:54:05'), (5687, 'http://iopscience.iop.org/0264-9381/29/12/124001/pdf/0264-9381_29_12_124001.pdf'), (5688, '2012-06-13 14:23:43'), (5689, 'A new definition of asymptotic flatness in both null and spacelike directions is introduced. Notions relevant to the null regime are borrowed directly from Penrose’s definition of weak asymptotic simplicity. In the spatial regime, however, a new approach is adopted. The key feature of this approach is that it uses only those notions which refer to space–time as a whole, thereby avoiding the use of a initial value formulation, and, consequently, of a splitting of space–time into space and time. It is shown that the resulting description of asymptotic flatness not only encompasses the essential physical ideas behind the more familiar approaches based on the initial value formulation, but also succeeds in avoiding the global problems that usually arise. A certain 4‐manifold—called Spi (spatial infinity) —is constructed using well‐behaved, asymptotically geodesic, spacelike curves in the physical space–time. The structure of Spi is discussed in detail; in many ways, Spi turns out to be the spatial analog of I. The group of asymptotic symmetries at spatial infinity is examined. In its structure, this group turns out to be very similar to the BMS group. It is further shown that for the class of asymptotically flat space–times satisfying an additional condition on the (asymptotic behavior of the ’’magnetic’’ part of the) Weyl tensor, a Poincaré (sub‐) group can be selected from the group of asymptotic symmetries in a canonical way. (This additional condition is rather weak: In essence, it requires only that the angular momentum contribution to the asymptotic curvature be of a higher order than the energy–momentum contribution.) Thus, for this (apparently large) class of space–times, the symmetry group at spatial infinity is just the Poincaré group. Scalar, electromagnetic and gravitational fields are then considered, and their limiting behavior at spatial infinity is examined. In each case, the asymptotic field satisfies a simple, linear differential equation. Finally, conserved quantities are constructed using these asymptotic fields. Total charge and 4‐momentum are defined for arbitrary asymptotically flat space–times. These definitions agree with those in the literature, but have a further advantage of being both intrinsic and free of ambiguities which usually arise from global problems. A definition of angular momentum is then proposed for the class of space–times satisfying the additional condition on the (asymptotic behavior of the) Weyl tensor. This definition is intimately intertwined with the fact that, for this class of space–times, the group of asymptotic symmetries at spatial infinity is just the Poincaré group; in particular, the definition is free of super‐translation ambiguities. It is shown that this angular momentum has the correct transformation properties. In the next paper, the formalism developed here will be seen to provide a platform for discussing in detail the relationship between the structure of the gravitational field at null infinity and that at spatial infinity.'), (5690, '0264-9381_21_23_008-1.pdf'), (5691, '2009-02-21 2009-02-21'), (5692, '048002'), (5693, '10.1088/0264-9381/26/4/048002'), (5694, 'http://iopscience.iop.org/0264-9381/26/4/048002'), (5695, 'A note on computations of angular momentum and its flux in numerical relativity'), (5696, '2012-06-13 14:25:16'), (5697, '1978-07-01 1978-07-01'), (5698, 'Practical formula for the radiated angular momentum'), (5699, '041502'), (5700, 'http://link.aps.org/doi/10.1103/PhysRevD.76.041502'), (5701, '10.1103/PhysRevD.76.041502'), (5702, 'We present a simple formula for the radiated angular momentum based on a spin-weighted spherical harmonic decomposition of the Weyl scalar ψ4 representing outgoing radiation in the Kinnersley tetrad. We test our formula by measuring the radiated angular momentum from three simulations of nonspinning equal-mass–black-hole binaries with orbital angular momentum aligned along the x, y, and z axes, respectively. We find that the radiated angular momentum agrees with the differences in the remnant horizon spins and the initial angular momentum for each system.'), (5703, '2012-06-13 14:25:23'), (5704, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i4/e041502'), (5705, '0264-9381_26_4_048002.pdf'), (5706, '1988-03-01 1988-03-01'), (5707, '423-435'), (5708, '10.1088/0264-9381/5/3/004'), (5709, 'http://iopscience.iop.org/0264-9381/5/3/004'), (5710, 'Supercentre of mass system at future null infinity'), (5711, '2012-06-13 16:16:36'), (5712, 'doi:10.1063/1.523863'), (5713, '0264-9381_5_3_004.pdf'), (5714, 'On angular momentum at future null infinity'), (5715, 503), (5716, 'http://stacks.iop.org/0264-9381/3/i=4/a=006'), (5717, 'A new definition of angular momentum at future null infinity is proposed which is free of supertranslation ambiguities. A prescription is given to single out a unique Bondi system.'), (5718, '0264-9381_3_4_006.pdf'), (5719, '1542-1566'), (5720, 'A unified treatment of null and spatial infinity in general relativity. I. Universal structure, asymptotic symmetries, and conserved quantities at spatial infinity'), (5721, '2012-06-14 17:49:33'), (5722, 'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/19/1542/1/pdf'), (5723, '2012-06-14 17:51:09'), (5724, 'One of the greatest theoretical challenges in the build-up to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly simplify this problem. We show that generic precessing-binary inspiral waveforms (covering a seven-dimensional parameter space) can be mapped to only a two-dimensional space of non-precessing binaries, characterized by the mass ratio and a single effective total spin. The mapping consists of a time-dependent rotation of the waveforms into the quadrupole-aligned frame, and is extremely accurate (matches $> 0.99$ with parameter biases in the total spin of $\\Delta \\chi \\leq 0.04$), even in the case of transitional precession. In addition, we demonstrate a simple method to construct hybrid post-Newtonian--numerical-relativity precessing-binary waveforms in the quadrupole-aligned frame, and provide evidence that our approximate mapping can be used all the way to the merger. Finally, based on these results, we outline a general proposal for the construction of generic waveform models, which will be the focus of future work.'), (5725, '2012-07-16 13:04:13'), (5726, '2012-06-17 20:17:26'), (5727, 'The Shift Operators and Translations of Spherical Harmonics'), (5728, 'Solid and surface spherical harmonics functions have very simple transformation properties with respect to the gradient and angular momentum operators. These properties can be utilized for the derivation of translation relations of the spherical harmonic functions. 1 Introduction Already many papers have been published about the transformational properties of the spherical harmonics functions. To cite a few: Hobson (1955), Rose (1957), Aardoom (1969), Giacaglia (1980) and Epton and Dembart (1994). The formulas presented in this paper are not new, but they are derived in a particular straightforward manner which we believe to be much simpler than often found in other literature. First we give some definitions, then we show the properties of the operators applied and finally we show how they can be used to derive translation relations for spherical harmonic functions and their coefficients. 2 General properties Since many definitions can be found for the spherical harmonic functions, w...'), (5729, 'CiteSeer'), (5730, 'Citeseer - Full Text PDF'), (5731, 'http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=A5E4773ABD84E7FCA5C5DB2619F75B00?doi=10.1.1.56.5257&rep=rep1&type=pdf'), (5732, '2012-06-18 17:54:49'), (5733, 'Energy of isolated systems at retarded times as the null limit of quasilocal energy'), (5734, '1977-1984'), (5735, '1997-02-15 February 15, 1997'), (5736, 'http://link.aps.org/doi/10.1103/PhysRevD.55.1977'), (5737, '10.1103/PhysRevD.55.1977'), (5738, 'We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy E. The result coincides with the Bondi-Sachs mass. Our E is the lapse-unity shift-zero boundary value of the gravitational Hamiltonian appropriate for the partial system Σ contained within a finite topologically spherical boundary B=∂Σ. Moreover, we show that with an arbitrary lapse and zero shift the same null limit of the Hamiltonian defines a physically meaningful element in the space dual to supertranslations. This result is specialized to yield an expression for the full Bondi-Sachs four-momentum in terms of Hamiltonian values.'), (5739, '2012-06-18 19:47:40'), (5740, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v55/i4/p1977_1'), (5741, '1946-00-00 1946'), (5742, '10.1119/1.1990764'), (5743, 'http://link.aip.org/link/?AJP/14/1/1&Agg=doi'), (5744, 'Probability, Frequency and Reasonable Expectation'), (5745, '2012-06-18 22:14:41'), (5746, 'On the Global Isometric Embedding of Pseudo-Riemannian Manifolds'), (5747, '1970-01-13 01/13/1970'), (5748, '10.1098/rspa.1970.0015'), (5749, 314), (5750, 1518), (5751, 'http://rspa.royalsocietypublishing.org/content/314/1518/417'), (5752, '417-428'), (5753, '2012-06-22 00:56:45'), (5754, "It is shown that any pseudo-Riemannian manifold has (in Nash's sense) a proper isometric embedding into a pseudo-Euclidean space, which can be made to be of arbitrarily high differentiability. The application of this to the positive definite case treated by Nash gives a new proof using a Euclidean space of substantially lower dimension. The general result is applied to the space-time of relativity, and the dimensions and signatures of the spaces needed to embed various cases are evaluated."), (5755, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v15/i10/p1768_s1'), (5756, 'Proc. R. Soc. Lond. A-1970-Clarke-417-28.pdf'), (5757, 'Spacetime algebra is employed to formulate classical relativistic mechanics without coordinates. Observers are treated on the same footing as other physical systems. The kinematics of a rigid body are expressed in spinor form and the Thomas precession is derived.'), (5758, '1974-10-01 1974-10-01'), (5759, 'doi:10.1063/1.1666540'), (5760, '1768-1777'), (5761, 'Proper particle mechanics'), (5762, '2012-06-26 15:24:01'), (5763, 'Detecting binary neutron star systems with spin in advanced gravitational-wave detectors'), (5764, '2012-07-26 2012-07-26'), (5765, 'JMathPhys_15_1768.pdf'), (5766, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v15/i10/p1778_s1'), (5767, "A spinor formulation of the classical Lorentz force is given which describes the precession of an electron's spin as well as its velocity. Solutions are worked out applicable to an electron in a uniform field, a plane wave, and a Coulomb field."), (5768, 'doi:10.1063/1.1666541'), (5769, '1778-1786'), (5770, 'Proper dynamics of a rigid point particle'), (5771, '2012-06-26 15:26:02'), (5772, 'http://arxiv.org/abs/1207.6406'), (5773, 'arXiv:1207.6406'), (5774, 'JMathPhys_15_1778.pdf'), (5775, 'Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation'), (5776, 'http://www.livingreviews.org/lrr-2009-6'), (5777, 'lrr-2009-6Color.pdf'), (5778, 'Quasi-Local Energy-Momentum and Angular Momentum in General Relativity'), (5779, 'Living Rev. Relativity'), (5780, 'http://relativity.livingreviews.org/Articles/lrr-2009-4/'), (5781, '2012-07-02 15:44:59'), (5782, 'relativity.livingreviews.org'), (5783, 'lrr-2009-4Color.pdf'), (5784, '1985-01-01 1985-01-01'), (5785, 'L7-L10'), (5786, '10.1088/0264-9381/2/1/002'), (5787, 'http://iopscience.iop.org/0264-9381/2/1/002'), (5788, 'Momentum flux at null infinity'), (5789, '2012-07-02 17:50:01'), (5790, '243 - 250'), (5791, '0264-9381_2_1_002.pdf'), (5792, '2012-00-00 2012'), (5793, '10.1016/j.jcp.2011.09.014'), (5794, 'http://www.sciencedirect.com/science/article/pii/S0021999111005468'), (5795, '1-s2.0-S0021999111005468-main-1.pdf'), (5796, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v3/i3/p566_s1?isAuthorized=yes'), (5797, 'A new approach to general relativity by means of a tetrad or spinor formalism is presented. The essential feature of this approach is the consistent use of certain complex linear combinations of Ricci rotation coefficients which give, in effect, the spinor affine connection. It is applied to two problems in radiation theory; a concise proof of a theorem of Goldberg and Sachs and a description of the asymptotic behavior of the Riemann tensor and metric tensor, for outgoing gravitational radiation.'), (5798, '1962-05-01 1962-05-01'), (5799, 'doi:10.1063/1.1724257'), (5800, '566-578'), (5801, '2012-07-07 12:13:58'), (5802, 'Recoil velocity at 2PN order for spinning black hole binaries'), (5803, '2008-12-23 2008-12-23'), (5804, 'http://arxiv.org/abs/0812.4413'), (5805, 'JMathPhys_3_566.pdf'), (5806, 'http://jmp.aip.org/resource/1/jmapaq/v4/i7/p998_s1?bypassSSO=1'), (5807, '1963-07-01 1963-07-01'), (5808, 'doi:10.1063/1.1704025'), (5809, '998-998'), (5810, 'Errata: An Approach to Gravitational Radiation by a Method of Spin Coefficients'), (5811, '2012-07-07 12:15:58'), (5812, 'Errata'), (5813, 'Phys.Rev.D80:044010,2009'), (5814, '10.1103/PhysRevD.80.044010'), (5815, 'JMathPhys_4_998.pdf'), (5816, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v2/i3/p290_s1?isAuthorized=yes'), (5817, "It is shown that a field of null rays is geodetic and shear‐free if and only if the associated family of null bivectors includes a solution to Maxwell's equations for charge‐free space."), (5818, '1961-05-01 1961-05-01'), (5819, 'doi:10.1063/1.1703712'), (5820, '290-291'), (5821, 'Null Electromagnetic Fields'), (5822, '2012-07-07 13:15:19'), (5823, 'arXiv:0812.4413'), (5824, "We compute the flux of linear momentum carried by gravitational waves emitted from spinning binary black holes at 2PN order for generic orbits. In particular we provide explicit expressions of three new types of terms, namely next-to-leading order spin-orbit terms at 1.5 PN order, spin-orbit tail terms at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to quasi-circular orbits, we integrate the linear momentum flux over time to obtain the recoil velocity as function of orbital frequency. We find that in the so-called superkick configuration the higher-order spin corrections can increase the recoil velocity up to about a factor 3 with respect to the leading-order PN prediction. Furthermore, we provide expressions valid for generic orbits, and accurate at 2PN order, for the energy and angular momentum carried by gravitational waves emitted from spinning binary black holes. Specializing to quasi-circular orbits we compute the spin-spin terms at 2PN order in the expression for the evolution of the orbital frequency and found agreement with Mik\\'oczi, Vas\\'uth and Gergely. We also verified that in the limit of extreme mass ratio our expressions for the energy and angular momentum fluxes match the ones of Tagoshi, Shibata, Tanaka and Sasaki obtained in the context of black hole perturbation theory."), (5825, '2012-09-03 00:31:21'), (5826, 'JMathPhys_2_290.pdf'), (5827, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v21/i8/p2245_s1?isAuthorized=yes'), (5828, 'The good cut equation (F2\u2009Z=σ) is the link between a physical asymptotically flat space–time (characterized by σ) and its associated H‐space (characterized by Z and interpreted by Penrose as a nonlinear graviton). In this work a class of regular, nontrivial (σ≠0) solutions to the good cut equation is obtained by writing σ in terms of a potential function ϕ.'), (5829, '1980-08-01 1980-08-01'), (5830, 'doi:10.1063/1.524660'), (5831, '2245-2247'), (5832, 'A note on the good cut equation'), (5833, '2012-07-08 22:20:01'), (5834, '0812.4413 PDF'), (5835, 'http://www.arxiv.org/pdf/0812.4413.pdf'), (5836, 'Aligned Spins: Orbital Elements, Decaying Orbits, and Last Stable Circular Orbit to high post-Newtonian Orders'), (5837, '2010-12-21 2010-12-21'), (5838, 245004), (5839, '10.1088/0264-9381/27/24/245004'), (5840, 'http://iopscience.iop.org/0264-9381/27/24/245004'), (5841, 'The generalized good cut equation'), (5842, '2012-07-08 22:21:49'), (5843, 'Towards models of gravitational waveforms from generic binaries'), (5844, 'JMathPhys_21_2245.pdf'), (5845, '0264-9381_27_24_245004.pdf'), (5846, '1207.3088 PDF'), (5847, 'http://www.arxiv.org/pdf/1207.3088.pdf'), (5848, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v27/i5/p1398_s1?isAuthorized=yes'), (5849, 'The Dirac and Kähler equations are separated in a class of spherically symmetric space‐times by using new techniques of Clifford analysis. New operators, which raise and lower the ‘‘spin weight’’ of spin‐weighted functions by (1)/(2), are also introduced. The separated solutions enable us to analyze the distinction between spinor solutions to the Dirac separation equation and Kähler solutions.'), (5850, '1986-05-01 1986-05-01'), (5851, 'doi:10.1063/1.527098'), (5852, '1398-1403'), (5853, 'Separation of Dirac and Kähler equations in spherically symmetric space‐times'), (5854, 'SPIE-AIP'), (5855, '2012-07-16 19:18:02'), (5856, '2012-07-30 2012-07-30'), (5857, 'http://arxiv.org/abs/1207.6961'), (5858, 'JMathPhys_27_1398.pdf'), (5859, 'JMathPhys_18_1849.pdf'), (5860, 'Towards wave extraction in numerical relativity: the quasi-Kinnersley frame'), (5861, '2004-07-02 2004-07-02'), (5862, 'http://arxiv.org/abs/gr-qc/0407013'), (5863, 'Phys.Rev. D72 (2005) 024014'), (5864, '10.1103/PhysRevD.72.024014'), (5865, 'arXiv:gr-qc/0407013'), (5866, 'The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times non-perturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time.'), (5867, '2012-07-16 20:19:08'), (5868, 'Towards wave extraction in numerical relativity'), (5869, 'gr-qc/0407013 PDF'), (5870, 'http://www.arxiv.org/pdf/gr-qc/0407013.pdf'), (5871, 'Unambiguous angular momentum of radiative spacetimes and asymptotic structure in terms of the center of mass system'), (5872, '2003-05-02 2003-05-02'), (5873, 'http://arxiv.org/abs/gr-qc/0305010'), (5874, 'arXiv:gr-qc/0305010'), (5875, 'We present a definition of angular momentum for radiative spacetimes which does not suffer from any ambiguity of supertranslations. We succeed in providing an appropriate notion of {\\it intrinsic} angular momentum; and at the same time a definition of center of mass frame at future null infinity. We use the center of mass frame to present the asymptotic structure equations for vacuum spacetimes.'), (5876, '2012-07-16 20:27:53'), (5877, 'gr-qc/0305010 PDF'), (5878, 'http://www.arxiv.org/pdf/gr-qc/0305010.pdf'), (5879, 'arXiv:1207.6961'), (5880, 'Report on GR16, Session A3: Mathematical Studies of the Field Equations'), (5881, 'Light cones in relativity: Real, complex, and virtual, with applications'), (5882, '2011-02-11 February 11, 2011'), (5883, 'http://link.aps.org/doi/10.1103/PhysRevD.83.044023'), (5884, '10.1103/PhysRevD.83.044023'), (5885, 'We study geometric structures associated with shear-free null geodesic congruences in Minkowski space-time and asymptotically shear-free null geodesic congruences in asymptotically flat space-times. We show how in both the flat and asymptotically flat settings, complexified future null infinity IC+ acts as a “holographic screen,” interpolating between two dual descriptions of the null geodesic congruence. One description constructs a complex null geodesic congruence in a complex space-time whose source is a complex worldline, a virtual source as viewed from the holographic screen. This complex null geodesic congruence intersects the real asymptotic boundary when its source lies on a particular open-string type structure in the complex space-time. The other description constructs a real, twisting, shear-free or asymptotically shear-free null geodesic congruence in the real space-time, whose source (at least in Minkowski space) is in general a closed-string structure: the caustic set of the congruence. Finally we show that virtually all of the interior space-time physical quantities that are identified at null infinity I+ (center of mass, spin, angular momentum, linear momentum, and force) are given kinematic meaning and dynamical descriptions in terms of the complex worldline.'), (5886, '2012-07-17 02:11:00'), (5887, 'Light cones in relativity'), (5888, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i4/e044023'), (5889, '2010-04-07 2010-04-07'), (5890, '10.1088/0264-9381/27/7/075009'), (5891, 'http://iopscience.iop.org/0264-9381/27/7/075009'), (5892, 'The real meaning of complex Minkowski-space world-lines'), (5893, '2012-07-17 02:13:06'), (5894, '2002-04-29 2002-04-29'), (5895, '0264-9381_27_7_075009.pdf'), (5896, 'fulltext-6.pdf'), (5897, 'Doran & Lasenby - Geometric Algebra For Physicists (only first chapter)-1.pdf'), (5898, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v39/i12/p6631_s1?isAuthorized=yes'), (5899, 'The notion of center of mass for an isolated system has been previously encoded in the definition of the so-called nice sections. In this article we present a generalization of the proof of existence of solutions to the linearized equation for nice sections, and formalize a local existence proof of nice sections relaxing the radiation condition. We report on the differentiable and non-self-crossing properties of this family of solutions. We also give a proof of the global existence of nice sections. © 1998 American Institute of Physics.'), (5900, '1998-12-01 1998-12-01'), (5901, 'doi:10.1063/1.532646'), (5902, '6631-6650'), (5903, 'Rest frame system for asymptotically flat space–times'), (5904, 39), (5905, '2012-07-17 18:40:59'), (5906, 'In this article the quasi-Keplerian parameterisation for the case that spins and orbital angular momentum in a compact binary system are aligned or anti-aligned with the orbital angular momentum vector is extended to 3PN point-mass, next-to-next-to-leading order spin-orbit, next-to-next-to-leading order spin(1)-spin(2), and next-to-leading order spin-squared dynamics in the conservative regime. In a further step, we use the expressions for the radiative multipole moments with spin to leading order linear and quadratic in both spins to compute radiation losses of the orbital binding energy and angular momentum. Orbital averaged expressions for the decay of energy and eccentricity are provided. An expression for the last stable circular orbit is given in terms of the angular velocity type variable $x$.'), (5907, '2012-09-03 00:31:51'), (5908, 'JMathPhys_39_6631.pdf'), (5909, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v40/i11/p6126_s1'), (5910, '© 1999 American Institute of Physics.'), (5911, '1999-11-01 1999-11-01'), (5912, 'doi:10.1063/1.533081'), (5913, '6126-6127'), (5914, 'Erratum: “Rest frame system for asymptotically flat space–times” [J. Math. Phys. 39, 6631 (1998)]'), (5915, '2012-07-17 18:42:49'), (5916, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000040000011006126000001&idtype=cvips&doi=10.1063/1.533081&prog=normal'), (5917, '2012-07-17 18:42:53'), (5918, 'Aligned Spins'), (5919, '1207.6961 PDF'), (5920, '2000-09-21 2000-09-21'), (5921, '3663-3672'), (5922, '10.1088/0264-9381/17/18/305'), (5923, 'http://iopscience.iop.org/0264-9381/17/18/305'), (5924, 'General existence proof for rest frame systems in asymptotically flat spacetime'), (5925, '2012-07-17 18:48:23'), (5926, 'http://arxiv.org/abs/gr-qc/0204087'), (5927, '0264-9381_17_18_305.pdf'), (5928, '1987-09-01 1987-09-01'), (5929, '1063-1084'), (5930, '10.1088/0264-9381/4/5/010'), (5931, 'http://iopscience.iop.org/0264-9381/4/5/010'), (5932, 'General future asymptotically flat spacetimes'), (5933, '2012-07-17 19:43:03'), (5934, 'arXiv:gr-qc/0204087'), (5935, '0264-9381_4_5_010.pdf'), (5936, 'In this report, which is an extended version of that appearing in the Proceedings of GR16, I will give a summary of the main topics covered in Session A.3. on mathematical relativity at GR16, Durban. The summary is mainly based on extended abstracts submitted by the speakers. I would like to thank all participants for their contributions and help with this summary.'), (5937, '2012-07-18 02:05:50'), (5938, 'Report on GR16, Session A3'), (5939, 'gr-qc/0204087 PDF'), (5940, 'http://www.arxiv.org/pdf/gr-qc/0204087.pdf'), (5941, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v22/i4/p803_s1'), (5942, 'For an asymptotically flat space–time in general relativity there exist certain integrals, called linkages, over cross sections of null infinity, which represent the energy, momentum, or angular momentum of the system. A new formulation of the linkages is introduced and applied. It is shown that there exists a flux, representing the contribution of gravitational and matter radiation to the linkage. A uniqueness conjecture for the linkages is formulated. The ambiguities due to the possible presence of supertranslations in asymptotic rotations are studied using the behavior of the linkages under first‐order perturbations in the metric. While in certain situations these ambiguities disappear in the first‐order treatment, an example is given which suggests that they are an essential feature of general relativity and its asymptotic structure.'), (5943, '1981-04-01 1981-04-01'), (5944, 'doi:10.1063/1.524987'), (5945, '803-812'), (5946, 'Linkages in general relativity'), (5947, '2012-07-18 03:09:42'), (5948, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000022000004000803000001&idtype=cvips&doi=10.1063/1.524987&prog=normal'), (5949, '2012-07-18 03:09:44'), (5950, 'http://www.arxiv.org/pdf/1207.6961.pdf'), (5951, 'A guide to rotations in quantum mechanics'), (5952, 'Uniqueness of Scalar Field Energy and Gravitational Energy in the Radiating Regime'), (5953, '5052-5055'), (5954, '1998-06-08 June 08, 1998'), (5955, 'http://link.aps.org/doi/10.1103/PhysRevLett.80.5052'), (5956, '10.1103/PhysRevLett.80.5052'), (5957, 'The usual approaches to the definition of energy give an ambiguous result for the energy of fields in the radiating regime. We show that for a massless scalar field in Minkowski spacetime the definition may be rendered unambiguously by adding the requirement that the energy cannot increase in retarded time. We present a similar theorem for the gravitational field, proved elsewhere, which establishes that the Trautman-Bondi energy is the unique (up to a multiplicative factor) functional, within a natural class, which is monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth “piece” of conformal null infinity I.'), (5958, '2012-07-18 13:15:31'), (5959, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v80/i23/p5052_1'), (5960, 'Uniqueness of the Trautman-Bondi mass'), (5961, '084001'), (5962, 'http://link.aps.org/doi/10.1103/PhysRevD.58.084001'), (5963, '10.1103/PhysRevD.58.084001'), (5964, 'It is shown that the only functionals, within a natural class, which are monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth “piece” of conformal null infinity I, are those depending on the metric only through a specific combination of the Bondi “mass aspect” and other next-to-leading order terms in the metric. Under the extra condition of passive BMS invariance, the unique such functional (up to a multiplicative factor) is the Trautman-Bondi energy. It is also shown that this energy remains well defined for a wide class of “polyhomogeneous” metrics.'), (5965, '2012-07-18 13:15:35'), (5966, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i8/e084001'), (5967, '805-822'), (5968, '10.1088/0305-4470/39/4/006'), (5969, 'http://iopscience.iop.org/0305-4470/39/4/006'), (5970, 'Relativistic spherical functions on the Lorentz group'), (5971, '2012-07-18 20:53:29'), (5972, '2008-07-21 2008-07-21'), (5973, '0305-4470_39_4_006.pdf'), (5974, "The detection of gravitational waves from binary neutron stars is a major goal of the gravitational-wave observatories Advanced LIGO and Advanced Virgo. Previous searches for binary neutron stars with LIGO and Virgo neglected the component stars' angular momentum (spin). We demonstrate that neglecting spin in matched-filter searches causes advanced detectors to lose more than 3% of the possible signal-to-noise ratio for 59% (6%) of sources, assuming that neutron star dimensionless spins, $cJ/GM^2$, are uniformly distributed with magnitudes between 0 and 0.4 (0.05) and that the neutron stars have isotropically distributed spin orientations. We present a new method of constructing filter banks for advanced-detector searches, which can create template banks of signals with non-zero spins that are (anti-)aligned with the orbital angular momentum. We show that this search loses more than 3% of the maximium signal-to-noise for only 9% (0.2%) of BNS sources with dimensionless spins between 0 and 0.4 (0.05) and isotropic spin orientations. Use of this template bank will prevent selection bias in gravitational-wave searches and allow a more accurate exploration of the distribution of spins in binary neutron stars."), (5975, 9780486411835), (5976, 'Chebyshev and Fourier Spectral Methods'), (5977, '2012-07-30 14:24:06'), (5978, '1207.6406 PDF'), (5979, 'Australian Journal of Physics'), (5980, 465), (5981, 607), (5982, 'Boyd1999.pdf'), (5983, 145001), (5984, '10.1088/0264-9381/25/14/145001'), (5985, 'http://iopscience.iop.org/0264-9381/25/14/145001'), (5986, 'On extracting physical content from asymptotically flat spacetime metrics'), (5987, '2012-07-23 21:38:42'), (5988, 'http://www.arxiv.org/pdf/1207.6406.pdf'), (5989, '0264-9381_25_14_145001.pdf'), (5990, 'Canonical choice of asymptotic retarded time in isolated gravitating systems'), (5991, 125), (5992, '6–7'), (5993, '291-293'), (5994, '1987-11-23 November 23, 1987'), (5995, '10.1016/0375-9601(87)90144-7'), (5996, 'http://www.sciencedirect.com/science/article/pii/0375960187901447'), (5997, 'We introduce a new notion of good sections at null infinity which permits one to define a desired canonical retarded time in isolated systems. This construction depends on the properties of the physical system at the fixed retarded time, in contrast to previous works where conditions at − ∞ (or + ∞) retarded time gave a global choice of preferred sections.'), (5998, '2012-07-23 22:28:56'), (5999, 'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271541&_user=492137&_pii=0375960187901447&_check=y&_origin=article&_zone=toolbar&_coverDate=23-Nov-1987&view=c&originContentFamily=serial&wchp=dGLbVlt-zSkzS&md5=064818a1d52f3c3e5b76d112d830f98c&pid=1-s2.0-0375960187901447-main.pdf'), (6000, 'Estimating total momentum at finite distances'), (6001, '2008-10-22 October 22, 2008'), (6002, 'http://link.aps.org/doi/10.1103/PhysRevD.78.084027'), (6003, '10.1103/PhysRevD.78.084027'), (6004, 'We study the difficulties associated with the evaluation of the total Bondi momentum at finite distances around the central source of a general (asymptotically flat) spacetime. Since the total momentum is only rigorously defined at future null infinity, both finite distance and gauge effects must be taken into account for a correct computation of this quantity. Our discussion is applicable in general contexts but is particularly relevant in numerically constructed spacetimes for both extracting important physical information and assessing the accuracy of additional quantities.'), (6005, '2012-07-24 15:03:37'), (6006, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i8/e084027'), (6007, 'Using curvature invariants for wave extraction in numerical relativity'), (6008, '2008-11-10 2008-11-10'), (6009, 'http://arxiv.org/abs/0811.1600'), (6010, 'arXiv:0811.1600'), (6011, 'We present a new expression for the Weyl scalar Psi_4 that can be used in numerical relativity to extract the gravitational wave content of a spacetime. The formula relies upon the identification of transverse tetrads, namely the ones in which Psi_1=Psi_3=0. It is well known that tetrads with this property always exist in a general Petrov type I spacetime. A sub-class of these tetrads naturally converges to the Kinnersley tetrad in the limit of Petrov type D spacetime. However, the transverse condition fixes only four of the six parameters coming from the Lorentz group of transformations applied to tetrads. Here we fix the tetrad completely, in particular by giving the expression for the spin-boost transformation that was still unclear. The value of Psi_4 in this optimal tetrad is given as a function of the two curvature invariants I and J.'), (6012, '2012-07-24 18:45:23'), (6013, '0811.1600 PDF'), (6014, 'http://www.arxiv.org/pdf/0811.1600.pdf'), (6015, 229), (6016, '2010-05-01 2010-05-01'), (6017, '012055'), (6018, '10.1088/1742-6596/229/1/012055'), (6019, 'http://iopscience.iop.org/1742-6596/229/1/012055'), (6020, 'On the use of curvature invariants in numerical relativity'), (6021, '2012-07-24 18:45:28'), (6022, 'http://iopscience.iop.org/1742-6596/229/1/012055/pdf/1742-6596_229_1_012055.pdf'), (6023, 'Quasigroups, asymptotic symmetries, and conservation laws in general relativity'), (6024, 'R7498-R7502'), (6025, '1997-12-15 December 15, 1997'), (6026, 'http://link.aps.org/doi/10.1103/PhysRevD.56.R7498'), (6027, '10.1103/PhysRevD.56.R7498'), (6028, 'A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat spacetime at future null infinity. The infinite-parameter Newman-Unti group of asymptotic symmetries is reduced to the Poincaré quasigroup, and the Noether charge associated with any element of the Poincaré quasialgebra is defined. The integral conserved quantities of energy-momentum and angular momentum are linear on generators of Poincaré quasigroup, are free of the supertranslation ambiguity, possess flux, and are identically equal to zero in Minkowski spacetime.'), (6029, '2012-07-24 18:45:41'), (6030, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v56/i12/pR7498_1'), (6031, 'Dealing with delicate issues in waveform calculations'), (6032, 124040), (6033, '2007-12-28 December 28, 2007'), (6034, 'http://link.aps.org/doi/10.1103/PhysRevD.76.124040'), (6035, '10.1103/PhysRevD.76.124040'), (6036, 'We revisit the calculation of gravitational radiation through the use of Weyl scalars. We point out several possible problems arising from gauge and tetrad ambiguities and ways to address them. Our analysis indicates how relatively simple corrections can be introduced to remove these ambiguities.'), (6037, '2012-07-25 17:33:31'), (6038, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i12/e124040'), (6039, '2012-07-30 14:24:24'), (6040, 'http://adsabs.harvard.edu/abs/1987AuJPh..40..465M'), (6041, 9780521715959), (6042, '4th print.'), (6043, 'Imaginary numbers are not real—The geometric algebra of spacetime'), (6044, '0015-9018'), (6045, '1175-1201'), (6046, 'http://www.springerlink.com.proxy.library.cornell.edu/content/k712q7283161g221/abstract/'), (6047, '10.1007/BF01883676'), (6048, '2012-08-02 20:13:20'), (6049, 'SpringerLink Full Text PDF'), (6050, 'http://www.springerlink.com.proxy.library.cornell.edu/content/k712q7283161g221/fulltext.pdf'), (6051, 'Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms'), (6052, 86), (6053, '024011'), (6054, '2012-07-05 July 05, 2012'), (6055, 'http://link.aps.org/doi/10.1103/PhysRevD.86.024011'), (6056, '10.1103/PhysRevD.86.024011'), (6057, 'This paper presents a tunable effective-one-body (EOB) model for black-hole (BH) binaries of arbitrary mass ratio and aligned spins. This new EOB model incorporates recent results of small-mass-ratio simulations based on Teukolsky’s perturbative formalism. The free parameters of the model are calibrated to numerical-relativity simulations of nonspinning BH-BH systems of five different mass ratios and to equal-mass nonprecessing BH-BH systems with dimensionless BH spins χi≃±0.44. The present analysis focuses on the orbital dynamics of the resulting EOB model, and on the dominant (ℓ,m)=(2,2) gravitational-wave mode. The calibrated EOB model can generate inspiral-merger-ringdown waveforms for nonprecessing, spinning BH binaries with any mass ratio and with individual BH spins -1≤χi≲0.7. Extremizing only over time and phase shifts, the calibrated EOB model has overlaps larger than 0.997 with each of the seven numerical-relativity waveforms for total masses between 20M⊙ and 200M⊙, using the Advanced LIGO noise curve. We compare the calibrated EOB model with two additional equal-mass highly spinning (χi≃-0.95,+0.97) numerical-relativity waveforms, which were not used during calibration. We find that the calibrated model has an overlap larger than 0.995 with the simulation with nearly extremal antialigned spins. Extension of this model to black holes with aligned spins χi≳0.7 requires improvements of our modeling of the plunge dynamics and inclusion of higher-order PN spin terms in the gravitational-wave modes and radiation-reaction force.'), (6058, '2012-08-04 12:10:05'), (6059, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i2/e024011'), (6060, 'Not Available'), (6061, '2012-09-27 16:07:19'), (6062, 'NASA/ADS Full Text PDF'), (6063, 'http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987AuJPh..40..465M&link_type=ARTICLE'), (6064, 'Spin effects on gravitational waves from inspiraling compact binaries at second post-Newtonian order'), (6065, '2012-09-27 2012-09-27'), (6066, 'http://arxiv.org/abs/1209.6349'), (6067, 'arXiv:1209.6349'), (6068, 'We calculate the gravitational waveform for spinning, precessing compact binary inspirals through second post-Newtonian order in the amplitude. When spins are collinear with the orbital angular momentum and the orbits are quasi-circular, we further provide explicit expressions for the gravitational-wave polarizations and the decomposition into spin-weighted spherical-harmonic modes. Knowledge of the second post-Newtonian spin terms in the waveform could be used to improve the physical content of analytical templates for data analysis of compact binary inspirals and for more accurate comparisons with numerical-relativity simulations.'), (6069, '2012-09-28 12:15:16'), (6070, 'http://www.nytimes.com/'), (6071, '2012-11-07 05:24:13'), (6072, '1209.6349v1.pdf'), (6073, 'Third post-Newtonian spin-orbit effect in the gravitational radiation flux of compact binaries'), (6074, '2012-10-02 2012-10-02'), (6075, 'http://arxiv.org/abs/1210.0764'), (6076, 'arXiv:1210.0764'), (6077, 'Gravitational waves contain tail effects that are due to the backscattering of linear waves in the curved space-time geometry around the source. The knowledge as well as the accuracy of the two-body inspiraling post-Newtonian (PN) dynamics and of the gravitational-wave signal has been recently improved, notably by computing the spin-orbit (SO) terms induced by tail effects in the gravitational-wave energy flux at the 3PN order. Here we sketch this derivation, which yields the phasing formula including SO tail effects through the same 3PN order. Those results can be employed to improve the accuracy of analytical templates aimed at describing the whole process of inspiral, merger, and ringdown.'), (6078, '2012-10-03 14:03:14'), (6079, '1210.0764 PDF'), (6080, 'http://www.arxiv.org/pdf/1210.0764.pdf'), (6081, 'Republication of: The dynamics of general relativity'), (6082, '1997-2027'), (6083, 'http://www.springerlink.com/content/068kj2p81113p2q8/abstract/'), (6084, 'This article—summarizing the authors’ then novel formulation of General Relativity—appeared as Chap. 7, pp. 227–264, in Gravitation: an introduction to current research , L. Witten, ed. (Wiley, New York, 1962), now long out of print. Intentionally unretouched, this republication as Golden Oldie is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed–but not section nor equation numbering, etc. Current institutional affiliations are encoded in: arnowitt@physics.tamu.edu, deser@brandeis.edu, misner@umd.edu.'), (6085, '10.1007/s10714-008-0661-1'), (6086, '2012-10-05 14:17:57'), (6087, 'Republication of'), (6088, 'http://www.springerlink.com/content/068kj2p81113p2q8/fulltext.pdf'), (6089, 'Fast evaluation of asymptotic waveforms from gravitational perturbations'), (6090, '2012-10-04 2012-10-04'), (6091, 'http://arxiv.org/abs/1210.1565'), (6092, 'arXiv:1210.1565'), (6093, 'In the context of blackhole perturbation theory, we describe both exact evaluation of an asymptotic waveform from a time series recorded at a finite radial location and its numerical approximation. From the user\'s standpoint our technique is easy to implement, affords high accuracy, and works for both axial (Regge-Wheeler) and polar (Zerilli) sectors. Our focus is on the ease of implementation with publicly available numerical tables, either as part of an existing evolution code or a post-processing step. Nevertheless, we also present a thorough theoretical discussion of asymptotic waveform evaluation and radiation boundary conditions, which need not be understood by a user of our methods. In particular, we identify (both in the time and frequency domains) analytical asymptotic waveform evaluation kernels, and describe their approximation by techniques developed by Alpert, Greengard, and Hagstrom. This paper also presents new results on the evaluation of far-field signals for the ordinary (acoustic) wave equation. We apply our method to study late-time decay tails at null-infinity, "teleportation" of a signal between two finite radial values, and luminosities from extreme-mass-ratio binaries. Through numerical simulations with the outer boundary as close in as r = 30M, we compute asymptotic waveforms with late-time t^{-4} decay (l = 2 perturbations), and also luminosities from circular and eccentric particle-orbits that respectively match frequency domain results to relative errors of better than 10^{-12} and 10^{-9}. Furthermore, we find that asymptotic waveforms are especially prone to contamination by spurious junk radiation.'), (6094, '2012-10-05 17:57:02'), (6095, '1210.1565 PDF'), (6096, 'http://www.arxiv.org/pdf/1210.1565.pdf'), (6097, '10.1103/PhysRevD.82.104057'), (6098, 'Intermediate-mass-ratio black hole binaries: Intertwining numerical and perturbative techniques'), (6099, 104057), (6100, 'http://link.aps.org/doi/10.1103/PhysRevD.82.104057'), (6101, '2010-11-30 November 30, 2010'), (6102, 'We describe in detail full numerical and perturbative techniques to compute the gravitational radiation from intermediate-mass-ratio black-hole-binary inspirals and mergers. We perform a series of full numerical simulations of nonspinning black holes with mass ratios q=1/10 and q=1/15 from different initial separations and for different finite-difference resolutions. In order to perform those full numerical runs, we adapt the gauge of the moving punctures approach with a variable damping term for the shift. We also derive an extrapolation (to infinite radius) formula for the waveform extracted at finite radius. For the perturbative evolutions we use the full numerical tracks, transformed into the Schwarzschild gauge, in the source terms of the Regge-Wheller-Zerilli Schwarzschild perturbations formalism. We then extend this perturbative formalism to take into account small intrinsic spins of the large black hole, and validate it by computing the quasinormal mode frequencies, where we find good agreement for spins |a/M|<0.3. Including the final spins improves the overlap functions when comparing full numerical and perturbative waveforms, reaching 99.5% for the leading (ℓ,m)=(2,2) and (3, 3) modes, and 98.3% for the nonleading (2, 1) mode in the q=1/10 case, which includes 8 orbits before merger. For the q=1/15 case, we obtain overlaps near 99.7% for all three modes. We discuss the modeling of the full inspiral and merger based on a combined matching of post-Newtonian, full numerical, and geodesic trajectories.'), (6103, '2012-10-05 18:17:20'), (6104, 'http://relativity.livingreviews.org/Articles/lrr-2012-2/'), (6105, 'PhysRevD.82.104057.pdf'), (6106, 'Gravitational Waves in General Relativity'), (6107, 186), (6108, 4724), (6109, '535-535'), (6110, 'http://dx.doi.org/10.1038/186535a0'), (6111, '10.1038/186535a0'), (6112, '1960-05-14 print May 14, 1960'), (6113, '186535a0.pdf'), (6114, 'A fully covariant information-theoretic ultraviolet cutoff? for scalar ?fields in expanding FRW spacetimes'), (6115, 'http://arxiv.org/abs/1210.0750'), (6116, 'arXiv:1210.0750'), (6117, "While a natural ultraviolet cutoff, presumably at the Planck length, is widely assumed to exist in nature, it has proven difficult to implement a minimum length scale covariantly. A key reason is that the presence of a fixed minimum length would seem to contradict the ability of Lorentz transformations to contract lengths. In this paper, we implement a fully covariant Planck scale cutoff by cutting off the spectrum of the d'Alembertian. In this scenario, consistent with Lorentz contractions, wavelengths that are arbitrarily smaller than the Planck length continue to exist. However, the dynamics of modes of wavelengths that are significantly smaller than the Planck length possess a very small bandwidth. This has the effect of freezing the dynamics of such modes. While both, wavelengths and bandwidths, are frame dependent, Lorentz contraction and time dilation conspire to make the freezing of modes of transplanckian wavelengths covariant. In particular, we show that this ultraviolet cutoff can be implemented covariantly also in curved spacetimes. We focus on Friedmann Robertson Walker (FRW) spacetimes and their much-discussed transplanckian question: The physical wavelength of each comoving mode was smaller than the Planck scale at sufficiently early times. What was the mode's dynamics then? Here, we show that in the presence of the covariant UV cutoff, the dynamical bandwidth of a comoving mode is essentially zero up until its physical wavelength starts exceeding the Planck length. In particular, we show that under general assumptions, the number of dynamical degrees of freedom of each comoving mode all the way up to some arbitrary finite time is actually finite. Our results also open the way to calculating the impact of this natural UV cutoff on inflationary predictions for the CMB."), (6118, '2012-10-08 19:27:52'), (6119, 'A fully covariant information-theoretic ultraviolet cutoff?'), (6120, '1210.0750 PDF'), (6121, 'http://www.arxiv.org/pdf/1210.0750.pdf'), (6122, '2012-10-09 15:06:49'), (6123, 'lrr-2012-2Color.pdf'), (6124, 'Impact of Higher-order Modes on the Detection of Binary Black Hole Coalescences'), (6125, '2012-10-05 2012-10-05'), (6126, 'http://arxiv.org/abs/1210.1891'), (6127, 'arXiv:1210.1891'), (6128, 'The inspiral and merger of black-hole binary systems are a promising source of gravitational waves. The most effective method to look for a signal with a well understood waveform, such as the binary black hole signal, is matched filtering against a library of model waveforms. Current model waveforms are comprised solely of the dominant radiation mode, the quadrupole mode, although it is known that there can be significant power in the higher-order modes. The binary black hole waveforms produced by numerical relativity are accurate through late inspiral, merger, and ringdown and include the higher-order modes. The available numerical-relativity waveforms span an increasing portion of the physical parameter space of unequal mass, spin and precession. In this paper, we investigate the degree to which gravitational-wave searches could be improved by the inclusion of higher modes in the model waveforms, for signals with a variety of initial mass ratios and generic spins. Our investigation studies how well the quadrupole-only waveform model matches the signal as a function of the inclination and orientation of the source and how the modes contribute to the distance reach into the Universe of Advanced LIGO for a fixed set of internal source parameters. The mismatch between signals and quadrupole-only waveform can be large, dropping below 0.97 for up to 65% of the source-sky for the non-precessing cases we studied, and over a larger area in one precessing case. There is a corresponding 30% increase in detection volume that could be achieved by adding higher modes to the search; however, this is mitigated by the fact that the mismatch is largest for signals which radiate the least energy and to which the search is therefore least sensitive. Likewise, the mismatch is largest in directions from the source along which the least energy is radiated.'), (6129, '2012-10-10 15:30:32'), (6130, '1210.1891 PDF'), (6131, 'http://www.arxiv.org/pdf/1210.1891.pdf'), (6132, '10.1103/PhysRevD.84.084037'), (6133, '084037'), (6134, 'http://link.aps.org/doi/10.1103/PhysRevD.84.084037'), (6135, '2011-10-17 October 17, 2011'), (6136, 'This paper presents a post-Newtonian (PN) template family of gravitational waveforms from inspiralling compact binaries with nonprecessing spins, where the spin effects are described by a single “reduced-spin” parameter. This template family, which reparametrizes all the spin-dependent PN terms in terms of the leading-order (1.5PN) spin-orbit coupling term in an approximate way, has very high overlaps (fitting factor >0.99) with nonprecessing binaries with arbitrary mass ratios and spins. We also show that this template family is “effectual” for the detection of a significant fraction of generic spinning binaries in the comparable-mass regime (m2/m1≲10), providing an attractive and feasible way of searching for gravitational waves from spinning low-mass binaries. We also show that the secular (nonoscillatory) spin-dependent effects in the phase evolution (which are taken into account by the nonprecessing templates) are more important than the oscillatory effects of precession in the comparable-mass (m1≃m2) regime. Hence the effectualness of nonspinning templates is particularly poor in this case, as compared to non-precessing-spin templates. For the case of binary neutron stars observable by Advanced LIGO, even moderate spins (L̂N·S/m2≃0.015–0.1) will cause considerable mismatches (∼3%–25%) with nonspinning templates. This is contrary to the expectation that neutron-star spins may not be relevant for gravitational wave detection.'), (6137, '2012-10-10 20:48:47'), (6138, '10.1103/RevModPhys.29.547'), (6139, 'PhysRevD.84.084037.pdf'), (6140, '10.1103/PhysRevD.78.044021'), (6141, 'Analysis of spin precession in binary black hole systems including quadrupole-monopole interaction'), (6142, '044021'), (6143, 'http://link.aps.org/doi/10.1103/PhysRevD.78.044021'), (6144, '2008-08-11 August 11, 2008'), (6145, 'We analyze in detail the spin precession equations in binary black hole systems, when the tidal torque on a Kerr black hole due to quadrupole-monopole coupling is taken into account. We show that completing the precession equations with this term reveals the existence of a conserved quantity at 2PN order when averaging over orbital motion. This quantity allows one to solve the (orbit-averaged) precession equations exactly in the case of equal masses and arbitrary spins, neglecting radiation reaction. For unequal masses, an exact solution does not exist in closed form, but we are still able to derive accurate approximate analytic solutions. We also show how to incorporate radiation-reaction effects into our analytic solutions adiabatically, and compare the results to solutions obtained numerically. For various configurations of the binary, the relative difference in the accumulated orbital phase computed using our analytic solutions versus a full numerical solution varies from ∼0.3% to ∼1.8% over ∼80–140 orbital cycles accumulated while sweeping over the orbital frequency range ∼20–300 Hz. This typically corresponds to a discrepancy of order ∼5–6 radians. While this may not be accurate enough for implementation in LIGO template banks, we still believe that our new solutions are potentially quite useful for comparing numerical relativity simulations of spinning binary black hole systems with post-Newtonian theory. They can also be used to gain more understanding of precession effects, with potential application to the gravitational recoil problem, and to provide semianalytical templates for spinning, precessing binaries.'), (6146, '2012-10-10 21:18:08'), (6147, 'http://prd.aps.org/pdf/PRD/v78/i4/e044021'), (6148, 'Precession during merger 1: Strong polarization changes are observationally accessible features of strong-field gravity during binary black hole merger'), (6149, '2012-09-17 2012-09-17'), (6150, 'http://arxiv.org/abs/1209.3712'), (6151, 'arXiv:1209.3712'), (6152, 'The short gravitational wave signal from the merger of compact binaries encodes a surprising amount of information about the strong-field dynamics of merger into frequencies accessible to ground-based interferometers. In this paper we describe a previously-unknown "precession" of the peak emission direction with time, both before and after the merger, about the total angular momentum direction. We demonstrate the gravitational wave polarization encodes the orientation of this direction to the line of sight. We argue the effects of polarization can be estimated nonparametrically, directly from the gravitational wave signal as seen along one line of sight, as a slowly-varying feature on top of a rapidly-varying carrier. After merger, our results can be interpreted as a coherent excitation of quasinormal modes of different angular orders, a superposition which naturally "precesses" and modulates the line-of-sight amplitude. Recent analytic calculations have arrived at a similar geometric interpretation. We suspect the line-of-sight polarization content will be a convenient observable with which to define new high-precision tests of general relativity using gravitational waves. Additionally, as the nonlinear merger process seeds the initial coherent perturbation, we speculate the amplitude of this effect provides a new probe of the strong-field dynamics during merger. To demonstrate the ubiquity of the effects we describe, we summarize the post-merger evolution of 104 generic precessing binary mergers. Finally, we provide estimates for the detectable impacts of precession on the waveforms from high-mass sources. These expressions may identify new precessing binary parameters whose waveforms are dissimilar from the existing sample.'), (6153, '2012-10-11 02:48:55'), (6154, 'Precession during merger 1'), (6155, '1209.3712 PDF'), (6156, 'http://www.arxiv.org/pdf/1209.3712.pdf'), (6157, 'Suitability of hybrid gravitational waveforms for unequal-mass binaries'), (6158, '2012-10-10 2012-10-10'), (6159, 'http://arxiv.org/abs/1210.3007'), (6160, 'arXiv:1210.3007'), (6161, 'This article studies sufficient accuracy criteria of hybrid post-Newtonian (PN) and numerical relativity (NR) waveforms for parameter estimation of strong binary black-hole sources in second- generation ground-based gravitational-wave detectors. We investigate equal-mass non-spinning binaries with a new 33-orbit NR waveform, as well as unequal-mass binaries with mass ratios 2, 3, 4 and 6. For equal masses, the 33-orbit NR waveform allows us to recover previous results and to extend the analysis toward matching at lower frequencies. For unequal masses, the errors between different PN approximants increase with mass ratio. Thus, at 3.5PN, hybrids for higher-mass-ratio systems would require NR waveforms with many more gravitational-wave (GW) cycles to guarantee no adverse impact on parameter estimation. Furthermore, we investigate the potential improvement in hybrid waveforms that can be expected from 4th order post-Newtonian waveforms, and find that knowledge of this 4th post-Newtonian order would significantly improve the accuracy of hybrid waveforms.'), (6162, '2012-10-11 14:50:19'), (6163, '1210.3007 PDF'), (6164, 'http://www.arxiv.org/pdf/1210.3007.pdf'), (6165, 'Synthesis of the Elements in Stars'), (6166, '547-650'), (6167, 'http://link.aps.org/doi/10.1103/RevModPhys.29.547'), (6168, '1957-10-01 October 1, 1957'), (6169, '2012-10-14 18:26:03'), (6170, 'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v29/i4/p547_1'), (6171, '10.1103/PhysRevD.86.084017'), (6172, 'http://link.aps.org/doi/10.1103/PhysRevD.86.084017'), (6173, '2012-10-02 October 2, 2012'), (6174, 'The detection of gravitational waves from binary neutron stars is a major goal of the gravitational-wave observatories Advanced LIGO and Advanced Virgo. Previous searches for binary neutron stars with LIGO and Virgo neglected the component stars’ angular momentum (spin). We demonstrate that neglecting spin in matched-filter searches causes advanced detectors to lose more than 3% of the possible signal-to-noise ratio for 59% (6%) of sources, assuming that neutron star dimensionless spins, cJ/GM2, are uniformly distributed with magnitudes between 0 and 0.4 (0.05) and that the neutron stars have isotropically distributed spin orientations. We present a new method for constructing template banks for gravitational-wave searches for systems with spin. We present a new metric in a parameter space in which the template placement metric is globally flat. This new method can create template banks of signals with nonzero spins that are (anti-)aligned with the orbital angular momentum. We show that this search loses more than 3% of the maximum signal-to-noise for only 9% (0.2%) of binary neutron star sources with dimensionless spins between 0 and 0.4 (0.05) and isotropic spin orientations. Use of this template bank will prevent selection bias in gravitational-wave searches and allow a more accurate exploration of the distribution of spins in binary neutron stars.'), (6175, '2012-10-16 20:06:40'), (6176, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i8/e084017'), (6177, 'ELynah.com'), (6178, '2011-07-10 2011-07-10'), (6179, 'arXiv:1212.5553'), (6180, 'Optimal extraction of information from gravitational-wave observations of binary black-hole coalescences requires detailed knowledge of the waveforms. Current approaches for representing waveform information are based on spin-weighted spherical harmonic decomposition. Higher-order harmonic modes carrying a few percent of the total power output near merger can supply information critical to determining intrinsic and extrinsic parameters of the binary. One obstacle to constructing a full multi-mode template of merger waveforms is the apparently complicated behavior of some of these modes; instead of settling down to a simple quasinormal frequency with decaying amplitude, some $|m| \\neq \\ell$ modes show periodic bumps characteristic of mode-mixing. We analyze the strongest of these modes -- the anomalous $(3,2)$ harmonic mode -- measured in a set of binary black-hole merger waveform simulations, and show that to leading order, they are due to a mismatch between the spherical harmonic basis used for extraction in 3D numerical relativity simulations, and the spheroidal harmonics adapted to the perturbation theory of Kerr black holes. Other causes of mode-mixing arising from gauge ambiguities and physical properties of the quasinormal ringdown modes are also considered and found to be small for the waveforms studied here.'), (6181, '2013-01-01 16:44:44'), (6182, 'http://web.archive.org/web/20110710184800/http://www.elynah.com/?cheers#goaliesieve'), (6183, '2012-10-21 16:15:29'), (6184, 'Rubiks_Bricks.pdf'), (6185, 'Rubiks_Cube_2x2x2_solving_guide.pdf'), (6186, 'Rubiks_cube_3x3_solution-en.pdf'), (6187, "Group Theory and the Rubik's Cube.pdf"), (6188, 'The gravitational waveform (GWF) generated by inspiralling compact\nbinaries moving in quasi-circular orbits is computed at the third\npost-Newtonian (3PN) approximation to general relativity. Our\nmotivation is two-fold: (i) to provide accurate templates for the data\nanalysis of gravitational wave inspiral signals in laser\ninterferometric detectors; (ii) to provide the associated\nspin-weighted spherical harmonic decomposition to facilitate\ncomparison and match of the high post-Newtonian prediction for the\ninspiral waveform to the numerically-generated waveforms for the\nmerger and ringdown. This extension of the GWF by half a PN order\n(with respect to previous work at 2.5PN order) is based on the\nalgorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and\nsource multipole moments for general sources at 3PN order. We also\nobtain the 3PN extension of the source multipole moments in the case\nof compact binaries, and compute the contributions of hereditary terms\n(tails, tails-of-tails and memory integrals) up to 3PN order. The end\nresults are given for both the complete plus and cross polarizations\nand the separate spin-weighted spherical harmonic modes.'), (6189, '0802.1249v3.pdf'), (6190, 'Note erratum'), (6191, 'Hofstadter_Mar1981_995410.pdf'), (6192, 'scientificamerican0381-20-7.pdf'), (6193, 'http://www.nytimes.com/2012/10/25/health/teff-and-oatmeal-pancakes-recipes-for-health.html'), (6194, '2012-10-23 2012-10-23'), (6195, 'Teff and Oatmeal Pancakes — Recipes for Health'), (6196, 'Health'), (6197, '1212.5553 PDF'), (6198, 'Teff and Oatmeal Pancakes — Recipes for Health - NYTimes.com'), (6199, 'http://www.arxiv.org/pdf/1212.5553.pdf'), (6200, '2012-10-27 18:19:00'), (6201, 9780521337076), (6202, 'Step 3'), (6203, 'http://www.speedcubing.com/chris/4-step3.html'), (6204, '2012-10-29 19:02:12'), (6205, "Rubik's 4x4 moves"), (6206, '2012-10-29 19:07:58'), (6207, '2012-11-07 05:24:25'), (6208, 'Obama Wins New Term as Electoral Advantage Holds - NYTimes.com'), (6209, 'http://www.nytimes.com/2012/11/07/us/politics/obama-romney-presidential-election-2012.html?hp&pagewanted=all'), (6210, '2012-11-07 05:25:02'), (6211, 'Obama wins re-election'), (6212, 'Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries'), (6213, 'http://arxiv.org/abs/1212.5520'), (6214, 'http://arxiv.org/abs/1403.6915'), (6215, 'We extend our previous work devoted to the computation of the next-to-next-to-leading order spin-orbit correction (corresponding to 3.5PN order) in the equations of motion of spinning compact binaries, by: (i) Deriving the corresponding spin-orbit terms in the evolution equations for the spins, the conserved integrals of the motion and the metric regularized at the location of the particles (obtaining also the metric all-over the near zone but with some lower precision); (ii) Performing the orbital reduction of the precession equations, near-zone metric and conserved integrals to the center- of-mass frame and then further assuming quasi-circular orbits (neglecting gravitational radiation reaction). The results are systematically expressed in terms of the spin variables with conserved Euclidean norm instead of the original antisymmetric spin tensors of the pole-dipole formalism. This work paves the way to the future computation of the next-to-next-to-leading order spin-orbit terms in the gravitational-wave phasing of spinning compact binaries.'), (6216, 'http://arxiv.org/abs/1405.0504'), (6217, '1212.5520 PDF'), (6218, 'http://www.arxiv.org/pdf/1212.5520.pdf'), (6219, 'Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems'), (6220, '2012-10-15 2012-10-15'), (6221, 'http://arxiv.org/abs/1210.4143'), (6222, 'arXiv:1210.4143'), (6223, "We compute next-to-next-to-leading order spin contributions to the post-Newtonian equations of motion for binaries of compact objects, such as black holes or neutron stars. For maximally spinning black holes, those contributions are of third-and-a-half post-Newtonian (3.5PN) order, improving our knowledge of the equations of motion, already known for non-spinning objects up to this order. Building on previous work, we represent the rotation of the two bodies using a pole-dipole matter stress-energy tensor, and iterate Einstein's field equations for a set of potentials parametrizing the metric in harmonic coordinates. Checks of the result include the existence of a conserved energy, the approximate global Lorentz invariance of the equations of motion in harmonic coordinates, and the recovery of the motion of a spinning object on a Kerr background in the test-mass limit. We verified the existence of a contact transformation, together with a redefinition of the spin variables that makes our result equivalent to a previously published reduced Hamiltonian, obtained from the Arnowitt-Deser-Misner (ADM) formalism."), (6224, '2013-01-02 05:40:20'), (6225, '1210.4143 PDF'), (6226, 'http://www.arxiv.org/pdf/1210.4143.pdf'), (6227, 'Fitting Smooth Paths to Spherical Data'), (6228, '2013-01-09 19:59:54'), (6229, '2013-01-16 2013-01-16'), (6230, '0264-9381_29_12_124001.pdf'), (6231, 'Index IUPAP Red Book « Applications of statistics in Measurement & Testing'), (6232, 'http://metrology.wordpress.com/measurement-process-index/iupap-red-book/index-iupap-red-book/'), (6233, '2013-01-10 15:50:34'), (6234, 'IUPAP Red Book'), (6235, '2013-01-10 15:51:05'), (6236, 'IUPAP Red book « Applications of statistics in Measurement & Testing'), (6237, 'http://metrology.wordpress.com/measurement-process-index/iupap-red-book/'), (6238, '2013-01-10 15:51:31'), (6239, "This thesis concerns numerical relativity, the attempt to study Einstein's theory of gravitation using numerical discretization. The goal of the field, the study of gravitational dynamics in cases where symmetry reduction or perturbation theory are not possible, finally seems to be coming to fruition, at least for the archetypal problem of the inspiral and coalescence of binary black hole systems. This thesis presents three episodes that each bear some relationship to this story.\n\n\n\n\n\nChapters 2 and 3 present previously published work in collaboration with Richard Price and others on the so-called periodic standing-wave (PSW) approximation for binary inspiral. The approximation is to balance outgoing radiation with incoming radiation, stabilizing the orbit and making the problem stationary in a rotating frame. Chapters 2 and 3 apply the method to the problem of co-orbiting charges coupled to a nonlinear scalar field in three dimensions.\n\n\n\n\n\nChapters 4, 5, and 6 concern the stability of constraint fields in conventional numerical relativity simulations. Chapter 4 (also previously published work, in collaboration with the Caltech numerical relativity group, along with Michael Holst and Lawrence Kidder) presents a method for immediately correcting violations of constraints after they have arisen. Chapters 5 and 6 present methods to ``damp' away constraint violations dynamically in two specific contexts. Chapter 5 (previously published work in collaboration with the Caltech numerical relativity group and Lawrence Kidder) presents a first-order linearly degenerate symmetric hyperbolic representation of Einstein's equations in generalized harmonic gauge. A representation is presented that stabilizes all constraints, including those that appear when the system is written in first-order form. Chapter 6 presents a generalization of the Kidder-Scheel-Teukolsky evolution systems that provides much-improved stability. This is investigated with numerical simulations of a single black hole spacetime. \n\n\n\n\n\nFinally, chapter 7 presents work in progress to implement code to calculate the spin of black holes in numerical simulations. This requires a well-defined generalization of the concept of ``rotation generators' on topological two-spheres that may not have any true Killing vectors. I present a new method for defining these fields, and results of a numerical code that computes them."), (6240, '10.1103/PhysRevD.76.041501'), (6241, '1 General recommendations.pdf'), (6242, 'Approximate Killing vectors on S^{2}'), (6243, '041501'), (6244, 'http://link.aps.org/doi/10.1103/PhysRevD.76.041501'), (6245, '2007-08-10 August 10, 2007'), (6246, '4 Recommended symbols for physical quantities.pdf'), (6247, 'We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S2. When solutions of Killing’s equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes.'), (6248, '5 Recommended mathematical symbols.pdf'), (6249, '3 Definitions of units and systems of units.pdf'), (6250, '2 Symbols for elememts, particles, states, and transitions.pdf'), (6251, '2013-02-04 20:50:09'), (6252, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i4/e041501'), (6253, '2010-09-07 2010-09-07'), (6254, 'LaTeX'), (6255, 'Revtex4-1 command and option summary.pdf'), (6256, 'http://iopscience.iop.org/0264-9381/27/17/173001'), (6257, '2013-02-06 03:31:07'), (6258, 'Revtex4-1 author guide.pdf'), (6259, 'http://arxiv.org/abs/1307.5098'), (6260, 'Reports on Progress in Physics'), (6261, 'Phys Rev style guide and journal abbreviations.pdf'), (6262, '0034-4885, 1361-6633'), (6263, 'APS author guide.pdf'), (6264, 'SI'), (6265, '076901'), (6266, 'NIST guide to SI.pdf'), (6267, '10.1088/0034-4885/72/7/076901'), (6268, 'http://iopscience.iop.org/0034-4885/72/7/076901'), (6269, 'This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.'), (6270, 'Full brochure.pdf'), (6271, 'Pocket reference.pdf'), (6272, '2013-02-06 17:40:07'), (6273, 'Concise summary.pdf'), (6274, 'http://arxiv.org/abs/1301.3665'), (6275, 'arXiv:1301.3665'), (6276, 'This publication will deal with an explicit determination of the time evolution of the spin orientation axes and the evolution of the orbital phase in the case of circular orbits under next-to-leading order spin-orbit interactions. We modify the method of Schneider and Cui proposed in ["Theoreme \\"uber Bewegungsintegrale und ihre Anwendungen in Bahntheorien", Verlag der Bayerischen Akademie der Wissenschaften, volume 212, 2005.] to iteratively remove oscillatory terms in the equations of motion for different masses that were not present in the case of equal masses. Our smallness parameter is chosen to be the difference of the symmetric mass ratio to the value 1/4. Before the first Lie transformation, the set of conserved quantities consists of the total angular momentum, the amplitudes of the orbital angular momentum and of the spins, $L, S_1,$ and $S_2$. In contrary, the magnitude of the total spin $S=|S_1+S_2|$ is not conserved and we wish to shift its non-conservation to higher orders of the smallness parameter. We perform the iterations explicitly to first order, while performing higher orders would mean no structural difference or harder mathematical difficulties. To apply this method, we develop a canonical system of spin variables reduced by the conservation law of total angular momentum, which is imposed on the phase space as a constraint. The result is an asymptotic series in $\\epsilon$ that may be truncated appropriately considering the physical properties of the regarded system.'), (6277, '2013-01-17 20:27:52'), (6278, 'Canonical Angles In A Compact Binary Star System With Spinning Components'), (6279, '1301.3665 PDF'), (6280, 'http://www.arxiv.org/pdf/1301.3665.pdf'), (6281, '2008-10-29 2008-10-29'), (6282, 'http://arxiv.org/abs/0810.5336'), (6283, 'Phys.Rev.D79:104023,2009; Erratum-ibid.D84:049901,2011'), (6284, '10.1103/PhysRevD.84.049901'), (6285, 'arXiv:0810.5336'), (6286, 'We provide ready-to-use time-domain gravitational waveforms for spinning compact binaries with precession effects through 1.5PN order in amplitude and compute their mode decomposition using spin-weighted -2 spherical harmonics. In the presence of precession, the gravitational-wave modes (l,m) contain harmonics originating from combinations of the orbital frequency and precession frequencies. We find that the gravitational radiation from binary systems with large mass asymmetry and large inclination angle can be distributed among several modes. For example, during the last stages of inspiral, for some maximally spinning configurations, the amplitude of the (2,0) and (2,1) modes can be comparable to the amplitude of the (2,2) mode. If the mass ratio is not too extreme, the l=3 and l=4 modes are generally one or two orders of magnitude smaller than the l = 2 modes. Restricting ourselves to spinning, non-precessing compact binaries, we apply the stationary-phase approximation and derive the frequency-domain gravitational waveforms including spin-orbit and spin(1)- spin(2) effects through 1.5PN and 2PN order respectively in amplitude, and 2.5PN order in phase. Since spin effects in the amplitude through 2PN order affect only the first and second harmonics of the orbital phase, they do not extend the mass reach of gravitational-wave detectors. However, they can interfere with other harmonics and lower or raise the signal-to-noise ratio depending on the spin orientation. These ready-to-use waveforms could be employed in the data-analysis of the spinning, inspiraling binaries as well as in comparison studies at the interface between analytical and numerical relativity.'), (6287, '2013-01-21 19:19:58'), (6288, '0810.5336 PDF'), (6289, 'http://www.arxiv.org/pdf/0810.5336.pdf'), (6290, '10.1103/PhysRevD.86.104006'), (6291, 'Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation'), (6292, 104006), (6293, 'http://link.aps.org/doi/10.1103/PhysRevD.86.104006'), (6294, '2012-11-01 November 1, 2012'), (6295, 'There is a well-known, intuitive geometric correspondence between high-frequency quasinormal modes of Schwarzschild black holes and null geodesics that reside on the light ring (often called spherical photon orbits): the real part of the mode’s frequency relates to the geodesic’s orbital frequency, and the imaginary part of the frequency corresponds to the Lyapunov exponent of the orbit. For slowly rotating black holes, the quasinormal mode’s real frequency is a linear combination of the orbit’s precessional and orbital frequencies, but the correspondence is otherwise unchanged. In this paper, we find a relationship between the quasinormal-mode frequencies of Kerr black holes of arbitrary (astrophysical) spins and general spherical photon orbits, which is analogous to the relationship for slowly rotating holes. To derive this result, we first use the Wentzel-Kramers-Brillouin approximation to compute accurate algebraic expressions for large-l quasinormal-mode frequencies. Comparing our Wentzel-Kramers-Brillouin calculation to the leading-order, geometric-optics approximation to scalar-wave propagation in the Kerr spacetime, we then draw a correspondence between the real parts of the parameters of a quasinormal mode and the conserved quantities of spherical photon orbits. At next-to-leading order in this comparison, we relate the imaginary parts of the quasinormal-mode parameters to coefficients that modify the amplitude of the scalar wave. With this correspondence, we find a geometric interpretation of two features of the quasinormal-mode spectrum of Kerr black holes: First, for Kerr holes rotating near the maximal rate, a large number of modes have nearly zero damping; we connect this characteristic to the fact that a large number of spherical photon orbits approach the horizon in this limit. Second, for black holes of any spins, the frequencies of specific sets of modes are degenerate; we find that this feature arises when the spherical photon orbits corresponding to these modes form closed (as opposed to ergodically winding) curves.'), (6296, '2013-01-23 16:26:40'), (6297, 'http://prd.aps.org/pdf/PRD/v86/i10/e104006'), (6298, 'Phys. Rev. D 84, 084023 (2011)'), (6299, '10.1103/PhysRevD.84.084023'), (6300, 'arXiv:1105.3922'), (6301, 'Numerical simulations of binary black holes---an important predictive tool for the detection of gravitational waves---are computationally expensive, especially for binaries with high mass ratios or with rapidly spinning constituent holes. Existing codes for evolving binary black holes rely on explicit timestepping methods, for which the timestep size is limited by the smallest spatial scale through the Courant-Friedrichs-Lewy condition. Binary inspiral typically involves spatial scales (the spatial resolution required by a small or rapidly spinning hole) which are orders of magnitude smaller than the relevant (orbital, precession, and radiation-reaction) timescales characterizing the inspiral. Therefore, in explicit evolutions of binary black holes, the timestep size is typically orders of magnitude smaller than the relevant physical timescales. Implicit timestepping methods allow for larger timesteps, and they often reduce the total computational cost (without significant loss of accuracy) for problems dominated by spatial rather than temporal error, such as for binary-black-hole inspiral in corotating coordinates. However, fully implicit methods can be difficult to implement for nonlinear evolution systems like the Einstein equations. Therefore, in this paper we explore implicit-explicit (IMEX) methods and use them for the first time to evolve black-hole spacetimes. Specifically, as a first step toward IMEX evolution of a full binary-black-hole spacetime, we develop an IMEX algorithm for the generalized harmonic formulation of the Einstein equations and use this algorithm to evolve stationary and perturbed single-black-hole spacetimes. Numerical experiments explore the stability and computational efficiency of our method.'), (6302, '2013-01-23 21:37:45'), (6303, '10.1103/PhysRevD.74.104006'), (6304, 'Solving Einstein’s equations with dual coordinate frames'), (6305, 'http://link.aps.org/doi/10.1103/PhysRevD.74.104006'), (6306, '2006-11-02 November 2, 2006'), (6307, 'A method is introduced for solving Einstein’s equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original inertial coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einstein’s equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating-coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.'), (6308, '2013-01-23 21:40:19'), (6309, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104006'), (6310, 'Dynamical Excision Boundaries in Spectral Evolutions of Binary Black Hole Spacetimes'), (6311, '2012-11-26 2012-11-26'), (6312, 'http://arxiv.org/abs/1211.6079'), (6313, 'arXiv:1211.6079'), (6314, 'Simulations of binary black holes systems using the Spectral Einstein Code (SpEC) are done on a computational domain that excises the regions surrounding the black holes. It is imperative that the excision boundaries are outflow boundaries with respect to the hyperbolic evolution equations used in the simulation. We employ a time-dependent mapping between the fixed computational frame and the inertial frame through which the black holes move. The time-dependent parameters of the mapping are adjusted throughout the simulation by a feedback control system in order to follow the motion of the black holes, to adjust the shape and size of the excision surfaces so that they remain outflow boundaries, and to prevent large distortions of the grid. We describe in detail the mappings and control systems that we use. We show how these techniques have been essential in the evolution of binary black hole systems with extreme configurations, such as large spin magnitudes and high mass ratios, especially during the merger, when apparent horizons are highly distorted and the computational domain becomes compressed. The techniques introduced here may be useful in other applications of partial differential equations that involve time-dependent mappings.'), (6315, '2013-01-25 21:07:34'), (6316, '1211.6079 PDF'), (6317, 'http://www.arxiv.org/pdf/1211.6079.pdf'), (6318, 'Der Energiesatz in der allgemeinen Relativitätstheorie'), (6319, 'Wiley-VCH Verlag GmbH & Co. KGaA'), (6320, 9783527608959), (6321, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1002/3527608958.ch14/summary'), (6322, '154–166'), (6323, 'Albert Einstein: Akademie-Vorträge'), (6324, 'de'), (6325, 'Copyright © 2006 Wiley-VCH Verlag GmbH & Co. KGaA'), (6326, '2013-01-29 16:15:29'), (6327, '10.1103/PhysRevD.87.024009'), (6328, 'http://link.aps.org/doi/10.1103/PhysRevD.87.024009'), (6329, '2013-01-04 January 4, 2013'), (6330, 'This article studies sufficient accuracy criteria of hybrid post-Newtonian (PN) and numerical relativity (NR) waveforms for parameter estimation of strong binary black-hole sources in second-generation ground-based gravitational-wave detectors. We investigate equal-mass nonspinning binaries with a new 33-orbit NR waveform, as well as unequal-mass binaries with mass ratios 2, 3, 4 and 6. For equal masses, the 33-orbit NR waveform allows us to recover previous results and to extend the analysis toward matching at lower frequencies. For unequal masses, the errors between different PN approximants increase with mass ratio. Thus, at 3.5 PN, hybrids for higher-mass-ratio systems would require NR waveforms with many more gravitational-wave cycles to guarantee no adverse impact on parameter estimation. Furthermore, we investigate the potential improvement in hybrid waveforms that can be expected from fourth-order post-Newtonian waveforms and find that knowledge of this fourth post-Newtonian order would significantly improve the accuracy of hybrid waveforms.'), (6331, '2013-02-03 18:15:03'), (6332, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i2/e024009'), (6333, '10.1103/PhysRevD.86.064020'), (6334, 'Nonspinning searches for spinning black hole-neutron star binaries in ground-based detector data: Amplitude and mismatch predictions in the constant precession cone approximation'), (6335, '064020'), (6336, 'http://link.aps.org/doi/10.1103/PhysRevD.86.064020'), (6337, '2012-09-12 September 12, 2012'), (6338, 'Current searches for compact binary mergers by ground-based gravitational-wave detectors assume for simplicity the two bodies are not spinning. If the binary contains compact objects with significant spin, then this can reduce the sensitivity of these searches, particularly for black hole-neutron star binaries. In this paper we investigate the effect of neglecting precession on the sensitivity of searches for spinning binaries using nonspinning waveform models. We demonstrate that in the sensitive band of Advanced LIGO, the angle between the binary’s orbital angular momentum and its total angular momentum is approximately constant. Under this constant precession cone approximation, we show that the gravitational-wave phasing is modulated in two ways: a secular increase of the gravitational-wave phase due to precession and an oscillation around this secular increase. We show that this secular evolution occurs in precisely three ways, corresponding to physically different apparent evolutions of the binary’s precession about the line of sight. We estimate the best possible fitting factor between any nonprecessing template model and a single precessing signal, in the limit of a constant precession cone. Our closed-form estimate of the fitting factor depends only the geometry of the in-band precession cone; it does not depend explicitly on binary parameters, detector response, or details of either signal model. The precessing black hole-neutron star waveforms least accurately matched by nonspinning waveforms correspond to viewing geometries where the precession cone sweeps the orbital plane repeatedly across the line of sight, in an unfavorable polarization alignment.'), (6339, '2013-02-04 15:27:21'), (6340, 'Nonspinning searches for spinning black hole-neutron star binaries in ground-based detector data'), (6341, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i6/e064020'), (6342, '10.1103/PhysRevD.84.124002'), (6343, 'http://link.aps.org/doi/10.1103/PhysRevD.84.124002'), (6344, '2011-12-01 December 1, 2011'), (6345, 'Previous studies have demonstrated that gravitational radiation reliably encodes information about the natural emission direction of the source (e.g., the orbital plane). In this paper, we demonstrate that these orientations can be efficiently estimated by the principal axes of ⟨L(aLb)⟩, an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. Evaluating this average at each time provides the instantaneous emission direction. Further averaging across the entire signal yields an average orientation, closely connected to the angular components of the Fisher matrix. The latter direction is well-suited to data analysis and parameter estimation when the instantaneous emission direction evolves significantly. Finally, in the time domain, the average ⟨L(aLb)⟩ provides fast, invariant diagnostics of waveform quality.'), (6346, '2013-02-04 15:33:47'), (6347, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i12/e124002'), (6348, '10.1103/PhysRevD.86.104037'), (6349, 'Asymptotic frame selection for binary black hole spacetimes: Post-Newtonian limit'), (6350, 104037), (6351, 'http://link.aps.org/doi/10.1103/PhysRevD.86.104037'), (6352, '2012-11-15 November 15, 2012'), (6353, 'One way to select a preferred frame from gravitational radiation is via the principal axes of ⟨L(aLb)⟩, an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. In this paper we evaluate this time-domain average for a quasicircular binary using approximate (post-Newtonian) waveforms. For nonprecessing unequal-mass binaries, we show the dominant eigenvector of this tensor lies along the orbital angular momentum. For precessing binaries, this frame is not generally aligned with either the orbital or total angular momentum, working to leading order in the spins. The difference between these two quantities grows with time, as the binary approaches the end of the inspiral and both precession and higher harmonics become more significant.'), (6354, '2013-02-04 15:38:37'), (6355, 'Asymptotic frame selection for binary black hole spacetimes'), (6356, 'LIGO'), (6357, 'PhysRevD.86.104037.pdf'), (6358, 'http://www.nytimes.com/2012/10/25/health/teff-and-oatmeal-pancakes-recipes-for-health.html?_r=0'), (6359, 124012), (6360, '10.1088/0264-9381/29/12/124012'), (6361, 'http://iopscience.iop.org/0264-9381/29/12/124012'), (6362, 'Astronomy and astrophysics with gravitational waves in the advanced detector era'), (6363, '2013-02-06 17:40:09'), (6364, '2013-02-10 15:54:49'), (6365, '0264-9381_29_12_124012.pdf'), (6366, '0034-4885_72_7_076901.pdf'), (6367, 'Journal of Instrumentation'), (6368, '03'), (6369, '1748-0221'), (6370, '2012-03-29 2012-03-29'), (6371, 'P03012-P03012'), (6372, '10.1088/1748-0221/7/03/P03012'), (6373, 'http://iopscience.iop.org/1748-0221/7/03/P03012'), (6374, 'The Astronomical Journal'), (6375, '2013-02-06 17:46:54'), (6376, 'Virgo'), (6377, 135), (6378, '1748-0221_7_03_P03012.pdf'), (6379, 'Virgo: A laser interferometer to detect gravitational waves'), (6380, 'LIGO: The Laser Interferometer Gravitational-Wave Observatory'), (6381, 124007), (6382, '10.1088/0264-9381/29/12/124007'), (6383, 'http://iopscience.iop.org/0264-9381/29/12/124007'), (6384, 'Detector configuration of KAGRA–the Japanese cryogenic gravitational-wave detector'), (6385, '2013-02-06 17:51:06'), (6386, '0004-6256, 1538-3881'), (6387, '0264-9381_29_12_124007.pdf'), (6388, '10.1103/PhysRevLett.107.191104'), (6389, 'Beyond the Fisher-Matrix Formalism: Exact Sampling Distributions of the Maximum-Likelihood Estimator in Gravitational-Wave Parameter Estimation'), (6390, 107), (6391, 191104), (6392, 'http://link.aps.org/doi/10.1103/PhysRevLett.107.191104'), (6393, '2011-11-04 November 4, 2011'), (6394, 'Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise realizations, as well as the leading-order width of the posterior probability, but it is limited to high signal strengths often not realized in practice. By contrast, Monte Carlo Bayesian inference provides the full posterior for any signal strength, but it is too expensive to repeat for a representative set of noises. Here I describe an efficient semianalytical technique to map the exact sampling distribution of the maximum-likelihood estimator across noise realizations, for any signal strength. This technique can be applied to any estimation problem for signals in additive Gaussian noise.'), (6395, '2013-02-06 18:22:30'), (6396, 'Beyond the Fisher-Matrix Formalism'), (6397, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v107/i19/e191104'), (6398, '10.1103/PhysRevD.85.104045'), (6399, 'Estimating parameters of coalescing compact binaries with proposed advanced detector networks'), (6400, 85), (6401, 104045), (6402, 'http://link.aps.org/doi/10.1103/PhysRevD.85.104045'), (6403, '2012-05-24 May 24, 2012'), (6404, 'The advanced versions of the LIGO and Virgo ground-based gravitational-wave detectors are expected to operate from three sites: Hanford, Livingston, and Cascina. Recent proposals have been made to place a fourth site in Australia or India, and there is the possibility of using the Large Cryogenic Gravitational Wave Telescope in Japan to further extend the network. Using Bayesian parameter-estimation analyses of simulated gravitational-wave signals from a range of coalescing-binary locations and orientations at fixed distance or signal-to-noise ratio, we study the improvement in parameter estimation for the proposed networks. We find that a fourth detector site can break degeneracies in several parameters; in particular, the localization of the source on the sky is improved by a factor of ∼3–4 for an Australian site, or ∼2.5–3.5 for an Indian site, with more modest improvements in distance and binary inclination estimates. This enhanced ability to localize sources on the sky will be crucial in any search for electromagnetic counterparts to detected gravitational-wave signals.'), (6405, '2013-02-06 18:23:51'), (6406, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i10/e104045'), (6407, '1996-06-01 1996-06-01'), (6408, '1279-1307'), (6409, '10.1088/0264-9381/13/6/004'), (6410, 'http://iopscience.iop.org/0264-9381/13/6/004'), (6411, 'On the estimation of parameters of the gravitational-wave signal from a coalescing binary by a network of detectors'), (6412, '2013-02-06 18:32:26'), (6413, '2008-06-01 2008-06-01'), (6414, 739), (6415, '10.1088/0004-637X/739/2/99'), (6416, 'http://iopscience.iop.org/0004-637X/739/2/99'), (6417, 'LOCALIZING COMPACT BINARY INSPIRALS ON THE SKY USING GROUND-BASED GRAVITATIONAL WAVE INTERFEROMETERS'), (6418, '2013-02-06 18:43:50'), (6419, '2298-2322'), (6420, '2011-05-21 2011-05-21'), (6421, 105021), (6422, '10.1088/0264-9381/28/10/105021'), (6423, 'http://iopscience.iop.org/0264-9381/28/10/105021'), (6424, 'Source localization with an advanced gravitational wave detector network'), (6425, '2013-02-06 18:43:56'), (6426, '10.1088/0004-6256/135/6/2298'), (6427, '10.1103/PhysRevD.84.104020'), (6428, 'Application of asymptotic expansions for maximum likelihood estimators’ errors to gravitational waves from inspiraling binary systems: The network case'), (6429, 'http://link.aps.org/doi/10.1103/PhysRevD.84.104020'), (6430, '2011-11-08 November 8, 2011'), (6431, 'This paper describes the most accurate analytical frequentist assessment to date of the uncertainties in the estimation of physical parameters from gravitational waves generated by nonspinning binary systems and Earth-based networks of laser interferometers. The paper quantifies how the accuracy in estimating the intrinsic parameters mostly depends on the network signal to noise ratio (SNR), but the resolution in the direction of arrival also strongly depends on the network geometry. We compare results for six different existing and possible global networks and two different choices of the parameter space. We show how the fraction of the sky where the one sigma angular resolution is below 2 square degrees increases about 3 times when transitioning from the Hanford (USA), Livingston (USA) and Cascina (Italy) network to a network made of five interferometers (while keeping the network SNR fixed). The technique adopted here is an asymptotic expansion of the uncertainties in inverse powers of the SNR where the first order is the inverse Fisher information matrix. We show that the commonly employed approach of using a simplified parameter spaces and only the Fisher information matrix can largely underestimate the uncertainties (the combined effect would lead to a factor 7 for the one sigma sky uncertainty in square degrees at a network SNR of 15).'), (6432, '2013-02-06 18:43:59'), (6433, 'Application of asymptotic expansions for maximum likelihood estimators’ errors to gravitational waves from inspiraling binary systems'), (6434, 'http://iopscience.iop.org/0004-6256/135/6/2298'), (6435, '10.1103/PhysRevD.81.082001'), (6436, 'Geometrical expression for the angular resolution of a network of gravitational-wave detectors'), (6437, '082001'), (6438, 'http://link.aps.org/doi/10.1103/PhysRevD.81.082001'), (6439, '2010-04-08 April 8, 2010'), (6440, 'We report for the first time general geometrical expressions for the angular resolution of an arbitrary network of interferometric gravitational-wave (GW) detectors when the arrival time of a GW is unknown. We show explicitly elements that decide the angular resolution of a GW detector network. In particular, we show the dependence of the angular resolution on areas formed by projections of pairs of detectors and how they are weighted by sensitivities of individual detectors. Numerical simulations are used to demonstrate the capabilities of the current GW detector network. We confirm that the angular resolution is poor along the plane formed by current LIGO-Virgo detectors. A factor of a few to more than ten fold improvement of the angular resolution can be achieved if the proposed new GW detectors LCGT or AIGO are added to the network. We also discuss the implications of our results for the design of a GW detector network, optimal localization methods for a given network, and electromagnetic follow-up observations.'), (6441, '2013-02-06 18:44:03'), (6442, '1982-05-08 05/08/1982'), (6443, '10.1103/PhysRevD.83.102001'), (6444, 'Localization of gravitational wave sources with networks of advanced detectors'), (6445, 102001), (6446, 'http://link.aps.org/doi/10.1103/PhysRevD.83.102001'), (6447, '2011-05-17 May 17, 2011'), (6448, 'Coincident observations with gravitational wave (GW) detectors and other astronomical instruments are among the main objectives of the experiments with the network of LIGO, Virgo, and GEO detectors. They will become a necessary part of the future GW astronomy as the next generation of advanced detectors comes online. The success of such joint observations directly depends on the source localization capabilities of the GW detectors. In this paper we present studies of the sky localization of transient GW sources with the future advanced detector networks and describe their fundamental properties. By reconstructing sky coordinates of ad hoc signals injected into simulated detector noise, we study the accuracy of the source localization and its dependence on the strength of injected signals, waveforms, and network configurations.'), (6449, '2013-02-06 18:44:07'), (6450, '2013-02-13 20:44:27'), (6451, '2010-12-10 2010-12-10'), (6452, '496-514'), (6453, '10.1088/0004-637X/725/1/496'), (6454, 'http://iopscience.iop.org/0004-637X/725/1/496'), (6455, 'EXPLORING SHORT GAMMA-RAY BURSTS AS GRAVITATIONAL-WAVE STANDARD SIRENS'), (6456, '2013-02-06 18:44:10'), (6457, 'http://iopscience.iop.org/1538-3881/135/6/2298/pdf/1538-3881_135_6_2298.pdf'), (6458, 184011), (6459, '10.1088/0264-9381/25/18/184011'), (6460, 'http://iopscience.iop.org/0264-9381/25/18/184011'), (6461, 'Parameter estimation of spinning binary inspirals using Markov chain Monte Carlo'), (6462, '2013-02-06 18:44:14'), (6463, 'Simple, regular, and efficient numerical integration of rotational motion'), (6464, 688), (6465, '2008-12-01 2008-12-01'), (6466, 'L61-L64'), (6467, '10.1086/595279'), (6468, 'http://iopscience.iop.org/595279'), (6469, 'Gravitational-Wave Astronomy with Inspiral Signals of Spinning Compact-Object Binaries'), (6470, '2013-02-06 18:44:17'), (6471, 'Spin-s Spherical Harmonics and $\\eth$'), (6472, '2013-02-06 18:44:22'), (6473, 'Positive energy theorems in General Relativity'), (6474, 'General relativistic null-cone evolutions with a high-order scheme'), (6475, '2012-08-19 2012-08-19'), (6476, 'http://arxiv.org/abs/1208.3891'), (6477, 'arXiv:1208.3891'), (6478, 'We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. The scheme can offer significantly more accuracy with relatively low computational cost compared to previous methods as a result of the higher-order discretization. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.'), (6479, '2013-02-06 23:41:04'), (6480, '1208.3891 PDF'), (6481, 'http://www.arxiv.org/pdf/1208.3891.pdf'), (6482, '2013-02-14 2013-02-14'), (6483, 'http://arxiv.org/abs/1302.3405'), (6484, 'arXiv:1302.3405'), (6485, 'The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that has been proved remarkably difficult to solve. They constitute one of the major results in classical General Relativity and they uncover a deep self-consistence of the theory.'), (6486, '2013-02-15 22:34:40'), (6487, '1302.3405 PDF'), (6488, 'http://www.arxiv.org/pdf/1302.3405.pdf'), (6489, '2013-02-19 20:48:02'), (6490, 'Neutron star spin–kick velocity correlation effect on binary neutron star coalescence rates and spin–orbit misalignment of the components'), (6491, '2008-03-11 03/11/2008'), (6492, '10.1111/j.1365-2966.2007.12635.x'), (6493, 'MNRAS'), (6494, 384), (6495, 'http://mnras.oxfordjournals.org/content/384/4/1393'), (6496, '1393-1398'), (6497, '0035-8711, 1365-2966'), (6498, '2013-02-19 21:01:27'), (6499, 'mnras.oxfordjournals.org'), (6500, 'We study the effect of the neutron star spin–kick velocity alignment observed in young radio pulsars on the coalescence rate of binary neutron stars. Two scenarios are considered for neutron star formation: when the kick is always present, and when it is small or absent if a neutron star is formed in a binary system as a result of electron-capture degenerate core collapse. The effect is shown to be especially strong for large kick amplitudes and tight alignments, reducing the expected galactic rate of binary neutron star coalescence compared to calculations with randomly directed kicks. The spin–kick correlation also leads to a much narrower neutron star spin–orbit misalignment.'), (6501, 'http://mnras.oxfordjournals.org/content/384/4/1393.full.pdf'), (6502, 'Resonant-plane locking and spin alignment in stellar-mass black-hole binaries: a diagnostic of compact-binary formation'), (6503, '2013-02-18 2013-02-18'), (6504, 'http://arxiv.org/abs/1302.4442'), (6505, 'arXiv:1302.4442'), (6506, 'We study the influence of astrophysical formation scenarios on the precessional dynamics of spinning black-hole binaries by the time they enter the observational window of second- and third-generation gravitational-wave detectors, such as Advanced LIGO/Virgo, LIGO-India, KAGRA and the Einstein Telescope. Under the plausible assumption that tidal interactions are efficient at aligning the spins of few-solar mass black-hole progenitors with the orbital angular momentum, we find that black-hole spins should be expected to preferentially lie in a plane when they become detectable by gravitational-wave interferometers. This "resonant plane" is identified by the conditions \\Delta\\Phi=0{\\deg} or \\Delta\\Phi=+/-180{\\deg}, where \\Delta\\Phi is the angle between the components of the black-hole spins in the plane orthogonal to the orbital angular momentum. If the angles \\Delta \\Phi can be accurately measured for a large sample of gravitational-wave detections, their distribution will constrain models of compact binary formation. In particular, it will tell us whether tidal interactions are efficient, and whether mass transfer between the binary members is strong enough to produce mass-ratio reversal (so that the heavier black hole is produced by the initially lighter stellar progenitor). Therefore our model offers a concrete observational link between gravitational-wave measurements and astrophysics. We also hope that it will stimulate further studies of precessional dynamics, gravitational-wave template placement and parameter estimation for binaries locked in the resonant plane.'), (6507, '2013-02-20 03:58:28'), (6508, 'Resonant-plane locking and spin alignment in stellar-mass black-hole binaries'), (6509, '1302.4442 PDF'), (6510, 'http://www.arxiv.org/pdf/1302.4442.pdf'), (6511, '2013-02-20 04:10:54'), (6512, 'Scholarpedia'), (6513, '1941-6016'), (6514, 7445), (6515, '10.4249/scholarpedia.7445'), (6516, 'http://www.scholarpedia.org/article/Spin-coefficient_formalism'), (6517, 'Spin-coefficient formalism'), (6518, '2013-02-25 05:21:04'), (6519, 'Studies of waveform requirements for intermediate mass-ratio coalescence searches with advanced detectors'), (6520, '2013-02-25 2013-02-25'), (6521, 'http://arxiv.org/abs/1302.6049'), (6522, 'arXiv:1302.6049'), (6523, 'The coalescence of a stellar-mass compact object into an intermediate-mass black hole (intermediate mass-ratio coalescence; IMRAC) is an important astrophysical source for ground-based gravitational-wave interferometers in the so-called advanced configuration. However, the ability to carry out effective matched-filter based searches for these systems is limited by the lack of reliable waveforms. Here we consider binaries in which the intermediate-mass black hole has mass in the range 24 - 200 solar masses with a stellar-mass companion having masses in the range 1.4 - 18.5 solar masses. In addition, we constrain the mass ratios, q, of the binaries to be in the range 1/140 < q < 1/10 and we restrict our study to the case of circular binaries with non-spinning components. We investigate the relative contribution to the signal-to-noise ratio (SNR) of the three different phases of the coalescence: inspiral, merger and ringdown. We show that merger and ringdown contribute to a substantial fraction of the total SNR over a large portion of the mass parameter space, although in a limited portion the SNR is dominated by the inspiral phase. We further identify three regions in the IMRAC mass-space in which: (i) inspiral-only searches could be performed with losses in detection rates L in the range 10% < L < 27%, (ii) searches based on inspiral-only templates lead to a loss in detection rates in the range 27% < L < 50%$, and (iii) templates that include merger and ringdown are essential to prevent losses in detection rates greater than 50%. We investigate the effectiveness with which the inspiral-only portion of the IMRAC waveform space is covered by comparing several existing waveform families in this regime. Our results reinforce the importance of extensive numerical relativity simulations of IMRACs and the need for further studies of suitable approximation schemes in this mass range.'), (6524, '2013-02-26 13:16:56'), (6525, '1302.6049 PDF'), (6526, 'http://www.arxiv.org/pdf/1302.6049.pdf'), (6527, 'Angular velocity of gravitational radiation from precessing binaries and the corotating frame'), (6528, '2013-02-12 2013-02-12'), (6529, 'http://arxiv.org/abs/1302.2919'), (6530, 'arXiv:1302.2919'), (6531, 'This paper defines an angular velocity for time-dependent functions on the sphere, and applies it to gravitational waveforms from compact binaries. Because it is geometrically meaningful and has a clear physical motivation, the angular velocity is uniquely useful in helping to solve an important---and largely ignored---problem in models of compact binaries: the inverse problem of deducing the physical parameters of a system from the gravitational waves alone. It is also used to define the corotating frame of the waveform. When decomposed in this frame, the waveform has no rotational dynamics and is therefore as slowly evolving as possible. The resulting simplifications lead to straightforward methods for accurately comparing waveforms and constructing hybrids. As formulated in this paper, the methods can be applied robustly to both precessing and nonprecessing waveforms, providing a clear, comprehensive, and consistent framework for waveform analysis. Explicit implementations of all these methods are provided in accompanying computer code.'), (6532, '2013-03-01 01:08:45'), (6533, '10.1098/rspa.1982.0058'), (6534, 381), (6535, 1780), (6536, 'http://rspa.royalsocietypublishing.org/content/381/1780/53'), (6537, '53-63'), (6538, '2013-03-01 18:42:01'), (6539, 'rspa.royalsocietypublishing.org'), (6540, 'A new approach to defining energy-momentum and angular momentum in general relativity is presented which avoids some of the difficulties of previous definitions and which can be applied quasi-locally. It depends on the construction of a twistor space T$^\\alpha$(S) associated with any spacelike topological 2-sphere S. Though several problems of interpretation remain to be solved, the new definition works well at T$^+$, reproducing the Bondimass-momentum as four of the ten precisely determined quantities at each cut of T$^+$. The remaining six quantities provide a definition of angular momentum which appears to be new.'), (6541, 'http://rspa.royalsocietypublishing.org/content/381/1780/53.full.pdf'), (6542, 'Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian'), (6543, '10.1103/PhysRevD.81.084001'), (6544, '2013-03-13 2013-03-13'), (6545, 'http://arxiv.org/abs/1303.3225'), (6546, 'Estimating energy-momentum and angular momentum near null infinity'), (6547, 'http://link.aps.org/doi/10.1103/PhysRevD.81.084001'), (6548, '2010-04-01 April 1, 2010'), (6549, '2013-03-02 21:07:17'), (6550, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084001'), (6551, 'Minimal Length Scale Scenarios for Quantum Gravity'), (6552, '2013-00-00 2013'), (6553, 'http://relativity.livingreviews.org/Articles/lrr-2013-2/'), (6554, '2013-03-02 21:29:02'), (6555, 'Minimal Length Scale Scenarios for Quantum Gravity - lrr-2013-2Color.pdf'), (6556, 'http://relativity.livingreviews.org/Articles/lrr-2013-2/download/lrr-2013-2Color.pdf'), (6557, '2013-03-02 21:30:12'), (6558, 'lrr-2013-2Color.pdf'), (6559, 'arXiv:1303.3225'), (6560, "A new type of algebra for Minkowski space‐time is described, in terms of which it is possible to express any conformally covariant or Poincaré covariant operation. The elements of the algebra (twistors) are combined according to tensor‐type rules, but they differ from tensors or spinors in that they describe locational properties in addition to directional ones. The representation of a null line by a pair of two‐component spinors, one of which defines the direction of the line and the other, its moment about the origin, gives the simplest type of twistor, with four complex components. The rules for generating other types of twistor are then determined by the geometry. One‐index twistors define a four‐dimensional, four‐valued (``spinor'') representation of the (restricted) conformal group. For the Poincaré group a skew‐symmetric metric twistor is introduced. Twistor space defines a complex projective three‐space C, which gives an alternative picture equivalent to the Minkowski space‐time M (which must be completed by a null cone at infinity). Points in C represent null lines or ``complexified'' null lines in M; lines in C represent real or complex points in M (so M, when complexified, is the Klein representation of C. Conformal transformations of M, including space and time reversals (and complex conjugation) are discussed in detail in twistor terms. A theorem of Kerr is described which shows that the complex analytic surfaces in C define the shear‐free null congruences in the real space M. Twistors are used to derive new theorems about the real geometry of M. The general twistor description of physical fields is left to a later paper."), (6561, '1967-02-01 1967-02-01'), (6562, 'doi:10.1063/1.1705200'), (6563, '345-366'), (6564, 'Twistor Algebra'), (6565, 'AIP'), (6566, 'The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as function of orbital angular frequency. Apart from a single coefficient, which is known solely numerically, all the coefficients are given as exact numbers. The shown Hamiltonian is presented in the center-of-mass frame and out of its 57 coefficients 51 are given fully explicitly. Those coefficients are six coefficients more than previously achieved [Jaranowski/Sch\\"afer, Phys. Rev. D 86, 061503(R) (2012)]. The local divergences in the point-mass model are uniquely controlled by the method of dimensional regularization. As application, the last stable circular orbit is determined as function of the symmetric-mass-ratio parameter.'), (6567, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v8/i2/p345_s1'), (6568, '2013-04-05 17:41:41'), (6569, '2013-03-02 22:23:36'), (6570, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000008000002000345000001&idtype=cvips&doi=10.1063/1.1705200&prog=normal'), (6571, '2013-03-02 22:23:38'), (6572, '2013-03-02 22:24:10'), (6573, 'The twistor programme'), (6574, 'Reports on Mathematical Physics'), (6575, '65-76'), (6576, '0034-4877'), (6577, '10.1016/0034-4877(77)90047-7'), (6578, 'http://www.sciencedirect.com/science/article/pii/0034487777900477'), (6579, "The formalism of twistors provides a new approach to the description of basic physics. The points of Minkowski space-time are represented by 2-dimensional linear subspaces of a complex 4-dimensional vector space (flat twistor space) on which a Hermitian form of signature ++-- is defined. Free massless fields can be represented in terms of the sheaf cohomology of portions of this space. Twistor space (or a suitable part of it) can be expressed in two different ways as a complex fibration. If one or the other fibration structure is deformed, the resulting space represents not empty Minkowski space but, in one case, the general “right-flat” solution of Einstein's vacuum equations and, in the other, the general (left-handed) solution of Maxwell's equations. These provide the most primitive types of interaction (gravitational or electromagnetic) which may generalize to other fields in a comprehensive twistor scheme for the description of elementary particles."), (6580, '1977-08-00 August 1977'), (6581, '2013-03-02 22:25:28'), (6582, 'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271950&_user=492137&_pii=0034487777900477&_check=y&_origin=article&_zone=toolbar&_coverDate=1977--31&view=c&originContentFamily=serial&wchp=dGLbVlV-zSkzS&md5=2dd3759c5bcfea2ffaa8c9c4c3c84d04&pid=1-s2.0-0034487777900477-main.pdf'), (6583, 'Twistors in Geometric Algebra'), (6584, '2008-09-01 2008/09/01'), (6585, 'Advances in Applied Clifford Algebras'), (6586, 'AACA'), (6587, '3-4'), (6588, '10.1007/s00006-008-0083-x'), (6589, '373-394'), (6590, '0188-7009, 1661-4909'), (6591, 'http://link.springer.com/article/10.1007/s00006-008-0083-x'), (6592, '2013-03-02 22:30:34'), (6593, 'link.springer.com.proxy.library.cornell.edu'), (6594, 'Twistors are re-interpreted in terms of geometric algebra as 4-d spinors with a position dependence. This allows us to construct their properties as observables of a quantum system. The Robinson congruence is derived and extended to non-Euclidean spaces where it is represented in terms of d-lines. Different conformal spaces are constructed through the infinity twistors for Friedmann-Robertson-Walker spaces. Finally, we give a 6-d spinor representation of a twistor, which allows us to define the geometrical properties of the twistors as observables of this higher dimensional space.'), (6595, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs00006-008-0083-x'), (6596, 'The construction of spinors in geometric algebra'), (6597, 317), (6598, '383-409'), (6599, '10.1016/j.aop.2004.11.008'), (6600, 'http://www.sciencedirect.com/science/article/pii/S0003491604002209'), (6601, 'The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some real geometric algebra, the gap among algebraic, geometric, and physical methods is closed. Spinors are developed in any number of dimensions from a discussion of spin groups, followed by the specific cases of U (1), SU (2), and SL ( 2 , C ) spinors. The physical observables in Schrödinger–Pauli theory and Dirac theory are found, and the relationship between Dirac, Lorentz, Weyl, and Majorana spinors is made explicit. The use of a real geometric algebra, as opposed to one defined over the complex numbers, provides a simpler construction and advantages of conceptual and theoretical clarity not available in other approaches.'), (6602, '2005-06-00 June 2005'), (6603, '2013-03-03 17:13:16'), (6604, 'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272507&_user=492137&_pii=S0003491604002209&_check=y&_origin=article&_zone=toolbar&_coverDate=2005--30&view=c&originContentFamily=serial&wchp=dGLzVlV-zSkWb&md5=0aaf6c3702d07fcdefa2cdbb5ec411a7&pid=1-s2.0-S0003491604002209-main.pdf'), (6605, 'Angular momentum of isolated systems'), (6606, '2007-12-01 2007/12/01'), (6607, 'Gen Relativ Gravit'), (6608, '10.1007/s10714-007-0509-0'), (6609, '2125-2147'), (6610, 'http://link.springer.com/article/10.1007/s10714-007-0509-0'), (6611, '2013-03-05 22:38:45'), (6612, 'link.springer.com'), (6613, 'Penrose’s twistorial approach to the definition of angular momentum at null infinity is developed so that angular momenta at different cuts can be meaningfully compared. This is done by showing that the twistor spaces associated with different cuts of J+\\mathcal{J}^+ can be identified as manifolds (but not as vector spaces). The result is a well-defined, Bondi–Metzner–Sachs-invariant notion of angular momentum in a radiating space–time; the difficulties and ambiguities previously encountered are attached to attempts to express this in special-relativistic terms, and in particular to attempts to identify a single Minkowski space of origins. Unlike the special-relativistic case, the angular momentum cannot be represented by a purely j = 1 quantity M ab , but has higher-j contributions as well. Applying standard kinematic prescriptions, these higher-j contributions are shown to correspond precisely to the shear. Thus it appears that shear and angular momentum should be regarded as different aspects of a single unified concept.'), (6614, 'http://link.springer.com/content/pdf/10.1007%2Fs10714-007-0509-0'), (6615, 'I-Love-Q Relations in Neutron Stars and their Applications to Astrophysics, Gravitational Waves and Fundamental Physics'), (6616, '2013-03-06 2013-03-06'), (6617, 'http://arxiv.org/abs/1303.1528'), (6618, 'arXiv:1303.1528'), (6619, "The exterior gravitational field of a slowly-rotating neutron star can be characterized by its multipole moments, the first few being the neutron star mass, moment of inertia, and quadrupole moment. In principle, all of these quantities depend on the neutron star's internal structure, and thus, on unknown nuclear physics at supra-nuclear energy densities. We here find relations between the moment of inertia, the Love numbers and the quadrupole moment (I-Love-Q relations) that do not depend sensitively on the neutron star's internal structure. Such universality may arise for two reasons: (i) these relations depend most sensitively on the internal structure far from the core, where all realistic equations of state mostly approach each other; (ii) as the NS compactness increases, the I-Love-Q trio approaches that of a BH, which does not have an internal-structure dependence. Three important consequences derive from these I-Love-Q relations. On an observational astrophysics front, the measurement of a single member of the I-Love-Q trio would automatically provide information about the other two, even when the latter may not be observationally accessible. On a gravitational wave front, the I-Love-Q relations break the degeneracy between the quadrupole moment and the neutron-star spins in binary inspiral waveforms, allowing second-generation ground-based detectors to determine the (dimensionless) averaged spin to 0.01. On a fundamental physics front, the I-Love-Q relations allow for tests of General Relativity in the neutron-star strong-field that are both theory- and internal structure-independent. As an example, by combining gravitational-wave and electromagnetic observations, one may constrain dynamical Chern-Simons gravity in the future by more than 6 orders of magnitude more stringently than Solar System and table-top constraints."), (6620, '2013-03-08 15:10:21'), (6621, '1303.1528 PDF'), (6622, 'http://www.arxiv.org/pdf/1303.1528.pdf'), (6623, 'Recent progress in spin calculations in the post-Newtonian framework and applications'), (6624, '2013-03-04 2013-03-04'), (6625, 'http://arxiv.org/abs/1303.0666'), (6626, 'arXiv:1303.0666'), (6627, 'Recently we derived the next-to-next-to-leading order post-Newtonian Hamiltonians at spin-orbit and spin(1)-spin(2) level for a binary system of compact objects. In this talk the derivation of them will be shortly outlined at an introductory level. We will also discuss some checks of our (complicated and long) results in the first part of the talk. In the second part we will show how to apply our results to the calculation of the last stable circular orbit of such a binary system of black holes or neutron stars.'), (6628, '2013-03-08 15:10:38'), (6629, '1303.0666 PDF'), (6630, 'http://www.arxiv.org/pdf/1303.0666.pdf'), (6631, 'A first-order secular theory for the post-Newtonian two-body problem with spin -- I: The restricted case'), (6632, '2013-03-01 2013-03-01'), (6633, 'http://arxiv.org/abs/1303.0232'), (6634, 'MNRAS (January 21, 2013) 428 (3): 2295-2310'), (6635, '10.1093/mnras/sts198'), (6636, 'arXiv:1303.0232'), (6637, 'We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces well-known relativistic effects such as the precession of the pericentre and the Lense-Thirring and geodetic effects. Additionally, our theory takes into full account the complex interplay between the various relativistic effects, and provides a new explicit solution of the averaged equations of motion in terms of elliptic functions. Our analysis reveals the presence of particular configurations for which non-periodical behaviour can arise. The application of our results to real astrodynamical systems (such as Mercury-like and pulsar planets) highlights the contribution of relativistic effects to the long-term evolution of the spin and orbit of the secondary body.'), (6638, '2013-03-08 15:10:44'), (6639, 'A first-order secular theory for the post-Newtonian two-body problem with spin -- I'), (6640, '1303.0232 PDF'), (6641, 'http://www.arxiv.org/pdf/1303.0232.pdf'), (6642, '10.1103/PhysRevD.86.104063'), (6643, 'Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and nonprecessing inspiral signals'), (6644, 104063), (6645, 'http://link.aps.org/doi/10.1103/PhysRevD.86.104063'), (6646, '2012-11-27 November 27, 2012'), (6647, 'One of the greatest theoretical challenges in the buildup to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly simplify this problem. We show that generic precessing-binary inspiral waveforms (covering a seven-dimensional space of intrinsic parameters) can be mapped to a two-dimensional space of nonprecessing binaries, characterized by the mass ratio and a single effective total spin. The mapping consists of a time-dependent rotation of the waveforms into the quadrupole-aligned frame and is extremely accurate (matches >0.99 with parameter biases in the total spin of Δχ≤0.04), even in the case of transitional precession. In addition, we demonstrate a simple method to construct hybrid post-Newtonian–numerical relativity precessing-binary waveforms in the quadrupole-aligned frame and provide evidence that our approximate mapping can be used all the way to the merger. Finally, based on these results, we outline a general proposal for the construction of generic waveform models, which will be the focus of future work.'), (6648, '2013-03-12 02:49:29'), (6649, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i10/e104063'), (6650, '1987-02-05 1987-02-05'), (6651, 'Spinors and Space-Time'), (6652, '10.1088/0264-9381/17/21/304'), (6653, '2013-08-14 18:09:07'), (6654, 'Twistor quantisation and curved space-time'), (6655, '1968-05-01 1968/05/01'), (6656, 'International Journal of Theoretical Physics'), (6657, 'Int J Theor Phys'), (6658, '10.1007/BF00668831'), (6659, '61-99'), (6660, '0020-7748, 1572-9575'), (6661, 'http://link.springer.com/article/10.1007/BF00668831'), (6662, '2013-03-25 20:26:15'), (6663, 'The formalism of twistors [the ‘spinors’ for the group O(2,4)] is employed to give a concise expression for the solution of the zero rest-mass field equations, for each spin (s=0, 1/2, 1, ...), in terms of an arbitrary complex analytic functionf(Z α) (homogeneous of degree −2s −2). The four complex variablesZ α are the components of a twistor. In terms of twistor space (C-picture) it is analytic structure which takes the place of field equations in ordinary Minkowski space-time (M-picture). By requiring that the singularities off(Z α) form a disconnected pair of regions in the upper half of twistor space, fields of positive frequency are generated. The twistor formalism is adapted so as to be applicable in curved space-times. The effect of conformai curvature in theM-picture is studied by consideration of plane (-fronted) gravitational ‘sandwich’ waves. TheC-picture still exists, but its complex structure ‘shifts’ as it is ‘viewed’ from different regions of the space-time. A weaker symplectic structure remains. The shifting of complex structure is naturally described in terms of Hamiltonian equations and Poisson brackets, in the twistor variablesZ α, \\bar Z_\\alpha . This suggests the correspondence TeX\\bar Z_\\alpha = \\partial /\\partial Z^\\alpha as a basis for quantization. The correspondence is then shown to be, in fact, valid for the Hubert space of functionsf(Z α), which give the above twistor description of zero rest-mass fields. For this purpose, the Hubert space scalar product is described in (conformally invariant) twistor terms. The twistor expressions for the charge and the mass, momentum and angular momentum (both in ‘inertial’ and ‘active’ versions, in linearised theory) are also given. It is suggested that twistors may supply a link between quantum theory and space-time curvature. On this view, curvature arises whenever a ‘shift’ occurs in the interpretation of the twistor variablesZ α, TeX\\bar Z_\\alpha as the twistor ‘position’ and ‘momentum’ operators, respectively.'), (6664, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF00668831'), (6665, "Some Examples of Penrose's Quasi-Local Mass Construction"), (6666, '1983-08-08 08/08/1983'), (6667, '10.1098/rspa.1983.0092'), (6668, 388), (6669, 1795), (6670, 'http://rspa.royalsocietypublishing.org/content/388/1795/457'), (6671, '457-477'), (6672, '2013-03-25 21:59:49'), (6673, "Penrose's quasi-local mass (Penrose, Proc. R. Soc. Lond. A 381, 253 (1982)) is calculated for a variety of two-surfaces in particular space-times. The results are compared with other definitions of mass where these are available."), (6674, 'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/388/1795/457.full.pdf'), (6675, 'More on quasi-local mass'), (6676, 'Twistor Newsletter'), (6677, 'No18 26 July 1984.pdf'), (6678, '1984-07-26 July 26, 1984'), (6679, 'http://people.maths.ox.ac.uk/lmason/Tn/TN1-25/No18%2026%20July%201984.pdf'), (6680, 'Next-to-next-to-leading order spin-orbit effects in the gravitational wave flux and orbital phasing of compact binaries'), (6681, 'arXiv:1405.0504 [astro-ph, physics:gr-qc]'), (6682, 'http://arxiv.org/abs/1303.7412'), (6683, '2014-05-02 2014-05-02'), (6684, "We compute the next-to-next-to-leading order spin-orbit contributions in the total energy flux emitted in gravitational waves by compact binary systems. Such contributions correspond to the post-Newtonian order 3.5PN for maximally spinning compact objects. Continuing our recent work on the next-to-next-to-leading spin-orbit terms at 3.5PN order in the equations of motion, we obtain the spin-orbit terms in the multipole moments of the compact binary system up to the same order within the multipolar post-Newtonian wave generation formalism. Our calculation of the multipole moments is valid for general orbits and in an arbitrary frame; the moments are then reduced to the center-of-mass frame and the resulting energy flux is specialized to quasi-circular orbits. The test-mass limit of our final result for the flux agrees with the already known Kerr black hole perturbation limit. Furthermore the various multipole moments of the compact binary reduce in the one-body case to those of a single boosted Kerr black hole. We briefly discuss the implications of our result for the gravitational-wave flux in terms of the binary's phase evolution, and address its importance for the future detection and parameter estimation of signals in gravitational wave detectors."), (6685, '2014-05-06 20:47:34'), (6686, '1303.7412 PDF'), (6687, 'http://www.arxiv.org/pdf/1303.7412.pdf'), (6688, '1303.3225 PDF'), (6689, 'http://www.arxiv.org/pdf/1303.3225.pdf'), (6690, 'http://link.aps.org/doi/10.1103/PhysRevD.87.104006'), (6691, 'http://arxiv.org/abs/1403.5672'), (6692, 'arXiv:1403.5672 [astro-ph, physics:gr-qc]'), (6693, '2014-03-22 2014-03-22'), (6694, '2014-03-25 18:58:00'), (6695, 'Google Scholar'), (6696, 'Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we have found that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the compactness of the progenitor stars. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We have tested our approach with simulated data and verified it works well for all the equations of state considered.'), (6697, 'Constraining the equation of state of neutron stars from binary mergers'), (6698, 'http://www.arxiv.org/pdf/1403.5672.pdf'), (6699, '1403.5672 PDF'), (6700, 'Practical Parameterization of Rotations Using the Exponential Map'), (6701, '29-48'), (6702, '10.1080/10867651.1998.10487493'), (6703, 'http://www.tandfonline.com/doi/abs/10.1080/10867651.1998.10487493'), (6704, 'Abstract Paramet erizing three degree-of-freedom (DOF) rotat ions is difficult to do well. Many graphics applications demand that we be able to compute and differentiate positions and orientations of articulated figures with respect to their rotational (and other) parameters, as well as integrate differential equations, optimize rotation parameters, and interpolate orientations. Widely used parameterizations such as Euler angles and quaternions are well suited to only a few of these operations. The exponential map maps a vector in R 3 describing the axis and magnitude of a three-DOF rotation to the corresponding rotation. Several graphics researchers have applied it with limited success to interpolation of orientations, but it has been virtually ignored with respect to the other operations mentioned above. In this paper we present formulae for computing, differentiating, and integrating three-DOF rotations with the exponential map. We show that our formulation is numerically stable in the face of machine precision issues, and that for most applications all singularities in the map can be avoided through a simple technique of dynamic reparameterization. We demonstrate how to use the exponential map to solve both the “free ly rotating body” problem, and the important ball-and-socket joint required to accurately model shoulder and hip joints in art iculated figures. Examining several common graphics applications, we explaint he benefits of our formulation of t he exponential map over Euler angles and quaternions, including robustness, sm all state vectors, lack of explicitconst raints, good modeling capabilities, simplicity of solving ordinary differential equations, and good interpolation behavior.'), (6705, '1086-7651'), (6706, 'Taylor and Francis+NEJM'), (6707, '2013-04-09 21:20:27'), (6708, '10.1103/PhysRevD.87.044009'), (6709, '10867651.1998.pdf'), (6710, 'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/10867651.1998.10487493'), (6711, '2013-04-09 21:22:07'), (6712, '044009'), (6713, 'http://link.aps.org/doi/10.1103/PhysRevD.87.044009'), (6714, '2013-02-05 February 5, 2013'), (6715, 'We calculate the gravitational waveform for spinning, precessing compact binary inspirals through second post-Newtonian order in the amplitude. When spins are collinear with the orbital angular momentum and the orbits are quasicircular, we further provide explicit expressions for the gravitational-wave polarizations and the decomposition into spin-weighted spherical-harmonic modes. Knowledge of the second post-Newtonian spin terms in the waveform could be used to improve the physical content of analytical templates for data analysis of compact binary inspirals and for more accurate comparisons with numerical-relativity simulations.'), (6716, '2013-04-09 21:56:21'), (6717, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i4/e044009'), (6718, 'Next-to-next-to-leading order spin–orbit effects in the near-zone metric and precession equations of compact binaries'), (6719, '2013-04-07 2013-04-07'), (6720, '10.1088/0264-9381/30/7/075017'), (6721, 'We extend our previous work devoted to the computation of the next-to-next-to-leading order spin–orbit correction (corresponding to 3.5PN order) in the equations of motion of spinning compact binaries by (i) deriving the corresponding spin–orbit terms in the evolution equations for the spins, the conserved integrals of the motion and the metric regularized at the location of the particles (obtaining also the metric all over the near zone but with some lower precision); (ii) performing the orbital reduction of the precession equations, near-zone metric and conserved integrals to the center-of-mass frame and then further assuming quasi-circular orbits (neglecting gravitational radiation reaction). The results are systematically expressed in terms of the spin variables with a conserved Euclidean norm instead of the original antisymmetric spin tensors of the pole–dipole formalism. This work paves the way to the future computation of the next-to-next-to-leading order spin–orbit terms in the gravitational-wave phasing of spinning compact binaries.'), (6722, '075017'), (6723, 'http://iopscience.iop.org/0264-9381/30/7/075017'), (6724, '2013-04-09 22:03:16'), (6725, 'Wave-Functions for Spin-3/2 and Integer Spin Fields'), (6726, 'Next-to-next-to-leading order spin–orbit effects in the equations of motion of compact binary systems'), (6727, '2013-03-07 2013-03-07'), (6728, '10.1088/0264-9381/30/5/055007'), (6729, "We compute next-to-next-to-leading order spin contributions to the post-Newtonian equations of motion for binaries of compact objects, such as black holes or neutron stars. For maximally spinning black holes, those contributions are of third-and-a-half post-Newtonian (3.5 PN) order, improving our knowledge of the equations of motion, already known for non-spinning objects up to this order. Building on previous work, we represent the rotation of the two bodies using a pole–dipole matter stress–energy tensor and iterate Einstein's field equations for a set of potentials parametrizing the metric in harmonic coordinates. Checks of the result include the existence of a conserved energy, the approximate global Lorentz invariance of the equations of motion in harmonic coordinates and the recovery of the motion of a spinning object on a Kerr background in the test-mass limit. We verified the existence of a contact transformation, together with a redefinition of the spin variables that makes our result equivalent to a previously published reduced Hamiltonian, obtained from the Arnowitt–Deser–Misner formalism."), (6730, '055007'), (6731, 'http://iopscience.iop.org/0264-9381/30/5/055007'), (6732, '2013-04-09 22:06:20'), (6733, '10.1007/s00006-008-0077-8'), (6734, '0264-9381_30_5_055007.pdf'), (6735, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/30/5/055007/pdf/0264-9381_30_5_055007.pdf'), (6736, '2013-04-09 22:06:49'), (6737, '0264-9381_30_7_075017.pdf'), (6738, 'ProofResponse1.txt'), (6739, 'Statistical and systematic errors for gravitational-wave inspiral signals: A principal component analysis'), (6740, 'A single-spin precessing gravitational wave in closed form'), (6741, '2013-04-11 2013-04-11'), (6742, 'http://arxiv.org/abs/1304.3332'), (6743, 'arXiv:1304.3332'), (6744, 'Current searches for gravitational waves from compact binaries use templates where the binary does not precess. By contrast, generic black hole-neutron star binaries will significantly precess, inducing modulations that nonprecessing searches are particularly ill-suited to recover. In this paper we provide a closed-form representation of the single-spin precessing waveform in the frequency domain by reorganizing the signal as a sum over harmonics, each of which resembles a nonprecessing waveform. This form enables simple analytic calculations (e.g., a Fisher matrix) and computationally fast frequency-domain templates. We have verified that our \\texttt{SpinTaylorF2SingleSpin} model is faithful to the time-domain \\texttt{SpinTaylorT2} model: for the majority of generic BH-NS binaries, the corresponding signals generated from each model agree to better than 1%. Our waveform model is now available as part of the publicly-available \\texttt{lalsimulation} waveform-generation code.'), (6745, '2013-04-12 02:49:22'), (6746, '1304.3332 PDF'), (6747, 'http://www.arxiv.org/pdf/1304.3332.pdf'), (6748, '353-372'), (6749, 'http://link.springer.com/article/10.1007/s00006-008-0077-8'), (6750, '2013-04-17 15:59:32'), (6751, 'Following the Bargmann-Wigner formalism, wave-functions for integer and spin-3/2 fields are constructed within geometric algebra. This is achieved through the multiparticle space-time algebra, where the number of copies of the space-time algebra corresponds to the number of spinor fields needed to construct the wave-function. However, this formalism breaks down if a gauge field is introduced. This is resolved by introducing a symmetrised version of the covariant derivative, such that it obeys the Duffin-Kemmer algebra. Furthermore, new interesting results are found for the energy-momentum tensors.'), (6752, 'http://link.springer.com/content/pdf/10.1007%2Fs00006-008-0077-8'), (6753, 'http://arxiv.org/abs/1403.5301'), (6754, 'arXiv:1403.5301 [astro-ph, physics:gr-qc, physics:nucl-th]'), (6755, '2014-03-20 2014-03-20'), (6756, '2014-03-25 19:04:11'), (6757, 'We present a novel method for revealing the equation of state of high-density neutron star matter through gravitational waves emitted during the postmerger phase of a binary neutron star system. The method relies on a small number of detections of the peak frequency in the postmerger phase for binaries of different (relatively low) masses, in the most likely range of expected detections. From such observations, one can construct the derivative of the peak frequency versus the binary mass, in this mass range. Through a detailed study of binary neutron star mergers for a large sample of equations of state, we show that one can extrapolate the above information to the highest possible mass (the threshold mass for black hole formation in a binary neutron star merger). In turn, this allows for an empirical determination of the maximum mass of cold, nonrotating neutron stars to within 0.1 M_sun, while the corresponding radius is determined to within a few percent. Combining this with the determination of the radius of cold, nonrotating neutron stars of 1.6 M_sun (to within a few percent, as was demonstrated in Bauswein et al., PRD, 86, 063001, 2012), allows for a clear distinction of a particular candidate equation of state among a large set of other candidates. Our method is particularly appealing because it reveals simultaneously the moderate and very high-density parts of the equation of state, enabling the distinction of mass-radius relations even if they are similar at typical neutron star masses. Furthermore, our method also allows to deduce the maximum central energy density and maximum central rest-mass density of cold, nonrotating neutron stars with an accuracy of a few per cent.'), (6758, 'Geometric Algebra Techniques for General Relativity'), (6759, '2003-11-03 2003-11-03'), (6760, 'http://arxiv.org/abs/gr-qc/0311007'), (6761, 'Annals Phys. 311 (2004) 459-502'), (6762, 'arXiv:gr-qc/0311007'), (6763, '2013-04-22 22:28:24'), (6764, 'gr-qc/0311007 PDF'), (6765, 'http://www.arxiv.org/pdf/gr-qc/0311007.pdf'), (6766, '2.5PN kick from black-hole binaries in circular orbit: Nonspinning case'), (6767, '2013-04-22 2013-04-22'), (6768, 'http://arxiv.org/abs/1304.5915'), (6769, 'arXiv:1304.5915'), (6770, 'Using the Multipolar post-Minskowskian formalism, we compute the linear momentum flux from black-hole binaries in circular orbits and having no spins. The total linear momentum flux contains various types of instantaneous (which are functions of the retarded time) and hereditary (which depends on the dynamics of the binary in the past) terms both of which are analytically computed. In addition to the inspiral contribution, we use a simple model of plunge to compute the kick or recoil accumulated during this phase.'), (6771, '2013-04-23 13:39:42'), (6772, '2.5PN kick from black-hole binaries in circular orbit'), (6773, '1304.5915 PDF'), (6774, 'http://www.arxiv.org/pdf/1304.5915.pdf'), (6775, 'How Black Holes Get Their Kicks:Radiation Recoil in Binary Black Hole Mergers'), (6776, '2005-01-01 2005/01/01'), (6777, 'Springer Berlin Heidelberg'), (6778, '978-3-540-25275-7, 978-3-540-31639-8'), (6779, '333-339'), (6780, 'http://link.springer.com/chapter/10.1007/11403913_64'), (6781, '2013-04-23 15:08:04'), (6782, 'Growing Black Holes: Accretion in a Cosmological Context'), (6783, '©2005 Springer-Verlag Berlin/Heidelberg'), (6784, 'ESO Astrophysics Symposia'), (6785, 'Gravitational waves from the coalescence of binary black holes carry linear momentum, causing center of mass recoil. This “radiation rocket” has important implications for systems with escape speeds of order the recoil velocity. We describe new recoil calculations using high precision black hole perturbation theory to estimate the magnitude of the recoil for the slow “inspiral” coalescence phase; coupled with a cruder calculation for the final “plunge”, we estimate the total recoil imparted to a merged black hole. We find that velocities of many tens to a few hundred km/sec can be achieved fairly easily. The recoil probably never exceeds about 500 km/sec.'), (6786, 'How Black Holes Get Their Kicks'), (6787, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F11403913_64.pdf'), (6788, '10.1103/PhysRev.128.2471'), (6789, 'Classical Radiation Recoil'), (6790, '2471-2475'), (6791, 'http://link.aps.org/doi/10.1103/PhysRev.128.2471'), (6792, '1962-12-01 December 1, 1962'), (6793, 'The conditions under which a material system may recoil while emitting electromagnetic or gravitational radiation are investigated. The lowest order secular effects in the electromagnetic case arise from an interference of the electric dipole radiation with the electric quadrupole or magnetic dipole radiations. In the gravitational case, the lowest order terms involve the interference of the mass quadrupole radiation with the mass octopole or the flow quadrupole radiations. The investigation of the gravitational radiation recoil is carried out in complete analogy with the more elementary electromagnetic case, so that this paper should be accessible to physicists having no previous knowledge of general relativity theory.'), (6794, '2013-04-23 15:08:49'), (6795, '2013-04-25 2013-04-25'), (6796, 'Binary Black Hole Coalescence'), (6797, '2007-10-05 2007-10-05'), (6798, 'http://arxiv.org/abs/0710.1338'), (6799, 'arXiv:0710.1338'), (6800, 'The two-body problem in general relativity is reviewed, focusing on the final stages of the coalescence of the black holes as uncovered by recent successes in numerical solution of the field equations.'), (6801, '2013-04-23 15:11:40'), (6802, '0710.1338 PDF'), (6803, 'http://www.arxiv.org/pdf/0710.1338.pdf'), (6804, 'Gravitational Recoil of Inspiraling Black Hole Binaries to Second Post-Newtonian Order'), (6805, '2005-12-10 2005-12-10'), (6806, 635), (6807, '10.1086/497332'), (6808, 'The loss of linear momentum by gravitational radiation and the resulting gravitational recoil of black hole binary systems may play an important role in the growth of massive black holes in early galaxies. We calculate the gravitational recoil of nonspinning black hole binaries at the second post-Newtonian order (2 PN) beyond the dominant effect, obtaining, for the first time, the 1.5 PN correction term due to tails of waves and the next 2 PN term. We find that the maximum value of the net recoil experienced by the binary due to the inspiral phase up to the innermost stable circular orbit (ISCO) is of the order of 22 km s-1. We then estimate the kick velocity accumulated during the plunge from the ISCO up to the horizon by integrating the momentum flux using the 2 PN formula along a plunge geodesic of the Schwarzschild metric. We find that the contribution of the plunge dominates over that of the inspiral. For a mass ratio m2/m1 = , we estimate a total recoil velocity (due to both adiabatic and plunge phases) of 100 ± 20 km s-1. For a ratio of 0.38, the recoil is maximum, and we estimate it to be 250 ± 50 km s-1. In the limit of small mass ratio, we estimate V/c ≈ 0.043(±20%)(m2/m1)2. Our estimates are consistent with, but span a substantially narrower range than, those of Favata and coworkers.'), (6809, 508), (6810, 'http://iopscience.iop.org/0004-637X/635/1/508'), (6811, '2013-04-23 15:17:41'), (6812, 'http://encompass.library.cornell.edu/cgi-bin/checkIP.cgi?access=gateway_standard%26url=http://iopscience.iop.org/0004-637X/635/1/508/pdf/0004-637X_635_1_508.pdf'), (6813, '10.1103/PhysRevD.46.1517'), (6814, 'Coalescing binary systems of compact objects to (post)^{5/2}-Newtonian order. II. Higher-order wave forms and radiation recoil'), (6815, '1517-1539'), (6816, 'http://link.aps.org/doi/10.1103/PhysRevD.46.1517'), (6817, '1992-08-15 August 15, 1992'), (6818, 'Using formulas developed by Blanchet, Damour, and Iyer, we obtain a symmetric trace-free multipolar expansion of the gravitational radiation from a coalescing binary system which is sufficiently accurate to allow a post-Newtonian calculation of the linear momentum carried off by the gravitational radiation prior to a binary coalescence. We briefly examine the structure of the post-quadrupole corrections to the wave form for an orbiting binary system near coalescence. The post-Newtonian correction to the momentum ejection allows a more accurate calculation of the system recoil velocity (radiation rocket effect). We find that the higher-order correction actually reduces the net momentum ejection. Furthermore, the post-Newtonian correction to the momentum flux has only a weak dependence on the mass ratio of the objects in the binary, suggesting that previous test mass calculations may be quite accurate. We estimate an upper bound of the center-of-mass velocity of 1 km s-1 for neutron star binaries very near coalescence. In an appendix we give a self-contained (albeit less rigorous) derivation of the gravitational wave form using the Epstein-Wagoner formalism.'), (6819, '2013-04-23 15:17:49'), (6820, 'http://arxiv.org/abs/1304.7017'), (6821, 'kerr_schild1.pdf'), (6822, 'http://www.mrao.cam.ac.uk/~clifford/publications/ps/kerr_schild1.pdf'), (6823, '2013-04-23 21:04:42'), (6824, 'INTEGRAL EQUATIONS AND KERR-SCHILD FIELDS I. TIME-DEPENDENT, SPHERICALLY-SYMMETRIC FIELDS'), (6825, '2013-05-03 May 3, 2013'), (6826, '2013-04-23 21:04:48'), (6827, 'arXiv:1304.7017'), (6828, 'Identifying the source parameters from a gravitational-wave measurement alone is limited by our ability to discriminate signals from different sources and the accuracy of the waveform family employed in the search. Here we address both issues in the framework of an adapted coordinate system that allows for linear Fisher-matrix type calculations of waveform differences that are both accurate and computationally very efficient. We investigate statistical errors by using principal component analysis of the post-Newtonian (PN) expansion coefficients, which is well conditioned despite the Fisher matrix becoming ill-conditioned for larger numbers of parameters. We identify which combinations of physical parameters are most effectively measured by gravitational-wave detectors for systems of neutron stars and black holes with aligned spin. We confirm the expectation that the dominant parameter of the inspiral waveform is the chirp mass. The next dominant parameter depends on a combination of the spin and the symmetric mass ratio. In addition, we can study the systematic effect of various spin contributions to the PN phasing within the same parametrization, showing that the inclusion of spin-orbit corrections up to next-to-leading order, but not necessarily of spin-spin contributions, is crucial for an accurate inspiral waveform model. This understanding of the waveform structure throughout the parameter space is important to set up an efficient search strategy and correctly interpret future gravitational-wave observations.'), (6829, '2013-04-29 13:09:38'), (6830, 'Statistical and systematic errors for gravitational-wave inspiral signals'), (6831, '1304.7017 PDF'), (6832, 'http://www.arxiv.org/pdf/1304.7017.pdf'), (6833, 'Revealing the high-density equation of state through binary neutron star mergers'), (6834, 'http://www.arxiv.org/pdf/1403.5301.pdf'), (6835, 'Precession-tracking coordinates for simulations of compact-object-binaries'), (6836, '2013-04-10 2013-04-10'), (6837, 'http://arxiv.org/abs/1304.3067'), (6838, 'arXiv:1304.3067'), (6839, 'Binary black hole simulations with black hole excision using spectral methods require a coordinate transformation into a co-rotating coordinate system where the black holes are essentially at rest. This paper presents and discusses two coordinate transformations that are applicable to precessing binary systems, one based on Euler angles, the other on quaternions. Both approaches are found to work well for binaries with moderate precession, i.e. for cases where the orientation of the orbital plane changes by much less than 90 degrees. For strong precession, performance of the Euler-angle parameterization deteriorates, eventually failing for a 90 degree change in orientation because of singularities in the parameterization ("gimbal lock"). In contrast, the quaternion representation is invariant under an overall rotation, and handles any orientation of the orbital plane as well as the Euler-angle technique handles non-precessing binaries.'), (6840, '2013-04-29 16:53:18'), (6841, '1304.3067 PDF'), (6842, 'http://www.arxiv.org/pdf/1304.3067.pdf'), (6843, '1403.5301 PDF'), (6844, 135009), (6845, '2013-07-07 2013-07-07'), (6846, 'http://doi.acm.org/10.1145/2365934.2365942'), (6847, '10.1088/0264-9381/30/13/135009'), (6848, '10.1119/1.1621029'), (6849, 'http://link.aip.org/link/AJPIAS/v72/i1/p92/s1&Agg=doi'), (6850, 'A geometric algebra reformulation of geometric optics'), (6851, 'http://iopscience.iop.org/0067-0049/189/2/255'), (6852, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000072000001000092000001&idtype=cvips&doi=10.1119/1.1621029&prog=normal'), (6853, '2013-05-01 00:44:24'), (6854, '2013-05-01 00:44:28'), (6855, '0807.1382v1.pdf'), (6856, 'http://arxiv.org/pdf/0807.1382v1.pdf?fname=cm&font=TypeI'), (6857, '2013-05-01 00:47:13'), (6858, 'Electromagnetic energy-momentum equation without tensors: a geometric algebra approach'), (6859, 'arXiv preprint arXiv:0807.1382'), (6860, 'http://arxiv.org/abs/0807.1382'), (6861, '2013-05-01 00:47:17'), (6862, 'Electromagnetic energy-momentum equation without tensors'), (6863, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000060000009000788000001&idtype=cvips&doi=10.1119/1.17060&prog=normal'), (6864, '2013-05-01 00:51:01'), (6865, 788), (6866, '10.1119/1.17060'), (6867, 'http://link.aip.org/link/?AJP/60/788/1&Agg=doi'), (6868, 'Why i?'), (6869, '2013-05-01 00:51:09'), (6870, '0809.0351v1.pdf'), (6871, 'http://arxiv.org/pdf/0809.0351v1.pdf?fname=cm&font=TypeI'), (6872, '2013-05-01 01:52:33'), (6873, 'Taxonomy of Clifford Cl_ ${$3, 0$}$ subgroups: Choir and band groups'), (6874, 'arXiv preprint arXiv:0809.0351'), (6875, 'http://arxiv.org/abs/0809.0351'), (6876, '2013-05-01 01:52:35'), (6877, 'Taxonomy of Clifford Cl_ ${$3, 0$}$ subgroups'), (6878, 'This paper defines an angular velocity for time-dependent functions on the sphere and applies it to gravitational waveforms from compact binaries. Because it is geometrically meaningful and has a clear physical motivation, the angular velocity is uniquely useful in helping to solve an important—and largely ignored—problem in models of compact binaries: the inverse problem of deducing the physical parameters of a system from the gravitational waves alone. It is also used to define the corotating frame of the waveform. When decomposed in this frame, the waveform has no rotational dynamics and is therefore as slowly evolving as possible. The resulting simplifications lead to straightforward methods for accurately comparing waveforms and constructing hybrids. As formulated in this paper, the methods can be applied robustly to both precessing and nonprecessing waveforms, providing a clear, comprehensive, and consistent framework for waveform analysis. Explicit implementations of all these methods are provided in accompanying computer code.'), (6879, '2013-05-09 13:49:59'), (6880, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i10/e104006'), (6881, 'NEW_GRAVITY.pdf'), (6882, 'http://geocalc.clas.asu.edu/pdf/NEW_GRAVITY.pdf'), (6883, '2013-05-10 15:17:09'), (6884, 189), (6885, '2013-05-10 15:17:11'), (6886, 'Spacetime calculus for gravitation theory'), (6887, 'Tutorial on Geometric Calculus.pdf'), (6888, 'http://geocalc.clas.asu.edu/pdf/Tutorial%20on%20Geometric%20Calculus.pdf'), (6889, '2013-05-10 21:58:43'), (6890, '2013-05-10'), (6891, 'Tutorial on Geometric Calculus'), (6892, 'Spin&grv.pdf'), (6893, 'http://geocalc.clas.asu.edu/pdf/Spin&grv.pdf'), (6894, '2013-05-11 04:03:24'), (6895, 'DLAandG.pdf'), (6896, 'http://geocalc.clas.asu.edu/pdf/DLAandG.pdf'), (6897, '2013-05-11 04:06:52'), (6898, 'Spinor Approach to Gravitational Motion and Precession'), (6899, '589--598'), (6900, 'Int. J. Theor. Phys.'), (6901, 'The Design of Linear Algebra and Geometry'), (6902, 'Acta Applicandae Mathematicae'), (6903, '65--93'), (6904, 'UGA.pdf'), (6905, 'http://geocalc.clas.asu.edu/pdf/UGA.pdf'), (6906, '2013-05-11 04:15:55'), (6907, 'Universal geometric algebra'), (6908, 255), (6909, 'The Astrophysical Journal Supplement Series'), (6910, 'http://www.lomont.org/Math/GeometricAlgebra/Universal%20Geometric%20Algebra%20-%20Hestenes%20-%201988.pdf'), (6911, '2013-05-11 04:15:57'), (6912, 'Quarterly Journal of Pure and Applied Mathematics'), (6913, '253–-274'), (6914, 'PGwithCA.pdf'), (6915, 'http://geocalc.clas.asu.edu/pdf/PGwithCA.pdf'), (6916, '2013-05-11 04:17:08'), (6917, 'Projective geometry with Clifford algebra'), (6918, 'Acta Applicandae Mathematica'), (6919, '25–63'), (6920, 'http://link.springer.com/article/10.1007/BF00046919'), (6921, '2013-05-11 04:17:11'), (6922, 'LGasSG.pdf'), (6923, 'http://geocalc.clas.asu.edu/pdf/LGasSG.pdf'), (6924, '2013-05-11 04:17:50'), (6925, 'Lie groups as spin groups'), (6926, 34), (6927, '0067-0049'), (6928, '1993-08-00 August 1993'), (6929, '3642--3669'), (6930, 'NFMPchapt1.pdf'), (6931, 'http://geocalc.clas.asu.edu/pdf/NFMPchapt1.pdf'), (6932, '2013-05-11 04:29:55'), (6933, 'New foundations for mathematical physics'), (6934, 'NFMPchapt2.pdf'), (6935, 'http://geocalc.clas.asu.edu/pdf/NFMPchapt2.pdf'), (6936, '2013-05-11 04:30:49'), (6937, 'http://geocalc.clas.asu.edu/pdf/Hamilton.pdf'), (6938, '2013-05-11 12:18:59'), (6939, '2010-08-01 2010-08-01'), (6940, 'Dordercht/Boston'), (6941, 'UnifiedLang.pdf'), (6942, 'http://geocalc.clas.asu.edu/pdf/UnifiedLang.pdf'), (6943, '2013-05-11 12:27:51'), (6944, 'A unified language for mathematics and physics'), (6945, 'Clifford Algebras and their Applications in Mathematical Physics'), (6946, '1–23'), (6947, 'http://link.springer.com/chapter/10.1007/978-94-009-4728-3_1'), (6948, '2013-05-11 12:27:56'), (6949, 'DIF_FORM.pdf'), (6950, 'http://geocalc.clas.asu.edu/pdf/DIF_FORM.pdf'), (6951, '2013-05-11 12:38:13'), (6952, 'Differential forms in geometric calculus'), (6953, '269–285'), (6954, 'http://link.springer.com/chapter/10.1007/978-94-011-2006-7_31'), (6955, '2013-05-11 12:38:16'), (6956, 'SIMP_CAL.pdf'), (6957, 'http://geocalc.clas.asu.edu/pdf/SIMP_CAL.pdf'), (6958, '2013-05-11 16:36:08'), (6959, 'Simplicial calculus with geometric algebra'), (6960, 'MultCalc.pdf'), (6961, 'http://geocalc.clas.asu.edu/pdf/MultCalc.pdf'), (6962, '2013-05-11 16:51:53'), (6963, 'Multivector calculus'), (6964, 'J. Math. Anal. Appl'), (6965, '313–325'), (6966, '1968-00-00 1968'), (6967, 'http://ckw.phys.ncku.edu.tw/public/pub/Notes/Mathematics/Geometry/Hestenes/CAtoGA/MultCalc.pdf'), (6968, '2013-05-11 16:51:59'), (6969, 'MultFunc.pdf'), (6970, 'http://geocalc.clas.asu.edu/pdf/MultFunc.pdf'), (6971, '2013-05-11 16:53:54'), (6972, 'Multivector functions'), (6973, 'J. Math. Anal. and Appl.'), (6974, '467–-473'), (6975, 'Shape in GC-2012.pdf'), (6976, 'http://geocalc.clas.asu.edu/pdf/Shape%20in%20GC-2012.pdf'), (6977, '2013-05-11 16:56:35'), (6978, 'ApJS'), (6979, 'Guide to Geometric Algebra in Practice'), (6980, 'Springer Verlag'), (6981, '393--410'), (6982, 'The Shape of Di\x0bfferential Geometry in Geometric Calculus'), (6983, 'Open WorldCat'), (6984, 'English'), (6985, 'http://dx.doi.org/10.1007/978-0-85729-811-9'), (6986, 'Guide to geometric algebra in practice'), (6987, 'London; New York'), (6988, '9780857298119 0857298119'), (6989, '2013-05-13 19:49:12'), (6990, 232), (6991, 3540570632), (6992, 'Algebraic Theory of Spinors and Clifford Algebras: Collected Works of Claude Chevalley'), (6993, 'This volume is the first in a projected series devoted to the mathematical and philosophical works of the late Claude Chevalley. It covers the main contributions by the author to the theory of spinors. Since its appearance in 1954, "The Algebraic Theory of Spinors" has been a much sought after reference. It presents the whole story of one subject in a concise and especially clear manner. The reprint of the book is supplemented by a series of lectures on Clifford Algebras given by the author in Japan at about the same time. Also included is a postface by J.-P. Bourguignon describing the many uses of spinors in differential geometry developed by mathematical physicists from the 1970s to the present day. An insightful review of "Spinors" by J. Dieudonne is also made available to the reader in this new edition.'), (6994, '1997-00-00 1997'), (6995, 'Algebraic Theory of Spinors and Clifford Algebras'), (6996, 'http://books.google.com/books?id=bzBDRgyhRP4C'), (6997, '2013-05-14 18:43:15'), (6998, 'astrop.pdf'), (6999, 'http://www.mrao.cam.ac.uk/~clifford/publications/ps/astrop.pdf'), (7000, '2013-05-15 16:00:39'), (7001, 'Astrophysical and Cosmological Consequences of a Gauge Theory of Gravity'), (7002, 'Advances in Astrofundamental Physics. Erice 1994'), (7003, 'World Scientific Publishing Co.'), (7004, '359--401'), (7005, "A new gauge-theory description of gravity is presented, employing gauge fields in a flat background spacetime. These fields ensure that all physical relations are independent of the position and orientation of the matter fields in this background. The language of 'geometric algebra' best expresses the physical and mathematical content of the theory and is employed throughout. A method of working directly with the physical fields is developed and applied to the case of a radially-symmetric time-varying perfect fluid. A gauge is found in which the physics reduces to a set of Newtonian equations. The insistence on finding global solutions alters the physical picture of the horizon around a black hole, and enables one to discuss the properties of field lines inside the horizon created by a point charge held at rest outside it. Some applications to cosmology are discussed, and a study of the Dirac equation in a cosmological background reveals that the only models consistent with homogeneity are spatially flat."), (7006, 'Physical Applications of Geometric Algebra'), (7007, "An optional minor course in Cambridge's math tripos III"), (7008, 'lect01.pdf'), (7009, 'lect02.pdf'), (7010, 'lect03.pdf'), (7011, 'lect04.pdf'), (7012, 'lect05.pdf'), (7013, 'lect06.pdf'), (7014, 'lect07.pdf'), (7015, 'lect08.pdf'), (7016, 'lect09.pdf'), (7017, 'lect10.pdf'), (7018, 'lect11.pdf'), (7019, 'lect12.pdf'), (7020, 'lect13.pdf'), (7021, 'lect14.pdf'), (7022, 'lect15.pdf'), (7023, 'lect16.pdf'), (7024, '3dsummary.pdf'), (7025, 'examples1_answers.pdf'), (7026, 'examples1.pdf'), (7027, 'examples2_answers.pdf'), (7028, 'examples2.pdf'), (7029, 'examples3_answers.pdf'), (7030, 'examples3.pdf'), (7031, 'formula_sheet.pdf'), (7032, 'hout01.pdf'), (7033, 'hout02.pdf'), (7034, 'hout03.pdf'), (7035, 'hout04.pdf'), (7036, 'hout05.pdf'), (7037, 'hout06.pdf'), (7038, 'hout07.pdf'), (7039, 'hout08.pdf'), (7040, 'hout09.pdf'), (7041, 'hout10.pdf'), (7042, 'hout11.pdf'), (7043, 'hout12.pdf'), (7044, 'hout13.pdf'), (7045, 'hout14.pdf'), (7046, 'hout15.pdf'), (7047, 'hout16.pdf'), (7048, 'sample_tripos.pdf'), (7049, 'http://arxiv.org/abs/math-ph/0308039'), (7050, 'arXiv:math-ph/0308039'), (7051, 'siggraph_2003_next_no_linked.ppt'), (7052, 'Modeling the Cosmos: The Shape of the Universe'), (7053, 'SIGGRAPH 2003'), (7054, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_1'), (7055, '©2011 Springer-Verlag London Limited'), (7056, 'Springer London'), (7057, '3-24'), (7058, '978-0-85729-810-2, 978-0-85729-811-9'), (7059, '2011-01-01 2011/01/01'), (7060, '2013-05-17 17:41:22'), (7061, 'We discuss a fully covariant Lagrangian-based description of 3D rigid body motion, employing spinors in 5D conformal space. The use of this space enables the translational and rotational degrees of freedom of the body to be expressed via a unified rotor structure, and the equations of motion in terms of a generalised ‘moment of inertia tensor’ are given. The development includes the effects of external forces and torques on the body. To illustrate its practical applications, we give a brief overview of a prototype multi-rigid-body physics engine implemented using 5D conformal objects as the variables.'), (7062, 'Rigid Body Dynamics and Conformal Geometric Algebra'), (7063, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_1.pdf'), (7064, '2013-05-17 17:41:55'), (7065, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_2'), (7066, '25-45'), (7067, 'The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some advantages over matrix formulations. It allows motors to be estimated from a variety of geometric data such as points, spheres, circles, lines, planes, directions, and tangents; and the different types of geometric data are combined naturally in a single framework. Also, it excludes the possibility of a reflection unlike some matrix formulations. It returns the motor with the smallest translation and rotation angle when the optimal motor is not unique.'), (7068, 'Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra'), (7069, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_2.pdf'), (7070, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_6'), (7071, '105-125'), (7072, 'Several applications require the tracking of attitude and position of a body based on velocity data. It is tempting to use direction cosine matrices (DCM), for example, to track attitude based on angular velocity data, and to integrate the linear velocity data separately in a suitable frame. In this chapter we make the case for using bivectors as the attitude tracking method of choice since several features make their performance and flexibility superior to that of DCMs, Euler angles or even rotors. We also discuss potential advantages in using CGA to combine the integration of angular and linear velocities in one step, as the features that make bivectors attractive for tracking rotations extend to bivectors that represent general displacements.'), (7073, 'Attitude and Position Tracking'), (7074, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_6.pdf'), (7075, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_3'), (7076, '47-62'), (7077, 'This paper describes a novel iterative Inverse Kinematics (IK) solver, FABRIK, that is implemented using Conformal Geometric Algebra (CGA). FABRIK uses a forward and backward iterative approach, finding each joint position via locating a point on a line. We use the IK of a human hand as an example of implementation where a constrained version of FABRIK was employed for pose tracking. The hand is modelled using CGA, taking advantage of CGA’s compact and geometrically intuitive framework and that basic entities in CGA, such as spheres, lines, planes and circles, are simply represented by algebraic objects. This approach can be used in a wide range of computer animation applications and is not limited to the specific problem discussed here. The proposed hand pose tracker is real-time implementable and exploits the advantages of CGA for applications in computer vision, graphics and robotics.'), (7078, 'Inverse Kinematics Solutions Using Conformal Geometric Algebra'), (7079, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_3.pdf'), (7080, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_4'), (7081, '63-78'), (7082, 'We describe a new algorithm to reconstruct a rigid body motion from point correspondences. The algorithm works by constructing a series of reflections which align the points with their correspondences one by one. This is naturally and efficiently implemented in the conformal model of geometric algebra, where the resulting transformation is represented by a versor. As a direct result of this algorithm, we also present a very compact and fast formula to compute a quaternion from two vector correspondences, a surprisingly elementary result which appears to be new.'), (7083, 'Reconstructing Rotations and Rigid Body Motions from Exact Point Correspondences Through Reflections'), (7084, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_4.pdf'), (7085, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_5'), (7086, '81-104'), (7087, 'Conformal transformations are described by rotors in the conformal model of geometric algebra (CGA). In applications there is a need for interpolation of such transformations, especially for the subclass of 3D rigid body motions. This chapter gives explicit formulas for the square root and the logarithm of rotors in 3D CGA. It also classifies the types of conformal transformations and their orbits. To derive the results, we employ a novel polar decomposition for the even subalgebra of 3D CGA and an associated norm-like expression.'), (7088, 'Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition'), (7089, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_5.pdf'), (7090, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_8'), (7091, '151-173'), (7092, 'In this work we introduce a new kernel for image processing called the atomic function. This kernel is compact in the spatial domain, and it can be adapted to the behavior of the input signal by broadening or narrowing its band ensuring a maximum signal-to-noise ratio. It can be used for smooth differentiation of images in the quaternion algebra framework. We discuss the role of the quaternion atomic function with respect to monogenic signals. We then propose a steerable quaternion wavelet scheme for image structure and contour detection. Making use of the generalized Radon transform and images processed with the quaternion wavelet atomic function transform, we detect shape contours in color images. We believe that the atomic function is a promising kernel for image processing and scene analysis.'), (7093, 'Quaternion Atomic Function for Image Processing'), (7094, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_8.pdf'), (7095, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_10'), (7096, '195-215'), (7097, 'The bottleneck in symbolic geometric computation is middle expression swell. Another embarrassing problem is geometric explanation of algebraic results, which is often impossible because the results are not invariant under coordinate transformations. In classical invariant-theoretical methods, the two difficulties are more or less alleviated but stay, while new difficulties arise. In this chapter, we introduce a new framework for symbolic geometric computing based on conformal geometric algebra: the algebra for describing geometric configuration is null Grassmann–Cayley algebra, the algebra for advanced invariant manipulation is null bracket algebra, and the algebra underlying both algebras is null geometric algebra. When used in geometric computing, the new approach not only brings about amazing simplifications in algebraic manipulation, but can be used to extend and generalize existing theorems by removing some geometric constraints from the hypotheses.'), (7098, 'On Geometric Theorem Proving with Null Geometric Algebra'), (7099, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_10.pdf'), (7100, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_9'), (7101, '175-191'), (7102, 'The aim of this chapter is to propose two different approaches for color object recognition, both using the recently defined color Clifford Fourier transform. The first one deals with so-called Generalized Fourier Descriptors, the definition of which relies on plane motion group actions. The proposed color extension leads to more compact descriptors, with lower complexity and better recognition rates, than the already existing descriptors based on the processing of the r, g and b channels separately. The second approach concerns color phase correlation for color images. The idea here is to generalize in the Clifford framework the usual means of measuring correlation from the well-known shift theorem. Both methods necessitate to choose a 2-blade B of ℝ4 which corresponds to an analysis plane in the color space. The relevance of proposed methods for classification purposes is discussed on several color image databases. In particular, the influence of parameter B is studied regarding the type of images.'), (7103, 'Color Object Recognition Based on a Clifford Fourier Transform'), (7104, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_9.pdf'), (7105, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_12'), (7106, '233-249'), (7107, 'We show how a number of combinatorial problems, such as determining the number of cycles in graphs, can be recast using a graded commutative algebra constructed within a real Grassmann exterior algebra. The computational complexity of this approach is then measured by considering operations at the basis blade level of the algebra. In particular, the worst-case time complexity of counting arbitrary length cycles in simple n-vertex graphs via nilpotent adjacency matrix methods is shown to be , where α≤3 is the exponent representing the complexity of matrix multiplication. The storage complexity of the nilpotent adjacency matrix approach is . A probabilistic model is used to describe a class of graphs in which the average-case time complexity of cycle enumeration is for fixed 0<q<1. For reference, experimental results detailing computation times (in seconds) are compared with algorithms based on the approaches of Bax and Tarjan.'), (7108, 'On the Complexity of Cycle Enumeration for Simple Graphs'), (7109, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_12.pdf'), (7110, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_7'), (7111, '127-148'), (7112, 'This chapter describes an algorithm for calibrating the 3D positions of multiple stationary point targets which form part of an optical positioning system. A group of rigidly co-located calibrated cameras are moved to several positions and images of the targets acquired. The target pixel coordinates are extracted and transformed into 3D lines which are used as input data to the algorithm. A nonlinear solution is developed using geometric algebra and geometric calculus and expressed in the conformal model of Euclidean 3D space. A coordinate free approach to differentiating rotors is developed and used in the algorithm to differentiate motion rotors. Experiments are performed to evaluate the algorithm, and the results show that it performs well and is robust in the presence of noise.'), (7113, 'Calibration of Target Positions Using Conformal Geometric Algebra'), (7114, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_7.pdf'), (7115, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_11'), (7116, '217-232'), (7117, 'To model a geometrical part in Computer Aided Design systems, declarative modeling is a well-adapted solution to declare and specify geometric objects and constraints. In this chapter, we are interested in the representation of geometric objects and constraints using a new language of description and representation, Geometric Algebra (GA). GA is used here in association with the conformal model of Euclidean geometry (CGA) which requires two extra dimensions comparing to the usual vector space model. Topologically and Technologically Related Surfaces (TTRS) Theory is introduced here as a unified framework for geometric objects representation and geometric constraints solving. Based on TTRS, this chapter shows the capability of the CGA to represent geometric objects and geometric constraints through symbolic geometric constraints solving and algebraic classification.'), (7118, 'On the Use of Conformal Geometric Algebra in Geometric Constraint Solving'), (7119, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_11.pdf'), (7120, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_15'), (7121, '297-327'), (7122, 'We attach the degenerate signature (n,0,1) to the dual Grassmann algebra of projective space to obtain a real Clifford algebra which provides a powerful, efficient model for Euclidean geometry. We avoid problems with the degenerate metric by constructing an algebra isomorphism between the Grassmann algebra and its dual that yields non-metric meet and join operators. We focus on the cases of n=2 and n=3 in detail, enumerating the geometric products between k-blades and m-blades. We identify sandwich operators in the algebra that provide all Euclidean isometries, both direct and indirect. We locate the spin group, a double cover of the direct Euclidean group, inside the even subalgebra of the Clifford algebra, and provide a simple algorithm for calculating the logarithm of group elements. We conclude with an elementary account of Euclidean kinematics and rigid body motion within this framework.'), (7123, 'On the Homogeneous Model of Euclidean Geometry'), (7124, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_15.pdf'), (7125, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_14'), (7126, '273-294'), (7127, 'This chapter introduces global visibility computation using Grassmann Algebra. Visibility computation is a fundamental task in computer graphics, as in many other scientific domains. While it is well understood in two dimensions, this does not remain true in higher-dimensional spaces. Grassmann Algebra allows to think about visibility at a high level of abstraction and to design a framework for solving visibility problems in any n-dimensional space for n≥2. Contrary to Stolfi’s framework which allows only the representation of geometric lines, its algebraic nature deals means general applicability, with no exceptional cases. This chapter shows how the space of lines can be defined as a projective space over the bivector vector space. Then line classification, a key point for the visibility computation, is achieved using the exterior product. Actually, line classification turns out to be equivalent to point vs. hyperplane classification relative to a nondegenerate bilinear form. This ensures it is well defined and computationally robust. Using this, the lines stabbing an n-dimensional convex face are characterized. This set of lines appears to be the intersection of the decomposable bivectors set (i.e., bivectors that represent a line) and a convex polytope. Moreover, this convex polytope is proved to be minimal. This property allows useful algorithmic improvements. To illustrate the use of our framework in practice, we present the computation of soft shadows for three-dimensional illuminated scenes.'), (7128, 'A Framework for n-Dimensional Visibility Computations'), (7129, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_14.pdf'), (7130, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_13'), (7131, '253-272'), (7132, 'In this chapter, the classical line geometry is modeled in ℝ3,3, where lines are represented by null vectors, and points and planes by null 3-blades. The group of 3D special projective transformations SL(4) when acting upon points in space induces a Lie group isomorphism, with SO(3,3) acting upon lines. As an application of the use of the ℝ3,3 model of line geometry, this chapter analyzes the inverse singularity analysis of generalized Stewart platforms, using vectors of ℝ3,3 to encode the force and torque wrenches to classify their singular configurations.'), (7133, 'Line Geometry in Terms of the Null Geometric Algebra over ℝ3,3, and Application to the Inverse Singularity Analysis of Generalized Stewart Platforms'), (7134, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_13.pdf'), (7135, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_16'), (7136, '329-352'), (7137, 'We construct a homogeneous model for Computer Graphics using the Clifford Algebra for ℝ3. To incorporate points as well as vectors within this model, we employ the odd-dimensional elements of this graded eight-dimensional algebra to represent mass-points by exploiting the pseudoscalars to represent mass. The even-dimensional elements of this Clifford Algebra are isomorphic to the quaternions, which operate on the odd-dimensional elements by sandwiching. Along with the standard sandwiching formulas for rotations and reflections, this paradigm allows us to use sandwiching to compute perspective projections.'), (7138, 'A Homogeneous Model for Three-Dimensional Computer Graphics Based on the Clifford Algebra for ℝ3'), (7139, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_16.pdf'), (7140, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_18'), (7141, '371-389'), (7142, 'We discuss a ‘1D up’ approach to Conformal Geometric Algebra, which treats the dynamics of rigid bodies in 3D spaces with constant curvature via a 4D conformal representation. All equations are derived covariantly from a 4D Lagrangian, and definitions of energy and momentum in the curved space are given. Some novel features of the dynamics of rigid bodies in these spaces are pointed out, including a simple non-relativistic version of the Papapetrou force in General Relativity. The final view of ordinary translational motion that emerges is perhaps surprising, in that it is shown to correspond to precession in the 1D up conformal space. We discuss the alternative approaches to Euclidean motions and rigid body dynamics outlined by Gunn in Chap. 15 and Mullineux and Simpson in Chap. 17 of this volume, which also use only one extra dimension, and compare these with the Euclidean space limit of the current approach.'), (7143, 'Rigid Body Dynamics in a Constant Curvature Space and the ‘1D-up’ Approach to Conformal Geometric Algebra'), (7144, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_18.pdf'), (7145, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_17'), (7146, '353-369'), (7147, 'There is a requirement to be able to represent three-dimensional objects and their transforms in many applications, including computer graphics and mechanism and machine design. A geometric algebra is constructed which can model three-dimensional geometry and rigid-body transforms. The representation is exact since the square of one of the basis vectors is treated symbolically as being infinite. The non-zero, even-grade elements of the algebra represent precisely all rigid-body transforms. By allowing the transform to vary, smooth motions are obtained. This can be achieved using Bézier and B-spline combinations of even-grade elements.'), (7148, 'Rigid-Body Transforms Using Symbolic Infinitesimals'), (7149, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_17.pdf'), (7150, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_20'), (7151, '411-434'), (7152, 'A tutorial on the modern definition and application of moving frames, with a variety of examples and exercises, is given. We show three types of invariants; differential, joint and integral, and the running example is the linear action of SL(2) on smooth surfaces, on sets of points in the plane, and path integrals over curves in the plane. We also give details of moving frames for the group of rotations and translations acting on smooth curves, and on discrete sets of points, in the conformal geometric algebra.'), (7153, 'On the Modern Notion of a Moving Frame'), (7154, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_20.pdf'), (7155, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_19'), (7156, '393-410'), (7157, 'We review the foundations for coordinate-free differential geometry in Geometric Calculus. In particular, we see how both extrinsic and intrinsic geometry of a manifold can be characterized by a single bivector-valued one-form called the Shape Operator. The challenge is to adapt this formalism to Conformal Geometric Algebra for wide application in computer science and engineering.'), (7158, 'The Shape of Differential Geometry in Geometric Calculus'), (7159, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_19.pdf'), (7160, 'http://link.springer.com/content/pdf/bfm%3A978-0-85729-811-9%2F1.pdf'), (7161, '2013-05-17 17:49:56'), (7162, '10.1088/0067-0049/189/2/255'), (7163, 'http://books.google.com/books?hl=en&lr=&id=O7jO2pmUFOgC&oi=fnd&pg=PR3&dq=%22book+is+organized+in+themes+of+application+%EF%AC%81elds,+corresponding+to+the%22+%22one+algebra,+but+rather+a+family+of+algebras,+all+with+the+same+essential%22+%22as+homogeneous+coordinates,+since+geometric+algebra+has+a+particularly%22+&ots=ZqzdtEFoNU&sig=IfsrNgtgMio_00ggXpNTtXuX8ds'), (7164, 'Springerverlag London Limited'), (7165, '2013-05-17 17:49:59'), (7166, '2013-06-05 17:43:34'), (7167, 'http://link.springer.com/content/pdf/bfm%3A978-0-85729-811-9%2F1%2F1.pdf'), (7168, '2013-05-17 17:50:50'), (7169, 'We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the computation of several distinct spin transforms simultaneously. Specifically, only one set of special functions is computed for transforms of quantities with any spin, namely the Wigner d matrices evaluated at π/2, which may be computed with efficient recursions. For any spin, the computation scales as , where L is the band limit of the function. Our publicly available numerical implementation permits very high accuracy at modest computational cost. We discuss applications to the cosmic microwave background and gravitational lensing.'), (7170, 'Part I - Rigid Body Motion.pdf'), (7171, 'http://link.springer.com/content/pdf/bfm%3A978-0-85729-811-9%2F2%2F1.pdf'), (7172, '2013-05-17 17:53:51'), (7173, 'Fast and Exact Spin-s Spherical Harmonic Transforms'), (7174, 'Part II - Interpolation and Tracking.pdf'), (7175, 'http://link.springer.com/content/pdf/bfm%3A978-0-85729-811-9%2F3%2F1.pdf'), (7176, '2013-05-17 17:54:43'), (7177, 'http://iopscience.iop.org/0067-0049/189/2/255/pdf/0067-0049_189_2_255.pdf'), (7178, 'Part III - Image Processing.pdf'), (7179, 'http://link.springer.com/content/pdf/bfm%3A978-0-85729-811-9%2F4%2F1.pdf'), (7180, '2013-05-17 17:55:17'), (7181, 'http://fexpr.blogspot.com/2014/03/the-great-vectors-versus-quaternions.html'), (7182, '2013-06-05 17:45:47'), (7183, 'Part IV - Theorem Proving and Combinatorics.pdf'), (7184, 'http://link.springer.com/content/pdf/bfm%3A978-0-85729-811-9%2F5%2F1.pdf'), (7185, '2013-05-17 17:56:11'), (7186, '1306.3901'), (7187, 'Part V - Applications of Line Geometry.pdf'), (7188, 'http://link.springer.com/content/pdf/bfm%3A978-0-85729-811-9%2F6%2F1.pdf'), (7189, '2013-05-17 17:56:44'), (7190, "Advanced LIGO's ability to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem through compact binary coalescence detections"), (7191, 'Part VI - Alternatives to Conformal Geometric Algebra.pdf'), (7192, 'http://link.springer.com/content/pdf/bfm%3A978-0-85729-811-9%2F7%2F1.pdf'), (7193, '2013-05-17 17:57:27'), (7194, 'Fast and exact spin-s spherical harmonic transforms -- spinsfast code'), (7195, 'Part VII - Towards Coordinate-Free Differential Geometry.pdf'), (7196, 'http://link.springer.com/content/pdf/bbm%3A978-0-85729-811-9%2F1.pdf'), (7197, '2013-05-17 17:57:59'), (7198, 'http://arxiv.org/abs/1303.1782'), (7199, 'Index.pdf'), (7200, '2013-06-10 16:20:56'), (7201, 'Front matter.pdf'), (7202, 'http://link.springer.com/chapter/10.1007/978-0-85729-811-9_21'), (7203, '435-453'), (7204, '2013-05-17 17:59:04'), (7205, 'Using conformal geometric algebra, Euclidean motions in n-D are represented as orthogonal transformations of a representational space of two extra dimensions, and a well-chosen metric. Orthogonal transformations are representable as multiple reflections, and by means of the geometric product this takes an efficient and structure preserving form as a ‘sandwiching product’. The antisymmetric part of the geometric product produces a spanning operation that permits the construction of lines, planes, spheres and tangents from vectors, and since the sandwiching operation distributes over this construction, ‘objects’ are fully integrated with ‘motions’. Duality and the logarithms complete the computational techniques. The resulting geometric algebra incorporates general conformal transformations and can be implemented to run almost as efficiently as classical homogeneous coordinates. It thus becomes a high-level programming language which naturally integrates quantitative computation with the automatic administration of geometric data structures. This appendix provides a concise introduction to these ideas and techniques. Editorial note: This appendix is a slightly improved version of (Dorst in: Bayro-Corrochano, E., Scheuermann, G. (eds.) Geometric Algebra Computing for Engineering and Computer Science, pp. 457–476, [2011]). We provide it to make this book more self-contained.'), (7206, 'Tutorial Appendix: Structure Preserving Representation of Euclidean Motions Through Conformal Geometric Algebra'), (7207, 'Tutorial Appendix'), (7208, 'http://link.springer.com/content/pdf/10.1007%2F978-0-85729-811-9_21.pdf'), (7209, 9780521005), (7210, 'Clifford algebras and spinors'), (7211, 9783540570), (7212, 'arXiv e-print'), (7213, 9780521551), (7214, 'Clifford algebras and the classical groups'), (7215, 'World Scientific'), (7216, 9789812708), (7217, 'Invariant algebras and geometric reasoning'), (7218, 'Chamseddine and Connes have shown how the action for Einstein gravity, coupled to the $SU(3)\\times SU(2)\\times U(1)$ standard model of particle physics, may be elegantly recast as the "spectral action" on a certain "non-commutative geometry." In this paper, we show how this formalism may be extended to "non-associative geometries," and explain the motivations for doing so. As a guiding illustration, we present the simplest non-associative geometry (based on the octonions) and evaluate its spectral action: it describes Einstein gravity coupled to a $G_2$ gauge theory, with 8 Dirac fermions (which transform as a singlet and a septuplet under $G_2$). We use this example to illustrate how non-associative geometries may be naturally linked to ordinary (associative) geometries by a certain twisting procedure. This is just the simplest example: in a forthcoming paper we show how to construct realistic models that include Higgs fields, spontaneous symmetry breaking and fermion masses.'), (7219, 'New Jersey'), (7220, 'The algebraic theory of spinors and Clifford algebras'), (7221, 'http://link.springer.com/article/10.1007/s10714-010-1110-5'), (7222, '901-922'), (7223, '2011-03-01 2011/03/01'), (7224, '10.1007/s10714-010-1110-5'), (7225, '2013-05-17 20:38:04'), (7226, 'This is a reprinting of a paper by Roger Penrose, first published in a volume of conference proceedings in 1964, no longer easily accessible, in which he first presented the now-standard description of asymptotically flat spacetimes with the help of a conformal mapping, now called a Penrose transform. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Helmut Friedrich.'), (7227, 'Republication of: Conformal treatment of infinity'), (7228, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs10714-010-1110-5.pdf'), (7229, '2013-09-30 16:54:50'), (7230, '1212.5520'), (7231, 'http://link.aps.org/doi/10.1103/PhysRevD.87.081503'), (7232, '081503'), (7233, '2013-04-23 April 23, 2013'), (7234, '10.1103/PhysRevD.87.081503'), (7235, '2013-10-01 09:35:33'), (7236, 'The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as a function of orbital angular frequency. Apart from a single coefficient, which is known solely numerically, all the coefficients are given as exact numbers. The shown Hamiltonian is presented in the center-of-mass frame and out of its 57 coefficients, 51 are given fully explicitly. Those coefficients are six coefficients more than previously achieved [P. Jaranowski and G. Schäfer, Phys. Rev. D 86 061503(R) (2012)]. The local divergences in the point-mass model are uniquely controlled by the method of dimensional regularization. As an application, the last stable circular orbit is determined as a function of the symmetric-mass-ratio parameter.'), (7237, 'Dimensional regularization of local singularities in the fourth post-Newtonian two-point-mass Hamiltonian'), (7238, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i8/e081503'), (7239, 'Introduction to Elementary Particles - D. Griffiths.djvu'), (7240, 'http://link.aps.org/doi/10.1103/PhysRevD.85.064039'), (7241, 'http://arxiv.org/abs/1205.5935'), (7242, 'arXiv:1205.5935'), (7243, '2012-05-27 2012-05-27'), (7244, '2013-05-20 14:06:15'), (7245, 'This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines a product that\'s strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane. This system was invented by William Clifford and is more commonly known as Clifford algebra. It\'s actually older than the vector algebra that we use today (due to Gibbs) and includes it as a subset. Over the years, various parts of Clifford algebra have been reinvented independently by many people who found they needed it, often not realizing that all those parts belonged in one system. This suggests that Clifford had the right idea, and that geometric algebra, not the reduced version we use today, deserves to be the standard "vector algebra." My goal in these notes is to describe geometric algebra from that standpoint and illustrate its usefulness. The notes are work in progress; I\'ll keep adding new topics as I learn them myself.'), (7246, 'Geometric Algebra'), (7247, 'http://www.arxiv.org/pdf/1205.5935.pdf'), (7248, '1205.5935 PDF'), (7249, 'http://faculty.luther.edu/~macdonal/GAConstruct.pdf'), (7250, '2013-05-20 14:29:12'), (7251, 'GAConstruct.pdf'), (7252, 'http://link.springer.com/article/10.1007/BF03161249'), (7253, '1-6'), (7254, '2002-06-01 2002/06/01'), (7255, '10.1007/BF03161249'), (7256, '2013-05-20 14:33:11'), (7257, 'We give a simple, elementary, direct, and motivated construction of the geometric algebra overR n .'), (7258, 'An elementary construction of the geometric algebra'), (7259, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF03161249.pdf'), (7260, 'http://arxiv.org/abs/1011.3698'), (7261, 'arXiv:1011.3698'), (7262, '2010-11-16 2010-11-16'), (7263, '2013-05-20 14:48:31'), (7264, 'This is a simple way rigorously to construct Grassmann, Clifford and Geometric Algebras, allowing degenerate bilinear forms, infinite dimension, using fields or certain modules (characteristic 2 with limitation) - and characterize the algebras in a coordinate free form. The construction is done in an orthogonal basis, and the algebras characterized by universality. The basic properties with short proofs provides a clear foundation for further development of the algebras.'), (7265, 'Direct Construction of Grassmann, Clifford and Geometric Algebras'), (7266, 'http://www.arxiv.org/pdf/1011.3698.pdf'), (7267, '1011.3698 PDF'), (7268, 'http://arxiv.org/abs/1305.4306'), (7269, 'arXiv:1305.4306'), (7270, '2013-05-18 2013-05-18'), (7271, '2013-05-21 13:46:42'), (7272, 'The analytical understanding of quasinormal mode ringing requires an accurate knowledge of the Green\'s function describing the response of the black hole to external perturbations. We carry out a comprehensive study of quasinormal mode excitation for Kerr black holes. Relying on the formalism developed by Mano, Suzuki and Takasugi, we improve and extend previous calculations of the quasinormal mode residues in the complex frequency plane ("excitation factors" B_q). Using these results we compute the "excitation coefficients" C_q (essentially the mode amplitudes) in the special case where the source of the perturbations is a particle falling into the black hole along the symmetry axis. We compare this calculation with numerical integrations of the perturbation equations, and we show quantitatively how the addition of higher overtones improves the agreement with the numerical waveforms. Our results should find applications in models of the ringdown stage and in the construction of semianalytical template banks for gravitational-wave detectors, especially for binaries with large mass ratios and/or fast-spinning black holes.'), (7273, 'Quasinormal ringing of Kerr black holes. II. Excitation by particles falling radially with arbitrary energy'), (7274, 'http://www.arxiv.org/pdf/1305.4306.pdf'), (7275, '1305.4306 PDF'), (7276, '2013-05-22 18:44:27'), (7277, 'Spin-coefficient formalism - Scholarpedia'), (7278, 'http://arxiv.org/abs/1305.5188'), (7279, 'arXiv:1305.5188'), (7280, '2013-05-22 2013-05-22'), (7281, '2013-05-23 14:27:07'), (7282, 'Gravitational-wave detection has been pursued relentlessly for over 40 years. With the imminent operation of a new generation of laser interferometers, it is expected that detections will become a common occurrence. The research into more ambitious detectors promises to allow the field to move beyond detection and into the realm of precision science using gravitational radiation. In this article, I review the state of the art for the detectors and describe an outlook for the coming decades.'), (7283, 'Gravitational Radiation Detection with Laser Interferometry'), (7284, 'http://www.arxiv.org/pdf/1305.5188.pdf'), (7285, '1305.5188 PDF'), (7286, '047130932X'), (7287, '1998-08-10 1998-08-10'), (7288, 'Classical Electrodynamics Third Edition'), (7289, 808), (7290, '2013-07-18 2013-07-18'), (7291, '2013-07-22 03:22:36'), (7292, 'We present an electromagnetic analog of gravitational wave memory. That is, we consider what change has occurred to a detector of electromagnetic radiation after the wave has passed. Rather than a distortion in the detector, as occurs in the gravitational wave case, we find a residual velocity (a "kick") to the charges in the detector. In analogy with the two types of gravitational wave memory ("ordinary" and "nonlinear") we find two types of electromagnetic kick.'), (7293, 'Classical Electrodynamics by J.D. Jackson (Answers to sel. problems).pdf'), (7294, 'Penrose R., Rindler W. - Spinors and Space-time. Vol 1.djvu'), (7295, "Companion to J.D. Jackson's Classical Electrodynamics 3rd ed. - R. Magyar.pdf"), (7296, 'Classical Electrodynamics 3rd ed. - J.D. Jackson.djv'), (7297, 9780521347860), (7298, '1307.5098'), (7299, 'Spinors and Space-time'), (7300, 516), (7301, 'Within the framework of the Penrose conformal approach to asymptotical flatness we find minimal conditions on the Ricci tensor of the physical metric which guarantee that the Bondi mass and momentum are well defined. The energy-momentum vector, the Bondi news functions and the energy loss formula are expressed in terms of the Penrose conformal factor. An approximate Bondi-Sachs form of the metric is constructed. The Robinson-Trautman metrics are considered as an example.'), (7302, '10.2307/1968551'), (7303, 'http://www.jstor.org/stable/1968929'), (7304, 'On Unitary Representations of the Inhomogeneous Lorentz Group'), (7305, 'http://www.jstor.org/stable/1968551'), (7306, 'Copyright © 1939 Annals of Mathematics'), (7307, '149-204'), (7308, 'Annals of Mathematics'), (7309, '0003-486X'), (7310, '1939-01-01 January 1, 1939'), (7311, 'ArticleType: research-article / Full publication date: Jan., 1939 / Copyright © 1939 Annals of Mathematics'), (7312, '2013-05-29 00:04:25'), (7313, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1968551.pdf?acceptTC=true'), (7314, '1303.1782'), (7315, '2013-05-29 00:06:52'), (7316, 'Nature is the international weekly journal of science: a magazine style journal that publishes full-length research papers in all disciplines of science, as well as News and Views, reviews, news, features, commentaries, web focuses and more, covering all branches of science and how science impacts upon all aspects of society and life.'), (7317, 'The Motion of the Spinning Electron : Abstract : Nature'), (7318, 'The Motion of the Spinning Electron'), (7319, 'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v117/n2945/pdf/117514a0.pdf'), (7320, '1926-00-00 1926'), (7321, 117), (7322, '514--514'), (7323, '10.1038/117514a0'), (7324, 'http://www.nature.com/nature/journal/v117/n2945/abs/117514a0.html'), (7325, 'http://www.mrao.cam.ac.uk/~clifford/publications/ps/grass_mech.pdf'), (7326, '2013-05-30 15:45:29'), (7327, 'grass_mech.pdf'), (7328, 'Grassmann Mechanics, Multivector Derivatives and Geometric Algebra'), (7329, 'Non-Associative Geometry and the Spectral Action Principle'), (7330, 'Dordrecht'), (7331, '215--226'), (7332, "A method of incorporating the results of Grassmann calculus within the framework of geometric algebra is presented, and shown to lead to a new concept, the multivector Lagrangian. A general theory for multivector Lagrangians is outlined, and the crucial role of the multivector derivative is emphasised. A generalisation of Noether's theorem is derived, from which conserved quantities can be found conjugate to discrete symmetries."), (7333, '2-spinors, Twistors and Supersymmetry in the Spacetime Algebra'), (7334, 'http://www.arxiv.org/pdf/1303.1782.pdf'), (7335, '233--245'), (7336, 'We present a new treatment of 2-spinors and twistors, using the spacetime algebra. The key rôle of bilinear covariants is emphasized. As a by-product, an explicit representation is found, composed entirely of real spacetime vectors, for the Grassmann entities of supersymmetric field theory.'), (7337, 'http://www.mrao.cam.ac.uk/~clifford/publications/ps/2-spin_twist.pdf'), (7338, '2013-05-30 15:56:20'), (7339, '2-spin_twist.pdf'), (7340, 'http://www.mrao.cam.ac.uk/~clifford/publications/ps/chris_thesis.pdf'), (7341, '2013-05-31 01:11:24'), (7342, 'chris_thesis.pdf'), (7343, '1303.1782 PDF'), (7344, 'http://www.jstor.org/stable/2689497'), (7345, 'Copyright © 1977 Mathematical Association of America'), (7346, '2013-05-31 01:11:29'), (7347, '115-122'), (7348, '1994-02-00 February 1994'), (7349, 188), (7350, 'http://www.mrao.cam.ac.uk/~clifford/publications/abstracts/chris_thesis.html'), (7351, 'Cambridge'), (7352, "Clifford algebras have been studied for many years and their algebraic properties are well known. In particular, all Clifford algebras have been classified as matrix algebras over one of the three division algebras. But Clifford Algebras are far more interesting than this classification suggests; they provide the algebraic basis for a unified language for physics and mathematics which offers many advantages over current techniques. This language is called geometric algebra - the name originally chosen by Clifford for his algebra - and this thesis is an investigation into the properties and applications of Clifford's geometric algebra. The work falls into three broad categories:\n\n The formal development of geometric algebra has been patchy and a number of important subjects have not yet been treated within its framework. A principle feature of this thesis is the development of a number of new algebraic techniques which serve to broaden the field of applicability of geometric algebra. Of particular interest are an extension of the geometric algebra of spacetime (the spacetime algebra) to incorporate multiparticle quantum states, and the development of a multivector calculus for handling differentiation with respect to a linear function.\n A central contention of this thesis is that geometric algebra provides the natural language in which to formulate a wide range of subjects from modern mathematical physics. To support this contention, reformulations of Grassmann calculus, Lie algebra theory, spinor algebra and Lagrangian field theory are developed. In each case it is argued that the geometric algebra formulation is computationally more efficient than standard approaches, and that it provides many novel insights.\n The ultimate goal of a reformulation is to point the way to new mathematics and physics, and three promising directions are developed. The first is a new approach to relativistic multiparticle quantum mechanics. The second deals with classical models for quantum spin-1/2. The third details an approach to gravity based on gauge fields acting in a flat spacetime. The Dirac equation forms the basis of this gauge theory, and the resultant theory is shown to differ from general relativity in a number of its features and predictions."), (7353, 'Geometric Algebra and its Application to Mathematical Physics'), (7354, 'Mathematics Magazine'), (7355, 'g25_user_manual.pdf'), (7356, 'Gaigen'), (7357, '1202.2788'), (7358, 'All-sky search for gravitational-wave bursts in the second joint LIGO-Virgo run'), (7359, 'This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter.'), (7360, 'Introduction to Two Spinors in General Relativity'), (7361, 208), (7362, '1815-1837'), (7363, '2013-10-25 00:54:50'), (7364, 'http://web4.uwindsor.ca/users/b/baylis/main.nsf/9d019077a3c4f6768525698a00593654/e639e0cdf0d162c985256bb2004c8fde/$FILE/baylis1.pdf'), (7365, '2013-06-02 04:38:56'), (7366, 'baylis1.pdf'), (7367, 'GEOMETRY OF PARAVECTOR SPACE, WITH APPLICATIONS TO RELATIVISTIC PHYSICS'), (7368, 'http://web4.uwindsor.ca/users/b/baylis/main.nsf/9d019077a3c4f6768525698a00593654/e639e0cdf0d162c985256bb2004c8fde/$FILE/cainphys.pdf'), (7369, '2013-06-02 16:42:40'), (7370, 'http://link.springer.com/chapter/10.1007/978-0-8176-8190-6_4'), (7371, '91–133'), (7372, '2013-06-02 16:42:47'), (7373, 'Applications of Clifford algebras in physics'), (7374, 'Lectures on Clifford (Geometric) Algebras and Applications'), (7375, '2013-06-02 16:46:16'), (7376, 'Geometric Algebra: A Unified Mathematical Language for Physics'), (7377, 'AAPT Winter Meeting'), (7378, '2013-01-12 January 12, 2013'), (7379, 'http://www.damtp.cam.ac.uk/user/tong/qft/four.pdf'), (7380, '2013-06-03 03:15:37'), (7381, 'four.pdf'), (7382, 'http://www.arxiv.org/pdf/1306.3901.pdf'), (7383, 'Quantum Field Theory 4: The Dirac equation'), (7384, 'These lecture notes are based on an introductory course on quantum field theory, aimed at Part III (i.e. masters level) students. The full set of lecture notes can be downloaded here, together with videos of the course when it was repeated at the Perimeter Institute. Individual sections can be downloaded below. Last updated October 2012.'), (7385, 'http://www.damtp.cam.ac.uk/user/tong/qft.html'), (7386, '2013-06-02'), (7387, '0025-570X'), (7388, 'ArticleType: research-article / Full publication date: May, 1977 / Copyright © 1977 Mathematical Association of America'), (7389, '10.2307/2689497'), (7390, '2013-06-11 16:05:20'), (7391, 'Fractional Calculus'), (7392, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2689497.pdf?acceptTC=true'), (7393, 'http://arxiv.org/abs/1210.5016'), (7394, '2012-10-17 2012-10-17'), (7395, '2013-06-11 17:15:18'), (7396, 'A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as a set of non-overlapping cubic regions, plus a set of maps to identify the faces of adjoining regions. The differential structure on these manifolds is fixed by specifying a smooth reference metric tensor. Matching conditions that ensure the appropriate levels of continuity and differentiability across region boundaries are developed for arbitrary tensor fields. Standard numerical methods are then used to solve the equations with the appropriate boundary conditions, which are determined from these inter-region matching conditions. Numerical examples are presented which use pseudo-spectral methods to solve simple elliptic equations on multi-cube representations of manifolds with the topologies T^3, S^2 x S^1 and S^3. Examples are also presented of numerical solutions of simple hyperbolic equations on multi-cube manifolds with the topologies R x T^3, R x S^2 x S^1 and R x S^3.'), (7397, '1210.5016'), (7398, 'Solving Partial Differential Equations Numerically on Manifolds with Arbitrary Spatial Topologies'), (7399, 'http://www.arxiv.org/pdf/1210.5016.pdf'), (7400, '1210.5016 PDF'), (7401, 'http://arxiv.org/abs/1207.3744'), (7402, '2012-07-16 2012-07-16'), (7403, '2013-06-11 17:15:30'), (7404, 'A new method for solving the relativistic inverse stellar structure problem is presented. This method determines a spectral representation of the unknown high density portion of the stellar equation of state from a knowledge of the total masses M and radii R of the stars. Spectral representations of the equation of state are very efficient, generally requiring only a few spectral parameters to achieve good accuracy. This new method is able, therefore, to determine the high density equation of state quite accurately from only a few accurately measured [M,R] data points. This method is tested here by determining the equations of state from mock [M,R] data computed from tabulated "realistic" neutron-star equations of state. The spectral equations of state obtained from these mock data are shown to agree on average with the originals to within a few percent (over the entire high density range of the neutron-star interior) using only two [M,R] data points. Higher accuracies are achieved when more data are used. The accuracies of the equations of state determined in these examples are shown to be nearly optimal, in the sense that their errors are comparable to the errors of the best-fit spectral representations of these realistic equations of state.'), (7405, '1207.3744'), (7406, 'A Spectral Approach to the Relativistic Inverse Stellar Structure Problem'), (7407, 'http://www.arxiv.org/pdf/1207.3744.pdf'), (7408, '1207.3744 PDF'), (7409, 'An electromagnetic analog of gravitational wave memory'), (7410, 'http://www.arxiv.org/pdf/1307.5098.pdf'), (7411, '1307.5098 PDF'), (7412, '064039'), (7413, '2012-03-27 March 27, 2012'), (7414, '10.1103/PhysRevD.85.064039'), (7415, '2013-10-01 09:41:55'), (7416, 'First laws of black hole mechanics, or thermodynamics, come in a variety of different forms. In this paper, from a purely post-Newtonian (PN) analysis, we obtain a first law for binary systems of point masses moving along an exactly circular orbit. Our calculation is valid through 3PN order and includes, in addition, the contributions of logarithmic terms at 4PN and 5PN orders. This first law of binary point-particle mechanics is then derived from first principles in general relativity, and analogies are drawn with the single and binary black hole cases. Some consequences of the first law are explored for PN spacetimes. As one such consequence, a simple relation between the PN binding energy of the binary system and Detweiler’s redshift observable is established. Through it, we are able to determine with high precision the numerical values of some previously unknown high-order PN coefficients in the circular-orbit binding energy. Finally, we propose new gauge-invariant notions for the energy and angular momentum of a particle in a binary system.'), (7417, '2013-06-13 14:02:33'), (7418, '1210.1565'), (7419, 'http://arxiv.org/abs/1202.1038'), (7420, '2012-02-05 2012-02-05'), (7421, '2013-06-13 14:07:04'), (7422, "We present a new fully first order strongly hyperbolic representation of the BSSN formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity properties, and present two numerical implementations and simulations: one using finite differences, adaptive mesh refinement and in particular binary black holes, and another one using the discontinuous Galerkin method in spherical symmetry. The results of this paper constitute a first step in an effort to combine the robustness of BSSN evolutions with very high accuracy numerical techniques, such as spectral collocation multi-domain or discontinuous Galerkin methods."), (7423, '1202.1038'), (7424, "Numerical simulations with a first order BSSN formulation of Einstein's field equations"), (7425, 'http://www.arxiv.org/pdf/1202.1038.pdf'), (7426, '1202.1038 PDF'), (7427, 'http://iopscience.iop.org/0264-9381/19/5/308'), (7428, 953), (7429, '2002-03-07 2002-03-07'), (7430, '10.1088/0264-9381/19/5/308'), (7431, '2013-06-13 14:14:40'), (7432, 'This paper shows that the backscattering of electromagnetic and gravitational waves can be dominant when the radiation is produced very close to a spherical black hole. Numerical investigation shows that almost 50 per cent of the outgoing quadrupole gravitational wave is backscattered for a class of initial data. A similar analysis reveals at least a 20 per cent effect for a dipole electromagnetic radiation. Numerical results confirm theoretical predictions that the backscatter of short wavelength radiation is negligible. In the long-radiation band a rather weak dependence on the wavelength is observed. Our studies are based on the linear approximation. They can be of relevance for the determination of the total energy of backscattering tails and quasinormal modes.'), (7433, 'Backscattering of electromagnetic and gravitational waves off Schwarzschild geometry'), (7434, '1306.3901 PDF'), (7435, '0264-9381_19_5_308.pdf'), (7436, 'http://arxiv.org/abs/gr-qc/0103033'), (7437, '2001-03-09 2001-03-09'), (7438, 'Phys.Rev.D64:044012,2001'), (7439, '2013-06-13 14:35:41'), (7440, 'Gravitational waves in the linear approximation propagate in the Schwarzschild spacetime similarly as electromagnetic waves. A fraction of the radiation scatters off the curvature of the geometry. The energy of the backscattered part of an initially outgoing pulse of the quadrupole gravitational radiation is estimated by compact formulas depending on the initial energy, the Schwarzschild radius, and the location and width of the pulse. The backscatter becomes negligible in the short wavelength regime.'), (7441, 'gr-qc/0103033'), (7442, 'Can Schwarzschildean gravitational fields suppress gravitational waves?'), (7443, 'http://www.arxiv.org/pdf/gr-qc/0103033.pdf'), (7444, 'gr-qc/0103033 PDF'), (7445, 'First law of binary black hole mechanics in general relativity and post-Newtonian theory'), (7446, 'Oxford University Press'), (7447, 9780198503705), (7448, '1998-01-01 1998-01-01'), (7449, "Part of the reissued Oxford Classic Texts in the Physical Sciences series, this book was first published in 1983, and has swiftly become one of the great modern classics of relativity theory. It represents a personal testament to the work of the author, who spent several years writing and working-out the entire subject matter. The theory of black holes is the most simple and beautiful consequence of Einstein's relativity theory. At the time of writing there was no physical evidence for the existence of these objects, therefore all that Professor Chandrasekhar used for their construction were modern mathematical concepts of space and time. Since that time a growing body of evidence has pointed to the truth of Professor Chandrasekhar's findings, and the wisdom contained in this book has become fully evident."), (7450, 'The Mathematical Theory of Black Holes'), (7451, 676), (7452, 'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/400/3/1366'), (7453, 400), (7454, 'Misner, Thorne, Wheeler - Gravitation (english) (Freeman & Co. 1973)(1304p)(T).djvu'), (7455, 9780387953854), (7456, '2002-01-01 2002-01-01'), (7457, '"Lang\'s Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." \xa0NOTICES OF THE AMS "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."\xa0MATHEMATICAL REVIEWS This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. \xa0For the revised third edition, the author has added exercises and made numerous corrections to the text.'), (7458, 'Algebra'), (7459, 950), (7460, '1366-1372'), (7461, '2009-12-11 12/11/2009'), (7462, 'Serge Lang - Algebra.djvu'), (7463, 9780387903286), (7464, '1978-08-24 1978-08-24'), (7465, '"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year\'s course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book." --MATHSCINET'), (7466, 'Functions of One Complex Variable I'), (7467, 344), (7468, '10.1111/j.1365-2966.2009.15529.x'), (7469, '2013-07-23 19:56:37'), (7470, 'Conway J.B. Functions of one complex variable (2ed., Springer, 1978)(L)(T)(167s).djvu'), (7471, 'American Mathematical Soc.'), (7472, 9780821874332), (7473, 'The authors present topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem.'), (7474, 'Introduction to Complex Analysis'), (7475, 376), (7476, 'mnras.oxfordjournals.org.proxy.library.cornell.edu'), (7477, 'Points on the surface of a sphere can be mapped by stereographic projection to points on the plane of complex numbers. If the points on the sphere are identified with the directions of incoming light rays, then the effect of a Lorentz transformation, a rotation plus a boost, is represented by a bilinear or Möbius transformation applied to points on the complex plane. This procedure allows the effects of the aberration of light, precession and nutation, required for computing the mean and apparent positions of celestial objects, to be accounted for in a common framework and yields expressions that are readily evaluated in practice. The general form of the bilinear transformation representing a pure Lorentz boost is derived. Explicit expressions are given for the bilinear transformations representing aberration, precession and nutation as well as frame bias and transformations to the Celestial Intermediate Reference System. The approach described simplifies, and is an alternative to, the standard matrix methods commonly used to perform coordinate system rotations.'), (7478, 'Nevanlinna Paatero - Introduction to complex analysis (AW)(354s)(T).djvu'), (7479, 'Hawking S. Ellis G.F. The Large Scale Structure of Space-Time (1973)(CUP)(399s).djvu'), (7480, 'Geometric Algebra and its Application to Mathematical Physics - C. Doran.pdf'), (7481, 'Spacetime calculus'), (7482, 'Spacetime Calculus - with applications - D. Hestenes.djv'), (7483, 'Random House UK'), (7484, 9780099440680), (7485, 'In a single work of colossal scope one of the world’s greatest scientists has given us a complete and unrivalled guide to the glories of the universe.The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader — for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book.Roger Penrose’s purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. Rarely less than challenging, the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams.The Road to Reality was a Sunday Times top-ten bestseller in the hardcover edition, with over 40,000 copies sold.'), (7486, 'The Road to Reality'), (7487, 1138), (7488, 'Applications of complex analysis to precession, nutation and aberration'), (7489, 'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/400/3/1366.full.pdf'), (7490, 'The Road to Reality - A Complete Guide to the Laws of the Universe - Penrose, Roger.pdf'), (7491, 'Chandrasekhar-Mathematical_theory_of_black_holes-CH01-Mathematical_preliminaries(T).djvu'), (7492, 'Chandrasekhar-Mathematical_theory_of_black_holes-CH03-Schwarzschild_space-time(T).djvu'), (7493, 'Chandrasekhar-Mathematical_theory_of_black_holes-CH06-Kerr_metric(T).djvu'), (7494, 'Chandrasekhar-Mathematical_theory_of_black_holes-CH07-Geodesics_in_kerr_space-time(T).djvu'), (7495, 'Pearson Education, Limited'), (7496, 9780321856562), (7497, '2012-09-26 2012-09-26'), (7498, 'For junior/senior-level electricity and magnetism courses. This book is known for its clear, concise, and accessible coverage of standard topics in a logical and pedagogically sound order. The highly polished Fourth Edition features a clear, accessible treatment of the fundamentals of electromagnetic theory, providing a sound platform for the exploration of related applications (ac circuits, antennas, transmission lines, plasmas, optics, etc.). Its lean and focused approach employs numerous new examples and problems.'), (7499, 'Introduction to Electrodynamics'), (7500, 624), (7501, 'http://arxiv.org/abs/1307.6237'), (7502, '2013-07-23 2013-07-23'), (7503, 'Griffiths D.J. Introduction to electrodynamics (3ed., PH, 1999)(T)(596s).djvu'), (7504, 'John Wiley & Sons'), (7505, 9783527618477), (7506, '2008-09-26 2008-09-26'), (7507, 'This is the first quantitative treatment of elementary particle theory that is accessible to undergraduates. Using a lively, informal writing style, the author strikes a balance between quantitative rigor and intuitive understanding. The first chapter provides a detailed historical introduction to the subject. Subsequent chapters offer a consistent and modern presentation, covering the quark model, Feynman diagrams, quantum electrodynamics, and gauge theories. A clear introduction to the Feynman rules, using a simple model, helps readers learn the calculational techniques without the complications of spin. And an accessible treatment of QED shows how to evaluate tree-level diagrams. Contains an abundance of worked examples and many end-of-chapter problems.'), (7508, 'Introduction to Elementary Particles'), (7509, 403), (7510, '2013-07-25 15:30:53'), (7511, "We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes 0.8 of the maximum allowed) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, to the directions of the total angular momentum and the orbital angular momentum$. We find that the radiated angular momentum approximately follows the orbital angular momentum throughout the evolution. During the orbital evolution and merger, we observe that the angle between the orbital angular momentum and total spin is approximately conserved, which allows us to propose and test models for the merger remnant black hole's mass and spin. For instance, we verify that the hangup effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also find that the total angular momentum, while significantly decreasing in magnitude during the simulations, varies from its initial direction by < 5 deg. The maximum variation in the direction of the total angular momentum occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of the total angular momentum, is not possible for similar-mass binaries."), (7512, 'http://arxiv.org/abs/1305.5663'), (7513, '2013-05-24 2013-05-24'), (7514, 'Advances in Applied Clifford Algebras: Volume 23, Issue 2 (2013), Page 377-404'), (7515, '2013-06-18 16:07:29'), (7516, "We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond."), (7517, '1305.5663'), (7518, "Applications of Clifford's Geometric Algebra"), (7519, 'http://www.arxiv.org/pdf/1305.5663.pdf'), (7520, '1305.5663 PDF'), (7521, 'http://arxiv.org/abs/1306.4065'), (7522, '2013-06-19 13:01:05'), (7523, 'Using an extended set of equations of state and a multiple-group multiple-code collaborative effort to generate waveforms, we improve numerical-relativity-based data-analysis estimates of the measurability of matter effects in neutron-star binaries. We vary two parameters of a parameterized piecewise-polytropic equation of state (EOS) to analyze the measurability of EOS properties, via a parameter {\\Lambda} that characterizes the quadrupole deformability of an isolated neutron star. We find that, to within the accuracy of the simulations, the departure of the waveform from point-particle (or spinless double black-hole binary) inspiral increases monotonically with {\\Lambda}, and changes in the EOS that did not change {\\Lambda} are not measurable. We estimate with two methods the minimal and expected measurability of {\\Lambda} in second- and third- generation gravitational-wave detectors. The first estimate, using numerical waveforms alone, shows two EOS which vary in radius by 1.3km are distinguishable in mergers at 100Mpc. The second estimate relies on the construction of hybrid waveforms by matching to post-Newtonian inspiral, and estimates that the same EOS are distinguishable in mergers at 300Mpc. We calculate systematic errors arising from numerical uncertainties and hybrid construction, and we estimate the frequency at which such effects would interfere with template-based searches.'), (7524, '1306.4065'), (7525, 'Matter effects on binary neutron star waveforms'), (7526, 'http://www.arxiv.org/pdf/1306.4065.pdf'), (7527, '1306.4065 PDF'), (7528, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i6/e064039'), (7529, 'http://link.aps.org/doi/10.1103/PhysRevD.85.064010'), (7530, 'http://montgomerycollege.edu/Departments/planet/planet/Numerical_Relativity/bookGA.pdf'), (7531, '2013-06-19 14:30:56'), (7532, 'bookGA.pdf'), (7533, '2013-06-19 14:31:04'), (7534, 'An Introduction to Geometric Algebra and Calculus'), (7535, '2012-10-11 October 11, 2012'), (7536, '064010'), (7537, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_1'), (7538, '©2012 Springer Science+Business Media, LLC'), (7539, 'Birkhäuser Boston'), (7540, '1-2'), (7541, '978-0-8176-8282-8, 978-0-8176-8283-5'), (7542, '2012-01-01 2012/01/01'), (7543, '2013-06-19 16:48:38'), (7544, 'This text is intended for a one-semester course in differential geometry, although there is enough material for two quarters. The only prerequisite is completion of the calculus – linear algebra sequence. Solutions of differential equations are discussed in the text but do not appear in the problem sets. Thus, completion of a course in differential equations would be useful but not necessary.'), (7545, 'http://www.jstor.org/stable/3219300'), (7546, "A New Approach to Differential Geometry using Clifford's Geometric Algebra"), (7547, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_1.pdf'), (7548, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_3'), (7549, '27-46'), (7550, 'When the speed of sound is measured, it is found that the speed is independent of direction only if it is measured with respect to the air. If the air is moving at a rate of 20km per hour, an observer on the ground will discover that sound moving in the direction of the wind will move 20km per hour faster than it would when the air is still. Similarly, sound moving against the wind will be slowed down.'), (7551, 'Copyright © 2003 Mathematical Association of America'), (7552, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_3.pdf'), (7553, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_4'), (7554, '47-120'), (7555, 'The word “geometry”is derived from a greek word meaning “to measure land.”The starting point for differential geometry is the definition of an infinitesimal distance. Generally, such an infinitesimal distance ds is defined in terms of a coordinate system. For the Cartesian coordinate system applied to an n-dimensional Euclidean space, we have 4.1 $${(\\mathrm{d}s)}^{2} ={ \\sum \\nolimits }_{j=1}^{n}{(\\mathrm{d}{x}^{j})}^{2}.$$'), (7556, 'Penrose R., Rindler W. Spinors and space-time. Vol 2..djvu'), (7557, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_4.pdf'), (7558, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_2'), (7559, '3-25'), (7560, 'One frequently represents a vector x in the 3-dimensional Euclidean space E 3 by $\\mathbf{x} = x\\mathbf{i} + y\\mathbf{j} + z\\mathbf{k}$ or (x,y,z).'), (7561, 'http://arxiv.org/abs/1007.2481'), (7562, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_2.pdf'), (7563, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_5'), (7564, '121-179'), (7565, 'The simplest example of a curved surface is the ordinary 2-dimensional sphere in Euclidean 3-space. Furthermore the geometry of the sphere serves a major motivation for much of the mathematical work that has been done for more general surfaces. For this reason it is useful to examine some basic results associated with the geometry of a sphere.'), (7566, '2010-07-15 2010-07-15'), (7567, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_5.pdf'), (7568, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_6'), (7569, '181-226'), (7570, 'We can define the exterior derivative d by the equation: 6.1 $$\\mathbf{dA} = {\\gamma }^{k} \\wedge {\\nabla }_{ k}\\mathbf{A}\\text{,}$$'), (7571, '7th International Conference on Clifford Algebras and their Applications, Toulouse (France) : France (2005)'), (7572, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_6.pdf'), (7573, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_7'), (7574, '227-298'), (7575, 'A curve in E n is a one parameter mapping x(t) from some open interval in E1 to E n . Generally, a “curve”is considered a function so that a change in parameterization results in a “different curve”even though the path (or trace) remains the same.'), (7576, '2013-07-03 15:01:15'), (7577, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_7.pdf'), (7578, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_8'), (7579, '299-331'), (7580, 'You should be forewarned that a prerequisite for this chapter is a strong familiarity with the basic manipulations of complex numbers – multiplication, the polar representation, and the notion of complex conjugate. The non-Euclidean geometry of Bolyai and Lobachevsky eventually became known as hyperbolic geometry because the ordinary trigonometric functions sine and cosine that appear in formulas for the surface of a sphere are replaced by the hyperbolic functions sinhϕ and coshϕ for surfaces of constant negative Gaussian curvature.'), (7581, 'In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the link between the two approaches. Finally, we give some notions of the generalisations to arbitrary spacetimes, by the introduction of the spin and spinor bundles.'), (7582, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_8.pdf'), (7583, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_9'), (7584, '333-345'), (7585, 'Although a multitude of directrices can be used for a given ruled surface, there are particular directrices that are worth discussing.'), (7586, '1007.2481'), (7587, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_9.pdf'), (7588, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_10'), (7589, '347-373'), (7590, 'In this section, I will discuss lines of curvature. A curve x(t) is said to be a line of curvature if 10.1 $$\\frac{\\mathrm{d}\\mathbf{x}(t)} {\\mathrm{d}t} = \\mathbf{v}(t)\\text{, where}$$'), (7591, 'Spin and Clifford algebras, an introduction'), (7592, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_10.pdf'), (7593, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_11'), (7594, '375-394'), (7595, 'The term minimal surface is applied to any 2-dimensional surface embedded in E3 with zero mean curvature. It is understood that mean curvature is the average of the two principal curvatures.'), (7596, 'http://www.arxiv.org/pdf/1007.2481.pdf'), (7597, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_11.pdf'), (7598, 'http://link.springer.com/chapter/10.1007/978-0-8176-8283-5_12'), (7599, '395-430'), (7600, 'It was in 1905 that Einstein wrote his Ph.D. thesis and three papers each of which would individually receive nominations for the Nobel Prize. He would soon be working on his General Theory of Relativity. The Special Theory of Relativity clearly predicts how measurements for the same phenomena will differ when the observers and objects move at constant speeds relative to one another. But what happens when these relative speeds are not constant?'), (7601, '1007.2481 PDF'), (7602, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_12.pdf'), (7603, 'http://arxiv.org/abs/1307.1757'), (7604, '2013-07-06 2013-07-06'), (7605, '2013-07-09 12:54:49'), (7606, "Gravitational waves radiated by the coalescence of compact-object binaries containing a neutron star and a black hole are one of the most interesting sources for the ground-based gravitational-wave observatories Advanced LIGO and Advanced Virgo. Advanced LIGO will be sensitive to the inspiral of a $1.4\\, M_\\odot$ neutron star into a $10\\,M_\\odot$ black hole to a maximum distance of $\\sim 900$ Mpc. Achieving this sensitivity and extracting the physics imprinted in observed signals requires accurate modeling of the binary to construct template waveforms. In a NSBH binary, the black hole may have significant angular momentum (spin), which affects the phase evolution of the emitted gravitational waves. We investigate the ability of post-Newtonian (PN) templates to model the gravitational waves emitted during the inspiral phase of NSBH binaries. We restrict the black hole's spin to be aligned with the orbital angular momentum and compare several approximants. We examine restricted amplitude waveforms that are accurate to 3.5PN order in the orbital dynamics and complete to 2.5PN order in the spin dynamics. We also consider PN waveforms with the recently derived 3.5PN spin-orbit and 3PN spin-orbit tail corrections. We compare these approximants to the effective-one-body model. For all these models, large disagreements start at low to moderate black hole spins, particularly for binaries where the spin is anti-aligned with the orbital angular momentum. We show that this divergence begins in the early inspiral at $v \\sim 0.2$ for $\\chi_{BH} \\sim 0.4$. PN spin corrections beyond those currently known will be required for optimal detection searches and to measure the parameters of neutron star--black hole binaries. While this complicates searches, the strong dependence of the gravitational-wave signal on the spin dynamics will make it possible to extract significant astrophysical information."), (7607, '1307.1757'), (7608, 'Accuracy of gravitational waveform models for observing neutron-star--black-hole binaries in Advanced LIGO'), (7609, 'http://www.arxiv.org/pdf/1307.1757.pdf'), (7610, '1307.1757 PDF'), (7611, '1307.6237'), (7612, '10. *Lines of Curvature'), (7613, '01. Introduction'), (7614, '02. Clifford Algebra in Euclidean 3-Space'), (7615, '03. Clifford Algebra in Minkowski 4-Space'), (7616, '04. Clifford Algebra in Flat n-Space'), (7617, '05. Curved Spaces'), (7618, '06. The Gauss–Bonnet Formula'), (7619, 'http://link.aps.org/doi/10.1103/PhysRevD.61.084027'), (7620, '08. *Non-Euclidean (Hyperbolic) Geometry'), (7621, '09. *Ruled Surfaces Continued'), (7622, '11. *Minimal Surfaces'), (7623, '12. Some General Relativity'), (7624, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/bfm%3A978-0-8176-8283-5%2F1.pdf'), (7625, '2013-06-19 16:56:07'), (7626, 'bfm978-0-8176-8283-51.pdf'), (7627, 'http://books.google.com/books?hl=en&lr=&id=qlX3CqMUHpUC&oi=fnd&pg=PR7&dq=%22embedded+in+our+current+curriculum+is+an+accident+of+history.%22+%22%EF%AC%81rst+paper+on+what+is+now+known+as+Clifford+algebra+appeared+in+the%22+%221946+and+1958,+Marcel+Riesz+published+some+results+on+Clifford%22+&ots=lu3YKN2z3M&sig=l-pFazTbddgyM0VR-irqAxEwFD4'), (7628, '2013-06-19 16:56:14'), (7629, '2000-03-28 March 28, 2000'), (7630, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/bbm%3A978-0-8176-8283-5%2F1.pdf'), (7631, '2013-06-19 16:57:26'), (7632, 'bbm978-0-8176-8283-51.pdf'), (7633, '13. Appendices and Index'), (7634, '07. Some Extrinsic Geometry in E^n'), (7635, '10.1103/PhysRevD.61.084027'), (7636, '431-465'), (7637, "A new approach to differential geometry using Clifford's geometric algebra"), (7638, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v11/i11/p3145_s1'), (7639, '3145-3154'), (7640, '1970-11-01 1970-11-01'), (7641, 'doi:10.1063/1.1665105'), (7642, '2013-06-19 20:16:12'), (7643, 'A direct connection between the spin and conformally weighted functions on the sphere and geometric objects in Minkowski space is established through the isomorphism of the conformal group of the sphere to the restricted Lorentz group. It is shown that with the use of these functions one can duplicate all the standard work on the representations of the Lorentz group. It is shown further that these functions can be used to obtain a generalization of the classical equations of motion in which internal degrees of freedom arise naturally.'), (7644, 'The Lorentz Group and the Sphere'), (7645, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000011000011003145000001&idtype=cvips&doi=10.1063/1.1665105&prog=normal'), (7646, '2013-06-19 20:16:14'), (7647, 'http://iopscience.iop.org/0264-9381/1/4/001'), (7648, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/17/21/304/pdf/q02104.pdf'), (7649, '2013-06-19 21:15:57'), (7650, 'q02104.pdf'), (7651, 'http://iopscience.iop.org/0264-9381/17/21/304'), (7652, 4397), (7653, '2013-06-19 21:16:05'), (7654, 'Bondi mass in terms of the Penrose conformal factor'), (7655, 'Bondi Mass in Classical Field Theory'), (7656, 'Acta Physica Polonica B'), (7657, '2013-07-11 17:55:56'), (7658, '1998-03-00 March 1998'), (7659, '667--744'), (7660, 'http://th-www.if.uj.edu.pl/acta/vol29/abs/v29p0667.htm'), (7661, 'http://th-www.if.uj.edu.pl/acta/vol29/pdf/v29p0667.pdf'), (7662, '2013-06-19 21:46:50'), (7663, 'v29p0667.pdf'), (7664, 'http://arxiv.org/abs/1102.0589'), (7665, '2011-02-02 2011-02-02'), (7666, 'Advances in Mathematical Physics, vol. 2012, Article ID 197385, 2012'), (7667, '2013-06-20 00:51:03'), (7668, 'The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. As in the Bondi-Metzner-Sachs gauge, it is shown to be isomorphic to the direct sum of the abelian algebra of infinitesimal conformal rescalings with bms4. The latter algebra is the semi-direct sum of infinitesimal supertranslations with the conformal Killing vectors of the Riemann sphere. Infinitesimal local conformal transformations can then consistently be included. We work out the local conformal properties of the relevant Newman-Penrose coefficients, construct the surface charges and derive their algebra.'), (7669, '1102.0589'), (7670, 'A note on the Newman-Unti group and the BMS charge algebra in terms of Newman-Penrose coefficients'), (7671, 'http://www.arxiv.org/pdf/1102.0589.pdf'), (7672, '1102.0589 PDF'), (7673, 'Barnich and Lambert - 2011 - A note on the Newman-Unti group and the BMS charge.pdf'), (7674, '2012-03-07 March 7, 2012'), (7675, 'http://adsabs.harvard.edu/abs/1980grg1.conf..469G'), (7676, 'In general relativity, the notion of mass and other conserved quantities at spatial infinity can be defined in a natural way via the Hamiltonian framework: Each conserved quantity is associated with an asymptotic symmetry and the value of the conserved quantity is defined to be the value of the Hamiltonian which generates the canonical transformation on phase space corresponding to this symmetry. However, such an approach cannot be employed to define “conserved quantities” in a situation where symplectic current can be radiated away (such as occurs at null infinity in general relativity) because there does not, in general, exist a Hamiltonian which generates the given asymptotic symmetry. (This fact is closely related to the fact that the desired “conserved quantities” are not, in general, conserved.) In this paper we give a prescription for defining “conserved quantities” by proposing a modification of the equation that must be satisfied by a Hamiltonian. Our prescription is a very general one, and is applicable to a very general class of asymptotic conditions in arbitrary diffeomorphism covariant theories of gravity derivable from a Lagrangian, although we have not investigated existence and uniqueness issues in the most general contexts. In the case of general relativity with the standard asymptotic conditions at null infinity, our prescription agrees with the one proposed by Dray and Streubel from entirely different considerations.'), (7677, 'General definition of “conserved quantities” in general relativity and other theories of gravity'), (7678, '1980-00-00 1980'), (7679, '2013-06-21 14:11:15'), (7680, 'adsabs.harvard.edu'), (7681, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v61/i8/e084027'), (7682, 'Invariant Transformations Conservation Laws and Energy-Momentum'), (7683, 'http://iopscience.iop.org/0264-9381/2/2/012'), (7684, '1985-03-01 1985-03-01'), (7685, 'General Relativity and Gravitation. Vol. 1. One hundred years after the birth of Albert Einstein'), (7686, '469-490'), (7687, 'http://arxiv.org/abs/1211.0503'), (7688, '2012-11-02 2012-11-02'), (7689, 'Phys. Lett. B722, 341 (2013)'), (7690, '2013-06-25 15:08:37'), (7691, 'We consider dark matter (DM) that interacts with ordinary matter exclusively through an electromagnetic anapole, which is the only allowed electromagnetic form factor for Majorana fermions. We show that unlike DM particles with an electric or magnetic dipole moment, anapole dark matter particles annihilate exclusively into fermions via purely p-wave interactions, while tree-level annihilations into photons are forbidden. We calculate the anapole moment needed to produce a thermal relic abundance in agreement with cosmological observations, and show that it is consistent with current XENON100 detection limits on the DM-nucleus cross-section for all masses, while lying just below the detection threshold for a mass ~ 30-40 GeV.'), (7692, '1211.0503'), (7693, 'Anapole Dark Matter'), (7694, 'http://www.arxiv.org/pdf/1211.0503.pdf'), (7695, '1211.0503 PDF'), (7696, 'http://arxiv.org/abs/1306.5500'), (7697, '2013-06-23 2013-06-23'), (7698, '2013-06-25 15:09:14'), (7699, "We construct a general relativistic conservation law for linear and angular momentum for matter and gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous construction of a general relativistic energy conservation law with the same features. Our approach uses the Brown and York quasilocal stress-energy-momentum tensor for matter and gravitational fields, plus the concept of a rigid quasilocal frame (RQF) introduced in previous work. The RQF approach allows us to construct, in a generic spacetime, frames of reference whose boundaries are rigid (their shape and size do not change with time), and that have precisely the same six arbitrary time-dependent degrees of freedom as the accelerating and tumbling rigid frames we are familiar with in Newtonian mechanics. These RQFs, in turn, give rise to a completely general conservation law for the six components of momentum (three linear and three angular) of a finite system of matter and gravitational fields. We compare in detail this quasilocal RQF approach to constructing conservation laws with the usual local one based on spacetime symmetries, and discuss the shortcomings of the latter. These RQF conservation laws lead to a deeper understanding of physics in the form of simple, exact, operational definitions of gravitational energy and momentum fluxes, which in turn reveal, for the first time, the exact, detailed mechanisms of gravitational energy and momentum transfer taking place in a wide variety of physical phenomena, including a simple falling apple. As a concrete example, we derive a general relativistic version of Archimedes' law that we apply to understand electrostatic weight and buoyant force in the context of a Reissner-Nordstrom black hole."), (7700, '1306.5500'), (7701, 'Momentum in General Relativity: Local versus Quasilocal Conservation Laws'), (7702, 'Momentum in General Relativity'), (7703, 'http://www.arxiv.org/pdf/1306.5500.pdf'), (7704, '1306.5500 PDF'), (7705, 'http://arxiv.org/abs/1306.5564'), (7706, '2013-06-24 2013-06-24'), (7707, '2013-06-25 15:12:06'), (7708, 'This work devises a formalism to obtain the equations of motion for a black hole-fluid configuration. Our approach is based on a Post-Newtonian expansion and adapted to scenarios where obtaining the relevant dynamics requires long time-scale evolutions. These systems are typically studied with Newtonian approaches, which have the advantage that larger time-steps can be employed than in full general-relativistic simulations, but have the downside that important physical effects are not accounted for. The formalism presented here provides a relatively straightforward way to incorporate those effects in existing implementations, up to 2.5PN order, with lower computational costs than fully relativistic simulations.'), (7709, '1306.5564'), (7710, 'A Post-Newtonian approach to black hole-fluid systems'), (7711, 'http://www.arxiv.org/pdf/1306.5564.pdf'), (7712, '1306.5564 PDF'), (7713, 'http://arxiv.org/abs/1306.5697'), (7714, '2013-06-25 15:17:59'), (7715, 'Since black holes can be formed through widely varying processes, the horizon structure is highly complicated in the dynamical phase. Nonetheless, as numerical simulations show, the final state appears to be universal, well described by the Kerr geometry. How are all these large and widely varying deviations from the Kerr horizon washed out? To investigate this issue, we introduce a well-suited notion of horizon multipole moments and equations governing their dynamics, thereby providing a coordinate and slicing independent framework to investigate the approach to equilibrium. In particular, our flux formulas for multipoles can be used as analytical checks on numerical simulations and, in turn, the simulations could be used to fathom possible universalities in the way black holes approach their final equilibrium.'), (7716, '1306.5697'), (7717, 'Dynamical Black Holes: Approach to the Final State'), (7718, 'Dynamical Black Holes'), (7719, 'http://www.arxiv.org/pdf/1306.5697.pdf'), (7720, '1306.5697 PDF'), (7721, 'http://rspa.royalsocietypublishing.org/content/354/1679/379'), (7722, 354), (7723, 1679), (7724, '379-405'), (7725, '1977-06-27 06/27/1977'), (7726, '10.1098/rspa.1977.0073'), (7727, '2013-06-26 22:26:54'), (7728, 'Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptotically-flat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.'), (7729, 'Angular Momentum in General Relativity. I. Definition and Asymptotic Behaviour'), (7730, 'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/354/1679/379.full.pdf'), (7731, '10.1088/0264-9381/2/2/012'), (7732, '2013-07-11 17:56:04'), (7733, "The construction of measures of energy-momentum and angular momentum using spinor methods is considered in the theory of linearised gravitation and in general relativity. A new measure of angular momentum is obtained by generalising Witten's identities (1981) for energy-momentum, and at null infinity, for the appropriate choice of Poincare group, agreement with Penrose's quasi-local expression (1982) is obtained. The expressions introduced here may be regarded as a form of the linkage expression given by Geroch and Winicour (1981), but with a new choice of the gauge conditions for asymptotic symmetries. The methods introduced here can also be applied quasi-locally and some simple examples are given."), (7734, 'Witten identities for rotations, spinor boundary-value problems and new gauge conditions for asymptotic symmetries'), (7735, 'Where angular momentum goes in a precessing black hole binary'), (7736, 'http://iopscience.iop.org/0264-9381/6/11/010'), (7737, 1547), (7738, '1989-11-01 1989-11-01'), (7739, '10.1088/0264-9381/6/11/010'), (7740, '2013-07-11 17:56:13'), (7741, 'The asymptotic structure of axisymmetric radiative spacetimes which need not admit global null infinity is discussed. It is shown that from the asymptotic symmetry group a unique translation subgroup can locally be singled out and the news tensor can be obtained. The asymptotic structure of axisymmetric spacetimes with an infinite cosmic string and some of the exact radiative solutions with boost-rotation symmetry are treated as examples.'), (7742, 'On the asymptotic structure of axisymmetric radiative spacetimes'), (7743, 'http://www.arxiv.org/pdf/1307.6237.pdf'), (7744, '0264-9381_6_11_010.pdf'), (7745, '0264-9381_2_2_012.pdf'), (7746, 'http://link.aps.org/doi/10.1103/PhysRevD.41.410'), (7747, 41), (7748, '410-417'), (7749, '1990-01-15 January 15, 1990'), (7750, '10.1103/PhysRevD.41.410'), (7751, '2013-07-11 17:58:50'), (7752, 'We define a superpotential for energy-momentum and rotation momentum which is built out of the conformal tensor and a bivector. This superpotential is identified with that used by Penrose in his definition of quasilocal energy. It is applied to the definition of energy-momentum and rotation momentum at spatial and at null infinities. At spatial infinity the results are in agreement with those of Ashtekar and Hansen. At null infinity the results are unsatisfactory; they are tied to a specific Bondi frame. Thus, they are not in agreement with the results of Tamburino and Winicour, Geroch and Winicour, nor with those of Dray and Streubel. Some reasons for this failure are discussed.'), (7753, 'Conserved quantities at spatial and null infinity: The Penrose potential'), (7754, 'Conserved quantities at spatial and null infinity'), (7755, '1307.6237 PDF'), (7756, 'http://iopscience.iop.org/0264-9381/14/8/023'), (7757, 2249), (7758, '1997-08-01 1997-08-01'), (7759, '10.1088/0264-9381/14/8/023'), (7760, '2013-07-11 17:59:20'), (7761, "In this paper the standard values for total energy, linear momentum and also angular momentum of asymptotically flat Bondi metrics at null infinity are obtained from differential conservation laws on asymptotically flat backgrounds, derived from a quadratic Lagrangian density by methods currently used in classical field theory. It is thus a matter of taste and commodity whether to use a reference spacetime in defining these globally conserved quantities. Backgrounds lead to N ther conserved currents; the use of backgrounds is in line with classical views on conservation laws. Moreover, the conserved quantities are explicitly related to the sources of gravity through Einstein's equations. The relations depend, however, on a rule for mapping spacetimes onto backgrounds."), (7762, 'On global conservation laws at null infinity'), (7763, 'http://arxiv.org/abs/1307.6793'), (7764, 'PhysRevD.41.410.pdf'), (7765, '0264-9381_14_8_023.pdf'), (7766, '2013-07-11 18:00:56'), (7767, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v23/i12/p2410_s1'), (7768, '2410-2417'), (7769, '1982-12-01 1982-12-01'), (7770, 'doi:10.1063/1.525283'), (7771, '2013-07-11 18:01:05'), (7772, 'The relation between the linkage and the symplectic approaches to conserved quantities associated with the Bondi–Metzner–Sachs groups in general relativity is examined.'), (7773, 'Linkages and Hamiltonians at null infinity'), (7774, 'http://iopscience.iop.org/0264-9381/1/1/005'), (7775, '1984-01-11 1984-01-11'), (7776, '10.1088/0264-9381/1/1/005'), (7777, '2013-07-11 18:01:29'), (7778, "The definition of angular momentum recently given by Penrose (1982) is analysed on I. It is shown that this definition is essentially a supertranslation of previous definitions. The origin dependence of Penrose's angular momentum is shown to have the correct form. Based on Penrose's expression, the authors then define a momentum for all elements of the BMS Lie algebra, which is the first such expression with the property that its flux vanishes identically in Minkowski space."), (7779, 'Angular momentum at null infinity'), (7780, '2013-07-25 2013-07-25'), (7781, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000023000012002410000001&idtype=cvips&doi=10.1063/1.525283&prog=normal'), (7782, '2013-07-11 18:01:37'), (7783, '0264-9381_17_21_304.pdf'), (7784, '0264-9381_1_1_005.pdf'), (7785, '2013-07-26 17:04:11'), (7786, 'The imprint of non-linearities in the propagation of gravitational waves --- the tail effect --- is responsible for new spin contributions to the energy flux and orbital phasing of spinning black hole binaries. The spin-orbit (linear in spin) contribution to this effect is currently known at leading post-Newtonian order, namely 3PN for maximally spinning black holes on quasi-circular orbits. In the present work, we generalize these tail-originated spin-orbit terms to the next-to-leading 4PN order. This requires in particular extending previous results on the dynamical evolution of precessing compact binaries. We show that the tails represent the only spin-orbit terms at that order for quasi-circular orbits, and we find perfect agreement with the known result for a test particle around a Kerr black hole, computed by perturbation theory. The BH-horizon absorption terms have to be added to the PN result computed here. Our work completes the knowledge of the spin-orbit effects to the phasing of compact binaries up to the 4PN order, and will allow the building of more faithful PN templates for the inspiral phase of black hole binaries, improving the capabilities of ground-based and space-based gravitational wave detectors.'), (7787, '1307.6793'), (7788, 'Next-to-leading tail-induced spin-orbit effects in the gravitational radiation flux of compact binaries'), (7789, 'http://www.arxiv.org/pdf/1307.6793.pdf'), (7790, '1307.6793 PDF'), (7791, 'L33'), (7792, '1984-07-11 1984-07-11'), (7793, '10.1088/0264-9381/1/4/001'), (7794, '2013-07-31 21:28:38'), (7795, 'The symplectic approach to obtaining fluxes of gravitational energy-momentum and angular momentum given by Ashtekar and Streubel (1981) is completed by giving explicit expressions for the charge integral associated with an arbitrary BMS vector at a given retarded time. The expressions are obtained by weakening the definition of angular momentum given by Penrose (1982) into a map dual to the entire BMS group.'), (7796, 'Symplectic geometry of null infinity and two-surface twistors'), (7797, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v22/i9/p1837_s1'), (7798, '0264-9381_1_4_001.pdf'), (7799, 'L7'), (7800, '2013-07-31 21:30:14'), (7801, 'It is shown that the expression proposed by Dray and Streubel (1984) for the momentum charge associated with the full BMS group at null infinity has precisely the flux derived by Ashtekar and Streubel (1981) using symplectic methods.'), (7802, '1837-1850'), (7803, '0264-9381_2_1_002-1.pdf'), (7804, '1981-09-01 1981-09-01'), (7805, 'doi:10.1063/1.525155'), (7806, '2013-08-01 17:46:19'), (7807, 'A generalization of the Lie group construction is proposed wherein the composition law depends, apart from the parameters of the transformations composed, also on the transformed variables. This construction is met, in particular, on the hypersurfaces specified by the first class constraints in phase space.'), (7808, 'Quasigroup construction and first class constraints'), (7809, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000022000009001837000001&idtype=cvips&doi=10.1063/1.525155&prog=normal'), (7810, '2013-08-01 17:46:21'), (7811, '2013-08-01 17:46:56'), (7812, 'http://www.sciencedirect.com/science/article/pii/S0375960198007683'), (7813, 250), (7814, '1–3'), (7815, '55-61'), (7816, '1998-12-21 December 21, 1998'), (7817, '10.1016/S0375-9601(98)00768-3'), (7818, '2013-08-01 18:22:44'), (7819, 'The quasigroup approach to the conservation laws [Phys. Rev. D 56 (1997) R7498] is completed by imposing new gauge conditions for asymptotic symmetries. Noether charge associated with an arbitrary element of the Poincaré quasialgebra is free from the supertranslational ambiguity and identically vanishes in a flat spacetime.'), (7820, 'On angular momentum of gravitational radiation'), (7821, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271541&_user=492137&_pii=S0375960198007683&_check=y&_origin=article&_zone=toolbar&_coverDate=21-Dec-1998&view=c&originContentFamily=serial&wchp=dGLbVlS-zSkWA&md5=3a04da43cad499721ea71ef5e39145bd&pid=1-s2.0-S0375960198007683-main.pdf'), (7822, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v9/i6/p861_s1'), (7823, '861-867'), (7824, '1968-06-01 1968-06-01'), (7825, 'doi:10.1063/1.1664652'), (7826, '2013-08-03 15:46:33'), (7827, 'The total energy, momentum, supermomentum, and angular momentum of asymptotically flat space‐times are calculated in terms of coordinate and conformally invariant expressions by taking the limit in an invariant way of the asymptotic symmetry linkages through a sequence of finite closed two‐spaces which converge to a sphere at null infinity. The resulting expressions consist of integrals over the sphere at null infinity of cordinate and conformally invariant quantities. In the case of energy and momentum these integrals may be reduced to expressions previously proposed by Penrose.'), (7828, 'Some Total Invariants of Asymptotically Flat Space‐Times'), (7829, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000009000006000861000001&idtype=cvips&doi=10.1063/1.1664652&prog=normal'), (7830, '2013-08-03 15:46:35'), (7831, '2013-08-03 15:47:06'), (7832, 'http://link.aps.org/doi/10.1103/PhysRevLett.10.66'), (7833, '66-68'), (7834, '1963-01-15 January 15, 1963'), (7835, '10.1103/PhysRevLett.10.66'), (7836, '2013-08-03 15:51:17'), (7837, 'Asymptotic Properties of Fields and Space-Times'), (7838, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v10/i2/p66_1'), (7839, 'http://rspa.royalsocietypublishing.org/content/376/1767/585'), (7840, 1767), (7841, '585-607'), (7842, '1981-05-28 05/28/1981'), (7843, '10.1098/rspa.1981.0109'), (7844, '2013-08-03 16:47:51'), (7845, "The Hamiltonian description of massless spin zero- and one-fields in Minkowski space is first recast in a way that refers only to null infinity and fields thereon representing radiative modes. With this framework as a guide, the phase space of the radiative degrees of freedom of the gravitational field (in exact general relativity) is introduced. It has the structure of an infinite-dimensional affine manifold (modelled on a Frechet space) and is equipped with a continuous, weakly non-degenerate symplectic tensor field. The action of the Bondi-Metzner-Sachs group on null infinity is shown to induce canonical transformations on this phase space. The corresponding Hamiltonians - i.e. generating functions - are computed and interpreted as fluxes of supermomentum and angular momentum carried away by gravitational waves. The discussion serves three purposes: it brings out, via symplectic methods, the universality of the interplay between symmetries and conserved quantities; it sheds new light on the issue of angular momentum of gravitational radiation; and, it suggests a new approach to the quantization of the 'true' degrees of freedom of the gravitational field."), (7846, 'Symplectic Geometry of Radiative Modes and Conserved Quantities at Null Infinity'), (7847, 'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/376/1767/585.full.pdf'), (7848, 'http://arxiv.org/abs/1308.1521'), (7849, '2013-08-07 2013-08-07'), (7850, '2013-08-08 13:28:29'), (7851, 'The extraction of the gravitational wave signal, within the context of a characteristic numerical evolution is revisited. A formula for the gravitational wave strain is developed and tested, and is made publicly available as part of the PITT code within the Einstein Toolkit. Using the new strain formula, we show that artificial non-linear drifts inherent in time integrated waveforms can be reduced for the case of a binary black hole merger configuration. For the test case of a rapidly spinning stellar core collapse model, however, we find that the drift must have different roots.'), (7852, '1308.1521'), (7853, 'The gravitational wave strain in the characteristic formalism of numerical relativity'), (7854, 'http://www.arxiv.org/pdf/1308.1521.pdf'), (7855, '1308.1521 PDF'), (7856, 'http://link.springer.com/article/10.1007/BF00669365'), (7857, '1107-1124'), (7858, '1987-11-01 1987/11/01'), (7859, '10.1007/BF00669365'), (7860, '2013-08-08 19:37:47'), (7861, "Space-times for whichI + (future null infinity) is not necessarily homeomorphic toR×S 2 are considered. It is shown that, depending on the global conformal structure ofI +, a given space-time either (1) possesses an asymptotic symmetry group with a normal subgroup of supertranslations, similar in structure to the BMS group, or (2) possesses a simpler kind of asymptotic symmetry group, not involving supertranslations, or (3) has no asymptotic symmetry. The setting is Newman and Unti's approach to asymptotically flat space-times and use is made of the characterization of the asymptotic symmetry transformation as a conformal motion ofI + that preserves null angles."), (7862, 'Asymptotic symmetry and the global structure of future null infinity'), (7863, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF00669365.pdf'), (7864, 'http://iopscience.iop.org/0305-4470/11/1/012'), (7865, '1978-01-01 1978-01-01'), (7866, '10.1088/0305-4470/11/1/012'), (7867, '2013-08-08 19:37:55'), (7868, 'The intuitive definition of symmetry is compared with more formal definitions due to Tamburino and Winicour (1966), and to Penrose (1963), and within the context of the approach of Newman and Unti (1962) to asymptotically flat empty space-times these are shown to be equivalent. Natural interpretations of the transformations inherent in the work of Newman and Unti are given in terms of the conformal approach of Penrose.'), (7869, 'Conformal structure of imath+ and asymptotic symmetry. I. Definitions and local theory'), (7870, 'http://iopscience.iop.org/0264-9381/30/5/055015'), (7871, '0305-4470_11_1_012.pdf'), (7872, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v47/i12/p123504_s1'), (7873, '055015'), (7874, '10.1088/0264-9381/30/5/055015'), (7875, '2013-08-15 15:10:46'), (7876, 'In the context of black hole perturbation theory, we describe both exact evaluation of an asymptotic waveform from a time series recorded at a finite radial location and its numerical approximation. From the user’s standpoint our technique is easy to implement, affords high accuracy, and works for both axial (Regge–Wheeler) and polar (Zerilli) sectors. Our focus is on the ease of implementation with publicly available numerical tables, either as part of an existing evolution code or a post-processing step. Nevertheless, we also present a thorough theoretical discussion of asymptotic waveform evaluation and radiation boundary conditions, which need not be understood by a user of our methods. In particular, we identify (both in the time and frequency domains) analytical asymptotic waveform evaluation kernels, and describe their approximation by techniques developed by Alpert, Greengard, and Hagstrom. This paper also presents new results on the evaluation of far-field signals for the ordinary (acoustic) wave equation. We apply our method to study late-time decay tails at null-infinity, ‘teleportation’ of a signal between two finite radial values, and luminosities from extreme-mass-ratio binaries. Through numerical simulations with the outer boundary as close in as r = 30M, we compute asymptotic waveforms with late-time t−4 decay (ℓ = 2 perturbations), and also luminosities from circular and eccentric particle-orbits that respectively match frequency domain results to relative errors of better than 10−12 and 10−9. Furthermore, we find that asymptotic waveforms are especially prone to contamination by spurious junk radiation.'), (7877, '417-419'), (7878, '0264-9381_30_5_055015.pdf'), (7879, '1939-04-01 April 1, 1939'), (7880, 'ArticleType: research-article / Full publication date: Apr., 1939 / Copyright © 1939 Annals of Mathematics'), (7881, '10.2307/1968929'), (7882, '2013-08-19 14:59:11'), (7883, 'Uber Die Ausdrucke Der Gesamtenergie Und Des Gesamtimpulses Eines Materiellen Systems in Der Allgemeinen Relativitatstheorie'), (7884, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1968929.pdf?acceptTC=true'), (7885, 'U.S. Classification 703/2, 703/22, 700/245, 703/1; International Classification G06T17/30, G06T15/70, G06F7/60, G06F17/10; Cooperative Classification G06T17/30, G06T2210/21, G06T13/00, G05B2219/49145; European Classification G06T17/30, G06T13/00'), (7886, 'David Hestenes,'), (7887, 'US6853964 B1'), (7888, '2005-02-08 Feb 8, 2005'), (7889, 'United States'), (7890, 'System for encoding and manipulating models of objects'), (7891, 'Jun 30, 2000'), (7892, 'http://patentimages.storage.googleapis.com/pdfs/US6853964.pdf'), (7893, '2013-08-20 14:04:56'), (7894, 'Google Patents PDF'), (7895, 'http://link.springer.com/chapter/10.1007/978-1-4684-0676-4_4'), (7896, '©1979 Springer-Verlag US'), (7897, 'The Lebedev Physics Institute Series'), (7898, 'Springer US'), (7899, '73-185'), (7900, '978-1-4684-0678-8, 978-1-4684-0676-4'), (7901, '1979-01-01 1979/01/01'), (7902, '2013-08-22 15:43:36'), (7903, 'This survey gives a systematic exposition of the New man-Penrose method and its application to physical problems. The paper discusses the geometric properties of congruences of light rays in a gravitational field, gives an account of the spinor formalism, and considers its use in studying the properties of a gravitational field. A survey is given of the known exact algebraically special solutions of the Einstein equations. A separate chapter is devoted to the asymptotic properties of a gravitational field and the problem of constructing a quantum theory in asymptotically flat spaces. The application of the method treated to the calculation of the energy flux of particles created under conditions of quantum evaporation of black holes is discussed.'), (7904, 'The Newman-Penrose Method in the Theory of General Relativity'), (7905, 'Problems in the General Theory of Relativity and Theory of Group Representations'), (7906, '123504-123504-10'), (7907, '2013-08-23 18:57:03'), (7908, '2006-12-07 2006-12-07'), (7909, 'On the Rôle of Quaternions in the Algebra of Vectors'), (7910, 'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v43/n1118/pdf/043511c0.pdf'), (7911, 'doi:10.1063/1.2375037'), (7912, '2013-08-23 18:57:08'), (7913, '2013-09-09 15:04:29'), (7914, 'Quaternions and the “Ausdehnungslehre”'), (7915, 'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v44/n1126/pdf/044079b0.pdf'), (7916, 'We motivate a notion of geometric equivalence that is not the usual notion of algebraic equivalence (or isomorphism of Clifford algebra). Using this definition tilting to the opposite metric is a geometric equivalence in contrast to such algebraic equivalences as Cℓ(3,0) ≅ Cℓ(1,2) which are not geometric. We define and discuss the classification of partitioned Clifford algebra and the geometric equivalence of Dirac formulations.'), (7917, '2013-08-23 18:57:14'), (7918, 'Geometric equivalence of Clifford algebras'), (7919, 'Quaternions and the Algebra of Vectors'), (7920, 'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v47/n1220/pdf/047463a0.pdf'), (7921, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000047000012123504000001&idtype=cvips&doi=10.1063/1.2375037&prog=normal'), (7922, '2013-08-23 18:57:17'), (7923, '2013-09-09 15:04:31'), (7924, 'Quaternions and Vector Analysis'), (7925, 'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v48/n1242/pdf/048364b0.pdf'), (7926, "Quaternions and the ``Ausdehnungslehre''"), (7927, 'On the R{\\^{o}}le of Quaternions in the Algebra of Vectors'), (7928, '1891-04-02 April 2, 1891'), (7929, '1891-05-28 May 28, 1891'), (7930, '1893-03-16 March 16, 1893'), (7931, '1893-08-17 August 17, 1893'), (7932, 48), (7933, '511--513'), (7934, '79--82'), (7935, '463--464'), (7936, '364--367'), (7937, 'http://www.nature.com/nature/journal/v48/n1242/abs/048364b0.html'), (7938, 'http://www.nature.com/nature/journal/v47/n1220/abs/047463a0.html'), (7939, 'http://www.nature.com/nature/journal/v44/n1126/abs/044079b0.html'), (7940, 'http://www.nature.com/nature/journal/v43/n1118/abs/043511c0.html'), (7941, '0486649555 9780486649559 0486679101 9780486679105'), (7942, '1985-00-00 1985'), (7943, 'A history of vector analysis: the evolution of the idea of a vectorial system'), (7944, 'A history of vector analysis'), (7945, 'http://www.arxiv.org/pdf/1202.2788.pdf'), (7946, '1202.2788 PDF'), (7947, 'http://arxiv.org/abs/1205.2216'), (7948, 'https://www.math.ucdavis.edu/~temple/MAT21D/SUPPLEMENTARY-ARTICLES/Crowe_History-of-Vectors.pdf'), (7949, '2013-08-23 20:13:22'), (7950, 'Crowe_History-of-Vectors.pdf'), (7951, 'http://littrell.rhcmath.com/pdfs/vectorcalchistory.pdf'), (7952, 'Univ. of Notre Dame Press, Notre Dame, Indiana, t967'), (7953, '2013-08-23 20:13:25'), (7954, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v13/i11/p1837_s1'), (7955, '1837-1842'), (7956, '1972-11-01 1972-11-01'), (7957, 'doi:10.1063/1.1665917'), (7958, '2013-08-23 22:02:14'), (7959, 'A simple example of an aymptotic symmetry group in two dimensions is described. The structure of the corresponding group for asymptotically flat (four‐dimensional) space‐times, the BMS group, is given explicitly. The recent result that all induced representations of the BMS group have discrete spins is explained in terms of the relationship between this group and the Poincaré group. In fact, it is shown that the BMS group is, in a sense, the smallest generalization of the Poincaré group which eliminates the (physically embarrassing) continuous spin representations of the Poincaré group.'), (7960, 'Structure of the Bondi‐Metzner‐Sachs Group'), (7961, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000013000011001837000001&idtype=cvips&doi=10.1063/1.1665917&prog=normal'), (7962, '2013-08-23 22:02:16'), (7963, '2013-08-23 22:02:47'), (7964, 'http://link.springer.com/article/10.1023/A%3A1024498001488'), (7965, '583-633'), (7966, '2003-03-01 2003/03/01'), (7967, '10.1023/A:1024498001488'), (7968, '2013-08-24 18:28:44'), (7969, "General solutions of relativistic wave equations are studied in terms of functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is established. A generalization of the Gel'fand-Yaglom theory for higher-spin equations is given. A two-dimensional complex sphere is associated with each point of Minkowski spacetime. The separation of variables in a general relativistically invariant system is obtained via the hyperspherical functions defined on the surface of the two-dimensional complex sphere. In virtue of this the wave functions are represented in the form of series in hyperspherical functions. Such a description allows one to consider all the physical fields on an equal footing. General solutions of the Dirac and Weyl equations, and also the Maxwell equations in the Majorana-Oppenheimer form, are given in terms of functions on the Lorentz group."), (7970, 'General Solutions of Relativistic Wave Equations'), (7971, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1023%2FA%3A1024498001488.pdf'), (7972, 'How can one observe gravitational angular momentum radiation near null infinity? Angular momentum and its gravitational radiation of the twisting spacetime in Bondi coordinate'), (7973, 'http://www.worldscientific.com.proxy.library.cornell.edu/doi/abs/10.1142/S0129055X01000922?prevSearch=%28pin+group%29+and+%5BContrib%3A+berg%5D&searchHistoryKey='), (7974, '08'), (7975, '953-1034'), (7976, 'Reviews in Mathematical Physics'), (7977, '0129-055X, 1793-6659'), (7978, '2001-08-00 08/2001'), (7979, '10.1142/S0129055X01000922'), (7980, '2013-09-09 15:07:24'), (7981, 'THE PIN GROUPS IN PHYSICS: C, P AND T'), (7982, 'THE PIN GROUPS IN PHYSICS'), (7983, 'http://link.springer.com/article/10.1007/BF01078610'), (7984, '166-168'), (7985, 'Functional Analysis and Its Applications'), (7986, '0016-2663, 1573-8485'), (7987, '1974-04-01 1974/04/01'), (7988, 'Funct Anal Its Appl'), (7989, '10.1007/BF01078610'), (7990, '2013-09-10 20:15:45'), (7991, 'The decomposition of certain tensor products of representations in the principal series with representations in the supplementary series of the group SL (n, C) into irreducible components'), (7992, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01078610.pdf'), (7993, "To answer a question of how can one observed angular momentum radiation near null infinity, one can transform the twisting vacuum solution to make it satisfy Bondi coordinate conditions in the asymptotical region of the null infinity. We then obtain the Bondi-Sachs news function and also find the relationship of how does the angular momentum contribute to the news functions from the exact solution sense. By using the Komar's integral of angular momentum, the gravitational angular momentum flux of the twisting space-time can be obtained. All of our results can be compared with the Kerr solution or Schwarzschild solution. This study can provide a theoretical basis to understand the correlations of gravitational radiations near a rotating dynamical horizon and null infinity."), (7994, '484-485'), (7995, '1982-04-01 1982-04-01'), (7996, 'doi:10.1063/1.525405'), (7997, 'http://arxiv.org/abs/1310.1599'), (7998, 'The principal and supplementary series representations of arbitrary semisimple Lie groups is analyzed in the framework of Auslander and Kostant’s theory of UIR’s of solvable Lie groups. As an illustration, we discuss a physically relevant symmetry group, Spin (4,2).'), (7999, 'Geometric quantization and UIR’s of semisimple Lie groups. III. Principal and supplementary series'), (8000, 'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v23/i4/p484_s1'), (8001, '2013-09-10 20:16:37'), (8002, '1310.1599'), (8003, 'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000023000004000484000001&idtype=cvips&doi=10.1063/1.525405&prog=normal'), (8004, '2013-09-10 20:16:40'), (8005, '2013-10-11 21:01:12'), (8006, 'http://projecteuclid.org/euclid.cmp/1103815085'), (8007, '251-270'), (8008, 'Communications in Mathematical Physics (1965-1997)'), (8009, '1966-00-00 1966'), (8010, '2013-09-10 20:34:00'), (8011, 'projecteuclid.org'), (8012, 'Analytic continuation of group representations'), (8013, '2013-09-25 15:26:57'), (8014, 'http://rspa.royalsocietypublishing.org/content/287/1411/532'), (8015, 287), (8016, 1411), (8017, '532-548'), (8018, '1965-09-28 09/28/1965'), (8019, '10.1098/rspa.1965.0195'), (8020, '2013-09-10 20:35:58'), (8021, 'A simple algebraic method based on multispinors with a complex number of indices is used to obtain the linear (and unitary) representations of non-compact groups. The method is illustrated in the case of the 2 + 1 Lorentz group. All linear representations of this group, their various realizations in Hilbert space as well as the matrix elements of finite transformations have been found. The problem of reduction of the direct product is also briefly discussed.'), (8022, 'On Non-Compact Groups. II. Representations of the 2 + 1 Lorentz Group'), (8023, 'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/287/1411/532.full.pdf'), (8024, 'We present the results of a search for gravitational waves associated with 154 gamma-ray bursts (GRBs) that were detected by satellite-based gamma-ray experiments in 2009-2010, during the sixth LIGO science run and the second and third Virgo science runs. We perform two distinct searches: a modeled search for coalescences of either two neutron stars or a neutron star and black hole; and a search for generic, unmodeled gravitational-wave bursts. We find no evidence for gravitational-wave counterparts, either with any individual GRB in this sample or with the population as a whole. For all GRBs we place lower bounds on the distance to the progenitor, under the optimistic assumption of a gravitational-wave emission energy of 10^-2 M c^2 at 150 Hz, with a median limit of 17 Mpc. For short hard GRBs we place exclusion distances on binary neutron star and neutron star-black hole progenitors, using astrophysically motivated priors on the source parameters, with median values of 16 Mpc and 28 Mpc respectively. These distance limits, while significantly larger than for a search that is not aided by GRB satellite observations, are not large enough to expect a coincidence with a GRB. However, projecting these exclusions to the sensitivities of Advanced LIGO and Virgo, which should begin operation in 2015, we find that the detection of gravitational waves associated with GRBs will become quite possible.'), (8025, '1205.2216'), (8026, 'Search for gravitational waves associated with gamma-ray bursts during LIGO science run 6 and Virgo science runs 2 and 3'), (8027, 'euclid.cmp.1103815085.pdf'), (8028, 'http://www.jstor.org/stable/1969129'), (8029, 'Copyright © 1947 Annals of Mathematics'), (8030, '568-640'), (8031, '1947-07-01 July 1, 1947'), (8032, 'ArticleType: research-article / Full publication date: Jul., 1947 / Copyright © 1947 Annals of Mathematics'), (8033, '10.2307/1969129'), (8034, '2013-09-10 20:41:40'), (8035, 'Irreducible Unitary Representations of the Lorentz Group'), (8036, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1969129.pdf?acceptTC=true'), (8037, 'http://arxiv.org/abs/1309.2581'), (8038, '2013-09-10 2013-09-10'), (8039, '2013-09-13 22:07:22'), (8040, 'Recent years have seen a burgeoning interest in using pulsar timing arrays (PTAs) as gravitational-wave (GW) detectors. To date, that interest has focused mainly on three particularly promising source types: supermassive--black-hole binaries, cosmic strings, and the stochastic background from early-Universe phase transitions. In this paper, by contrast, our aim is to investigate the PTA potential for discovering unanticipated sources. We derive significant constraints on the available discovery space based solely on energetic and statistical considerations: we show that a PTA detection of GWs at frequencies above ~3.e-5 Hz would either be an extraordinary coincidence or violate "cherished beliefs;" we show that for PTAs GW memory can be more detectable than direct GWs, and that, as we consider events at ever higher redshift, the memory effect increasingly dominates an event\'s total signal-to-noise ratio. The paper includes also a simple analysis of the effects of pulsar red noise in PTA searches, and a demonstration that the effects of periodic GWs in the 10^-8 -- 10^-4.5 Hz band would not be degenerate with small errors in standard pulsar parameters (except in a few narrow bands).'), (8041, '1309.2581'), (8042, 'The Gravitational-Wave Discovery Space of Pulsar Timing Arrays'), (8043, 'http://www.arxiv.org/pdf/1309.2581.pdf'), (8044, '1309.2581 PDF'), (8045, 'http://link.springer.com/article/10.1007/BF01336904'), (8046, 98), (8047, '145-154'), (8048, 'Zeitschrift für Physik'), (8049, '0044-3328'), (8050, '1935-03-01 1935/03/01'), (8051, 'Z. Physik'), (8052, '10.1007/BF01336904'), (8053, '2013-09-16 14:11:05'), (8054, 'Die Schrödinger-Gleichung für das Wasserstoffatom im Impulsraum erweist sich als identisch mit der Integralgleichung für die Kugelfunktionen der vierdimensionalen Potentialtheorie. Die Transformationsgruppe der Wasserstoffgleichung ist also die vierdimensionale Drehgruppe; dadurch wird die Entartung der Wasserstoffniveaus in bezug auf die Azimutalquantenzahl l erklärt. Die aus der potentialtheoretischen Deutung der Schrödinger-Gleichung folgenden Beziehungen (Additionstheorem usw.) erlauben mannigfache physikalische Anwendungen. Die Methode ermöglicht, die unendlichen Summen, die in der Theorie des Compton-Effektes an gebundenen Elektronen und in verwandten Problemen auftreten, fast ohne Rechnung auszuwerten. Unter Zugrundelegung eines vereinfachten Atommodells lassen sich ferner explizite Ausdrücke für die Dichtematrix im Impulsraum, für Atomformfaktoren, für das Abschirmungspotential usw. aufstellen.'), (8055, 'Zur Theorie des Wasserstoffatoms'), (8056, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01336904.pdf'), (8057, 'Nova Publishers'), (8058, 9781590339398), (8059, '2004-01-01 2004-01-01'), (8060, 'Physics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require innovations in mathematical physics. Mathematical physics is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. This includes such subjects as scattering theory for n bodies, quantum mechanics (both nonrelativistic and relativistic), atomic and molecular physics, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis and algebra to which such subjects lead. This book presents leading-edge research in this fast-moving field.'), (8061, 'Mathematical Physics Research at the Cutting Edge'), (8062, 286), (8063, 'http://books.google.com/books?id=hIBiM7fa43sC'), (8064, '2013-09-16 14:22:12'), (8065, '189--246'), (8066, 'Hyperspherical Functions and Harmonic Analysis on the Lorentz Group'), (8067, 'http://books.google.com/books?id=hIBiM7fa43sC&lpg=PA242&ots=AOR3p9K2dK&dq=Dolginov%20AZ%201956%20Relativistic%20spherical%20functions&pg=PA189#v=onepage&q=Dolginov%20AZ%201956%20Relativistic%20spherical%20functions&f=false'), (8068, 'http://arxiv.org/abs/math-ph/0108022'), (8069, '2001-08-26 2001-08-26'), (8070, '2013-09-17 14:25:47'), (8071, "Finite-dimensional representations of the proper orthochronous Lorentz group are studied in terms of spinor representations of the Clifford algebras. The Clifford algebras are understood as an `algebraic covering' of a full system of the finite-dimensional representations of the Lorentz group. Space-time discrete symmetries P, T and PT, represented by fundamental automorphisms of the Clifford algebras, are defined on all the representation spaces. Real, complex, quaternionic and octonionic representations of the Lorentz group are considered. Physical fields of the different types are formulated within such representations. The Atiyah-Bott-Shapiro periodicity is defined on the Lorentz group. It is shown that modulo 2 and modulo 8 periodicities of the Clifford algebras allow to take a new look at the de Broglie-Jordan neutrino theory of light and the Gell-Mann-Ne'emann eightfold way in particle physics. On the representation spaces the charge conjugation C is represented by a pseudoautomorphism of the complex Clifford algebra. Quotient representations of the Lorentz group are introduced. It is shown that quotient representations are the most suitable for description of the massless physical fields. By way of example, neutrino field is described via the simplest quotient representation. Weyl-Hestenes equations for neutrino field are given."), (8072, 'math-ph/0108022'), (8073, 'Clifford Algebras and Lorentz Group'), (8074, 'http://www.arxiv.org/pdf/math-ph/0108022.pdf'), (8075, 'math-ph/0108022 PDF'), (8076, 'http://arxiv.org/abs/1309.3956'), (8077, '2013-09-16 2013-09-16'), (8078, '2013-09-17 18:10:47'), (8079, 'The energy of a compact binary system at the fifth post-Newtonian order is explicitly computed in the post-Minkowskian approximation by means of the Effective Field Theory approach. This result allows to determine, for the first time beyond the test particle limit, one coefficient of the energy expression for binary point masses on circular orbit as a function of the orbital angular frequency.'), (8080, '1309.3956'), (8081, 'Gravitating binaries at 5PN in the post-Minkowskian approximation'), (8082, 'http://www.arxiv.org/pdf/1309.3956.pdf'), (8083, '1309.3956 PDF'), (8084, 'http://link.springer.com/article/10.1007/BF01883677'), (8085, '1203-1237'), (8086, '1993-09-01 1993/09/01'), (8087, 'Found Phys'), (8088, '10.1007/BF01883677'), (8089, '2013-09-17 18:21:13'), (8090, "This article reviews Hestenes' work on the Dirac theory, where his main achievement is a real formulation of the theory within thereal Clifford algebra Cl 1,3 ≃ M2 (H). Hestenes invented first in 1966 hisideal spinors ϕ∈Cl11,32(1−γ03)\\phi \\in Cl_{1,3 _2}^1 (1 - \\gamma _{03} ) and later 1967/75 he recognized the importance of hisoperator spinors ψ ∈ Cl 1,3 + ≃ M2 (C). This article starts from the conventional Dirac equation as presented with matrices by Bjorken-Drell. Explicit mappings are given for a passage between Hestenes' operator spinors and Dirac's column spinors. Hestenes' operator spinors are seen to be multiples of even parts of real parts of Dirac spinors (real part in the decompositionC ⊗ Cl 1,3 andnot inC ⊗ M4 (R)=M4 (C)). It will become apparent that the standard matrix formulation contains superfluous parts, which ought to be cut out by Occam's razor. Fierz identities of bilinear covariants are known to be sufficient to study the non-null case but are seen to be insufficient for the null case ψ†γ0ψ=0, ψ†γ0γ0123ψ=0. The null case is thoroughly scrutinized for the first time with a new concept calledboomerang. This permits a new intrinsically geometric classification of spinors. This in turn reveals a new class of spinors which has not been discussed before. This class supplements the spinors of Dirac, Weyl, and Majorana; it describes neither the electron nor the neutron; it is awaiting a physical interpretation and a possible observation. Projection operators P±, Σ± are resettled among their new relatives in End(Cl 1,3 ). Finally, a new mapping, calledtilt, is introduced to enable a transition from Cl 1,3 to the (graded) opposite algebra Cl 3,1 without resorting to complex numbers, that is, not using a replacement γμ →iγμ."), (8091, 'Clifford algebras and Hestenes spinors'), (8092, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01883677.pdf'), (8093, 'paper.pdf'), (8094, 'http://arxiv.org/abs/1310.5381'), (8095, '981-238-307-7'), (8096, 'http://www.arxiv.org/pdf/1205.2216.pdf'), (8097, 'River Edge, NJ'), (8098, 'Introduction_to_2-Spinors_in_General_Relativity.pdf'), (8099, 'Strings_with_a_twistDo_we_really_need_half-.PDF'), (8100, 'Strings with a twist'), (8101, '2004-07-31 July 31, 2004'), (8102, 'New Scientist'), (8103, 'http://arxiv.org/abs/1212.5605'), (8104, '2013-09-18 19:28:03'), (8105, 'We establish a direct connection between scattering amplitudes in planar four-dimensional theories and a remarkable mathematical structure known as the positive Grassmannian. The central physical idea is to focus on on-shell diagrams as objects of fundamental importance to scattering amplitudes. We show that the all-loop integrand in N=4 SYM is naturally represented in this way. On-shell diagrams in this theory are intimately tied to a variety of mathematical objects, ranging from a new graphical representation of permutations to a beautiful stratification of the Grassmannian G(k,n) which generalizes the notion of a simplex in projective space. All physically important operations involving on-shell diagrams map to canonical operations on permutations; in particular, BCFW deformations correspond to adjacent transpositions. Each cell of the positive Grassmannian is naturally endowed with positive coordinates and an invariant measure which determines the on-shell function associated with the diagram. This understanding allows us to classify and compute all on-shell diagrams, and give a geometric understanding for all the non-trivial relations among them. Yangian invariance of scattering amplitudes is transparently represented by diffeomorphisms of G(k,n) which preserve the positive structure. Scattering amplitudes in (1+1)-dimensional integrable systems and the ABJM theory in (2+1) dimensions can both be understood as special cases of these ideas. On-shell diagrams in theories with less (or no) supersymmetry are associated with exactly the same structures in the Grassmannian, but with a measure deformed by a factor encoding ultraviolet singularities. The Grassmannian representation of on-shell processes also gives a new understanding of the all-loop integrand for scattering amplitudes, presenting all integrands in a novel dLog form which directly reflects the underlying positive structure.'), (8106, '1212.5605'), (8107, 'Scattering Amplitudes and the Positive Grassmannian'), (8108, 'http://www.arxiv.org/pdf/1212.5605.pdf'), (8109, '1212.5605 PDF'), (8110, '1205.2216 PDF'), (8111, 'http://arxiv.org/abs/1304.0210'), (8112, '2013-03-31 2013-03-31'), (8113, '2013-09-25 15:29:17'), (8114, 'We derive a simple relationship between the energy emitted in gravitational waves for a narrowband source and the distance to which that emission can be detected by a single detector. We consider linearly polarized, elliptically polarized, and unpolarized gravitational waves, and emission patterns appropriate for each of these cases. We ignore cosmological effects.'), (8115, '1304.0210'), (8116, 'A Rule of Thumb for the Detectability of Gravitational-Wave Bursts'), (8117, 'http://www.arxiv.org/pdf/1304.0210.pdf'), (8118, '1304.0210 PDF'), (8119, 'http://arxiv.org/abs/1304.0670'), (8120, '2013-04-02 2013-04-02'), (8121, '2013-09-25 15:53:15'), (8122, 'We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. For concreteness, we focus primarily on gravitational-wave signals from the inspiral of binary neutron star (BNS) systems, as the source considered likely to be the most common for detection and also promising for multimessenger astronomy. We find that confident detections will likely require at least 2 detectors operating with BNS sensitive ranges of at least 100 Mpc, while ranges approaching 200 Mpc should give at least ~1 BNS detection per year even under pessimistic predictions of signal rates. The ability to localize the source of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and can be as large as thousands of square degrees with only 2 sensitive detectors operating. Determining the sky position of a significant fraction of detected signals to areas of 5 sq deg to 20 sq deg will require at least 3 detectors of sensitivity within a factor of ~2 of each other and with a broad frequency bandwidth. Should one of the LIGO detectors be relocated in India as expected, many gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.'), (8123, '1304.0670'), (8124, 'Prospects for Localization of Gravitational Wave Transients by the Advanced LIGO and Advanced Virgo Observatories'), (8125, 'http://www.arxiv.org/pdf/1304.0670.pdf'), (8126, '1304.0670 PDF'), (8127, 'http://arxiv.org/abs/1304.4984'), (8128, '2013-04-17 2013-04-17'), (8129, '2013-09-25 15:53:18'), (8130, 'The first generation of ground-based interferometric gravitational wave detectors, LIGO, GEO and Virgo, have operated and taken data at their design sensitivities over the last few years. The data has been examined for the presence of gravitational wave signals. Presented here is a comprehensive review of the most significant results. The network of detectors is currently being upgraded and extended, providing a large likelihood for observations. These future prospects will also be discussed.'), (8131, '1304.4984'), (8132, 'Searching for gravitational waves with the LIGO and Virgo interferometers'), (8133, 'http://www.arxiv.org/pdf/1304.4984.pdf'), (8134, '1304.4984 PDF'), (8135, 'http://arxiv.org/abs/1305.0816'), (8136, '2013-05-03 2013-05-03'), (8137, '2013-09-25 15:53:22'), (8138, 'Interferometric detectors will very soon give us an unprecedented view of the gravitational-wave sky, and in particular of the explosive and transient Universe. Now is the time to challenge our theoretical understanding of short-duration gravitational-wave signatures from cataclysmic events, their connection to more traditional electromagnetic and particle astrophysics, and the data analysis techniques that will make the observations a reality. This paper summarizes the state of the art, future science opportunities, and current challenges in understanding gravitational-wave transients.'), (8139, '1305.0816'), (8140, 'The Transient Gravitational-Wave Sky'), (8141, 'http://www.arxiv.org/pdf/1305.0816.pdf'), (8142, '1305.0816 PDF'), (8143, 'http://arxiv.org/abs/1309.6334'), (8144, '2013-09-24 2013-09-24'), (8145, '2013-09-27 20:26:33'), (8146, 'Measuring the spins of supermassive black holes (SMBHs) in active galactic nuclei (AGN) can inform us about the relative role of gas accretion vs. mergers in recent epochs of the life of the host galaxy and its AGN. Recent advances in theory and observation have enabled spin measurements for a handful of SMBHs thus far, but this science is still very much in its infancy. Herein, I discuss how and why we seek to measure black hole spin in AGN, using recent results from long X-ray observing campaigns on three radio-quiet AGN (MCG-6-30-15, NGC 3783 and Fairall 9) to illustrate this process and its caveats. I then present our current knowledge of the distribution of SMBH spins in the local universe. I also address prospects for improving the accuracy, precision and quantity of these spin constraints in the next decade and beyond with instruments such as NuSTAR, Astro-H and a future generation large-area X-ray telescope.'), (8147, '1309.6334'), (8148, 'Measuring Supermassive Black Hole Spins in Active Galactic Nuclei'), (8149, 'http://www.arxiv.org/pdf/1309.6334.pdf'), (8150, '1309.6334 PDF'), (8151, '10.1103/PhysRevD.85.064010'), (8152, '2013-10-01 09:48:08'), (8153, 'Using the main result of a companion paper, in which the binding energy of a circular-orbit nonspinning compact binary system is computed at leading-order beyond the test-particle approximation, the exact expression of the effective-one-body (EOB) metric component gtteff is obtained through first order in the mass ratio. Combining these results with the recent gravitational self-force calculation of the periastron advance for circular orbits in the Schwarzschild geometry, the EOB metric component grreff is also determined at linear order in the mass ratio. These results assume that the mapping between the real and effective Hamiltonians at the second and third post-Newtonian (PN) orders holds at all PN orders. Our findings also confirm the advantage of resumming the PN dynamics around the test-particle limit if the goal is to obtain a flexible model that can smoothly connect the test-mass and equal-mass limits.'), (8154, 'Complete nonspinning effective-one-body metric at linear order in the mass ratio'), (8155, 'http://arxiv.org/abs/1302.6723'), (8156, '2013-10-01 09:48:33'), (8157, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i6/e064010'), (8158, '2013-02-27 2013-02-27'), (8159, 'Ann. Phys. (Berlin) 525:359 (2013)'), (8160, '2013-10-01 11:10:19'), (8161, "The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter-only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short-range behavior of the integrands around the sources. The Hamiltonian of a test-spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post-Newtonian approximate) Poincar\\'e algebra are applied. Along the way a self-contained overview for the computation of the 3PN ADM point-mass Hamiltonian is provided, too."), (8162, '1302.6723'), (8163, 'Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians'), (8164, 'http://www.arxiv.org/pdf/1302.6723.pdf'), (8165, '1302.6723 PDF'), (8166, 'http://arxiv.org/abs/1211.5535'), (8167, '2012-11-23 2012-11-23'), (8168, 'Prog. Theor. Phys. 128 (2012) pp. 971-992'), (8169, '2013-10-01 13:07:04'), (8170, 'We extend our previous results of the 14th post-Newtonian (PN) order expansion of gravitational waves for a test particle in circular orbits around a Schwarzschild black hole to the 22PN order, i.e. $v^{44}$ beyond the leading Newtonian approximation where $v$ is the orbital velocity of a test particle. Comparing our 22PN formula for the energy flux with high precision numerical results, we find that the relative error of the 22PN flux at the innermost stable circular orbit is about $10^{-5}$. We also estimate the phase difference between the 22PN waveforms and numerical waveforms after a two-year inspiral. We find that the dephase is about $10^{-9}$ for $\\mu/M=10^{-4}$ and $10^{-2}$ for $\\mu/M=10^{-5}$ where $\\mu$ is the mass of the compact object and $M$ the mass of the central supermassive black hole. Finally, we construct a hybrid formula of the energy flux by supplementing the 4PN formula of the energy flux for circular and equatorial orbits around a Kerr black hole with all the present 22PN terms for the case of a Schwarzschild black hole. Comparing the hybrid formula with the the full numerical results, we examine the performance of the hybrid formula for the case of Kerr black hole.'), (8171, '1211.5535'), (8172, 'Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order'), (8173, 'http://www.arxiv.org/pdf/1211.5535.pdf'), (8174, '1211.5535 PDF'), (8175, 'http://download.springer.com.proxy.library.cornell.edu/static/pdf/131/bok%253A978-0-387-48101-2.pdf?auth66=1381075251_22a09d75eab2741b7d73f98882aedfd0&ext=.pdf'), (8176, '2013-10-04 16:14:29'), (8177, 'bok%3A978-0-387-48101-2.pdf'), (8178, 'http://site.ebrary.com/id/10229193'), (8179, '9780387481012 038748101X 0387480986 9780387480985'), (8180, '2013-10-04 16:14:40'), (8181, '"In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems."--Jacket.'), (8182, 'Introduction to manifolds'), (8183, 'http://arxiv.org/abs/1310.1528'), (8184, '2013-10-05 2013-10-05'), (8185, '2013-10-08 13:20:15'), (8186, 'To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (LISA, etc.), inspiralling compact binaries --- binary star systems composed of neutron stars and/or black holes in their late stage of evolution --- require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion, pay attention to the self-field regularizations at work, discuss several notions of innermost circular orbits, estimate the accuracy of the approximation and make a comparison with numerical gravitational self-force computations. The gravitational waveform and energy flux are obtained with high post-Newtonian precision. Some landmark results are discussed in the case of eccentric compact binaries moving on quasi-elliptical orbits, and on spin-orbit coupling effects in black hole binaries.'), (8187, '1310.1528'), (8188, 'http://www.arxiv.org/pdf/1310.1528.pdf'), (8189, '1310.1528 PDF'), (8190, 'http://matriisi.ee.tut.fi/courses/analyysinseminaari/EHitzer_slides.pdf'), (8191, '2013-10-08 14:43:06'), (8192, 'EHitzer_slides.pdf'), (8193, 'Clifford Fourier and Clifford Wavelet Transforms'), (8194, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-3-0348-0603-9.pdf'), (8195, '2013-10-08 14:46:18'), (8196, '10.1007978-3-0348-0603-9.pdf'), (8197, 'http://www.springer.com/birkhauser/mathematics/book/978-3-0348-0602-2'), (8198, '2013-10-08 15:02:48'), (8199, 'www.springer.com.proxy.library.cornell.edu'), (8200, 'Quaternion and\xa0Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. ...'), (8201, 'Quaternion and Clifford Fourier Transforms and Wavelets'), (8202, 'http://arxiv.org/abs/1310.1602'), (8203, '2013-10-06 2013-10-06'), (8204, 'http://arxiv.org/abs/1311.5854'), (8205, 'A four-dimensional asymptotic expansion scheme is used to study the next order effects of the nonlinearity near a spinning dynamical black hole. The angular momentum flux and energy flux formula are then obtained by asymptotic expansion and the compatibility of the coupling Newman-Penrose equations. After constructing the reference frame in terms of the compatible constant spinors, the energy-momentum flux is derived and it is related to the black hole area growth. Directly from the flux formula of the spinning dynamical horizon, we find that the physically reasonable condition on the positivity of the gravitational energy flux yields that the shear will monotonically decrease with time.'), (8206, '1310.1602'), (8207, 'Gravitational radiation and angular momentum flux from a spinning dynamical black hole'), (8208, 'http://www.arxiv.org/pdf/1310.1602.pdf'), (8209, '1310.1602 PDF'), (8210, 'http://arxiv.org/abs/gr-qc/0407091'), (8211, '2004-07-25 2004-07-25'), (8212, 'Phys.Rev.D71:024027,2005'), (8213, '2013-10-09 01:21:13'), (8214, 'We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass monopole/spin-induced quadrupole interaction terms. In the case of both quasi-circular and eccentric orbits, we search for the presence of chaos (using the method of Lyapunov exponents) for a large variety of initial conditions. For quasi-circular orbits, we find no chaotic behavior for black holes with total mass 10 - 40 solar masses when initially at a separation corresponding to a Newtonian gravitational-wave frequency less than 150 Hz. Only for rather small initial radial distances, for which spin-spin induced oscillations in the radial separation are rather important, do we find chaotic solutions, and even then they are rare. Moreover, these chaotic quasi-circular orbits are of questionable astrophysical significance, since they originate from direct parametrization of the equations of motion rather than from widely separated binaries evolving to small separations under gravitational radiation reaction. In the case of highly eccentric orbits, which for ground-based interferometers are not astrophysically favored, we again find chaotic solutions, but only at pericenters so small that higher order PN corrections, especially higher spin PN corrections, should also be taken into account.'), (8215, 'gr-qc/0407091'), (8216, 'The dynamics of precessing binary black holes using the post-Newtonian approximation'), (8217, 'http://www.arxiv.org/pdf/gr-qc/0407091.pdf'), (8218, 'gr-qc/0407091 PDF'), (8219, 'http://arxiv.org/abs/gr-qc/0010100'), (8220, '2000-10-26 2000-10-26'), (8221, 'Phys.Rev. D67 (2003) 044013'), (8222, '2013-10-09 01:21:29'), (8223, 'A typical stellar mass black hole with a lighter companion is shown to succumb to a chaotic precession of the orbital plane. As a result, the optimal candidates for the direct detection of gravitational waves by Earth based interferometers can show irregular modulation of the waveform during the last orbits before plunge. The precession and the subsequent modulation of the gravitational radiation depends on the mass ratio, eccentricity, and spins. The smaller the mass of the companion, the more prominent the effect of the precession. The most important parameters are the spin magnitudes and misalignments. If the spins are small and nearly aligned with the orbital angular momentum, then there will be no chaotic precession while increasing both the spin magnitudes and misalignments increases the erratic precession. A large eccentricity can be induced by large, misaligned spins but does not seem to be required for chaos. An irregular precession of the orbital plane will generate irregularities in the gravitational wave frequency but may have a lesser effect on the total number of cycles observed.'), (8224, 'gr-qc/0010100'), (8225, 'The fate of chaotic binaries'), (8226, 'http://www.arxiv.org/pdf/gr-qc/0010100.pdf'), (8227, 'gr-qc/0010100 PDF'), (8228, 'http://link.aps.org/doi/10.1103/PhysRevD.79.043016'), (8229, '043016'), (8230, '2009-02-27 February 27, 2009'), (8231, '10.1103/PhysRevD.79.043016'), (8232, '2013-10-09 01:25:17'), (8233, 'Although the orbits of comparable-mass, spinning black holes seem to defy simple decoding, we find a means to decipher all such orbits—in the absence of radiation reaction. The conservative dynamics is complicated by extreme perihelion precession compounded by spin-induced precession. We are able to quantitatively define and describe the fully three-dimensional motion of comparable-mass binaries with one black hole spinning and expose an underlying simplicity. To do so, we untangle the dynamics by capturing the motion in the orbital plane and explicitly separate out the precession of the plane itself. Our system is defined by the conservative third-order post-Newtonian Hamiltonian plus spin-orbit coupling for one spinning black hole with a nonspinning companion. Our results are twofold: (1) We derive highly simplified equations of motion in a nonorthogonal orbital basis, and (2) we define a complete taxonomy for fully three-dimensional orbits. More than just a naming system, the taxonomy provides unambiguous and quantitative descriptions of the orbits, including a determination of the zoom-whirliness of any given orbit. Through a correspondence with the rationals, we are able to show that zoom-whirl behavior is prevalent in comparable-mass binaries in the strong-field regime, as it is for extreme-mass-ratio binaries in the strong field. A first significant conclusion that can be drawn from this analysis is that all generic orbits in the final stages of inspiral under gravitational radiation losses are characterized by precessing clovers with few leaves, and that no orbit will behave like the tightly precessing ellipse of Mercury. The gravitational waveform produced by these low-leaf clovers will reflect the natural harmonics of the orbital basis—harmonics that, importantly, depend only on radius. The significance for gravitational wave astronomy will depend on the number of windings the pair executes in the strong-field regime. The third-order post-Newtonian system studied provides an example of a general method that can be applied to any effective description of black hole pairs.'), (8234, 'Dynamics of black hole pairs. I. Periodic tables'), (8235, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i4/e043016'), (8236, 'http://link.aps.org/doi/10.1103/PhysRevD.79.043017'), (8237, '043017'), (8238, '10.1103/PhysRevD.79.043017'), (8239, 'arXiv:1311.5854 [gr-qc]'), (8240, 'Spinning black hole pairs exhibit a range of complicated dynamical behaviors. An interest in eccentric and zoom-whirl orbits has ironically inspired the focus of this paper: the constant radius orbits. When black hole spins are misaligned, the constant radius orbits are not circles but, rather, they lie on the surface of a sphere and have acquired the name “spherical orbits.” The spherical orbits are significant as they energetically frame the distribution of all orbits. In addition, each unstable spherical orbit is asymptotically approached by an orbit that whirls an infinite number of times, known as a homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the zoom-whirl spectrum and has a further significance as the separatrix between inspiral and plunge for eccentric orbits. We work in the context of two spinning black holes of comparable mass as described in the third-order post-Newtonian Hamiltonian with spin-orbit coupling included. As such, the results could provide a testing ground for the accuracy of the post-Newtonian expansion. Further, the spherical orbits could provide useful initial data for numerical relativity. Finally, we comment that the spinning black hole pairs should give way to chaos around the homoclinic orbit when spin-spin coupling is incorporated.'), (8241, 'Dynamics of black hole pairs. II. Spherical orbits and the homoclinic limit of zoom-whirliness'), (8242, 'How can one observe gravitational angular momentum radiation near null infinity?'), (8243, 'http://link.aps.org/doi/10.1103/PhysRevD.81.084045'), (8244, '084045'), (8245, '2010-04-23 April 23, 2010'), (8246, '10.1103/PhysRevD.81.084045'), (8247, '2013-11-22 2013-11-22'), (8248, 'The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum, and spin variables [X,P,S1,S2] compose its phase space. This may give a convenient application of perturbation theory to the derivation of the post-Newtonian formulation, but also makes classic theories of a symplectic Hamiltonian system a serious obstacle in application, especially in diagnosing integrability and nonintegrability from a dynamical system theory perspective. To completely understand the dynamical characteristic of the integrability or nonintegrability for the binary system, we construct a set of conjugate spin variables and reexpress the spin Hamiltonian part so as to make the complete Hamiltonian formulation symplectic. As a result, it is directly shown with the least number of independent isolating integrals that a conservative Hamiltonian compact binary system with both one spin and the pure orbital part to any post-Newtonian order is typically integrable and not chaotic. And a conservative binary system consisting of two spins restricted to the leading order spin-orbit interaction and the pure orbital part at all post-Newtonian orders is also integrable, independently on the mass ratio. For all other various spinning cases, the onset of chaos is possible.'), (8249, 'Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries'), (8250, '1310.1599 PDF'), (8251, 'http://link.aps.org/doi/10.1103/PhysRevD.79.124014'), (8252, 124014), (8253, '2009-06-11 June 11, 2009'), (8254, '10.1103/PhysRevD.79.124014'), (8255, '2013-12-05 14:37:38'), (8256, 'In paper I in this series, we found exact expressions for the equatorial homoclinic orbits: the separatrix between bound and plunging, whirling and not whirling motion. As a companion to that physical space study, in this paper we paint a phase space portrait of the homoclinic orbits that includes exact expressions for the actions and fundamental frequencies. Additionally, we develop a reduced Hamiltonian description of Kerr motion that allows us to track groups of trajectories with a single global clock. This facilitates a variational analysis, whose stability exponents and eigenvectors could potentially be useful for future studies of families of black hole orbits and their associated gravitational waveforms.'), (8257, 'Homoclinic orbits around spinning black holes. II. The phase space portrait'), (8258, 'http://www.arxiv.org/pdf/1310.1599.pdf'), (8259, 'We define the center of mass and spin of an isolated system in General Relativity. The resulting relationships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their newtonian counterparts, though no postnewtonian approximation has been taken. We also derive equations of motion linking their time evolution to the emitted gravitational radiation. These equations should be useful when describing highly energetic processes where a considerable fraction of the total mass is emitted as gravitational waves.'), (8260, 175001), (8261, '2011-09-07 2011-09-07'), (8262, '10.1088/0264-9381/28/17/175001'), (8263, 'Spin and Center of Mass in Asymptotically Flat Spacetimes'), (8264, 'http://www.arxiv.org/pdf/1311.5854.pdf'), (8265, 'Inspiral of generic black hole binaries: spin, precession and eccentricity'), (8266, 'Inspiral of generic black hole binaries'), (8267, '2013-10-11 21:01:33'), (8268, 'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/28/17/175001/pdf/0264-9381_28_17_175001.pdf'), (8269, '2013-10-09 01:28:39'), (8270, '0264-9381_28_17_175001.pdf'), (8271, 'http://stacks.iop.org/0264-9381/28/i=17/a=175001?key=crossref.2b737ee1e057955acd1b16531f3a5ba4'), (8272, '2013-10-09 01:28:47'), (8273, '1311.5854 PDF'), (8274, 'http://szeliski.org/Book/drafts/SzeliskiBook_20100903_draft.pdf'), (8275, '2013-10-09 01:29:53'), (8276, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i12/e124014'), (8277, '2013-10-09 01:30:17'), (8278, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i4/e043017'), (8279, '2013-10-09 01:33:19'), (8280, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084045'), (8281, 'http://arxiv.org/abs/1304.1775'), (8282, '2013-04-05 2013-04-05'), (8283, '2013-10-09 03:00:21'), (8284, 'Compact binary systems with neutron stars or black holes are one of the most promising sources for ground-based gravitational wave detectors. Gravitational radiation encodes rich information about source physics; thus parameter estimation and model selection are crucial analysis steps for any detection candidate events. Detailed models of the anticipated waveforms enable inference on several parameters, such as component masses, spins, sky location and distance that are essential for new astrophysical studies of these sources. However, accurate measurements of these parameters and discrimination of models describing the underlying physics are complicated by artifacts in the data, uncertainties in the waveform models and in the calibration of the detectors. Here we report such measurements on a selection of simulated signals added either in hardware or software to the data collected by the two LIGO instruments and the Virgo detector during their most recent joint science run, including a "blind injection" where the signal was not initially revealed to the collaboration. We exemplify the ability to extract information about the source physics on signals that cover the neutron star and black hole parameter space over the individual mass range 1 Msun - 25 Msun and the full range of spin parameters. The cases reported in this study provide a snap-shot of the status of parameter estimation in preparation for the operation of advanced detectors.'), (8285, '1304.1775'), (8286, 'Parameter estimation for compact binary coalescence signals with the first generation gravitational-wave detector network'), (8287, 'http://www.arxiv.org/pdf/1304.1775.pdf'), (8288, '1304.1775 PDF'), (8289, '2013-10-09 03:01:05'), (8290, 'http://arxiv.org/abs/1209.6533'), (8291, '2012-09-28 2012-09-28'), (8292, 'Phys. Rev. D 87, 022002 (2013)'), (8293, '2013-10-09 03:03:49'), (8294, 'We report a search for gravitational waves from the inspiral, merger and ringdown of binary black holes (BBH) with total mass between 25 and 100 solar masses, in data taken at the LIGO and Virgo observatories between July 7, 2009 and October 20, 2010. The maximum sensitive distance of the detectors over this period for a (20,20) Msun coalescence was 300 Mpc. No gravitational wave signals were found. We thus report upper limits on the astrophysical coalescence rates of BBH as a function of the component masses for non-spinning components, and also evaluate the dependence of the search sensitivity on component spins aligned with the orbital angular momentum. We find an upper limit at 90% confidence on the coalescence rate of BBH with non-spinning components of mass between 19 and 28 Msun of 3.3 \\times 10^-7 mergers /Mpc^3 /yr.'), (8295, '1209.6533'), (8296, 'Search for Gravitational Waves from Binary Black Hole Inspiral, Merger and Ringdown in LIGO-Virgo Data from 2009-2010'), (8297, 'http://www.arxiv.org/pdf/1209.6533.pdf'), (8298, '1209.6533 PDF'), (8299, '2013-10-09 03:19:58'), (8300, 'http://arxiv.org/abs/0904.4718'), (8301, '2009-04-29 2009-04-29'), (8302, 'Phys.Rev.D80:062002,2009'), (8303, '2013-10-09 11:43:37'), (8304, 'We report on a matched-filter search for gravitational wave bursts from cosmic string cusps using LIGO data from the fourth science run (S4) which took place in February and March 2005. No gravitational waves were detected in 14.9 days of data from times when all three LIGO detectors were operating. We interpret the result in terms of a frequentist upper limit on the rate of gravitational wave bursts and use the limits on the rate to constrain the parameter space (string tension, reconnection probability, and loop sizes) of cosmic string models.'), (8305, '0904.4718'), (8306, 'First LIGO search for gravitational wave bursts from cosmic (super)strings'), (8307, 'http://www.arxiv.org/pdf/0904.4718.pdf'), (8308, '0904.4718 PDF'), (8309, 'http://onlinelibrary.wiley.com/doi/10.1002/3527608958.ch12/summary'), (8310, '135–149'), (8311, '2013-10-09 13:57:22'), (8312, 'Über Gravitationswellen'), (8313, '2013-10-15 15:28:15'), (8314, 'SzeliskiBook_20100903_draft.pdf'), (8315, '2013-10-20 2013-10-20'), (8316, '2013-10-29 17:43:36'), (8317, 'We study how to extract information on the neutron star equation of state from the gravitational wave signal emitted during the coalescence of a binary system composed by two neutron stars or a neutron star and a black hole. We use Post-Newtonian templates which include the tidal deformability parameter and, when tidal disruption occurs before merger, a frequency cut-off. Assuming that this signal is detected by Advanced LIGO/Virgo or ET, we evaluate the uncertainties on these parameters using different data analysis strategies based on the Fisher matrix approach, and on recently obtained analytical fits of the relevant quantities. We find that the tidal deformability is more effective than the stellar compactness to discriminate among different possible equations of state.'), (8318, '1310.5381'), (8319, 'Constraining the equation of state of nuclear matter with gravitational wave observations: tidal deformability and tidal disruption'), (8320, 'Constraining the equation of state of nuclear matter with gravitational wave observations'), (8321, 'http://www.arxiv.org/pdf/1310.5381.pdf'), (8322, '1310.5381 PDF'), (8323, 'http://arxiv.org/abs/1310.5745'), (8324, '2013-10-21 2013-10-21'), (8325, '2013-10-29 17:43:51'), (8326, 'We consider the formation of extreme mass-ratio inspirals (EMRIs) sourced from a stellar cusp centred on a primary supermassive black hole (SMBH) and perturbed by an inspiraling less massive secondary SMBH. The problem is approached numerically, assuming the stars are non-interacting over these short timescales and performing an ensemble of restricted three-body integrations. From these simulations we see that not only can EMRIs be produced during this process, but the dynamics are also quite rich. In particular, most of the EMRIs are produced through a process akin to the Kozai-Lidov mechanism, but with strong effects due to the non-Keplerian stellar potential, general relativity, and non-secular oscillations in the angular momentum on the orbital timescale of the binary SMBH system.'), (8327, '1310.5745'), (8328, 'Production of EMRIs in Supermassive Black Hole Binaries'), (8329, 'http://www.arxiv.org/pdf/1310.5745.pdf'), (8330, '1310.5745 PDF'), (8331, 'http://arxiv.org/abs/1310.5633'), (8332, '2013-10-29 17:46:31'), (8333, "We demonstrate the implementation of a sensitive search pipeline for gravitational waves from coalescing binary black holes whose components have spins aligned with the orbital angular momentum. We study the pipeline recovery of simulated gravitational wave signals from aligned-spin binary black holes added to real detector noise, comparing the pipeline performance with aligned-spin filter templates to the same pipeline with non-spinning filter templates. Our results exploit a three-parameter phenomenological waveform family that models the full inspiral-merger-ringdown coalescence and treats the effect of aligned spins with a single effective spin parameter \\chi. We construct template banks from these waveforms by a stochastic placement method and use these banks as filters in the recently-developed gstlal search pipeline. We measure the observable volume of the analysis pipeline for binary black hole signals with total mass in [15,25] solar masses and \\chi in [0, 0.85]. We find an increase in observable volume of up to 45% for systems with 0.2 <= \\chi <= 0.85 with almost no loss of sensitivity to signals with 0 <= \\chi <= 0.2. We demonstrate this analysis on 25.9 days of data obtained from the Hanford and Livingston detectors in LIGO's fifth observation run."), (8334, '1310.5633'), (8335, 'Improving the sensitivity of a search for coalescing binary black holes with non-precessing spins in gravitational wave data'), (8336, 'http://www.arxiv.org/pdf/1310.5633.pdf'), (8337, '1310.5633 PDF'), (8338, 'http://arxiv.org/abs/1310.4771'), (8339, '2013-10-17 2013-10-17'), (8340, '2013-10-29 17:48:18'), (8341, 'This paper argues that the effect of Hawking radiation on an astrophysical black hole situated in a realistic cosmological context is not total evaporation of the black hole; rather there will always be a remnant mass. The key point is that the locus of emission of Hawking radiation is not the globally defined event horizon. Rather the emission domain lies just outside a timelike Marginal Outer Trapped Surface that is locally defined. The emission domain is mainly located inside the event horizon. A spacelike singularity forms behind the event horizon, and most of the Hawking radiation ends up at this singularity rather than at infinity. Whether any Hawking radiation reaches infinity depends on the relation between the emission domain and the event horizon. From the outside view, even if radiation is seen as always being emitted, the black hole never evaporates away, rather its mass and entropy asymptote to finite non-zero limits, and the event horizon always acts as a sink for matter and information. From an inside view, the matter and information disappear into the singularity, which is the boundary of spacetime. The argument is based on the nature of the processes at work plus a careful delineation of the relevant causal domains; in order to confirm this model and determine details of the outcome, detailed calculations of the expectation value of the stress-energy-momentum tensor are needed to determine back reaction effects.'), (8342, '1310.4771'), (8343, 'Astrophysical black holes may radiate, but they do not evaporate'), (8344, 'http://www.arxiv.org/pdf/1310.4771.pdf'), (8345, '1310.4771 PDF'), (8346, 'http://arxiv.org/abs/1310.2871'), (8347, '2013-10-10 2013-10-10'), (8348, '2013-10-29 17:50:49'), (8349, 'Gravitational wave detectors are typically described as responding to gravitational wave metric perturbations, which are gauge-dependent and --- correspondingly --- unphysical quantities. This is particularly true for ground-based interferometric detectors, like LIGO, space-based detectors, like LISA and its derivatives, spacecraft doppler tracking detectors, and pulsar timing arrays detectors. The description of gravitational waves, and a gravitational wave detector\'s response, to the unphysical metric perturbation has lead to a proliferation of false analogies and descriptions regarding how these detectors function, and true misunderstandings of the physical character of gravitational waves. Here we provide a fully physical and gauge invariant description of the response of a wide class of gravitational wave detectors in terms of the Riemann curvature, the physical quantity that describes gravitational phenomena in general relativity. In the limit of high frequency gravitational waves, the Riemann curvature separates into two independent gauge invariant quantities: a "background" curvature contribution and a "wave" curvature contribution. In this limit the gravitational wave contribution to the detector response reduces to an integral of the gravitational wave contribution of the curvature along the unperturbed photon path between components of the detector. The description presented here provides an unambiguous physical description of what a gravitational wave detector measures and how it operates, a simple means of computing corrections to a detectors response owing to general detector motion, a straightforward way of connecting the results of numerical relativity simulations to gravitational wave detection, and a basis for a general and fully relativistic pulsar timing formula.'), (8350, '1310.2871'), (8351, 'Gravitational wave detector response in terms of spacetime Riemann curvature'), (8352, 'http://www.arxiv.org/pdf/1310.2871.pdf'), (8353, '1310.2871 PDF'), (8354, 'http://arxiv.org/abs/1307.6232'), (8355, '2013-10-31 15:50:46'), (8356, "We describe a general procedure to generate spinning, precessing waveforms that include inspiral, merger and ringdown stages in the effective-one-body (EOB) approach. The procedure uses a precessing frame in which precession-induced amplitude and phase modulations are minimized, and an inertial frame, aligned with the spin of the final black hole, in which we carry out the matching of the inspiral-plunge to merger-ringdown waveforms. As a first application, we build spinning, precessing EOB waveforms for the gravitational modes l=2 such that in the nonprecessing limit those waveforms agree with the EOB waveforms recently calibrated to numerical-relativity waveforms. Without recalibrating the EOB model, we then compare EOB and post-Newtonian precessing waveforms to two numerical-relativity waveforms produced by the Caltech-Cornell-CITA collaboration. The numerical waveforms are strongly precessing and have 35 and 65 gravitational-wave cycles. We find a remarkable agreement between EOB and numerical-relativity precessing waveforms and spins' evolutions. The phase difference is ~ 0.2 rad at merger, while the mismatches, computed using the advanced-LIGO noise spectral density, are below 2% when maximizing only on the time and phase at coalescence and on the polarization angle."), (8357, '1307.6232'), (8358, 'Inspiral-merger-ringdown waveforms of spinning, precessing black-hole binaries in the effective-one-body formalism'), (8359, 'http://www.arxiv.org/pdf/1307.6232.pdf'), (8360, '1307.6232 PDF'), (8361, 'http://arxiv.org/abs/1310.8288'), (8362, '2013-10-30 2013-10-30'), (8363, '2013-10-31 16:05:04'), (8364, 'The coalescence of two neutron stars is an important gravitational wave source for LIGO and other ground-based detectors. Numerous studies have considered the precision with which binary parameters (masses, spins, Love numbers) can be measured. Here I consider the accuracy with which these parameters can be determined in the presence of systematic errors due to waveform approximations. These approximations include truncation of the post-Newtonian (PN) series and neglect of neutron star (NS) spin, tidal deformation, or orbital eccentricity. All of these effects can yield systematic errors that exceed statistical errors for plausible parameter values. In particular, neglecting 4PN and higher-order terms causes a significant bias in the NS Love number. Tidal effects will not be measurable with PN inspiral waveforms if these systematic errors are not controlled.'), (8365, '1310.8288'), (8366, 'Systematic parameter errors in inspiraling neutron star binaries'), (8367, 'http://www.arxiv.org/pdf/1310.8288.pdf'), (8368, '1310.8288 PDF'), (8369, 'http://arxiv.org/abs/1304.3176'), (8370, 88), (8371, '2013-07-00 7/2013'), (8372, 'arXiv:1304.3176 [astro-ph, physics:gr-qc]'), (8373, '10.1103/PhysRevD.88.024040'), (8374, '2013-12-06 21:07:17'), (8375, "Previous analytic and numerical calculations suggest that, at each instant, the emission from a precessing black hole binary closely resembles the emission from a nonprecessing analog. In this paper we quantitatively explore the validity and limitations of that correspondence, extracting the radiation from a large collection of roughly two hundred generic black hole binary merger simulations both in the simulation frame and in a corotating frame that tracks precession. To a first approximation, the corotating-frame waveforms resemble nonprecessing analogs, based on similarity over a band-limited frequency interval defined using a fiducial detector (here, advanced LIGO) and the source's total mass $M$. By restricting attention to masses $M\\in 100, 1000 M_\\odot$, we insure our comparisons are sensitive only to our simulated late-time inspiral, merger, and ringdown signals. In this mass region, every one of our precessing simulations can be fit by some physically similar member of the \\texttt{IMRPhenomB} phenomenological waveform family to better than 95%; most fit significantly better. The best-fit parameters at low and high mass correspond to natural physical limits: the pre-merger orbit and post-merger perturbed black hole. Our results suggest that physically-motivated synthetic signals can be derived by viewing radiation from suitable nonprecessing binaries in a suitable nonintertial reference frame. While a good first approximation, precessing systems have degrees of freedom (i.e., the transverse spins) which a nonprecessing simulation cannot reproduce. We quantify the extent to which these missing degrees of freedom limit the utility of synthetic precessing signals for detection and parameter estimation."), (8376, 'Comparing gravitational waves from nonprecessing and precessing black hole binaries in the corotating frame'), (8377, 'http://www.arxiv.org/pdf/1304.3176.pdf'), (8378, '1304.3176 PDF'), (8379, 'http://arxiv.org/abs/1305.4884'), (8380, 'arXiv:1305.4884 [gr-qc]'), (8381, '2013-05-21 2013-05-21'), (8382, '2013-12-06 21:55:22'), (8383, 'We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing the gravitational interaction of two bodies within the effective one-body formalism. The (non logarithmic) coefficient a_5 (nu) measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio nu. Its nu-independent part a_5 (0) is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation. Its nu-linear part a_5 (nu) - a_5 (0) is deduced from recent results of Jaranowski and Sch\\"afer, and is found to be significantly negative.'), (8384, 'Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation'), (8385, 'http://www.arxiv.org/pdf/1305.4884.pdf'), (8386, '1305.4884 PDF'), (8387, 'http://casa.colorado.edu/~ajsh/phys5770_08/grtetrad.pdf'), (8388, '2013-12-10 16:07:49'), (8389, 'grtetrad.pdf'), (8390, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/ebook.jsf?bid=CBO9780511790904'), (8391, 'http://www.sciencedirect.com/science/article/pii/0165168496000710'), (8392, '1-13'), (8393, 'Signal Processing'), (8394, '0165-1684'), (8395, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A005;jsessionid=DAD056502B05D010D438DDC4ADEB5B46?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8396, '2013-12-10 16:17:12'), (8397, 'http://arxiv.org/abs/0802.1249'), (8398, '2008-08-21 2008-08-21'), (8399, '0511140479 9780511140471 0511137958 9780511137952 0521829518 9780521829519 0511139721 9780511139727 9780511790904 0511790902'), (8400, '2013-12-10 16:17:17'), (8401, "Written for advanced undergraduate and graduate students, this is a clear mathematical introduction to Einstein's theory of general relativity and its physical applications. Concentrating on the theory's physical consequences, this approachable textbook contains over 300 exercises to illuminate and extend the discussion."), (8402, 'General relativity an introduction for physicists'), (8403, 'arXiv:0802.1249 [gr-qc]'), (8404, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A006?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8405, '2013-12-10 16:18:31'), (8406, '10.1088/0264-9381/25/16/165003'), (8407, '2014-01-07 14:44:31'), (8408, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A007?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8409, '2013-12-10 16:20:09'), (8410, 'The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) To provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) To provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.'), (8411, '1996-08-00 August 1996'), (8412, '10.1016/0165-1684(96)00071-0'), (8413, 'The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits'), (8414, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A008?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8415, '2013-12-10 16:21:41'), (8416, 'http://www.arxiv.org/pdf/0802.1249.pdf'), (8417, '01 - The spacetime of special relativity.pdf'), (8418, '0802.1249 PDF'), (8419, 175004), (8420, '2012-09-07 2012-09-07'), (8421, '2014-01-12 17:00:58'), (8422, 'http://jila.colorado.edu/~ajsh/phys5770_13/grbook.pdf'), (8423, '2013-12-10 16:32:57'), (8424, 'grbook.pdf'), (8425, 'General Relativity, Black Holes, and Cosmology (snapshot of proto-book 2013/08/02)'), (8426, 'http://arxiv.org/abs/1312.2503'), (8427, 'arXiv:1312.2503 [gr-qc]'), (8428, '2013-12-09 2013-12-09'), (8429, '2013-12-10 17:04:52'), (8430, "We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the 4th post-Newtonian approximation recently obtained by us. This extension is done to linear order in the mass ratio by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determination of the (linear in mass ratio) radial potential to the 6th post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In principle, our analytical method can be extended to arbitrarily high post-Newtonian orders."), (8431, 'High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations'), (8432, 'http://www.arxiv.org/pdf/1312.2503.pdf'), (8433, '1312.2503 PDF'), (8434, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A186?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8435, '2013-12-10 19:32:32'), (8436, 'arXiv:1204.1043 [gr-qc]'), (8437, '13 - The Kerr geometry.pdf'), (8438, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A274?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8439, '2013-12-10 19:35:46'), (8440, '10.1088/0264-9381/29/17/175004'), (8441, '18 - Gravitational waves.pdf'), (8442, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A025?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8443, '2013-12-10 19:36:39'), (8444, '2014-01-07 14:47:01'), (8445, '02 - Manifolds and coordinates.pdf'), (8446, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A042?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8447, '2013-12-10 19:37:15'), (8448, 'We compute the quadrupole mode of the gravitational waveform of inspiralling compact binaries at the third and a half post-Newtonian (3.5PN) approximation of general relativity. The computation is performed using the multipolar post-Newtonian formalism, and restricted to binaries without spins moving on quasi-circular orbits. The new inputs mainly include the 3.5PN terms in the mass quadrupole moment of the source, and the control of required subdominant corrections to the contributions of hereditary integrals (tails and non-linear memory effect). The result is given in the form of the quadrupolar mode (2,2) in a spin-weighted spherical harmonic decomposition of the waveform, and may be used for comparison with the counterpart quantity computed in numerical relativity. It is a step towards the computation of the full 3.5PN waveform, whose knowledge is expected to reduce the errors on the location parameters of the source.'), (8449, '03 - Vector calculus on manifolds.pdf'), (8450, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A299?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8451, '2013-12-10 19:37:53'), (8452, '2013-02-00 2/2013'), (8453, '20 - Bibliography.pdf'), (8454, 'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A300?pubCode=CUP&urlPrefix=cambridge&productCode=cbo'), (8455, '2013-12-10 19:38:20'), (8456, 'arXiv:1209.6349 [gr-qc]'), (8457, '21 - Index.pdf'), (8458, '00 - A - Front matter.pdf'), (8459, '00 - B - Contents.pdf'), (8460, '00 - C - Preface.pdf'), (8461, 'http://faculty.luther.edu/~macdonal/GA&GC.pdf'), (8462, '2013-12-16 03:35:15'), (8463, 'GA&GC.pdf'), (8464, 'http://www.montgomerycollege.edu/Departments/planet/planet/Numerical_Relativity/GA-SIG/GA%26GC.pdf'), (8465, '2013-12-16 03:35:21'), (8466, 'A survey of geometric algebra and geometric calculus'), (8467, 'http://link.springer.com/article/10.1023/A%3A1007901028047'), (8468, '191-213'), (8469, 'International Journal of Computer Vision'), (8470, '0920-5691, 1573-1405'), (8471, '1998-02-01 1998/02/01'), (8472, '10.1023/A:1007901028047'), (8473, '2013-12-16 05:10:20'), (8474, 'We discuss a coordinate-free approach to the geometry of computer vision problems. The technique we use to analyse the three-dimensional transformations involved will be that of geometric algebra: a framework based on the algebras of Clifford and Grassmann. This is not a system designed specifically for the task in hand, but rather a framework for all mathematical physics. Central to the power of this approach is the way in which the formalism deals with rotations; for example, if we have two arbitrary sets of vectors, known to be related via a 3D rotation, the rotation is easily recoverable if the vectors are given. Extracting the rotation by conventional means is not as straightforward. The calculus associated with geometric algebra is particularly powerful, enabling one, in a very natural way, to take derivatives with respect to any multivector (general element of the algebra). What this means in practice is that we can minimize with respect to rotors representing rotations, vectors representing translations, or any other relevant geometric quantity. This has important implications for many of the least-squares problems in computer vision where one attempts to find optimal rotations, translations etc., given observed vector quantities. We will illustrate this by analysing the problem of estimating motion from a pair of images, looking particularly at the more difficult case in which we have available only 2D information and no information on range. While this problem has already been much discussed in the literature, we believe the present formulation to be the only one in which least-squares estimates of the motion and structure are derived simultaneously using analytic derivatives.'), (8475, 'New Geometric Methods for Computer Vision: An Application to Structure and Motion Estimation'), (8476, 'New Geometric Methods for Computer Vision'), (8477, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1023%2FA%3A1007901028047.pdf'), (8478, 'http://geocalc.clas.asu.edu/pdf/CrystalGA.pdf'), (8479, '2013-12-16 18:33:30'), (8480, 'CrystalGA.pdf'), (8481, 'The Crystallographic Space Groups in Geometric Algebra'), (8482, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/54/5/10.1063/1.4802878;jsessionid=8g6q1gphp8flm.x-aip-live-01'), (8483, '052501'), (8484, '0022-2488, 1089-7658'), (8485, '2013-05-07 2013/05/07'), (8486, '10.1063/1.4802878'), (8487, '2013-12-16 18:36:31'), (8488, 'scitation.aip.org.proxy.library.cornell.edu'), (8489, 'The “observer space” of a Lorentzian spacetime is the space of future-timelike unit tangent vectors. Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract observer space geometries for which no underlying spacetime is assumed. We propose taking observer space as fundamental in general relativity, and prove integrability conditions under which spacetime can be reconstructed as a quotient of observer space. Additional field equations on observer space then descend to Einstein's equations on the reconstructed spacetime. We also consider the case where no such reconstruction is possible, and spacetime becomes an observer-dependent, relative concept. Finally, we discuss applications of observer space, including a geometric link between covariant and canonical approaches to gravity.'), (8490, 'Lifting general relativity to observer space'), (8491, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/54/5/1.4802878.pdf?itemId=/content/aip/journal/jmp/54/5/10.1063/1.4802878&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (8492, 'http://www.ams.org/bull/1972-78-05/S0002-9904-1972-12971-9/'), (8493, '635-652'), (8494, 'Bulletin of the American Mathematical Society'), (8495, '0002-9904, 1936-881X'), (8496, '1972-00-00 1972'), (8497, 'Bull. Amer. Math. Soc.'), (8498, '10.1090/S0002-9904-1972-12971-9'), (8499, '2013-12-16 18:46:51'), (8500, 'www.ams.org.proxy.library.cornell.edu'), (8501, 'Missed opportunities'), (8502, 'http://www.ams.org.proxy.library.cornell.edu/bull/1972-78-05/S0002-9904-1972-12971-9/S0002-9904-1972-12971-9.pdf'), (8503, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/33/1/10.1063/1.529955'), (8504, 33), (8505, '161-170'), (8506, '1992-01-01 1992/01/01'), (8507, '10.1063/1.529955'), (8508, '2013-12-16 19:20:21'), (8509, 'A unified mathematical approach to spinors and multivectors or superalgebra is constructed in a form useful to study the mathematical description of matter and its interaction fields. The formalism then encompasses both points of view: m u l t i v e c t o r s for the description of (space‐time) geometry and the description of the integer spin, interaction fields, and s p i n o r representations suitable for the description of half odd integer, matter fields. An application is made to study the change of the Dirac equation under the spinors to multivectors (to scalars) mapping. The physical and geometric content of the multivector solutions of the Dirac–Hestenes equation is clearly shown.'), (8510, 'Geometric superalgebra and the Dirac equation'), (8511, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/33/1/1.529955.pdf?itemId=/content/aip/journal/jmp/33/1/10.1063/1.529955&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (8512, 'http://geocalc.clas.asu.edu/pdf/crystalsymmetry.pdf'), (8513, '2013-12-16 19:39:50'), (8514, 'crystalsymmetry.pdf'), (8515, 'http://link.springer.com/chapter/10.1007/978-1-4612-0089-5_1'), (8516, '3–34'), (8517, '2013-12-16 19:39:55'), (8518, 'Point groups and space groups in geometric algebra'), (8519, 'Applications of Geometric Algebra in Computer Science and Engineering'), (8520, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aapt/journal/ajp/70/9/10.1119/1.1475326'), (8521, '958-963'), (8522, '0002-9505, 1943-2909'), (8523, '2002-08-13 2002/08/13'), (8524, '10.1119/1.1475326'), (8525, '2013-12-16 20:39:07'), (8526, 'Vectors and quaternions are quite different mathematical quantities because they have different symmetry properties. Gibbs and Heaviside created their vector system starting from the quaternion system invented by Hamilton. They identified a pure quaternion as a vector and introduced some changes in the product of two vectors defined by Hamilton without realizing that the scalar product and vector product cannot be interpreted as the scalar part and vector part of the quaternion product. Toward the end of the 19th century some authors realized that there was an incompatibility between the vector and quaternion formalisms, but the central problem was not altogether clear. This paper will show that the main difficulty arose from Hamilton’s contradictory use of i, j, and k both as versors and as vectors.'), (8527, 'Polar and axial vectors versus quaternions'), (8528, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aapt/journal/ajp/70/9/1.1475326.pdf?itemId=/content/aapt/journal/ajp/70/9/10.1119/1.1475326&mimeType=pdf&containerItemId=content/aapt/journal/ajp'), (8529, 'http://arxiv-web3.library.cornell.edu/abs/1311.2565'), (8530, '2013-11-11 2013/11/11'), (8531, '2013-12-18 16:28:57'), (8532, 'arxiv-web3.library.cornell.edu'), (8533, 'Stability of nonspinning effective-one-body model in approximating two-body dynamics and gravitational-wave emission'), (8534, 'http://arxiv.org/pdf/1311.2565'), (8535, 'http://arxiv-web3.library.cornell.edu/abs/1311.2544'), (8536, '2013-12-18 16:30:13'), (8537, 'Effective-one-body model for black-hole binaries with generic mass ratios and spins'), (8538, 'http://arxiv.org/pdf/1311.2544'), (8539, 'http://arxiv.org/abs/1312.3641'), (8540, 'arXiv:1312.3641 [gr-qc]'), (8541, '2013-12-12 2013-12-12'), (8542, '2013-12-19 17:28:32'), (8543, 'The inspiral and merger of two orbiting black holes is among the most promising sources for the first (hopefully imminent) direct detection of gravitational waves (GWs), and measurements of these signals could provide a wealth of information about astrophysics, fundamental physics and cosmology. Detection and measurement require a theoretical description of the GW signals from all possible black-hole-binary configurations, which can include complicated precession effects due to the black-hole spins. Modelling the GW signal from generic precessing binaries is therefore one of the most urgent theoretical challenges facing GW astronomy. This article briefly reviews the phenomenology of generic-binary dynamics and waveforms, and recent advances in modelling them.'), (8544, 'Modelling gravitational waves from precessing black-hole binaries: Progress, challenges and prospects'), (8545, 'Modelling gravitational waves from precessing black-hole binaries'), (8546, 'http://www.arxiv.org/pdf/1312.3641.pdf'), (8547, '1312.3641 PDF'), (8548, 'http://arxiv.org/abs/1312.6871'), (8549, 'arXiv:1312.6871 [gr-qc]'), (8550, '2013-12-24 2013-12-24'), (8551, '2014-01-01 19:42:26'), (8552, "We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein's equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when expressed in terms of manifestly gauge invariant quantities. Therefore we derive all our results from the perturbed Weyl tensor rather than the perturbed metric. We derive gravitational wave memory for the Einstein equations coupled to a general energy-momentum tensor that reaches null infinity."), (8553, 'A perturbative and gauge invariant treatment of gravitational wave memory'), (8554, 'http://www.arxiv.org/pdf/1312.6871.pdf'), (8555, '1312.6871 PDF'), (8556, 'http://arxiv.org/abs/1312.5375'), (8557, 'arXiv:1312.5375 [gr-qc]'), (8558, '2013-12-18 2013-12-18'), (8559, '2014-01-01 19:43:08'), (8560, "We report on recent results obtained in the post-Newtonian framework for the modelling of the gravitational waves emitted by binary systems of spinning compact objects (black holes and/or neutron stars). These new results are obtained at the spin-orbit (linear-in-spin) level and solving Einstein's field equations iteratively in harmonic coordinates as well as the multipolar post-Newtonian formalism. The dynamics of the binary was tackled at the next-to-next-to-leading order, corresponding to the 3.5 post-Newtonian (PN) order for maximally spinning objects, and the result is found to be consistent with a previously obtained reduced Hamiltonian in the ADM approach. The corresponding contribution to the energy flux emitted by the binary was obtained at the 3.5PN order, as well as the next-to-leading 4PN tail contribution to this flux, an imprint of the non-linearity in the propagation of the wave. These new terms can be used to build more accurate PN templates for the next generation of gravitational wave detectors. We give an illustrative estimate of the quantitative relevance of the new terms in the orbital phasing of the binary."), (8561, 'Gravitational waves from spinning compact object binaries: New post-Newtonian results'), (8562, 'Gravitational waves from spinning compact object binaries'), (8563, 'http://www.arxiv.org/pdf/1312.5375.pdf'), (8564, '1312.5375 PDF'), (8565, 'http://link.springer.com/article/10.1007/s10714-009-0781-2'), (8566, '2579-2586'), (8567, '2009-11-01 2009/11/01'), (8568, '10.1007/s10714-009-0781-2'), (8569, '2014-01-03 16:06:56'), (8570, 'We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painlevé–Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.'), (8571, 'Painlevé–Gullstrand coordinates for the Kerr solution'), (8572, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs10714-009-0781-2.pdf'), (8573, 'http://arxiv.org/abs/gr-qc/0411060'), (8574, 519), (8575, 'arXiv:gr-qc/0411060'), (8576, '10.1119/1.2830526'), (8577, '2014-01-03 16:32:39'), (8578, 'This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. %that can by understood by non-experts. In the river model, space itself flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. We show that the river model works also for rotating (Kerr-Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, the river has at each point not only a velocity but also a rotation, or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation), not just three (velocity). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point, and that encapsulates all the properties of a stationary rotating black hole.'), (8579, 'The river model of black holes'), (8580, 'http://www.arxiv.org/pdf/gr-qc/0411060.pdf'), (8581, 'gr-qc/0411060 PDF'), (8582, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/4/10.1063/1.1705280'), (8583, '809-812'), (8584, '1402.0053 PDF'), (8585, '10.1063/1.1705280'), (8586, '2014-01-03 17:21:20'), (8587, 'Spinor fields can be classified according to the invariants of their derivatives. It is suggested that different invariants describe different interactions of elementary particles. Then the classification of spinor fields becomes a classification of elementary particles and their interactions. A geometric interpretation of isospin is suggested and is used in a model of nucleoninteractions. This theory entails an intimate connection between spin and isospin which appears to have some experimental support. Among other things, it connects the pseudoscalar and isospin properties of the pion and accounts for the polarization of the third axis in isospace by the electromagnetic interactions.'), (8588, 'Spin and Isospin'), (8589, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/4/1.1705280.pdf?itemId=/content/aip/journal/jmp/8/4/10.1063/1.1705280&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (8590, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/4/10.1063/1.1705279'), (8591, '798-808'), (8592, '10.1063/1.1705279'), (8593, '2014-01-03 17:23:08'), (8594, 'The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (−1)½ which appears explicitly in the Dirac equation. In the modification of the Dirac electron theory which ensues, the (−1)½ appears as the generator of rotations in the spacelike plane orthogonal to the plane containing the electron current and spin vectors. This amounts to a further ``relativistic'' constraint on the spinor theory and so may be expected to have physical consequences. It does not, however, conflict with well‐substantiated features of the Dirac theory.'), (8595, 'Real Spinor Fields'), (8596, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/4/1.1705279.pdf?itemId=/content/aip/journal/jmp/8/4/10.1063/1.1705279&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (8597, 'http://link.springer.com/chapter/10.1007/978-94-009-4728-3_27'), (8598, '©1986 Springer Science+Business Media B.V.'), (8599, 'NATO ASI Series'), (8600, 'Springer Netherlands'), (8601, '321-346'), (8602, '978-94-010-8602-8, 978-94-009-4728-3'), (8603, '1986-01-01 1986/01/01'), (8604, '2014-01-03 17:29:10'), (8605, 183), (8606, 'The Dirac theory has a hidden geometric structure. This talk traces the conceptual steps taken to uncover that structure and points out significant implications for the interpretation of quantum mechanics. The unit imaginary in the Dirac equation is shown to represent the generator of rotations in a spacelike plane related to the spin. This implies a geometric interpretation for the generator of electromagnetic gauge transformations as well as for the entire electroweak gauge group of the Weinberg-Salam model. The geometric structure also helps to reveal closer connections to classical theory than hitherto suspected, including exact classical solutions of the Dirac equation.'), (8607, 'Clifford Algebra and the Interpretation of Quantum Mechanics'), (8608, 'Clifford Algebras and Their Applications in Mathematical Physics'), (8609, '2014-01-07 14:53:38'), (8610, 'http://link.springer.com/chapter/10.1007/978-94-009-4728-3_2'), (8611, '25-37'), (8612, '2014-01-03 17:29:18'), (8613, 'A historical review of spinors is given together with a construction of spinor spaces as minimal left ideals of Clifford algebras. Spinor spaces of euclidean spaces over reals have a natural linear structure over reals, complex numbers or quaternions. Clifford algebras have involutions which induce bilinear forms or scalar products on spinor spaces. The automorphism groups of these scalar products of spinors are determined and also classified.'), (8614, 'Clifford Algebras and Spinors'), (8615, 'http://www.arxiv.org/pdf/1209.6349.pdf'), (8616, '87-98'), (8617, '2003-04-01 April 1, 2003'), (8618, '1967-00-00 1967'), (8619, '1.2830526.pdf'), (8620, 'http://www.nhlbi.nih.gov/health/public/heart/hbp/dash/new_dash.pdf'), (8621, '2014-01-04 16:37:31'), (8622, 'new_dash.pdf'), (8623, 'http://books.google.com/books?hl=en&lr=&id=A9j9vuDHbL4C&oi=fnd&pg=PR3&dq=%22eat.+I+limit+alcohol,+and+watch+my%22+%22each+step+alone+lowers+blood+pressure,+the+combination+of%22+%22and+1,500+milligrams+per+day.+Twenty-three%22+%22from+me+and+is+doing+the%22+&ots=oiiOlFeepb&sig=fDXp29Rv4JfIaixzq-yJ7_rk6o8'), (8624, 'DIANE Publishing'), (8625, '2014-01-04 16:37:36'), (8626, 'Your Guide to Lowering Your Blood Pressure with the DASH Eating Plan (rev'), (8627, 'http://link.springer.com/article/10.1007/BF01883781'), (8628, '1295-1327'), (8629, '1993-10-01 1993/10/01'), (8630, '10.1007/BF01883781'), (8631, '2014-01-06 14:42:50'), (8632, "A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether's theorem is found which is appropriate to both discrete and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-energy and angular-momentum tensors are derived, with spinors and vectors treated in a unified way. It is demonstrated that the antisymmetric terms in the stress-energy tensor are crucial to the correct treatment of angular momentum. The multivector derivative is extended to provide a functional calculus for linear functions which is more compact and more powerful than previous formalisms. This is demonstrated in a reformulation of the functional derivative with respect to the metric, which is then used to recover the full canonical stress-energy tensor. Unlike conventional formalisms, which result in a symmetric stress-energy tensor, our reformulation retains the potentially important antisymmetric contribution."), (8633, 'A multivector derivative approach to Lagrangian field theory'), (8634, 'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01883781.pdf'), (8635, '1209.6349 PDF'), (8636, 'CliffordAlgebraToGeometricCalculus.pdf'), (8637, 'This paper is devoted to the study of higher-order statistics for complex random variables. We introduce a general framework allowing the direct manipulation of complex quantities: the separation between the real and the imaginary parts of a variable is avoided. We give the rules to integrate and derive probability density functions and characteristic functions, so that calculations may be carried out. In the case of multidimensional variables, we use the natural framework of tensors. The study of complex variables leads to the extension of the notion of complex circular random variables already known in the Gaussian case.'), (8638, 'Statistics for complex variables and signals — Part I: Variables'), (8639, 'Statistics for complex variables and signals — Part I'), (8640, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0165168496000710/pdf?md5=b84de43000e46dff6ec45d40a51b9291&pid=1-s2.0-0165168496000710-main.pdf'), (8641, 'http://www.sciencedirect.com/science/article/pii/S0550321306007632'), (8642, 758), (8643, '1–2'), (8644, '161-184'), (8645, 'Nuclear Physics B'), (8646, '0550-3213'), (8647, '2006-12-04 December 4, 2006'), (8648, '10.1016/j.nuclphysb.2006.09.014'), (8649, '2014-01-12 17:18:34'), (8650, 'We consider the signature reversing transformation of the metric tensor g μ ν → − g μ ν induced by the chiral transformation of the curved space gamma matrices γ μ → γ γ μ in spacetimes with signature ( S , T ) , which also induces a ( − 1 ) T spacetime orientation reversal. We conclude: (1) It is a symmetry only for chiral theories with S − T = 4 k , with k integer. (2) Yang–Mills theories require dimensions D = 4 k with T even for which even rank antisymmetric tensor field strengths and mass terms are also allowed. For example, D = 10 super-Yang–Mills is ruled out. (3) Gravitational theories require dimensions D = 4 k + 2 with T odd, for which the symmetry is preserved by coupling to odd rank field strengths. In D = 10 , for example, it is a symmetry of N = 1 and type IIB supergravity but not type IIA. A cosmological term and also mass terms are forbidden but non-minimal R ϕ 2 coupling is permitted. (4) Spontaneous compactification from D = 4 k + 2 leads to interesting but different symmetries in lower dimensions such as D = 4 , so Yang–Mills terms, Kaluza–Klein masses and a cosmological constant may then appear. As a well-known example, IIB permits AdS 5 × S 5 .'), (8651, 'Signature reversal invariance'), (8652, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0550321306007632/pdfft?md5=e4142bfb37613c0921b3828f96b5a8db&pid=1-s2.0-S0550321306007632-main.pdf'), (8653, '10.2307/3219300'), (8654, '2014-02-15 22:19:00'), (8655, 'An Elementary Introduction to the Hopf Fibration'), (8656, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/3219300.pdf?acceptTC=true'), (8657, 'http://link.springer.com/article/10.1007/BF01457962'), (8658, '637-665'), (8659, 'Mathematische Annalen'), (8660, 'http://arxiv.org/pdf/math-ph/0012006v1.pdf?fname=cm&font=TypeI'), (8661, '2014-01-12 17:25:18'), (8662, '0012006v1.pdf'), (8663, 'http://www.worldscientific.com/doi/abs/10.1142/S0129055X01000922'), (8664, '953–1034'), (8665, '2014-01-12 17:25:23'), (8666, 'The pin groups in physics: C, P and T'), (8667, 'The pin groups in physics'), (8668, '0025-5831, 1432-1807'), (8669, 'The LaTeX Companion'), (8670, '1931-12-01 1931/12/01'), (8671, 'TeXBook.pdf'), (8672, 'TeXByTopic.pdf'), (8673, 'The LaTeX Companion 2e.djvu'), (8674, 'http://link.aps.org/doi/10.1103/PhysRevLett.60.1599'), (8675, '1599-1601'), (8676, '1988-04-18 April 18, 1988'), (8677, '10.1103/PhysRevLett.60.1599'), (8678, '2014-01-15 04:44:22'), (8679, 'The groups Pin(n,m) and Pin(m,n) are not isomorphic, and the obstruction classes to their respective bundles are different. It follows that for nonorientable superstring theories the contributions to a Polyakov path integral from surfaces with positive metric are different from the contributions from those with negative metrics.'), (8680, 'Where the sign of the metric makes a difference'), (8681, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v60/i16/p1599_1'), (8682, 'http://link.aps.org/doi/10.1103/PhysRevLett.60.2704'), (8683, '2704-2704'), (8684, '1988-06-20 June 20, 1988'), (8685, '10.1103/PhysRevLett.60.2704'), (8686, '2014-01-15 04:44:56'), (8687, 'Where the Sign of the Metric Makes a Difference'), (8688, 'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v60/i25/p2704_1'), (8689, '2003-08-28 2003-08-28'), (8690, '"Mathematical Physics Research at the Cutting Edge" (Ed. C. V. Benton), pp. 193-250 (Nova Science Publishers, New York, 2004)'), (8691, '2014-02-18 04:08:33'), (8692, 'Matrix elements of spinor and principal series representations of the Lorentz group are studied in the basis of complex angular momentum (helicity basis). It is shown that matrix elements are expressed via hyperspherical functions (relativistic spherical functions). In essence, the hyperspherical functions present itself a four-dimensional (with respect to a pseudo-euclidean metrics of Minkowski spacetime) generalization of the usual three-dimensional spherical functions. An explicit form of the hyperspherical functions is given. The hypespherical functions of the spinor representations are represented by a product of generalized spherical functions and Jacobi functions. It is shown that zonal hyperspherical functions are expressed via the Appell functions. The associated hyperspherical functions are defined as the functions on a two-dimensional complex sphere. Integral representations, addition theorems, symmetry and recurrence relations for hyperspherical functions are given. In case of the principal and supplementary series representations of the Lorentz group, the matrix elements are expressed via the functions represented by a product of spherical and conical functions. The hyperspherical functions of the principal series representations allow one to apply methods of harmonic analysis on the Lorentz group. Different forms of expansions of square integrable functions on the Lorentz group are studied. By way of example, an expansion of the wave function, representing the Dirac field $(1/2,0)\\oplus(0,1/2)$, is given.'), (8693, 'http://www.arxiv.org/pdf/math-ph/0308039.pdf'), (8694, 'math-ph/0308039 PDF'), (8695, 'http://arxiv.org/abs/1402.3586'), (8696, 'arXiv:1402.3586 [gr-qc, physics:hep-th]'), (8697, '2014-02-14 2014-02-14'), (8698, '2014-02-18 15:09:47'), (8699, 'We present a pedagogical introduction to the notions underlying the connection formulation of General Relativity - Loop Quantum Gravity (LQG) - with an emphasis on the physical aspects of the framework. We begin by reviewing General Relativity and Quantum Field Theory, to emphasise the similarities between them which establish a foundation upon which to build a theory of quantum gravity. We then explain, in a concise and clear manner, the steps leading from the Einstein-Hilbert action for gravity to the construction of the quantum states of geometry, known as \\emph{spin-networks}, which provide the basis for the kinematical Hilbert space of quantum general relativity. Along the way we introduce the various associated concepts of \\emph{tetrads}, \\emph{spin-connection} and \\emph{holonomies} which are a pre-requisite for understanding the LQG formalism. Having provided a minimal introduction to the LQG framework, we discuss its applications to the problems of black hole entropy and of quantum cosmology. A list of the most common criticisms of LQG is presented, which are then tackled one by one in order to convince the reader of the physical viability of the theory. An extensive set of appendices provide accessible introductions to several key notions such as the \\emph{Peter-Weyl theorem}, \\emph{duality} of differential forms and \\emph{Regge calculus}, among others. The presentation is aimed at graduate students and researchers who have some familiarity with the tools of quantum mechanics and field theory and/or General Relativity, but are intimidated by the seeming technical prowess required to browse through the existing LQG literature. Our hope is to make the formalism appear a little less bewildering to the un-initiated and to help lower the barrier for entry into the field.'), (8700, 'LQG for the Bewildered'), (8701, 'http://www.arxiv.org/pdf/1402.3586.pdf'), (8702, '1402.3586 PDF'), (8703, '68–78'), (8704, 'This paper describes an approach to implementing geometric algebra. The goal of the implementation was to create an efficient, general implementation of geometric algebras of relatively low dimension, based on an orthogonal basis of any signature, for use in applications like computer graphics, computer vision, physics and robotics. The approach taken is to let the user specify the properties of the geometric algebra required, and to automatically generate source code accordingly. The resulting source code consist of three layers, of which the lower two are automatically generated. The top layer hides the implementation and optimization details from the user and provides a dimension independent, object oriented interface to using geometric algebra in software, while the lower layers implement the algebra efficiently. Coordinates of multivectors are stored in a compressed form, which does not store coordinates of grade parts that are known to be equal to. Optimized implementations of products can be automatically generated according to a profile analysis of the user application. We present benchmarks that compare the performance of this approach to other GA implementations available to us and demonstrate the impact of various settings our code generator offers.'), (8705, 'Gaigen: a Geometric Algebra Implementation Generator'), (8706, 'FD03] FONTIJNE D., DORST L.: MODELING 3D EUCLIDEAN GEOMETRY. IEEE COMPUTER GRAPHICS AND APPLICATIONS 23, 2 (MARCHAPRIL 2003'), (8707, 'http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=4CAF7A1F3D1A6FAB425CEF8BD08A6F10?doi=10.1.1.114.9270&rep=rep1&type=pdf'), (8708, '2014-02-26 01:39:47'), (8709, 'http://www.tandfonline.com/doi/abs/10.1080/14786444808646139'), (8710, '435-439'), (8711, 'Philosophical Magazine Series 3'), (8712, '1941-5966'), (8713, '1848-00-00 1848'), (8714, '10.1080/14786444808646139'), (8715, '2014-02-26 03:31:47'), (8716, 'Berlin, Lehmanns Media-LOB.de'), (8717, 'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444808646139'), (8718, 'http://www.tandfonline.com/doi/abs/10.1080/14786444908646257'), (8719, '406-410'), (8720, '1849-00-00 1849'), (8721, '10.1080/14786444908646257'), (8722, '2014-02-26 03:41:24'), (8723, '978-3-86541-361-1'), (8724, 'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444908646257'), (8725, 'http://www.tandfonline.com/doi/abs/10.1080/14786444908646169'), (8726, 226), (8727, '37-47'), (8728, '10.1080/14786444908646169'), (8729, '2014-02-26 03:41:35'), (8730, 'Gaalet - a C++ expression template library for implementing geometric algebra'), (8731, 'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444908646169'), (8732, 'http://www.tandfonline.com/doi/abs/10.1080/14786445008646598'), (8733, '281-283'), (8734, '1850-00-00 1850'), (8735, '10.1080/14786445008646598'), (8736, '2014-02-26 03:41:41'), (8737, 'http://link.springer.com/article/10.1007/s00006-013-0424-2'), (8738, 'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786445008646598'), (8739, 'On a new imaginary in algebra'), (8740, 'On the symbols of algebra, and on the Theory of Tesarines'), (8741, 'On impossible equations, on impossible quantities, and on tessarines'), (8742, 'On certain functions resembling quaternions, and on a new imaginary in algebra'), (8743, 'http://download.springer.com.proxy.library.cornell.edu/static/pdf/316/bok%253A978-3-7643-7791-5.pdf?auth66=1389996833_f53e4819b8806cb562774f3eabbf6b15&ext=.pdf'), (8744, '2014-01-15 22:14:20'), (8745, 'bok%3A978-3-7643-7791-5.pdf'), (8746, 'Quaternions, Clifford algebras and relativistic physics'), (8747, 'Computer Vision: Algorithms and Applications'), (8748, 'SIGGRAPH 2003, San Diego'), (8749, 'http://arxiv.org/abs/1206.2943'), (8750, '2012-10-00 10/2012'), (8751, 'arXiv:1206.2943 [gr-qc]'), (8752, '10.1103/PhysRevD.86.084054'), (8753, '2014-01-16 22:01:46'), (8754, 'Initial data for numerical evolutions of binary-black holes have been dominated by "conformally flat" (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated "conformally curved" initial data (i.e., initial data in which the background metric is \\emph{not} explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild (SKS) black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using SKS initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within $\\delta \\phi \\lesssim 10^{-2}$ radians and the amplitudes agree to within $\\delta A/A \\lesssim 5 \\times 10^{-3}$, which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in $10^{5}'), (8755, 'Are different approaches to constructing initial data for binary black hole simulations of the same astrophysical situation equivalent?'), (8756, 'http://www.arxiv.org/pdf/1206.2943.pdf'), (8757, '1206.2943 PDF'), (8758, 'http://arxiv.org/abs/1401.3789'), (8759, 'arXiv:1401.3789 [gr-qc]'), (8760, '2014-01-15 2014-01-15'), (8761, '2014-01-17 15:16:49'), (8762, 'We give an elementary proof of positivity of the Trautman-Bondi mass of light-cones with complete generators.'), (8763, 'The mass of light-cones'), (8764, 'http://www.arxiv.org/pdf/1401.3789.pdf'), (8765, '1401.3789 PDF'), (8766, 'http://www.lboro.ac.uk/microsites/maths/research/preprints/papers04/04-35.pdf'), (8767, '2014-01-18 05:24:32'), (8768, '04-35.pdf'), (8769, 'Derivative formulas and errors for non-uniformly spaced points'), (8770, 'http://arxiv.org/abs/1401.4548'), (8771, 'arXiv:1401.4548 [astro-ph, physics:gr-qc, physics:hep-th, physics:math-ph]'), (8772, '2014-01-18 2014-01-18'), (8773, '2014-01-21 14:39:44'), (8774, 'We complete the analytical determination, at the 4th post-Newtonian (4PN) approximation, of the conservative dynamics of gravitationally interacting two-point-mass systems. This completion is obtained by resolving the infra-red ambiguity which had blocked a previous 4PN calculation [P.Jaranowski and G.Sch\\"afer, Phys. Rev. D 87, 081503(R) (2013)] by taking into account the 4PN breakdown of the usual near-zone expansion due to infinite-range tail-transported temporal correlations found long ago [L.Blanchet and T.Damour, Phys. Rev. D 37, 1410 (1988)]. This leads to a Poincar\\\'e-invariant 4PN-accurate effective action for two masses, which mixes instantaneous interaction terms (described by a usual Hamiltonian) with a (time-symmetric) non-local-in-time interaction.'), (8775, 'Non-local-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems'), (8776, 'http://www.arxiv.org/pdf/1401.4548.pdf'), (8777, '1401.4548 PDF'), (8778, 'http://www.sciencemag.org/content/228/4706/1422'), (8779, 228), (8780, 4706), (8781, '1422-1423'), (8782, 'Science'), (8783, '0036-8075, 1095-9203'), (8784, '1985-06-21 06/21/1985'), (8785, 'PMID: 17814485'), (8786, '10.1126/science.228.4706.1422'), (8787, '2014-01-21 17:21:28'), (8788, 'www.sciencemag.org'), (8789, 'Spinor Calculus Spinors and Space-Time.'), (8790, 'Math. Ann.'), (8791, 'Sixth High-End Visualization Workshop'), (8792, 'amsmath guide.pdf'), (8793, '1695702.pdf'), (8794, 'http://link.aps.org/doi/10.1103/PhysRevD.81.084025'), (8795, '2010-04-14 April 14, 2010'), (8796, '10.1103/PhysRevD.81.084025'), (8797, '2014-01-24 04:08:12'), (8798, 'We establish the set of independent variables suitable to monitor the complicated evolution of the spinning compact binary during the inspiral. Our approach is valid up to the second post-Newtonian order, including leading order spin-orbit, spin-spin and mass quadrupole-mass monopole effects, for generic (noncircular, nonspherical) orbits. Then, we analyze the conservative spin dynamics in terms of these variables. We prove that the only binary black hole configuration allowing for spin precessions with equal angular velocities about a common instantaneous axis roughly aligned to the normal of the osculating orbit, is the equal mass and parallel (aligned or antialigned) spin configuration. This analytic result puts limitations on what particular configurations can be selected in numerical investigations of compact binary evolutions, even in those including only the last orbits of the inspiral.'), (8799, 'Spinning compact binary inspiral: Independent variables and dynamically preserved spin configurations'), (8800, 'Spinning compact binary inspiral'), (8801, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084025'), (8802, '10.1007/BF01457962'), (8803, '2014-02-15 22:20:01'), (8804, 'Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche'), (8805, 'http://www.sciencedirect.com/science/article/pii/0040938364900035'), (8806, '3, Supplement 1'), (8807, 'HopfFibration.pdf'), (8808, 'http://www.sciencedirect.com/science/article/pii/S0393044002001213'), (8809, '125-150'), (8810, 'Journal of Geometry and Physics'), (8811, '0393-0440'), (8812, '2003-05-00 May 2003'), (8813, '10.1016/S0393-0440(02)00121-3'), (8814, '2014-02-15 22:37:35'), (8815, 'It is pointed out that the Hopf fibration—a special but very basic non-trivial principal fiber bundle—occurs in at least seven different situations in theoretical physics in various guises. Surprisingly, the gauge theory aspect is in the minority here.'), (8816, 'The Hopf fibration—seven times in physics'), (8817, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044002001213/pdfft?md5=00beb14dc52536f62e26332c24c0f2ba&pid=1-s2.0-S0393044002001213-main.pdf'), (8818, '3-38'), (8819, '0040-9383'), (8820, '1964-07-00 July 1964'), (8821, '10.1016/0040-9383(64)90003-5'), (8822, '2014-03-01 21:03:21'), (8823, 'Clifford modules'), (8824, 'http://www.sciencedirect.com/science/article/pii/0040938364900035/pdf?md5=f55e052338189ca79550217063b0aedf&pid=1-s2.0-0040938364900035-main.pdf'), (8825, 'arXiv:1403.6915 [astro-ph, physics:gr-qc]'), (8826, 'http://arxiv.org/abs/0805.0311'), (8827, '2014-03-27 2014-03-27'), (8828, '2014-04-01 20:43:58'), (8829, 'Clifford Algebras, Clifford Groups, and a Generalization of the Quaternions'), (8830, 'arXiv:0805.0311 [math]'), (8831, '2008-05-02 2008-05-02'), (8832, '2014-03-01 21:13:46'), (8833, "One of the main goals of these notes is to explain how rotations in reals^n are induced by the action of a certain group, Spin(n), on reals^n, in a way that generalizes the action of the unit complex numbers, U(1), on reals^2, and the action of the unit quaternions, SU(2), on reals^3 (i.e., the action is defined in terms of multiplication in a larger algebra containing both the group Spin(n) and reals^n). The group Spin(n), called a spinor group, is defined as a certain subgroup of units of an algebra, Cl_n, the Clifford algebra associated with reals^n. Since the spinor groups are certain well chosen subgroups of units of Clifford algebras, it is necessary to investigate Clifford algebras to get a firm understanding of spinor groups. These notes provide a tutorial on Clifford algebra and the groups Spin and Pin, including a study of the structure of the Clifford algebra Cl_{p, q} associated with a nondegenerate symmetric bilinear form of signature (p, q) and culminating in the beautiful ``8-periodicity theorem'' of Elie Cartan and Raoul Bott (with proofs)."), (8834, 'http://www.arxiv.org/pdf/0805.0311.pdf'), (8835, '0805.0311 PDF'), (8836, 'Plzen (Pilsen), University of West Bohemia, Czech Republic'), (8837, 'UNION Agency, Na Mazinach 9, CZ 322 00 Plzen, Czech Republic'), (8838, '978-80-86943-90-9'), (8839, 'Using Geometric Algebra for Navigation in Riemannian and Hard Disc Space'), (8840, 'GraVisMa 2009 - Computer Graphics, Vision and Mathematics for Scientific Computing'), (8841, 'Using Geometric Algebra for Navigation in Riemannina and Hard Disc Space.pdf'), (8842, 'This paper reports on some issues encountered when preparing the wealth of geometric algebra for its application in the computer sciences. They involve simply making the internal structure explicit (section 2.2); redesigning the operators (even the rather basic inner product can be improved, in section 2.3); the development of new techniques to enable the user to adapt the structure to his or her needs (section 2.4); and making mathematical isomorphisms explicit in applicable operators (section 2.5)'), (8843, 'Honing Geometric Algebra for Its Use in the Computer Sciences'), (8844, 'http://link.springer.com/article/10.1007/BF01877755'), (8845, '132-136'), (8846, '1971-06-01 1971/06/01'), (8847, 'Commun.Math. Phys.'), (8848, '10.1007/BF01877755'), (8849, '2014-03-03 04:14:50'), (8850, "Spherical functions of the Lorentz group with respect to the horyspheric subgroup are derived and their relation to Gelfand's homogeneous functions are discussed."), (8851, 'Spherical functions of the Lorentz group on the two dimensional complex sphere of zero radius'), (8852, 'VizWorkshop2010_Seybold.pdf'), (8853, 'BMS-374.pdf'), (8854, 'http://131.220.132.179/people/biblio/downloads/bms/BMS-374.pdf'), (8855, '179-192'), (8856, 'Mathematisches Institut der Universität'), (8857, '2014-03-03 04:17:00'), (8858, 'Gelfand pairs'), (8859, 'art%3A10.1007%2FBF01877755.pdf'), (8860, 'http://arxiv.org/abs/1403.0544'), (8861, 'arXiv:1403.0544 [astro-ph, physics:gr-qc]'), (8862, '2014-03-03 2014-03-03'), (8863, '2014-03-04 13:58:30'), (8864, 'Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binary\'s nature and inspiral kinematics. Using the lalinference\\_mcmc Markov-chain Monte Carlo parameter estimation code, we use two fiducial examples to illustrate how the geometry and kinematics are encoded into the modulated gravitational wave signal, using coordinates well-adapted to precession. Even for precessing binaries, we show the performance of detailed parameter estimation can be estimated by "effective" estimates: comparisons of a prototype signal with its nearest neighbors, adopting a fixed sky location and idealized two-detector network. We use detailed and effective approaches to show higher harmonics provide nonzero but small local improvement when estimating the parameters of precessing BH-NS binaries. That said, we show higher harmonics can improve parameter estimation accuracy for precessing binaries ruling out approximately-degenerate source orientations. Our work illustrates quantities gravitational wave measurements can provide, such as reliable component masses and the precise orientation of a precessing short gamma ray burst progenitor relative to the line of sight. "Effective" estimates may provide a simple way to estimate trends in the performance of parameter estimation for generic precessing BH-NS binaries in next-generation detectors. For example, our results suggest that the orbital chirp rate, precession rate, and precession geometry are roughly-independent observables, defining natural variables to organize correlations in the high-dimensional BH-NS binary parameter space.'), (8865, 'Parameter Estimation of Gravitational Waves from Precessing BH-NS Inspirals with higher harmonics'), (8866, 'http://www.arxiv.org/pdf/1403.0544.pdf'), (8867, '1403.0544 PDF'), (8868, 'http://arxiv.org/abs/1403.0129'), (8869, 'arXiv:1403.0129 [gr-qc]'), (8870, '2014-03-01 2014-03-01'), (8871, '2014-03-04 14:02:06'), (8872, "Compact binary coalescences are the most promising sources of gravitational waves (GWs) for ground based detectors. Binary systems containing one or two spinning black holes are particularly interesting due to spin-orbit (and eventual spin-spin) interactions, and the opportunity of measuring spins directly through GW observations. In this letter we analyze simulated signals emitted by spinning binaries with several values of masses, spins, orientation, and signal-to-noise ratio. We find that spin magnitudes and tilt angles can be estimated to accuracy of a few percent for neutron star--black hole systems and $\\sim$ 5-30% for black hole binaries. In contrast, the difference in the azimuth angles of the spins, which may be used to check if spins are locked into resonant configurations, cannot be constrained. We observe that the best performances are obtained when the line of sight is perpendicular to the system's total angular momentum, and that a sudden change of behavior occurs when a system is observed from angles such that the plane of the orbit can be seen both from above and below during the time the signal is in band. This study suggests that the measurement of black hole spin by means of GWs can be as precise as what can be obtained from X-ray binaries."), (8873, 'Measuring the spin of black holes in binary systems using gravitational waves'), (8874, 'http://www.arxiv.org/pdf/1403.0129.pdf'), (8875, '1403.0129 PDF'), (8876, 'http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.17.9599&rep=rep1&type=pdf'), (8877, '2014-04-07 15:18:04'), (8878, 'http://arxiv.org/abs/0810.2412'), (8879, 'arXiv:0810.2412 [math-ph]'), (8880, '2008-10-14 2008-10-14'), (8881, '2014-04-07 16:02:01'), (8882, 'The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, a package for Clifford algebra calculations for the computer algebra program Mathematica is introduced through a presentation of the main ideas of Clifford algebras and illustrative examples. This package can be a useful computational tool since allows the manipulation of all these mathematical objects. It also includes the possibility of visualize elements of a Clifford algebra in the 3-dimensional space.'), (8883, 'Clifford Algebra with Mathematica'), (8884, 'http://www.arxiv.org/pdf/0810.2412.pdf'), (8885, '0810.2412 PDF'), (8886, 'http://link.aps.org/doi/10.1103/PhysRevD.59.124022'), (8887, '1999-05-21 May 21, 1999'), (8888, '10.1103/PhysRevD.59.124022'), (8889, '2014-03-01 2014/03/01'), (8890, 'Geometric Algebra with Applications in Engineering'), (8891, '2014-04-07 18:41:00'), (8892, 'We investigate higher than the first order gravitational perturbations in the Newman-Penrose formalism. Equations for the Weyl scalar ψ4, representing outgoing gravitational radiation, can be uncoupled into a single wave equation to any perturbative order. For second order perturbations about a Kerr black hole, we prove the existence of a first and second order gauge (coordinates) and tetrad invariant waveform, ψI, by explicit construction. This waveform is formed by the second order piece of ψ4 plus a term, quadratic in first order perturbations, chosen to make ψI totally invariant and to have the appropriate behavior in an asymptotically flat gauge. ψI satisfies a single wave equation of the form 𝒯ψI=S, where 𝒯 is the same wave operator as for first order perturbations and S is a source term build up out of (known to this level) first order perturbations. We discuss the issues of imposition of initial data to this equation, computation of the energy and momentum radiated and wave extraction for direct comparison with full numerical approaches to solve Einstein equations.'), (8893, 'Second order gauge invariant gravitational perturbations of a Kerr black hole'), (8894, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.59.124022'), (8895, 'Adv. Appl. Clifford Algebras'), (8896, 'EmbeddedWorld2013-GAComputingForAPUs.pdf'), (8897, 'http://www.gaalop.de/wp-content/uploads/EmbeddedWorld2013-GAComputingForAPUs.pdf'), (8898, '2014-04-10 02:41:35'), (8899, 'Geometric Algebra Computing Technology for Accelerated Processing Units'), (8900, '10.1007/s00006-013-0424-2'), (8901, 'http://arxiv.org/abs/0809.4526'), (8902, 'arXiv:0809.4526 [math]'), (8903, '2008-09-25 2008-09-25'), (8904, '2014-04-13 15:05:33'), (8905, "A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green's and Stokes' theorem are discussed, as well as the new theory of monogenic functions, which generalizes the concept of an analytic function of a complex variable to higher dimensions."), (8906, 'Fundamental Theorem of Calculus'), (8907, 'http://www.arxiv.org/pdf/0809.4526.pdf'), (8908, '0809.4526 PDF'), (8909, '2014-03-11 17:38:27'), (8910, 'http://arxiv.org/abs/1404.3180'), (8911, 'arXiv:1404.3180 [gr-qc]'), (8912, '2014-04-11 2014-04-11'), (8913, '2014-04-15 15:39:36'), (8914, 'In this paper, we examine eigenvalue problem of a rotation matrix in Minkowski 3 space by using split quaternions. We express the eigenvalues and the eigenvectors of a rotation matrix in term of the coefficients of the corresponding unit timelike split quaternion. We give the characterizations of eigenvalues (complex or real) of a rotation matrix in Minkowski 3 space according to only first component of the corresponding quaternion. Moreover, we find that the casual characters of rotation axis depend only on first component of the corresponding quaternion. Finally, we give the way to generate an orthogonal basis for 𝔼31{\\mathbb{E}^{3}_{1}} by using eigenvectors of a rotation matrix.'), (8915, 'We study the performance of various analytical frequency-domain templates for detection and parameter estimation of gravitational waves from spin-precessing, quasi-circular, compact binary inspirals. We begin by assessing the extent to which non-spinning, spin-aligned, and the new (analytical, frequency-domain, small-spin) double-precessing frequency-domain templates can be used to detect signals from such systems. For effective, dimensionless spin values above $0.2$, the use of non-spinning or spin-aligned templates for detection purposes will result in a loss of up to $30%$ of all events, while in the case of the double-precessing model, this never exceeds $6%$. Moreover, even for signals from systems with small spins, non-spinning and spin-aligned templates introduce large biases in the extracted masses and spins. The use of a model that encodes spin-induced precession effects, such as the double-precessing model, improves the mass and spin extraction by up to an order of magnitude. The additional information encoded in the spin-orbit interaction is invaluable if one wishes to extract the maximum amount of information from gravitational wave signals.'), (8916, 'Detection and Parameter Estimation of Gravitational Waves from Compact Binary Inspirals with Analytical Double-Precessing Templates'), (8917, 'http://www.arxiv.org/pdf/1404.3180.pdf'), (8918, '1404.3180 PDF'), (8919, 'On the Eigenvalues and Eigenvectors of a Lorentzian Rotation Matrix by Using Split Quaternions'), (8920, 'http://arxiv.org/abs/1404.3197'), (8921, 'arXiv:1404.3197 [gr-qc]'), (8922, '2014-04-15 15:39:57'), (8923, 'While black hole perturbation theory predicts a rich quasi-normal mode structure, technical challenges have limited the numerical study of excitations to the fundamental, lowest order modes caused by the coalescence of black holes. Here, we present a robust method to identify quasi-normal mode excitations beyond the fundamentals within currently available numerical relativity waveforms. In applying this method to waveforms of initially non-spinning black hole binaries, of mass ratios 1 to 15, we find not only the fundamental quasi-normal mode amplitudes, but also overtones, and evidence for 2nd order quasi-normal modes. We find that the mass-ratio dependence of quasi-normal mode excitation is very well modeled by a Post-Newtonian like sum in symmetric mass ratio. Concurrently, we find that the mass ratio dependence of some quasi-normal modes is qualitatively different from their Post-Newtonian inspired counterparts, suggesting that the imprints of nonlinear merger are more evident in some modes than in others. We present new fitting formulas for the related quasi-normal mode excitations, as well as for remnant black hole spin and mass. We also discuss the relevance of our results in terms of gravitational wave detection and characterization.'), (8924, '1584887729.pdf'), (8925, 'Modeling Ringdown: Beyond the Fundamental Quasi-Normal Modes'), (8926, 'Modeling Ringdown'), (8927, 'http://www.arxiv.org/pdf/1404.3197.pdf'), (8928, '1404.3197 PDF'), (8929, 'art%3A10.1007%2Fs00006-013-0424-2.pdf'), (8930, 'http://arxiv.org/abs/1307.4418'), (8931, '2013-09-00 9/2013'), (8932, 'arXiv:1307.4418 [gr-qc]'), (8933, '10.1103/PhysRevD.88.063011'), (8934, 'Taylor & Francis'), (8935, '2014-04-15 16:20:48'), (8936, 'We obtain analytical gravitational waveforms in the frequency-domain for precessing, quasi-circular compact binaries with small spins, applicable, for example, to binary neutron star inspirals. We begin by calculating an analytic solution to the precession equations, obtained by expanding in the dimensionless spin parameters and using multiple-scale analysis to separate timescales. We proceed by analytically computing the Fourier transform of time-domain waveform through the stationary phase approximation. We show that the latter is valid for systems with small spins. Finally, we show that these waveforms have a high overlap with numerical waveforms obtained through direct integration of the precession equations and discrete Fourier transformations. The resulting, analytic waveform family is ideal for detection and parameter estimation of gravitational waves emitted by inspiraling binary neutron stars with ground-based detectors.'), (8937, '1584887729 9781584887720'), (8938, 'Gravitational Waveforms for Precessing, Quasicircular Compact Binaries with Multiple Scale Analysis: Small Spin Expansion'), (8939, 'Gravitational Waveforms for Precessing, Quasicircular Compact Binaries with Multiple Scale Analysis'), (8940, 'http://www.arxiv.org/pdf/1307.4418.pdf'), (8941, '1307.4418 PDF'), (8942, 'http://arxiv.org/abs/1305.1932'), (8943, 'arXiv:1305.1932 [astro-ph, physics:gr-qc]'), (8944, '2013-05-08 2013-05-08'), (8945, '2014-04-15 16:20:52'), (8946, 'We calculate analytical gravitational waveforms in the time- and frequency-domain for precessing quasi-circular binaries with spins of arbitrary magnitude, but nearly aligned with the orbital angular momentum. We first derive an analytical solution to the precession equations by expanding in the misalignment angle and using multiple scale analysis to separate timescales. We then use uniform asymptotic expansions to analytically Fourier transform the time-domain waveform, thus extending the stationary-phase approximation, which fails when precession is present. The resulting frequency-domain waveform family has a high overlap with numerical waveforms obtained by direct integration of the post-Newtonian equations of motion and discrete Fourier transformations. Such a waveform family lays the foundations for the accurate inclusion of spin precession effects in analytical gravitational waveforms, and thus, it can aid in the detection and parameter estimation of gravitational wave signals from the inspiral phase of precessing binary systems.'), (8947, 'http://www.springer.com/computer/image+processing/book/978-3-540-89067-6'), (8948, '2014-03-04 17:42:25'), (8949, 'www.springer.com'), (8950, 'The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will ...'), (8951, 'bok%3A978-3-540-89068-3.pdf'), (8952, 'Addison Wesley Longman'), (8953, '0201021153'), (8954, '1970-01-01 January 1, 1970'), (8955, '2014-03-27 12:15:22'), (8956, 'Gravitational Waveforms for Precessing, Quasi-circular Binaries via Multiple Scale Analysis and Uniform Asymptotics: The Near Spin Alignment Case'), (8957, 'Gravitational Waveforms for Precessing, Quasi-circular Binaries via Multiple Scale Analysis and Uniform Asymptotics'), (8958, "The first direct observation of gravitational waves' action upon matter has recently been reported by the BICEP2 experiment. Advanced ground-based gravitational-wave detectors are being installed. They will soon be commissioned, and then begin searches for high-frequency gravitational waves at a sensitivity level that is widely expected to reach events involving compact objects like stellar mass black holes and neutron stars. Pulsar timing arrays continue to improve the bounds on gravitational waves at nanohertz frequencies, and may detect a signal on roughly the same timescale as ground-based detectors. The science case for space-based interferometers targeting millihertz sources is very strong. The decade of gravitational-wave discovery is poised to begin. In this writeup of a talk given at the 2013 TAUP conference, we will briefly review the physics of gravitational waves and gravitational-wave detectors, and then discuss the promise of these measurements for making cosmological measurements in the near future."), (8959, 'The Feynman Lectures on Physics'), (8960, 'http://arxiv.org/abs/1403.0677'), (8961, 'arXiv:1403.0677 [astro-ph]'), (8962, '2014-03-05 21:26:03'), (8963, 'If binaries consisting of two 100 Msun black holes exist they would serve as extraordinarily powerful gravitational-wave sources, detectable to redshifts of z=2 with the advanced LIGO/Virgo ground-based detectors. Large uncertainties about the evolution of massive stars preclude definitive rate predictions for mergers of these massive black holes. We show that rates as high as hundreds of detections per year, or as low as no detections whatsoever, are both possible. It was thought that the only way to produce these massive binaries was via dynamical interactions in dense stellar systems. This view has been challenged by the recent discovery of several stars with mass greater than 150 Msun in the R136 region of the Large Magellanic Cloud. Current models predict that when stars of this mass leave the main sequence, their expansion is insufficient to allow common envelope evolution to efficiently reduce the orbital separation. The resulting black-hole--black-hole binary remains too wide to be able to coalesce within a Hubble time. If this assessment is correct, isolated very massive binaries do not evolve to be gravitational-wave sources. However, other formation channels exist. For example, the high multiplicity of massive stars, and their common formation in relatively dense stellar associations, opens up dynamical channels for massive black hole mergers (e.g., via Kozai cycles or repeated binary-single interactions). We identify key physical factors that shape the population of very massive black-hole--black-hole binaries. Advanced gravitational-wave detectors will provide important constraints on the formation and evolution of very massive stars.'), (8964, 'The Formation and Gravitational-Wave Detection of Massive Stellar Black-Hole Binaries'), (8965, 'http://www.arxiv.org/pdf/1403.0677.pdf'), (8966, '1403.0677 PDF'), (8967, 'http://vizworkshop.cct.lsu.edu/viz2010/default/list_papers'), (8968, 'http://sourceforge.net/apps/trac/gaalet/'), (8969, '2014-03-07 03:40:33'), (8970, 'Gaalet'), (8971, '2014-03-07 03:40:35'), (8972, 'gaalet_tutorial_gravisma_2010.pdf'), (8973, 'http://www.gaalop.de/download/'), (8974, '2014-03-07 04:19:41'), (8975, 'Download | Gaalop'), (8976, 'GPC_Manual.pdf'), (8977, 'http://sourceforge.net/p/glucat/git/ci/master/tree/'), (8978, '2014-03-07 05:21:06'), (8979, 'GluCat: Clifford algebra templates / Code / [371660]'), (8980, '2014-03-07 05:21:08'), (8981, 'http://www.sciencedirect.com/science/article/pii/S016892741100081X'), (8982, '989-1000'), (8983, 'Applied Numerical Mathematics'), (8984, '0168-9274'), (8985, '2011-09-00 September 2011'), (8986, '10.1016/j.apnum.2011.05.001'), (8987, '2014-03-07 18:36:12'), (8988, 'In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of O(hd+1−k)O(hd+1−k) as h→0h→0, where d is the degree of the polynomial or spline. In this paper we establish, in the important cases k=1,2k=1,2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polynomial interpolants of degree d.'), (8989, 'Convergence rates of derivatives of a family of barycentric rational interpolants'), (8990, 'http://www.sciencedirect.com/science/article/pii/S016892741100081X/pdf?md5=fe9b54cede43def71cccfcf00ffa862e&pid=1-s2.0-S016892741100081X-main.pdf'), (8991, 'http://link.springer.com/chapter/10.1007/3-7643-7356-3_3'), (8992, '©2005 Birkhäuser Verlag'), (8993, 'ISNM International Series of Numerical Mathematics'), (8994, 'Birkhäuser Basel'), (8995, '27-51'), (8996, '978-3-7643-7124-1, 978-3-7643-7356-6'), (8997, '2014-03-07 19:08:58'), (8998, 151), (8999, 'In 1945, W. Taylor discovered the barycentric formula for evaluating the interpolating polynomial. In 1984, W. Werner has given first consequences of the fact that the formula usually is a rational interpolant. We review some advances since the latter paper in the use of the formula for rational interpolation.'), (9000, 'Recent Developments in Barycentric Rational Interpolation'), (9001, 'Trends and Applications in Constructive Approximation'), (9002, 'http://link.springer.com/content/pdf/10.1007%2F3-7643-7356-3_3.pdf'), (9003, 'http://epubs.siam.org/doi/abs/10.1137/110827156'), (9004, '643-656'), (9005, 'SIAM Journal on Numerical Analysis'), (9006, '0036-1429, 1095-7170'), (9007, '2012-01-00 01/2012'), (9008, '10.1137/110827156'), (9009, '2014-03-07 19:14:12'), (9010, 'Linear Rational Finite Differences from Derivatives of Barycentric Rational Interpolants'), (9011, 'http://dx.doi.org/10.1007/s00211-007-0093-y'), (9012, '315–331'), (9013, 'Numer. Math.'), (9014, '0029-599X'), (9015, '2007-08-00 August 2007'), (9016, '10.1007/s00211-007-0093-y'), (9017, '2014-03-07 19:19:50'), (9018, 'It is well known that rational interpolation sometimes gives better approximations than polynomial interpolation, especially for large sequences of points, but it is difficult to control the occurrence of poles. In this paper we propose and study a family of barycentric rational interpolants that have no real poles and arbitrarily high approximation orders on any real interval, regardless of the distribution of the points. These interpolants depend linearly on the data and include a construction of Berrut as a special case.'), (9019, 'Barycentric Rational Interpolation with No Poles and High Rates of Approximation'), (9020, '110827156.pdf'), (9021, 'http://link.springer.com/chapter/10.1007/11499251_19'), (9022, '©2005 Springer-Verlag Berlin Heidelberg'), (9023, 'Lecture Notes in Computer Science'), (9024, '229-238'), (9025, '978-3-540-26296-1, 978-3-540-32119-4'), (9026, '2014-03-09 22:54:27'), (9027, 'Averaging measured data is an important issue in computer vision and robotics. Integrating the pose of an object measured with multiple cameras into a single mean pose is one such example. In many applications data does not belong to a vector space. Instead, data often belongs to a non-linear group manifold as it is the case for orientation data and the group of three-dimensional rotations SO(3). Averaging on the manifold requires the utilization of the associated Riemannian metric resulting in a rather complicated task. Therefore the Euclidean mean with best orthogonal projection is often used as an approximation. In SO(3) this can be done by rotation matrices or quaternions. Clifford algebra as a generalization of quaternions allows a general treatment of such approximated averaging for all classical groups. Results for the two-dimensional Lorentz group SO(1,2) and the related groups SL(2,ℝ) and SU(1,1) are presented. The advantage of the proposed Clifford framework lies in its compactness and easiness of use.'), (9028, 'On Averaging in Clifford Groups'), (9029, 'Computer Algebra and Geometric Algebra with Applications'), (9030, 'Geometric algebra and applications to physics'), (9031, 'Averaging.pdf'), (9032, 'In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that the Riemannian mean rotation shares many common features with the geometric mean of positive numbers and the geometric mean of positive Hermitian operators. We give some examples with closed-form solutions of both notions of mean.'), (9033, 'Means and Averaging in the Group of Rotations'), (9034, 'http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.16.5040&rep=rep1&type=pdf'), (9035, '2014-03-10 05:04:28'), (9036, 'Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations.'), (9037, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/10/7/10.1063/1.1664958'), (9038, '1195-1203'), (9039, '2003-11-04 2003/11/04'), (9040, '2014-03-13 16:04:18'), (9041, 'Using the Newman‐Penrose formalism, the vacuum field equations are solved for Petrov type D. An exhaustive set of ten metrics is obtained, including among them a new rotating solution closely related to the Ehlers‐Kundt ``C'' metric. They all possess at least two Killing vectors and depend only on a small number of arbitrary constants.'), (9042, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/10/7/1.1664958.pdf?itemId=/content/aip/journal/jmp/10/7/10.1063/1.1664958&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (9043, 'http://epubs.siam.org.proxy.library.cornell.edu/doi/abs/10.1137/S0895479801383877'), (9044, '1-16'), (9045, 'SIAM Journal on Matrix Analysis and Applications'), (9046, '0895-4798, 1095-7162'), (9047, '2002-01-00 01/2002'), (9048, '10.1137/S0895479801383877'), (9049, '2014-03-17 14:22:06'), (9050, 's0895479801383877.pdf'), (9051, 'b2_respap_arxiv_v1.pdf'), (9052, 'b2_instr_arxiv_v1.pdf'), (9053, 'We investigate the effects of using the {\\it full} waveform (FWF) over the conventional {\\it restricted} waveform (RWF) of the inspiral signal from a coalescing compact binary (CCB) system in extracting the parameters of the source, using a global network of second generation interferometric detectors. We study a hypothetical population of (1.4-10)$M_\\odot$ NS-BH binaries (uniformly distributed and oriented in the sky) by employing the full post-Newtonian waveforms, which not only include contributions from various harmonics other than the dominant one (quadrupolar mode) but also the post-Newtonian amplitude corrections associated with each harmonic, of the inspiral signal expected from this system. It is expected that the GW detector network consisting of the two LIGO detectors and a Virgo detector will be joined by KAGRA and by proposed LIGO-India. We study the problem of parameter estimation with all 16 possible detector configurations. Comparing medians of error distributions obtained using FWFs with those obtained using RWFs (which only include contributions from the dominant harmonic with Newtonian amplitude) we find that the measurement accuracies for luminosity distance and the cosine of the inclination angle improve almost by a factor of 1.5-2 depending upon the network under consideration. Although the use of FWF does not improve the source localization accuracy much, the global network consisting of five detectors will improve the source localization accuracy by a factor of 4 as compared to the estimates using a 3 detector LIGO-Virgo network for the same waveform model.'), (9054, 'Bicep2 II: Experiment and three-year data set'), (9055, 'Biecp2 I: Detection of B-mode polarization at degree angular scales'), (9056, 'Volume 1 edition'), (9057, 'Wiley-VCH'), (9058, '0471504475'), (9059, '1989-01-04 January 4, 1989'), (9060, 'Methods of Mathematical Physics, Vol. 1'), (9061, 'Gravitational wave astronomy and cosmology'), (9062, 'http://www.arxiv.org/pdf/1405.0504.pdf'), (9063, 'CourantHilbert-MethodsOfMathematicalPhysicsVol.1.pdf'), (9064, 'http://link.aps.org/doi/10.1103/PhysRevD.89.021501'), (9065, 89), (9066, '021501'), (9067, '2014-01-06 January 6, 2014'), (9068, '10.1103/PhysRevD.89.021501'), (9069, '2014-03-19 13:18:41'), (9070, 'We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes |S⃗ 1,2/m21,2|=0.8) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, δJˆrad(t), to the directions of the total angular momentum, J^(t), and the orbital angular momentum, L^(t). We find that δJˆrad(t) approximately follows L^ throughout the evolution. During the orbital evolution and merger, we observe that the angle between L⃗ and total spin S⃗ is approximately conserved to within 1°, which allows us to propose and test models for the merger remnant’s mass and spin. For instance, we verify that the hang-up effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than ∼5∘. The maximum variation in the direction of J⃗ occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of J⃗ , is not possible for similar-mass binaries and would require a mass ratio m1/m2≲1/4.'), (9071, 'Where angular momentum goes in a precessing black-hole binary'), (9072, 'http://journals.aps.org/prd/pdf/10.1103/PhysRevD.89.021501'), (9073, 'http://arxiv.org/abs/1312.5775'), (9074, 'arXiv:1312.5775 [astro-ph, physics:gr-qc]'), (9075, '2013-12-19 2013-12-19'), (9076, '2014-03-19 13:19:05'), (9077, 'We perform a set of 38 numerical simulations of equal-mass black-hole binaries in a configuration where the two black-hole spins in the binary are equal in both magnitude and direction, to study precession effects. We vary the initial direction of the total spin S with respect to the orbital angular momentum L, covering the 2 dimensional space of orientation angles with 38 configurations. In all cases, we set the initial dimensionless black-hole spins to 0.8. We observe that during the late-inspiral stage, the total angular momentum of the system J remains within 5 deg. of its original direction, with the largest changes in direction occurring when the spins are nearly (but not exactly) counter-aligned with the orbital angular momentum. We also observe that the angle between S and L is nearly conserved during the inspiral phase. These two dynamical properties allow us to propose a new phenomenological formula for the final mass and spin of merged black holes in terms of the individual masses and spins of the progenitor binary at far separations. We determine coefficients of this formula (in the equal-mass limit) using a least-squared fit to the results of this new set of 38 runs, an additional set of five new configurations with spins aligned/counteraligned with the orbital angular momentum, and over a hundred recent simulations. We find that our formulas reproduce the remnant mass and spin of these simulations to within a relative error of 2.5%. We discuss the region of validity of this dynamical picture for precessing unequal-mass binaries. Finally, we perform a statistical study to see the consequence of this new formula for distributions of spin-magnitudes and remnant masses with applications to black-hole-spin distributions and gravitational radiation in cosmological scenarios involving several mergers.'), (9078, 'Black-Hole Binary Remnant Mass and Spin Revisited: A New Phenomenological Formula'), (9079, 'Black-Hole Binary Remnant Mass and Spin Revisited'), (9080, 'http://www.arxiv.org/pdf/1312.5775.pdf'), (9081, '1312.5775 PDF'), (9082, 'Parameter estimation of neutron star-black hole binaries using an advanced gravitational-wave detector network: Effects of the full post-Newtonian waveform'), (9083, 'Parameter estimation of neutron star-black hole binaries using an advanced gravitational-wave detector network'), (9084, 'http://www.arxiv.org/pdf/1403.6915.pdf'), (9085, '1403.6915 PDF'), (9086, 'http://arxiv.org/abs/1308.3271'), (9087, 'arXiv:1308.3271 [gr-qc]'), (9088, '2013-08-14 2013-08-14'), (9089, '2014-04-02 19:45:59'), (9090, 'The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger and ringdown, is one of the most pressing theoretical problems in the build-up to the era of GW astronomy. We present such a model, "PhenomP", which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three physical parameters. Essentially, we simply "twist up" a two-parameter non-precessing-binary model with approximate expressions for the precessional motion, which require only one additional physical parameter, an effective precession spin. The model is constructed in the frequency domain, which will be essential for efficient GW searches and source measurements. We have tested the model\'s fidelity for GW applications by comparison against hybrid post-Newtonian-numerical-relativity waveforms at a variety of configurations - although we did not use these numerical simulations in the construction of the model. Our model can be used to develop GW searches, to study the implications for astrophysical measurements, and, perhaps most importantly, as a simple conceptual framework to form the basis of generic-binary waveform modelling in the advanced-detector era.'), (9091, 'Twist and shout: A simple model of complete precessing black-hole-binary gravitational waveforms'), (9092, 'Twist and shout'), (9093, 'http://www.arxiv.org/pdf/1308.3271.pdf'), (9094, '1308.3271 PDF'), (9095, 'http://link.aps.org/doi/10.1103/PhysRevLett.111.241104'), (9096, 111), (9097, 241104), (9098, '2013-12-11 December 11, 2013'), (9099, '10.1103/PhysRevLett.111.241104'), (9100, '2014-04-03 20:02:26'), (9101, 'This Letter presents a publicly available catalog of 174 numerical binary black hole simulations following up to 35 orbits. The catalog includes 91 precessing binaries, mass ratios up to 8∶1, orbital eccentricities from a few percent to 10−5, black hole spins up to 98% of the theoretical maximum, and radiated energies up to 11.1% of the initial mass. We establish remarkably good agreement with post-Newtonian precession of orbital and spin directions for two new precessing simulations, and we discuss other applications of this catalog. Formidable challenges remain: e.g., precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.'), (9102, 'Catalog of 174 Binary Black Hole Simulations for Gravitational Wave Astronomy'), (9103, 'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.111.241104'), (9104, 'http://link.aps.org/doi/10.1103/PhysRevD.88.124010'), (9105, 124010), (9106, '2013-12-03 December 3, 2013'), (9107, '10.1103/PhysRevD.88.124010'), (9108, '2014-04-03 21:27:05'), (9109, 'We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar Ψ4 at a finite distance from the source and Cauchy-characteristic extraction (CCE). The direct NP approach is simpler than CCE, but NP waveforms can be contaminated by near-zone effects—unless the waves are extracted at several distances from the source and extrapolated to infinity. Even then, the resulting waveforms can in principle be contaminated by gauge effects. In contrast, CCE directly provides, by construction, gauge-invariant waveforms at future null infinity. We verify the gauge invariance of CCE by running the same physical simulation using two different gauge conditions. We find that these two gauge conditions produce the same CCE waveforms but show differences in extrapolated-Ψ4 waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-Ψ4 and CCE waveforms. In some cases, we find that NP waveforms extrapolated to infinity agree with the corresponding CCE waveforms to within the estimated error bars. However, we find that in other cases extrapolated and CCE waveforms disagree, most notably for m=0 “memory” modes.'), (9110, 'Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations'), (9111, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.124010'), (9112, 'http://www.jstor.org/stable/2949580'), (9113, 'Copyright © 1970 Society for Industrial and Applied Mathematics'), (9114, '1-46'), (9115, '1970-03-01 March 1, 1970'), (9116, '2014-04-04 21:34:39'), (9117, 'When a Hermitian linear operator is slightly perturbed, by how much can its invariant subspaces change? Given some approximations to a cluster of neighboring eigenvalues and to the corresponding eigenvectors of a real symmetric matrix, and given an estimate for the gap that separates the cluster from all other eigenvalues, how much can the subspace spanned by the eigenvectors differ from the subspace spanned by our approximations? These questions are closely related; both are investigated here. The difference between the two subspaces is characterized in terms of certain angles through which one subspace must be rotated in order most directly to reach the other. These angles unify the treatment of natural geometric, operator-theoretic and error-analytic questions concerning those subspaces. Sharp bounds upon trigonometric functions of these angles are obtained from the gap and from bounds upon either the perturbation (1st question) or a computable residual (2nd question). An example is included.'), (9118, 'The Rotation of Eigenvectors by a Perturbation. III'), (9119, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2949580.pdf?acceptTC=true'), (9120, 'http://www.arxiv.org/pdf/1305.1932.pdf'), (9121, '1305.1932 PDF'), (9122, 'We present the three main mathematical constructs used to represent the attitude of a rigid body in threedimensional space. These are (1) the rotation matrix, (2) a triple of Euler angles, and (3) the unit quaternion. To these we add a fourth, the rotation vector, which has many of the benefits of both Euler angles and quaternions, but neither the singularities of the former, nor the quadratic constraint of the latter. There are several other subsidiary representations, such as Cayley-Klein parameters and the axis-angle representation, whose relations to the three main representations are also described. Our exposition is catered to those who seek a thorough and unified reference on the whole subject; detailed derivations of some results are not presented.'), (9123, 'Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors'), (9124, 'Representing Attitude'), (9125, 'http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.110.5134&rep=rep1&type=pdf'), (9126, '2014-04-17 20:11:19'), (9127, '1405.0504 PDF'), (9128, 'http://arxiv.org/abs/1405.1572'), (9129, 'arXiv:1405.1572 [gr-qc]'), (9130, '2014-05-07 2014-05-07'), (9131, '2014-05-08 14:50:12'), (9132, '(Abridged) High-order terms in the post-Newtonian (PN) expansions of various quantities for compact binaries exhibit a combinatorial increase in complexity, including ever-increasing numbers of transcendentals. Here we consider the gravitational wave energy flux at infinity from a point particle in a circular orbit around a Schwarzschild black hole, which is known to 22PN beyond the lowest-order Newtonian prediction, at which point each order has over 1000 terms. We introduce a factorization that considerably simplifies the spherical harmonic modes of the energy flux (and thus also the amplitudes of the spherical harmonic modes of the gravitational waves); it is likely that much of the complexity this factorization removes is due to curved-space wave propagation (e.g., tail effects). For the modes with azimuthal number l of 7 or greater, this factorization reduces the expressions for the modes that enter the 22PN total energy flux to pure integer PN series with rational coefficients, which amounts to a reduction of up to a factor of ~150 in the total number of terms in a given mode. The reduction in complexity becomes less dramatic for smaller l, due to the structure of the expansion, though the factorization is still able to remove all the half-integer PN terms. For the 22PN l = 2 modes, this factorization still reduces the total number of terms (and size) by a factor of ~10 and gives purely rational coefficients through 8PN. This factorization also improves the convergence of the series, though we find the exponential resummation introduced for the full energy flux by Isoyama et al. to be even more effective at improving the convergence of the individual modes, producing improvements of over four orders of magnitude over the original series for some modes. However, the exponential resummation is not as effective at simplifying the series, particularly for the higher-order modes.'), (9133, 'Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole'), (9134, 'Taming the post-Newtonian expansion'), (9135, 'http://www.arxiv.org/pdf/1405.1572.pdf'), (9136, '1405.1572 PDF'), (9137, 'http://arxiv.org/abs/1004.0679'), (9138, '2010-05-00 5/2010'), (9139, 'arXiv:1004.0679 [gr-qc, physics:physics]'), (9140, '10.1103/PhysRevD.81.104012'), (9141, '2014-05-08 18:12:26'), (9142, 'We study systems analogous to binary black holes with spin in order to gain some insight into the origin and nature of "bobbing" motion and "kicks" that occur in this system. Our basic tool is a general formalism for describing the motion of extended test bodies in an external electromagnetic field in curved spacetime and possibly subject to other forces. We first show that bobbing of exactly the type as observed in numerical simulations of the binary black hole system occurs in a simple system consisting of two spinning balls connected by an elastic band in flat spacetime. This bobbing may be understood as arising from the difference between a spinning body\'s "lab frame centroid" and its true center of mass, and is purely "kinematical" in the sense that it will appear regardless of the forces holding two spinning bodies in orbit. Next, we develop precise rules for relating the motion of charged bodies in a stationary external electromagnetic field in flat spacetime with the motion of bodies in a weakly curved stationary spacetime. We then consider the system consisting of two orbiting charges with magnetic dipole moment and spin at a level of approximation corresponding to 1.5 post-Newtonian order. Here we find that considerable amounts of momentum are exchanged between the bodies and the electromagnetic field; however, the bodies store this momentum entirely as "hidden" mechanical momentum, so that the interchange does not give rise to any net bobbing. The net bobbing that does occur is due solely to the kinematical spin effect, and we therefore argue that the net bobbing of the electromagnetic binary is not associated with possible kicks. We believe that this conclusion holds in the gravitational case as well.'), (9143, 'Bobbing and Kicks in Electromagnetism and Gravity'), (9144, 'http://www.arxiv.org/pdf/1004.0679.pdf'), (9145, '1004.0679 PDF'), (9146, 'http://link.aps.org/doi/10.1103/PhysRevLett.98.231102'), (9147, 231102), (9148, '2007-06-07 June 7, 2007'), (9149, '10.1103/PhysRevLett.98.231102'), (9150, '2014-05-11 20:48:21'), (9151, 'Recent calculations of gravitational radiation recoil generated during black-hole binary mergers have reopened the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy. Here we report the first systematic study of gravitational recoil of equal-mass binaries with equal, but counteraligned, spins parallel to the orbital plane. Such an orientation of the spins is expected to maximize the recoil. We find that recoil velocity (which is perpendicular to the orbital plane) varies sinusoidally with the angle that the initial spin directions make with the initial linear momenta of each hole and scales up to a maximum of ∼4000 km s−1 for maximally rotating holes. Our results show that the amplitude of the recoil velocity can depend sensitively on spin orientations of the black holes prior to merger.'), (9152, 'Maximum Gravitational Recoil'), (9153, 'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.98.231102'), (9154, 'http://iopscience.iop.org/1538-4357/659/1/L5'), (9155, 659), (9156, 'L5'), (9157, '1538-4357'), (9158, '2007-04-10 2007-04-10'), (9159, '10.1086/516712'), (9160, '2014-05-11 20:51:31'), (9161, 'We report the first results from the evolution of generic black hole binaries, i.e., binaries containing unequal-mass black holes with misaligned spins. Our configuration, which has a mass ratio of 2 : 1, consists of an initially nonspinning hole orbiting a larger, rapidly spinning hole (specific spin a/m = 0.885), with the spin direction oriented -45° with respect to the orbital plane. We track the inspiral and merger for ~2 orbits and find that the remnant receives a substantial kick of 454 km s-1, more than twice as large as the maximum kick from nonspinning binaries. The remnant spin direction is flipped by 103° with respect to the initial spin direction of the larger hole. We performed a second run with antialigned spins, a/m = ±0.5 lying in the orbital plane that produces a kick of ~1830 km s-1 off the orbital plane. This value scales to nearly 4000 km s-1 for maximally spinning holes. Such a large recoil velocity opens up the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy.'), (9162, 'Large Merger Recoils and Spin Flips from Generic Black Hole Binaries'), (9163, 'http://iopscience.iop.org/1538-4357/659/1/L5/pdf/1538-4357_659_1_L5.pdf'), (9164, 'http://link.aps.org/doi/10.1103/PhysRevLett.98.231101'), (9165, '10.1103/PhysRevLett.98.231101'), (9166, '2014-05-11 20:52:23'), (9167, 'Recent calculations of the recoil velocity in binary black-hole mergers have found the kick velocity to be of the order of a few hundred km/s in the case of nonspinning binaries and about 500 km/s in the case of spinning configurations, and have lead to predictions of a maximum kick of up to 1300 km/s. We test these predictions and demonstrate that kick velocities of at least 2500 km/s are possible for equal-mass binaries with antialigned spins in the orbital plane. Kicks of that magnitude are likely to have significant repercussions for models of black-hole formation, the population of intergalactic black holes, and the structure of host galaxies.'), (9168, 'Supermassive Recoil Velocities for Binary Black-Hole Mergers with Antialigned Spins'), (9169, 'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.98.231101'), (9170, 'http://link.aps.org/doi/10.1103/PhysRevD.80.044010'), (9171, '044010'), (9172, '2009-08-13 August 13, 2009'), (9173, '2014-05-12 03:05:27'), (9174, 'We compute the flux of linear momentum carried by gravitational waves emitted from spinning binary black holes at second post-Newtonian (2PN) order for generic orbits. In particular we provide explicit expressions of three new types of terms, namely, next-to-leading order spin-orbit terms at 1.5 post-Newtonian (1.5PN) order, spin-orbit tail terms at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to quasicircular orbits, we integrate the linear-momentum flux over time to obtain the recoil velocity as function of orbital frequency. We find that in the so-called superkick configuration the higher-order spin corrections can increase the recoil velocity up to a factor ∼3 with respect to the leading-order PN prediction. Whereas the recoil velocity computed in PN theory within the adiabatic approximation can accurately describe the early inspiral phase, we find that its fast increase during the late inspiral and plunge, and the arbitrariness in determining until when it should be trusted, makes the PN predictions for the total recoil not very accurate and robust. Nevertheless, the linear-momentum flux at higher PN orders can be employed to build more reliable resummed expressions aimed at capturing the nonperturbative effects until merger. Furthermore, we provide expressions valid for generic orbits, and accurate at 2PN order, for the energy and angular momentum carried by gravitational waves emitted from spinning binary black holes. Specializing to quasicircular orbits we compute the spin-spin terms at 2PN order in the expression for the evolution of the orbital frequency and found agreement with Mikóczi, Vasúth, and Gergely. We also verified that in the limit of extreme mass ratio our expressions for the energy and angular momentum fluxes match the ones of Tagoshi, Shibata, Tanaka, and Sasaki obtained in the context of black hole perturbation theory.'), (9175, 'Recoil velocity at second post-Newtonian order for spinning black hole binaries'), (9176, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.80.044010'), (9177, 'http://link.springer.com/article/10.1007/BF01808375'), (9178, '363-363'), (9179, '1975-08-01 1975/08/01'), (9180, '10.1007/BF01808375'), (9181, '2014-05-12 13:05:01'), (9182, 'Gravitationally radiated linear momentum flux'), (9183, 'http://epubs.siam.org.proxy.library.cornell.edu/doi/abs/10.1137/S1064827503422932'), (9184, '1416-1428'), (9185, 'SIAM Journal on Scientific Computing'), (9186, 'Une formule pour le rayonnement gravitationnel en première approximation'), (9187, '1064-8275'), (9188, "Compte Rendus de L'Académie des Sciences"), (9189, 225), (9190, '1578--1580'), (9191, '1962-11-05 November 5, 1962'), (9192, 'https://archive.org/stream/ComptesRendusAcademieDesSciences0255/ComptesRendusAcadmieDesSciences-Tome255-Juillet-dcembre1962Partie3#page/n5/mode/2up'), (9193, 'fr'), (9194, 'N0004003_PDF_261_263DM.pdf'), (9195, 'http://arxiv.org/abs/1404.7070'), (9196, 'arXiv:1404.7070 [gr-qc]'), (9197, '2014-04-28 2014-04-28'), (9198, '2014-05-12 13:38:12'), (9199, "Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally characterize this 'picture', the physical parameters of the system can be extracted more efficiently from the gravitational wave data, and interpreted more easily. We assess the performance of MCMC parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binary's spins and orbital angular momentum and (b) a time at which the detectors are most sensitive to the binary's gravitational wave emission. Using anticipated noise curves for the advanced-generation LIGO and Virgo gravitational wave detectors, we find that this careful choice of reference frame and reference time significantly improves parameter estimation efficiency for BNS, NS-BH, and BBH signals."), (9200, 'A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves'), (9201, 'http://www.arxiv.org/pdf/1404.7070.pdf'), (9202, '1404.7070 PDF'), (9203, 'http://link.springer.com/article/10.1007/s00023-010-0072-1'), (9204, '77-118'), (9205, 'Annales Henri Poincaré'), (9206, '1424-0637, 1424-0661'), (9207, '2011-02-01 2011/02/01'), (9208, 'Ann. Henri Poincaré'), (9209, '10.1007/s00023-010-0072-1'), (9210, '2014-05-12 14:32:51'), (9211, "In this paper, we employ a technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index J) of generic Wigner matrix elements DJMM′(g){D^{J}_{MM'}(g)} . We use this result to derive asymptotic formulae for the character χ J (g) of an SU(2) group element and for Wigner’s 3j symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for χ J (g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums."), (9212, 'Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j Symbols, and Character Localization'), (9213, 'Asymptotes in SU(2) Recoupling Theory'), (9214, '2004-01-01 January 1, 2004'), (9215, 'Wigners.pdf'), (9216, 'http://oxfordindex.oup.com/view/10.1093/acprof:oso/9780199205677.001.0001'), (9217, 9780199205677), (9218, '2008-04-10 2008-04-10'), (9219, '2014-05-12 14:53:18'), (9220, 'Introduction to 3+1 Numerical Relativity'), (9221, 'Appendices.pdf'), (9222, 'SIAM J. Sci. Comput.'), (9223, '10.1137/S1064827503422932'), (9224, '2014-05-14 21:59:53'), (9225, 'epubs.siam.org.proxy.library.cornell.edu (Atypon)'), (9226, 'Efficient storage schemes are presented for storing Clebsch--Gordan, Wigner 3j and 6j symbols, as well as Gaunt coefficients, which are the integral over three spherical harmonics. Use is hereby made of the large number of symmetries which these symbols exhibit. Computer codes have been written and benchmarked against well-known published programs which usually use recursion relations for the evaluation. It is shown that our codes can be an order of magnitude or more faster in execution speed, maintaining full double precision accuracy., Efficient storage schemes are presented for storing Clebsch--Gordan, Wigner 3j and 6j symbols, as well as Gaunt coefficients, which are the integral over three spherical harmonics. Use is hereby made of the large number of symmetries which these symbols exhibit. Computer codes have been written and benchmarked against well-known published programs which usually use recursion relations for the evaluation. It is shown that our codes can be an order of magnitude or more faster in execution speed, maintaining full double precision accuracy.'), (9227, 'Efficient Storage Scheme for Precalculated Wigner 3j, 6j and Gaunt Coefficients'), (9228, 'http://epubs.siam.org.proxy.library.cornell.edu/doi/pdf/10.1137/S1064827503422932'), (9229, 'http://arxiv.org/abs/1108.4376'), (9230, 749), (9231, '2012-04-10 2012-04-10'), (9232, 'arXiv:1108.4376 [astro-ph]'), (9233, '10.1088/0004-637X/749/1/31'), (9234, '2014-05-15 19:14:56'), (9235, 'Parity violation found in the Cosmic Microwave Background (CMB) radiation is a crucial clue for the non-standard cosmological model or the possible contamination of various foreground residuals and/or calibration of the CMB data sets. In this paper, we study the directional properties of the CMB parity asymmetry by excluding the $m=0$ modes in the definition of parity parameters. We find that the preferred directions of the parity parameters coincide with the CMB kinematic dipole, which implies that the CMB parity asymmetry may be connected with the possible contamination of the residual dipole component. We also find that such tendency is not only localized at $l=2,3$, but in the extended multipole ranges up to $l\\sim 22$.'), (9236, 'Is the CMB asymmetry due to the kinematic dipole?'), (9237, 'http://www.arxiv.org/pdf/1108.4376.pdf'), (9238, '1108.4376 PDF'), (9239, 'http://link.springer.com/article/10.1007/s10714-007-0570-8'), (9240, '1705-1729'), (9241, '2008-08-01 2008/08/01'), (9242, '2014-05-15 20:41:49'), (9243, 'We present expressions for the energy, linear momentum and angular momentum carried away from an isolated system by gravitational radiation based on spin-weighted spherical harmonics decomposition of the Weyl scalar Ψ 4. We also show that the expressions derived are equivalent to the common expressions obtained when using a framework based on perturbations of a Schwazschild background. The main idea is to collect together all the different expressions in a uniform and consistent way. The formulae presented here are directly applicable to the calculation of the radiated energy, linear momentum and angular momentum starting from the gravitational waveforms which are typically extracted from numerical simulations.'), (9244, 'Multiple expansions for energy and momenta carried by gravitational waves'), (9245, '2014-05-22 14:33:58'), (9246, 'RuizEtAl.pdf'), (9247, 'Hermann Grassmann was right'), (9248, '2014-05-22 14:34:22'), (9249, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.77.124047'), (9250, 'http://link.aps.org/doi/10.1103/PhysRevD.76.061502'), (9251, '061502'), (9252, '2007-09-10 September 10, 2007'), (9253, '10.1103/PhysRevD.76.061502'), (9254, '2014-05-22 14:40:07'), (9255, 'We present results from several simulations of equal mass black holes with spin. The spin magnitudes are S/m2=0.8 in all cases, but we vary the spin orientations arbitrarily, inside and outside the orbital plane. We find that in all but one case the final merged black hole acquires a kick of more than 1000 km/s, indicating that kicks of this magnitude are likely to be generic and should be expected for mergers with general spin orientations. The maximum kick velocity we find is 2500 km/s and occurs for initial spins which are antialigned in the initial orbital plane.'), (9256, 'Binary black hole mergers: Large kicks for generic spin orientations'), (9257, 'Binary black hole mergers'), (9258, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.76.061502'), (9259, '1986-05-01 May 1, 1986'), (9260, 'http://link.springer.com/chapter/10.1007/978-3-0346-0405-5_23'), (9261, '©2011 Springer Basel AG'), (9262, 'Springer Basel'), (9263, '261-274'), (9264, '978-3-0346-0404-8, 978-3-0346-0405-5'), (9265, '2014-05-23 03:15:17'), (9266, 'Grassmann’s planwas to develop a purely formal algebra tomodel natural operations on geometric objects: flat or linear pieces of space of all possible dimensions. His approach was to be synthetic, so that the symbols in his algebra would denote geometric objects themselves, not just numbers (typically, coordinates) that could be derived from those objects by measurement. His was not to be an algebra of numerical quantities, but an algebra of pieces of space.'), (9267, 'On Grassmann’s regressive product'), (9268, "From Past to Future: Graßmann's Work in Context"), (9269, 9780817638689), (9270, 'bok%3A978-3-0346-0405-5.pdf'), (9271, 'Many of the capabilities of Grassmann’s algebra are still not well-enough known in the scientific community. This paper discusses just two of them: the capability to distin- guish algebraically between points and vectors in space, and the capability to compute intersections of geometric entities with a simple product operation. The first may be little known due to the mainstreaming of Gibbs’ three-dimensional vector alge- bra; the second due to Grassmann’s choice of notation for his product operations. We explore two applications.'), (9272, '287--302'), (9273, 'Grassmann, geometry and mechanics'), (9274, 'http://link.springer.com/chapter/10.1007/978-1-84996-108-0_1'), (9275, '©2010 Springer-Verlag London Limited'), (9276, '3-33'), (9277, '978-1-84996-107-3, 978-1-84996-108-0'), (9278, '2010-01-01 2010/01/01'), (9279, '2014-05-25 03:30:42'), (9280, 'Conformal Geometric Algebraic (CGA) provides ideal mathematical tools for construction, analysis, and integration of classical Euclidean, Inversive & Projective Geometries, with practical applications to computer science, engineering, and physics. This paper is a comprehensive introduction to a CGA tool kit. Synthetic statements in classical geometry translate directly to coordinate-free algebraic forms. Invariant and covariant methods are coordinated by conformal splits, which are readily related to the literature using methods of matrix algebra, biquaternions, and screw theory. Designs for a complete system of powerful tools for the mechanics of linked rigid bodies are presented.'), (9281, 'New Tools for Computational Geometry and Rejuvenation of Screw Theory'), (9282, 'Geometric Algebra Computing'), (9283, '1996-08-22 1996-08-22'), (9284, 'bok%3A978-1-84996-108-0.pdf'), (9285, 'http://link.springer.com/10.1007/978-1-84996-108-0'), (9286, 'London'), (9287, '2014-05-25 03:31:54'), (9288, 'http://link.springer.com/article/10.1007/BF03161244'), (9289, '135-182'), (9290, '2002-12-01 2002/12/01'), (9291, '10.1007/BF03161244'), (9292, '2014-05-26 14:58:56'), (9293, 'Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions. The basic rules of multivector differentiation are derived explicitly, as well as a variety of basic multivector derivatives. Finally factorization, which relates functions of vector variables and multivector variables is discussed, and the concepts of both simplicial variables and derivatives are explained. Everything is proven explicitly in a very elementary level step by step approach. The paper is thus intended to serve as reference material, providing a number of details, which are usually skipped in more advanced discussions of the subject matter. The arrangement of the material closely followschapter 2 of [3].'), (9294, 'Multivector differential calculus'), (9295, 'Leading authorities in the emerging field of Clifford (geometric) algebras have contributed to this fundamental and comprehensive text. The subject of Clifford algebras is presented here in efficient geometric language: common concepts in physics are clarified, united and extended in new and sometimes surprising directions. The text may well serve as a pedagogical tool for either self study or in courses at both the undergraduate and graduate level. Bibliographies complete many chapters and an index covers the entire book. Those new to Clifford algebras may start by reading the Introduction, after which practically any set of chapters can be read independently of the others.'), (9296, 'art%3A10.1007%2FBF03161244.pdf'), (9297, '181-186'), (9298, 'Glasgow Mathematical Journal'), (9299, '10.1017/S0017089500005978'), (9300, 'The Fourier transform of vector-valued functions'), (9301, 'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?pageCode=100101&type=1&fid=5048576&jid=GMJ&volumeId=26&issueId=02&aid=5048568&fromPage=online'), (9302, '2014-05-26 15:57:49'), (9303, 'http://arxiv.org/abs/1307.3562'), (9304, '2014-01-13 2014-1-13'), (9305, 'arXiv:1307.3562 [astro-ph, physics:gr-qc]'), (9306, '10.1103/PhysRevD.89.024010'), (9307, '2014-05-26 18:35:58'), (9308, "The first direct detection of neutron-star-black-hole binaries will likely be made with gravitational-wave observatories. Advanced LIGO and Advanced Virgo will be able to observe neutron-star-black-hole mergers at a maximum distance of 900Mpc. To acheive this sensitivity, gravitational-wave searches will rely on using a bank of filter waveforms that accurately model the expected gravitational-wave signal. The angular momentum of the black hole is expected to be comparable to the orbital angular momentum. This angular momentum will affect the dynamics of the inspiralling system and alter the phase evolution of the emitted gravitational-wave signal. In addition, if the black hole's angular momentum is not aligned with the orbital angular momentum it will cause the orbital plane of the system to precess. In this work we demonstrate that if the effect of the black hole's angular momentum is neglected in the waveform models used in gravitational-wave searches, the detection rate of $(10+1.4)M_{\\odot}$ neutron-star--black-hole systems would be reduced by $33 - 37%$. The error in this measurement is due to uncertainty in the Post-Newtonian approximations that are used to model the gravitational-wave signal of neutron-star-black-hole inspiralling binaries. We describe a new method for creating a bank of filter waveforms where the black hole has non-zero angular momentum, but is aligned with the orbital angular momentum. With this bank we find that the detection rate of $(10+1.4)M_{\\odot}$ neutron-star-black-hole systems would be reduced by $26-33%$. Systems that will not be detected are ones where the precession of the orbital plane causes the gravitational-wave signal to match poorly with non-precessing filter waveforms. We identify the regions of parameter space where such systems occur and suggest methods for searching for highly precessing neutron-star-black-hole binaries."), (9309, 'Investigating the effect of precession on searches for neutron-star-black-hole binaries with Advanced LIGO'), (9310, 'http://www.arxiv.org/pdf/1307.3562.pdf'), (9311, '1307.3562 PDF'), (9312, 'http://link.aps.org/doi/10.1103/PhysRevD.89.024010'), (9313, '024010'), (9314, '2014-01-13 January 13, 2014'), (9315, '2014-05-26 18:36:19'), (9316, 'The first direct detection of neutron-star– black-hole binaries will likely be made with gravitational-wave observatories. Advanced LIGO and Advanced Virgo will be able to observe neutron-star– black-hole mergers at a maximum distance of 900 Mpc. To achieve this sensitivity, gravitational-wave searches will rely on using a bank of filter waveforms that accurately model the expected gravitational-wave signal. The emitted signal will depend on the masses of the black hole and the neutron star and also the angular momentum of both components. The angular momentum of the black hole is expected to be comparable to the orbital angular momentum when the system is emitting gravitational waves in Advanced LIGO’s and Advanced Virgo’s sensitive band. This angular momentum will affect the dynamics of the inspiralling system and alter the phase evolution of the emitted gravitational-wave signal. In addition, if the black hole’s angular momentum is not aligned with the orbital angular momentum, it will cause the orbital plane of the system to precess. In this work we demonstrate that if the effect of the black hole’s angular momentum is neglected in the waveform models used in gravitational-wave searches, the detection rate of (10+1.4)M⊙ neutron-star– black-hole systems with isotropic spin distributions would be reduced by 33%–37% in comparison to a hypothetical perfect search at a fixed signal-to-noise ratio threshold. The error in this measurement is due to uncertainty in the post-Newtonian approximations that are used to model the gravitational-wave signal of neutron-star– black-hole inspiralling binaries. We describe a new method for creating a bank of filter waveforms where the black hole has nonzero angular momentum that is aligned with the orbital angular momentum. With this bank we find that the detection rate of (10+1.4)M⊙ neutron-star– black-hole systems would be reduced by 26%–33%. Systems that will not be detected are ones where the precession of the orbital plane causes the gravitational-wave signal to match poorly with nonprecessing filter waveforms. We identify the regions of parameter space where such systems occur and suggest methods for searching for highly precessing neutron-star– black-hole binaries.'), (9317, 'Investigating the effect of precession on searches for neutron-star–black-hole binaries with Advanced LIGO'), (9318, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.024010'), (9319, 'http://link.aps.org/doi/10.1103/PhysRevD.83.084002'), (9320, '084002'), (9321, '2011-04-04 April 4, 2011'), (9322, '10.1103/PhysRevD.83.084002'), (9323, '2014-05-27 04:29:36'), (9324, 'We introduce a method for conducting a targeted, coherent search for compact binary coalescences. The search is tailored to be used as a follow-up to electromagnetic transients such as gamma-ray bursts. We derive the coherent search statistic for Gaussian detector noise and discuss the benefits of a coherent, multidetector search over coincidence methods. To mitigate the effects of nonstationary data, we introduce a number of signal consistency tests, including the null signal-to-noise ratio, amplitude consistency, and several χ2 tests. We demonstrate the search performance on Gaussian noise and on data from LIGO’s fourth science run and verify that the signal consistency tests are capable of removing the majority of noise transients, giving the search an efficiency comparable to that achieved in Gaussian noise.'), (9325, 'Targeted coherent search for gravitational waves from compact binary coalescences'), (9326, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.83.084002'), (9327, 'http://link.aps.org/doi/10.1103/PhysRevD.76.082001'), (9328, '2007-10-24 October 24, 2007'), (9329, '10.1103/PhysRevD.76.082001'), (9330, '2014-05-27 04:29:39'), (9331, 'We carry out two searches for periodic gravitational waves using the most sensitive few hours of data from the second LIGO science run. Both searches exploit fully coherent matched filtering and cover wide areas of parameter space, an innovation over previous analyses which requires considerable algorithm development and computational power. The first search is targeted at isolated, previously unknown neutron stars, covers the entire sky in the frequency band 160–728.8 Hz, and assumes a frequency derivative of less than 4×10−10 Hz/s. The second search targets the accreting neutron star in the low-mass x-ray binary Scorpius X-1 and covers the frequency bands 464–484 Hz and 604–624 Hz as well as the two relevant binary orbit parameters. Because of the high computational cost of these searches we limit the analyses to the most sensitive 10 hours and 6 hours of data, respectively. Given the limited sensitivity and duration of the analyzed data set, we do not attempt deep follow-up studies. Rather we concentrate on demonstrating the data analysis method on a real data set and present our results as upper limits over large volumes of the parameter space. In order to achieve this, we look for coincidences in parameter space between the Livingston and Hanford 4-km interferometers. For isolated neutron stars our 95% confidence level upper limits on the gravitational wave strain amplitude range from 6.6×10−23 to 1×10−21 across the frequency band; for Scorpius X-1 they range from 1.7×10−22 to 1.3×10−21 across the two 20-Hz frequency bands. The upper limits presented in this paper are the first broadband wide parameter space upper limits on periodic gravitational waves from coherent search techniques. The methods developed here lay the foundations for upcoming hierarchical searches of more sensitive data which may detect astrophysical signals.'), (9332, 'Searches for periodic gravitational waves from unknown isolated sources and Scorpius X-1: Results from the second LIGO science run'), (9333, 'Searches for periodic gravitational waves from unknown isolated sources and Scorpius X-1'), (9334, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.76.082001'), (9335, 'http://link.aps.org/doi/10.1103/PhysRevD.88.122002'), (9336, 122002), (9337, '2013-12-13 December 13, 2013'), (9338, '10.1103/PhysRevD.88.122002'), (9339, '2014-05-27 04:30:15'), (9340, 'We study an improved method for detecting gravitational wave signals from perturbed black holes by Earth-based detectors in the search for intermediate-mass black holes. Such signals, called ringdowns, are damped sinusoids whose frequency and damping constant can be used to measure a black hole’s mass and spin. Utilizing the output from a matched-filter analysis pipeline, we present an improved statistic for the detection of a ringdown signal that is found to be coincident in multiple detectors. The statistic addresses the non-Gaussianity of the data without the use of an additional signal-based waveform consistency test. We also develop coherent network statistics to check for consistency of signal amplitudes and phases in the different detectors with their different orientations and signal arrival times. We find that the detection efficiency can be improved at least by a few tens of percent by applying these multidetector statistics primarily because of the ineffectiveness of single detector–based discriminators of nonstationary noise, such as the chi-square test, in the case of ringdown signals studied here.'), (9341, 'Improved coincident and coherent detection statistics for searches for gravitational wave ringdown signals'), (9342, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.122002'), (9343, 'Clifford (Geometric) Algebras: With Applications in Physics, Mathematics, and Engineering'), (9344, 'Clifford (Geometric) Algebras'), (9345, 540), (9346, 'http://books.google.com/books?id=0Nji78YQKfQC'), (9347, '2014-05-27 20:51:02'), (9348, 'http://www.sciencedirect.com/science/article/pii/S0965997811001177'), (9349, '723-733'), (9350, 'Advances in Engineering Software'), (9351, '0965-9978'), (9352, '10.1016/j.advengsoft.2011.05.010'), (9353, '2014-05-31 04:24:27'), (9354, 'The integration of the rotation from a given angular velocity is often required in practice. The present paper explores how the choice of the parametrization of rotation, when employed in conjuction with different numerical time-integration schemes, effects the accuracy and the computational efficiency. Three rotation parametrizations – the rotational vector, the Argyris tangential vector and the rotational quaternion – are combined with three different numerical time-integration schemes, including classical explicit Runge–Kutta method and the novel midpoint rule proposed here. The key result of the study is the assessment of the integration errors of various parametrization–integration method combinations. In order to assess the errors, we choose a time-dependent function corresponding to a rotational vector, and derive the related exact time-dependent angular velocity. This is then employed in the numerical solution as the data. The resulting numerically integrated approximate rotations are compared with the analytical solution. A novel global solution error norm for discrete solutions given by a set of values at chosen time-points is employed. Several characteristic angular velocity functions, resulting in small, finite and fast oscillating rotations are studied.'), (9355, 'Integrating rotation from angular velocity'), (9356, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0965997811001177/pdfft?md5=479e8e81ed5935d037f657dea4cd4120&pid=1-s2.0-S0965997811001177-main.pdf'), (9357, 'http://arxiv.org/abs/1406.0401'), (9358, 'arXiv:1406.0401 [gr-qc]'), (9359, '2014-06-02 2014-06-02'), (9360, '2014-06-04 19:18:23'), (9361, 'We propose a new way of analyzing, and analytically representing, the ringdown part of the gravitational wave signal emitted by coalescing black hole binaries.By contrast with the usual {\\it linear} decomposition of the multipolar complex waveform $h(t)$ in a sum of quasi-normal modes, our procedure relies on a {\\it multiplicative} decomposition of $h(t)$ as the product of the fundamental quasi-normal mode with a remaining time-dependent complex factor whose amplitude and phase are separately fitted. As an illustrative example, we apply our analysis and fitting procedure to the ringdown part of a sample of sixteen $\\ell=m=2$ equal-mass, spinning, nonprecessing, numerical waveforms computed with the SP$_{\\rm E}$C code,now publicly available in the SXS catalogue. Our approach yields an efficient and accurate way to represent the ringdown waveform, thereby offering a new way to complete the analytical effective-one-body inspiral-plus-plunge waveform.'), (9362, 'A new analytic representation of the ringdown waveform of coalescing spinning black hole binaries'), (9363, 'http://www.arxiv.org/pdf/1406.0401.pdf'), (9364, '1406.0401 PDF'), (9365, 'http://arxiv.org/abs/1406.4664'), (9366, 'arXiv:1406.4664 [gr-qc]'), (9367, '2014-06-18 2014-06-18'), (9368, 'arXiv: 1406.4664'), (9369, '2014-06-20 17:31:05'), (9370, 'We describe an alternative approach to the analysis of gravitational-wave backgrounds, based on the formalism used to characterise the polarisation of the cosmic microwave background. An arbitrary background can be decomposed into modes whose angular dependence on the sky is given by gradients and curls of spherical harmonics. We derive the pulsar timing overlap reduction function for individual modes, which are given by simple combinations of spherical harmonics evaluated at the pulsar locations. We show how these can be used to recover the components of an arbitrary background, giving explicit results for both isotropic and anisotropic uncorrelated backgrounds. We also find that the response of a pulsar timing array to curl modes is identically zero, so half of the gravitational-wave sky will never be observed using pulsar timing, no matter how many pulsars are included in the array. An isotropic uncorrelated background can be accurately represented using only three components, and so a search of this type will be almost as sensitive as the standard cross-correlation search using the Hellings and Downs overlap reduction function. However, in our approach each individual mode on its own describes a background that is correlated between different points on the sky. A measurement of these components that is inconsistent with the expected values for an uncorrelated background would therefore indicate startling new physics.'), (9371, 'A CMB-based approach to mapping gravitational-wave backgrounds: application to pulsar timing arrays'), (9372, 'A CMB-based approach to mapping gravitational-wave backgrounds'), (9373, 'http://www.arxiv.org/pdf/1406.4664.pdf'), (9374, 'arXiv:1406.4664 PDF'), (9375, 'http://arxiv.org/abs/1406.5559'), (9376, 'arXiv:1406.5559 [gr-qc]'), (9377, '2014-06-20 2014-06-20'), (9378, 'arXiv: 1406.5559'), (9379, '2014-06-24 18:59:18'), (9380, 'Two different approaches to gravitational perturbation theory appear to give two different answers for the properties of gravitational wave memory. We show that this contradiction is only apparent and the two approaches actually agree.'), (9381, 'Resolving a gravitational wave memory paradox'), (9382, 'http://www.arxiv.org/pdf/1406.5559.pdf'), (9383, 'arXiv:1406.5559 PDF'), (9384, 'http://link.springer.com/article/10.1007/s10851-009-0161-2'), (9385, '155-164'), (9386, 'Journal of Mathematical Imaging and Vision'), (9387, '0924-9907, 1573-7683'), (9388, '2009-10-01 2009/10/01'), (9389, 'J Math Imaging Vis'), (9390, '10.1007/s10851-009-0161-2'), (9391, '2014-06-26 18:15:18'), (9392, '3D rotations arise in many computer vision, computer graphics, and robotics problems and evaluation of the distance between two 3D rotations is often an essential task. This paper presents a detailed analysis of six functions for measuring distance between 3D rotations that have been proposed in the literature. Based on the well-developed theory behind 3D rotations, we demonstrate that five of them are bi-invariant metrics on SO(3) but that only four of them are boundedly equivalent to each other. We conclude that it is both spatially and computationally more efficient to use quaternions for 3D rotations. Lastly, by treating the two rotations as a true and an estimated rotation matrix, we illustrate the geometry associated with iso-error measures.'), (9393, 'Metrics for 3D Rotations: Comparison and Analysis'), (9394, 'Metrics for 3D Rotations'), (9395, 'http://arxiv.org/abs/1406.6913'), (9396, 'Rmetric.pdf'), (9397, 'arXiv:1406.6913 [gr-qc]'), (9398, '2014-06-26 2014-06-26'), (9399, 'arXiv: 1406.6913'), (9400, '2014-07-07 15:03:31'), (9401, 'We present a new, tunable effective-one-body (EOB) model of the motion and radiation of coalescing black hole binaries with arbitrary mass ratio and aligned spins. The most novel feature of our formalism is the introduction, and systematic use, of the (gauge-invariant) concept of {\\it centrifugal radius} $r_{c}$. In the spinning small mass-ratio limit, the main radial potential expressed in terms of $r_{c}$ differs very little (and only multiplicatively so) from the usual Schwarzschild potential $1-2M/r_{c}$. This motivates a new, multiplicative way of blending finite-mass-ratio deformations with spin-deformations. In the present exploratory work we consider a minimal version of our spinning EOB model (containing essentially only two adjustable parameters: one in the Hamiltonian and one in the waveform) and calibrate its (dominant mode) waveform against a sample of fifteen equal-mass, equal-spin waveforms produced by the SXS collaboration, and covering the dimensionless spin range $-0.95\\leq \\chi \\leq +0.98$. The numerical relativity / EOB phasing disagreement remains remarkably small ($\\lesssim \\pm 0.15$ rad) over the entire spin range.'), (9402, 'A new effective-one-body description of coalescing nonprecessing spinning black-hole binaries'), (9403, 'http://www.arxiv.org/pdf/1406.6913.pdf'), (9404, 'arXiv:1406.6913 PDF'), (9405, 'http://iopscience.iop.org/0264-9381/27/8/084006'), (9406, '10.1088/0264-9381/27/8/084006'), (9407, 'A/204'), (9408, 'The Advanced LIGO gravitational wave detectors are next generation instruments which will replace the existing initial LIGO detectors. They are currently being constructed and installed. Advanced LIGO strain sensitivity is designed to be about a factor 10 better than initial LIGO over a broad band and usable to 10 Hz, in contrast to 40 Hz for initial LIGO. This is expected to allow for detections and significant astrophysics in most categories of gravitational waves. To achieve this sensitivity, all hardware subsystems are being replaced with improvements. Designs and expected performance are presented for the seismic isolation, suspensions, optics and laser subsystems. Possible enhancements to Advanced LIGO, either to resolve problems that may arise and/or to allow for improved performance, are now being researched. Some of these enhancements are discussed along with some potential technology being considered for detectors beyond Advanced LIGO.'), (9409, 'Advanced LIGO: the next generation of gravitational wave detectors'), (9410, 'Advanced LIGO'), (9411, 'http://arxiv.org/abs/1407.5989'), (9412, '2014-07-21 15:32:14'), (9413, '0264-9381_27_8_084006.pdf'), (9414, 'http://iopscience.iop.org/0004-637X/699/1/453'), (9415, 699), (9416, 453), (9417, '10.1088/0004-637X/699/1/453'), (9418, '2014-07-21 15:42:57'), (9419, 'We present a study of correlations between X-ray spectral and timing properties observed from a number of Galactic black hole (BH) binaries during hard-soft state spectral evolution. We analyze 17 transition episodes from eight BH sources observed with Rossi X-Ray Timing Explorer. Our scaling technique for BH mass determination uses a correlation between the spectral index and quasi-periodic oscillation (QPO) frequency. In addition, we use a correlation between the index and the normalization of the disk seed component to cross-check the BH mass determination and estimate the distance to the source. While the index-QPO correlations for two given sources contain information on the ratio of the BH masses in those sources, the index-normalization correlations depend on the ratio of the BH masses and the distance square ratio. In fact, the index-normalization correlation also discloses the index-mass accretion rate saturation effect given that the normalization of disk seed photon supply is proportional to the disk mass accretion rate. We present arguments that this observationally established index saturation effect is a signature of the bulk motion (converging) flow onto a BH, which was early predicted by the dynamical Comptonization theory. We use GRO J1655 – 40 as a primary reference source for which the BH mass, distance, and inclination angle are evaluated by dynamical measurements with unprecedented precision among other Galactic BH sources. We apply our scaling technique to determine BH masses and distances for Cygnus X-1, GX 339 – 4, 4U 1543 – 47, XTE J1550 – 564, XTE J1650 – 500, H 1743 – 322, and XTE J1859 – 226. A good agreement of our results for sources with known values of BH masses and distance provides independent verification for our scaling technique.'), (9420, 'Determination of Black Hole Masses in Galactic Black Hole Binaries Using Scaling of Spectral and Variability Characteristics'), (9421, 'http://iopscience.iop.org/0004-637X/699/1/453/pdf/0004-637X_699_1_453.pdf'), (9422, 'http://dx.doi.org/10.1146/annurev-astro-081913-040031'), (9423, 'null'), (9424, 'Ann. Rev. Astronomy and Astrophys.'), (9425, '2014-00-00 2014'), (9426, '10.1146/annurev-astro-081913-040031'), (9427, 'Numerical Relativity and Astrophysics'), (9428, 'annurev-astro-081913-040031.pdf'), (9429, 'http://arxiv.org/abs/1407.5033'), (9430, 'arXiv:1407.5033 [gr-qc]'), (9431, '2014-07-18 2014-07-18'), (9432, 'arXiv: 1407.5033'), (9433, '2014-07-22 15:07:57'), (9434, 'Gravitational waves emitted from a generic binary black-hole merger carry away linear momentum anisotropically, resulting in a gravitational recoil, or "kick", of the center of mass. For certain merger configurations the time evolution of the magnitude of the kick velocity has a local maximum followed by a sudden drop. Perturbative studies of this "antikick" in a limited range of black hole spins have found that the antikick decreases for retrograde orbits as a function of negative spin. We analyze this problem using a recently developed code to evolve gravitational perturbations from a point-particle in Kerr spacetime driven by an effective-one-body resummed radiation reaction force at linear order in the mass ratio $\\nu\\ll 1$. Extending previous studies to nearly-extremal negative spins, we find that the well-known decrease of the antikick is overturned and, instead of approaching zero, the antikick increases again to reach $\\Delta v/(c\\nu^{2})=3.37\\times10^{-3}$ for dimensionless spin $\\hat{a}=-0.9999$. The corresponding final kick velocity is $v_{end}/(c\\nu^{2})=0.076$. This result is connected to the nonadiabatic character of the emission of linear momentum during the plunge. We interpret it analytically by means of the quality factor of the flux to capture quantitatively the main properties of the kick velocity. The use of such quality factor of the flux does not require trajectories nor horizon curvature distributions and should therefore be useful both in perturbation theory and numerical relativity.'), (9435, 'The antikick strikes back: recoil velocities for nearly-extremal binary black hole mergers in the test-mass limit'), (9436, 'The antikick strikes back'), (9437, 'http://www.arxiv.org/pdf/1407.5033.pdf'), (9438, 'arXiv:1407.5033 PDF'), (9439, 'http://thesis.library.caltech.edu/143/'), (9440, 'http://resolver.caltech.edu/CaltechETD:etd-01122009-143851'), (9441, '2014-09-05 01:16:49'), (9442, 'http://link.aps.org/doi/10.1103/PhysRevD.76.124029'), (9443, '10.1103/PhysRevD.76.124029'), (9444, '2014-07-28 16:05:07'), (9445, 'Framework for large-scale relativistic simulations in the characteristic approach'), (9446, 'thesis.library.caltech.edu'), (9447, "RSWeb '12"), (9448, "We examine various topics involved in the creation of accurate theoretical gravitational waveforms from binary black-hole systems.\n\nIn Chapter 2 a pseudospectral numerical code is applied to a set of analytic or near-analytic solutions to Einstein's equations which comprise a testbed for numerical-relativity codes. We then discuss methods for extracting gravitational-wave data from numerical simulations of black-hole binary systems, and introduce a practical technique for obtaining the asymptotic form of that data from finite simulation domains in Chapter 3. A formula is also developed to estimate the size of near-field effects from a compact binary. In Chapter 4 the extrapolated data is then compared to post-Newtonian (PN) approximations. We compare the phase and amplitude of the numerical waveform to a collection of Taylor approximants, cross-validating the numerical and PN waveforms, and investigating the regime of validity of the PN waveforms. Chapter 5 extends that comparison to include Padé and effective-one-body models, and investigates components of the PN models. In each case, a careful accounting is made of errors. Finally, we construct a long post-Newtonian–numerical hybrid waveform and evaluate the performance of LIGO's current data-analysis methods with it. We suggest certain optimizations of those methods, including extending the range of template mass ratios to unphysical ranges for certain values of the total mass, and a simple analytic cutoff frequency for the templates which results in nearly optimal matches for both Initial and Advanced LIGO."), (9449, 'http://thesis.library.caltech.edu/143/1/Thesis.pdf'), (9450, 'PhysRevD.76.124029.pdf'), (9451, 'arXiv:1407.5989 [astro-ph, physics:gr-qc]'), (9452, '2014-07-22 2014-07-22'), (9453, 'arXiv: 1407.5989'), (9454, '2014-07-31 17:01:57'), (9455, 'We demonstrate that in binary black hole mergers there is a direct correlation between the frequency of the gravitational wave at peak amplitude and the mass and spin of the final black hole. This correlation could potentially assist with the analysis of gravitational wave observations from binary black hole mergers.'), (9456, 'Decoding the final state in binary black hole mergers'), (9457, 'http://www.arxiv.org/pdf/1407.5989.pdf'), (9458, 'arXiv:1407.5989 PDF'), (9459, '2013-02-05 2013-2-5'), (9460, 'arXiv: 1209.6349'), (9461, '2014-08-05 15:27:52'), (9462, 'arXiv:1209.6349 PDF'), (9463, '2014-08-05 21:31:23'), (9464, 'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1107/S0108767306017478/abstract'), (9465, '262-269'), (9466, 'Acta Crystallographica Section A'), (9467, '1600-5724'), (9468, '2006-07-01 July 1, 2006'), (9469, 'Acta Cryst. A'), (9470, '10.1107/S0108767306017478'), (9471, '2014-08-07 12:44:23'), (9472, 'The FFT calculation of spherical harmonics, Wigner D matrices and rotation function has been extended to all angular variables in the AMoRe molecular replacement software. The resulting code avoids singularity issues arising from recursive formulas, performs faster and produces results with at least the same accuracy as the original code. The new code aims at permitting accurate and more rapid computations at high angular resolution of the rotation function of large particles. Test calculations on the icosahedral IBDV VP2 subviral particle showed that the new code performs on the average 1.5 times faster than the original code.'), (9473, 'Calculation of spherical harmonics and Wigner d\xa0functions by FFT. Applications to fast rotational matching in molecular replacement and implementation into AMoRe'), (9474, 'S0108767306017478.pdf'), (9475, '© 2011 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.'), (9476, '442-442'), (9477, 'Nature Physics'), (9478, '1745-2473'), (9479, '2011-06-00 June 2011'), (9480, 'http://link.aps.org/doi/10.1103/PhysRevD.88.062001'), (9481, '062001'), (9482, '2013-09-04 September 4, 2013'), (9483, '10.1103/PhysRevD.88.062001'), (9484, '2014-08-09 04:10:31'), (9485, 'Compact binary systems with neutron stars or black holes are one of the most promising sources for ground-based gravitational-wave detectors. Gravitational radiation encodes rich information about source physics; thus parameter estimation and model selection are crucial analysis steps for any detection candidate events. Detailed models of the anticipated waveforms enable inference on several parameters, such as component masses, spins, sky location and distance, that are essential for new astrophysical studies of these sources. However, accurate measurements of these parameters and discrimination of models describing the underlying physics are complicated by artifacts in the data, uncertainties in the waveform models and in the calibration of the detectors. Here we report such measurements on a selection of simulated signals added either in hardware or software to the data collected by the two LIGO instruments and the Virgo detector during their most recent joint science run, including a “blind injection” where the signal was not initially revealed to the collaboration. We exemplify the ability to extract information about the source physics on signals that cover the neutron-star and black-hole binary parameter space over the component mass range 1 M⊙–25 M⊙ and the full range of spin parameters. The cases reported in this study provide a snapshot of the status of parameter estimation in preparation for the operation of advanced detectors.'), (9486, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.062001'), (9487, 'http://link.aps.org/doi/10.1103/PhysRevD.87.084008'), (9488, '084008'), (9489, '2013-04-02 April 2, 2013'), (9490, '10.1103/PhysRevD.87.084008'), (9491, '2014-08-09 04:14:54'), (9492, 'The inspiral and merger of black hole binary systems are a promising source of gravitational waves for the array of advanced interferometric ground-based gravitational-wave detectors currently being commissioned. The most effective method to look for a signal with a well understood waveform, such as the binary black hole signal, is matched filtering against a library of model waveforms. While current model waveforms are comprised solely of the dominant radiation mode, the quadrupole mode, it is known that there can be significant power in the higher-order modes for a broad range of physically relevant source parameters during the merger of the black holes. The binary black hole waveforms produced by numerical relativity are accurate through late inspiral, merger, and ringdown and include the higher-order modes. The available numerical-relativity waveforms span an increasing portion of the physical parameter space of unequal mass, spin and precession. In this paper, we investigate the degree to which gravitational-wave searches could be improved by the inclusion of higher modes in the model waveforms, for signals with a variety of initial mass ratios and generic spins. Our investigation studies how well the quadrupole-only waveform model matches the signal as a function of the inclination and orientation of the source and how the modes contribute to the distance reach into the Universe of Advanced LIGO for a fixed set of internal source parameters. The mismatch between signals and quadrupole-only waveforms can be large, dropping below 0.97 for up to 65% of the source sky for the nonprecessing cases we studied, and over a larger area in one precessing case. There is a corresponding 30% increase in detection volume that could be achieved by adding higher modes to the search; however, this is mitigated by the fact that the mismatch is largest for signals which radiate the least energy and to which the search is therefore least sensitive. Likewise, the mismatch is largest in the directions from the source along which the least energy is radiated.'), (9493, 'Impact of higher-order modes on the detection of binary black hole coalescences'), (9494, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.084008'), (9495, 'http://iopscience.iop.org/0264-9381/31/2/025012'), (9496, '025012'), (9497, '2013-01-21 2013-01-21'), (9498, '10.1088/0264-9381/31/2/025012'), (9499, '2014-08-11 21:46:11'), (9500, "The Numerical–Relativity–Analytical–Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ∼100–200M⊙, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios ⩽4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters."), (9501, 'Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration'), (9502, 'http://iopscience.iop.org/0264-9381/31/2/025012/pdf/0264-9381_31_2_025012.pdf'), (9503, 'http://iopscience.iop.org/0264-9381/26/11/114002'), (9504, '10.1088/0264-9381/26/11/114002'), (9505, '2014-08-11 21:52:49'), (9506, "At early times in numerical evolutions of binary black holes, current simulations contain an initial burst of spurious gravitational radiation (also called 'junk radiation') which is not astrophysically realistic. The spurious radiation is a consequence of how the binary-black-hole initial data are constructed: the initial data are typically assumed to be conformally flat. In this paper, I adopt a curved conformal metric that is a superposition of two boosted, non-spinning black holes that are approximately 15 orbits from merger. I compare junk radiation of the superposed-boosted-Schwarzschild (SBS) initial data with the junk of corresponding conformally flat, maximally sliced (CFMS) initial data. The SBS junk is smaller in amplitude than the CFMS junk, with the junk's leading-order spectral modes typically being reduced by a factor of order 2 or more."), (9507, 'Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data'), (9508, 'http://relativity.livingreviews.org/Articles/lrr-2004-1/'), (9509, 'http://link.aps.org/doi/10.1103/PhysRevD.70.104016'), (9510, '2004-11-12 November 12, 2004'), (9511, '10.1103/PhysRevD.70.104016'), (9512, '2014-08-11 21:57:23'), (9513, 'We define and extensively test a set of boundary conditions that can be applied at black-hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasicircular orbits and the determination of the innermost stable circular orbit. Our tests show that the boundary conditions work well.'), (9514, 'Excision boundary conditions for black-hole initial data'), (9515, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.70.104016'), (9516, '1433-8351'), (9517, '10.12942/lrr-2004-1'), (9518, '2014-08-14 12:39:59'), (9519, 'Conformal Infinity'), (9520, 'lrr-2004-1Color.pdf'), (9521, 'http://rspa.royalsocietypublishing.org/content/284/1397/159'), (9522, 284), (9523, 1397), (9524, '159-203'), (9525, '1965-02-23 02/23/1965'), (9526, '10.1098/rspa.1965.0058'), (9527, '2014-08-14 12:47:30'), (9528, "A zero rest-mass field of arbitrary spin s determines, at each event in space-time, a set of 2s principal null directions which are related to the radiative behaviour of the field. These directions exhibit the characteristic 'peeling-off' behaviour of Sachs, namely that to order r$^{-k-1}$ (k = 0, \\ldots, 2s), 2s-k of them coincide radially, r being a linear parameter in any advanced or retarded radial direction. This result is obtained in part I for fields of any spin in special relativity, by means of an inductive spinor argument which depends ultimately on the appropriate asymptotic behaviour of a very simple Hertz-type complex scalar potential. Spin (s - $\\frac{1}{2}$) fields are used as potentials for spin s fields, etc. Several examples are given to illustrate this, In particular, the method is used to obtain physically sensible singularity-free waves for each spin which can be of any desired algebraic type. In part II, a general technique is described, for discussing asymptotic properties of fields in curved space-times which is applicable to all asymptotically flat or asymptotically de Sitter space-times. This involves the introduction of 'points at infinity' in a consistent way. These points constitute a hypersurface boundary $\\mathscr{J}$ to a manifold whose interior is conformally identical with the original space-time. Zero rest-mass fields exhibit an essential conformal invariance, so their behaviour at 'infinity' can be studied at this hypersurface. Continuity at $\\mathscr{J}$ for the transformed field implies that the 'peeling-off' property holds. Furthermore, if the Einstein empty-space equations hold near $\\mathscr{J}$ then continuity at $\\mathscr{J}$ for the transformed gravitational field is a consequence. This leads to generalizations of results due to Bondi and Sachs. The case when the Einstein-Maxwell equations hold near $\\mathscr{J}$ is also similarly treated here. The hypersurface $\\mathscr{J}$ is space-like, time-like or null according as the cosmological constant is positive, negative or absent. The technique affords a covariant approach to the definition of radiation fields in general relativity. If $\\mathscr{J}$ is not null, however, the radiation field concept emerges as necessarily origin dependent. Further applications of the technique are also indicated."), (9529, 'Zero Rest-Mass Fields Including Gravitation: Asymptotic Behaviour'), (9530, 'Zero Rest-Mass Fields Including Gravitation'), (9531, 'http://link.springer.com/article/10.1007/BF00759146'), (9532, 'Proc. R. Soc. Lond. A-1965-Penrose-159-203.pdf'), (9533, 'http://link.aps.org/doi/10.1103/PhysRevD.86.084020'), (9534, '2012-10-03 October 3, 2012'), (9535, '10.1103/PhysRevD.86.084020'), (9536, '2014-08-14 19:07:14'), (9537, 'We investigate the suitability and properties of a quasi-Kinnersley tetrad and a geometrically motivated coordinate system as tools for quantifying both strong-field and wave-zone effects in numerical relativity (NR) simulations. We fix two of the coordinate degrees of freedom of the metric, namely, the radial and latitudinal coordinates, using the Coulomb potential associated with the quasi-Kinnersley transverse frame. These coordinates are invariants of the spacetime and can be used to unambiguously fix the outstanding spin-boost freedom associated with the quasi-Kinnersley frame (and thus can be used to choose a preferred quasi-Kinnersley tetrad). In the limit of small perturbations about a Kerr spacetime, these geometrically motivated coordinates and quasi-Kinnersley tetrad reduce to Boyer-Lindquist coordinates and the Kinnersley tetrad, irrespective of the simulation gauge choice. We explore the properties of this construction both analytically and numerically, and we gain insights regarding the propagation of radiation described by a super-Poynting vector, further motivating the use of this construction in NR simulations. We also quantify in detail the peeling properties of the chosen tetrad and gauge. We argue that these choices are particularly well-suited for a rapidly converging wave-extraction algorithm as the extraction location approaches infinity, and we explore numerically the extent to which this property remains applicable on the interior of a computational domain. Using a number of additional tests, we verify numerically that the prescription behaves as required in the appropriate limits regardless of simulation gauge; these tests could also serve to benchmark other wave extraction methods. We explore the behavior of the geometrically motivated coordinate system in dynamical binary-black-hole NR mergers; while we obtain no unexpected results, we do find that these coordinates turn out to be useful for visualizing NR simulations (for example, for vividly illustrating effects such as the initial burst of spurious junk radiation passing through the computational domain). Finally, we carefully scrutinize the head-on collision of two black holes and, for example, the way in which the extracted waveform changes as it moves through the computational domain.'), (9538, 'Geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad'), (9539, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.86.084020'), (9540, 'http://www.springer.com/computer/image+processing/book/978-3-540-41198-7'), (9541, '2014-08-14 20:27:58'), (9542, 'Clifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. Clifford or geometric algebra shows strong unifying aspects and turned out ...'), (9543, 'Geometric Computing with Clifford Algebras - Theoretical Foundations and Applications in Computer'), (9544, 'Spherical Conformal Geometry with Geometric Algebra'), (9545, 'CompGeom-ch3.pdf'), (9546, 'Geometric Computing with Clifford Algebras'), (9547, 'http://iopscience.iop.org/0264-9381/31/9/092001'), (9548, '092001'), (9549, '10.1088/0264-9381/31/9/092001'), (9550, '2014-08-14 21:20:05'), (9551, 'The Bondi–Metzner–Sachs group is shown to be the conformal extension of Lévy-Leblond’s ‘Carroll’ group. Further extension to the Newman–Unti group is also discussed in the Carroll framework.'), (9552, 'Conformal Carroll groups and BMS symmetry'), (9553, '1101-1113'), (9554, 'cqg_31_9_092001.pdf'), (9555, 'http://link.aps.org/doi/10.1103/PhysRevLett.105.111103'), (9556, 105), (9557, 111103), (9558, '2010-09-08 September 8, 2010'), (9559, '10.1103/PhysRevLett.105.111103'), (9560, 'clifford-intro.pdf'), (9561, 'It is shown that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semidirect sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a consequence, two-dimensional conformal field theory techniques will play as fundamental a role in this context of direct physical interest as they do in three-dimensional anti–de Sitter gravity.'), (9562, 'Symmetries of Asymptotically Flat Four-Dimensional Spacetimes at Null Infinity Revisited'), (9563, '10.1007/BF00759146'), (9564, '2014-08-14 21:23:28'), (9565, 'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.105.111103'), (9566, 'http://link.aps.org/doi/10.1103/PhysRevD.87.104003'), (9567, 104003), (9568, '2013-05-02 May 2, 2013'), (9569, '10.1103/PhysRevD.87.104003'), (9570, '2014-08-15 19:35:35'), (9571, 'Parameter estimation of binary black-hole merger events in gravitational-wave data relies on matched-filtering techniques which, in turn, depend on accurate model waveforms. Here we characterize the systematic biases introduced in measuring astrophysical parameters of binary black holes by applying the currently most accurate effective-one-body templates to simulated data containing nonspinning numerical-relativity waveforms. We quantify the systematic bias by using a Markov chain Monte Carlo algorithm to sample the posterior distribution function of noise-free data, and compare the offset of the maximum a priori waveform parameters (the bias) to the width of the distribution, which we refer to as the statistical error. For advanced ground-based detectors, we find that the systematic biases are well within the statistical error for realistic signal-to-noise ratios. These biases grow to be comparable to the statistical errors at high ground-based-instrument signal-to-noise ratios (SNR∼50), but never dominate the error budget. At the much larger signal-to-noise ratios expected for space-based detectors, these biases will become large compared to the statistical errors, but for astrophysical black hole mass estimates the absolute biases (of at most a few percent) are still fairly small.'), (9572, 'Systematic biases in parameter estimation of binary black-hole mergers'), (9573, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.104003'), (9574, 'http://arxiv.org/abs/1408.3406'), (9575, 'arXiv:1408.3406 [astro-ph, physics:gr-qc]'), (9576, '2014-08-14 2014-08-14'), (9577, 'arXiv: 1408.3406'), (9578, '2014-08-16 03:34:23'), (9579, 'Compact binaries that emit gravitational waves in the sensitivity band of ground-based detectors can have non-negligible eccentricities just prior to merger, depending on the formation scenario. We develop a purely analytic, frequency-domain model for gravitational waves emitted by compact binaries on orbits with small eccentricity, which reduces to the quasi-circular post-Newtonian approximant TaylorF2 at zero eccentricity and to the post-circular approximation of Yunes et al. (2009) at small eccentricity. Our model uses a spectral approximation to the (post-Newtonian) Kepler problem to model the orbital phase as a function of frequency, accounting for eccentricity effects up to ${\\cal{O}}(e^8)$ at each post-Newtonian order. Our approach accurately reproduces an alternative time-domain eccentric waveform model for eccentricities $e\\in [0, 0.4]$ and binaries with total mass less than 12 solar masses. As an application, we evaluate the signal amplitude that eccentric binaries produce in different networks of existing and forthcoming gravitational waves detectors. Assuming a population of eccentric systems containing black holes and neutron stars that is uniformly distributed in co-moving volume, we estimate that second generation detectors like Advanced LIGO could detect approximately 0.1-10 events per year out to redshift $z\\sim 0.2$, while an array of Einstein Telescope detectors could detect hundreds of events per year to redshift $z \\sim 2.3$.'), (9580, 'Accurate and efficient waveforms for compact binaries on eccentric orbits'), (9581, 'http://www.arxiv.org/pdf/1408.3406.pdf'), (9582, 'arXiv:1408.3406 PDF'), (9583, '2014-08-19 18:42:57'), (9584, 'The equations are developed for spacecraft Doppler detection of periodic gravitational waves from a single binary star source. Graphical examples are included to indicate the great variety of Doppler signals which can be generated by these systems.'), (9585, 'The Doppler response to gravitational waves from a binary star source'), (9586, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/6/9/10.1063/1.1704788'), (9587, 'art%3A10.1007%2FBF00759146.pdf'), (9588, '1387-1391'), (9589, '1965-09-01 1965/09/01'), (9590, '10.1063/1.1704788'), (9591, '2014-08-20 12:03:19'), (9592, 'A purely covariant approach to general relativity, using the equation of geodesic deviation, is adopted. The physical interpretation is essentially that due to Pirani, but instead of using clouds of particles to analyze the gravitational field, a ``gravitational compass'' is proposed which fulfills the same purpose. Particular attention is focussed on the different roles played by the matter and the free gravitational field. The latter splits up conveniently into a super‐position of a transverse wave component, a longitudinal component, and a ``Coulomb'' field, all of which introduce ``shearing'' forces on the gravitational compass, while the matter contributes a general contraction. Applications to the Friedmann cosmological models and the problem of interactinggravitational waves are discussed.'), (9593, 'The Gravitational Compass'), (9594, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/6/9/1.1704788.pdf;jsessionid=63gk0bka4s2l3.x-aip-live-06?itemId=/content/aip/journal/jmp/6/9/10.1063/1.1704788&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (9595, 'http://arxiv.org/abs/1408.4283'), (9596, 'arXiv:1408.4283 [gr-qc]'), (9597, '2014-08-19 2014-08-19'), (9598, 'arXiv: 1408.4283'), (9599, '2014-08-20 12:11:15'), (9600, 'The definition of relative accelerations and strains among a set of comoving particles is studied in connection with the geometric properties of the frame adapted to a "fiducial observer." We find that a relativistically complete and correct definition of strains must take into account the transport law of the chosen spatial triad along the observer\'s congruence. We use special congruences of (accelerated) test particles in some familiar spacetimes to elucidate such a point. The celebrated idea of Szekeres\' compass of inertia, arising when studying geodesic deviation among a set of free-falling particles, is here generalized to the case of accelerated particles. In doing so we have naturally contributed to the theory of relativistic gravity gradiometer. Moreover, our analysis was made in an observer-dependent form, a fact that would be very useful when thinking about general relativistic tests on space stations orbiting compact objects like black holes and also in other interesting gravitational situations.'), (9601, 'Strains in General Relativity'), (9602, 'http://www.arxiv.org/pdf/1408.4283.pdf'), (9603, 'arXiv:1408.4283 PDF'), (9604, 'Official seal and emblem of the United Nations'), (9605, '1946-12-00 December 1946'), (9606, 'NL460424.pdf'), (9607, 'Chicago'), (9608, 'University Of Chicago Press'), (9609, 9780226767475), (9610, 'As long as there have been maps, cartographers have grappled with the impossibility of portraying the earth in two dimensions. To solve this problem mapmakers have created hundreds of map projections, mathematical methods for drawing the round earth on a flat surface. Yet of the hundreds of existing projections, and the infinite number that are theoretically possible, none is perfectly accurate.Flattening the Earth is the first detailed history of map projections since 1863. John P. Snyder discusses and illustrates the hundreds of known projections created from 500 B.C. to the present, emphasizing developments since the Renaissance and closing with a look at the variety of projections made possible by computers.The book contains 170 illustrations, including outline maps from original sources and modern computerized reconstructions. Though the text is not mathematically based, a few equations are included to permit the more technical reader to plot some projections. Tables summarize the features of nearly two hundred different projections and list those used in nineteenth-and twentieth-century atlases."This book is unique and significant: a thorough, well-organized, and insightful history of map projections. Snyder is the world\'s foremost authority on the subject and a significant innovator in his own right."—Mark Monmonier, author of How to Lie with Maps and Mapping It Out: Expository Cartography for the Humanities and Social Sciences.'), (9611, 'Flattening the Earth: Two Thousand Years of Map Projections'), (9612, 'Flattening the Earth'), (9613, '1984-00-00 1984'), (9614, '24th printing'), (9615, 'http://link.springer.com/article/10.1007/s10701-008-9223-3'), (9616, 'http://arxiv.org/abs/1408.5158'), (9617, 'arXiv:1408.5158 [astro-ph, physics:gr-qc]'), (9618, '2014-08-21 2014-08-21'), (9619, 'arXiv: 1408.5158'), (9620, '2014-08-25 13:20:44'), (9621, 'The detection and characterization of gravitational wave signals from compact binary coalescence events relies on accurate waveform templates in the frequency domain. The stationary phase approximation (SPA) can be used to compute closed-form frequency-domain waveforms for non-precessing, quasi-circular binary inspirals. However, until now, no fast frequency-domain waveforms have existed for generic, spin-precessing quasi-circular compact binary inspirals. Templates for these systems have had to be computed via a discrete Fourier transform of finely sampled time-domain waveforms, which is far more computationally expensive than those constructed directly in the frequency-domain, especially for those systems that are dominated by the inspiral part. There are two obstacles to deriving frequency-domain waveforms for precessing systems: (i) the spin-precession equations do not admit closed-form solutions for generic systems; (ii) the SPA fails catastrophically. Presently there is no general solution to the first problem, so we must resort to numerical integration of the spin precession equations. This is not a significant obstacle, as numerical integration on the slow precession timescale adds very little to the computational cost of generating the waveforms. Our main result is to solve the second problem, by providing an alternative to the SPA that we call the method of Shifted Uniform Asymptotics, or SUA, that cures the divergences in the SPA. The construction of frequency-domain templates using the SUA can be orders of magnitude more efficient than the time-domain ones obtained through a discrete Fourier transform. Moreover, this method is very faithful to the discrete Fourier transform, with mismatches on the order of $10^{-5}$.'), (9622, 'Fast Frequency-domain Waveforms for Spin-Precessing Binary Inspirals'), (9623, 'http://www.arxiv.org/pdf/1408.5158.pdf'), (9624, 'arXiv:1408.5158 PDF'), (9625, 'http://arxiv.org/abs/1408.4145'), (9626, 'arXiv:1408.4145 [astro-ph]'), (9627, '2014-08-18 2014-08-18'), (9628, 'arXiv: 1408.4145'), (9629, '2014-08-25 13:52:11'), (9630, 'Stellar-mass black holes and neutron stars represent extremes in gravity, density, and magnetic fields. They therefore serve as key objects in the study of multiple frontiers of physics. In addition, their origin (mainly in core-collapse supernovae) and evolution (via accretion or, for neutron stars, magnetic spindown and reconfiguration) touch upon multiple open issues in astrophysics. In this review, we discuss current mass and spin measurements and their reliability for neutron stars and stellar-mass black holes, as well as the overall importance of spins and masses for compact object astrophysics. Current masses are obtained primarily through electromagnetic observations of binaries, although future microlensing observations promise to enhance our understanding substantially. The spins of neutron stars are straightforward to measure for pulsars, but the birth spins of neutron stars are more difficult to determine. In contrast, even the current spins of stellar-mass black holes are challenging to measure. As we discuss, major inroads have been made in black hole spin estimates via analysis of iron lines and continuum emission, with reasonable agreement when both types of estimate are possible for individual objects, and future X-ray polarization measurements may provide additional independent information. We conclude by exploring the exciting prospects for mass and spin measurements from future gravitational wave detections, which are expected to revolutionize our understanding of strong gravity and compact objects.'), (9631, 'The Masses and Spins of Neutron Stars and Stellar-Mass Black Holes'), (9632, 'http://www.arxiv.org/pdf/1408.4145.pdf'), (9633, 'arXiv:1408.4145 PDF'), (9634, 'http://arxiv.org/abs/1408.5505'), (9635, 'arXiv:1408.5505 [gr-qc]'), (9636, '2014-08-23 2014-08-23'), (9637, 'arXiv: 1408.5505'), (9638, '2014-08-27 05:47:35'), (9639, 'Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical methods in general relativity: the post-Newtonian formalism, black hole perturbation theory, numerical relativity simulations, and the effective one-body model. We review recent work at the multiple interfaces of these analytical and numerical techniques, emphasizing the use of coordinate-invariant relationships to perform meaningful comparisons. Such comparisons provide independent checks of the validity of the various calculations, they inform the development of a universal, semi-analytical model of the binary dynamics and gravitational-wave emission, and they help to delineate the respective domains of validity of each approximation method. For instance, several recent comparisons suggest that perturbation theory may find applications in a broader range of physical problems than previously thought, including the radiative inspiral of intermediate mass-ratio and comparable-mass black hole binaries.'), (9640, 'The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem'), (9641, 'http://www.arxiv.org/pdf/1408.5505.pdf'), (9642, 'arXiv:1408.5505 PDF'), (9643, 'Grade-free product formulae from Grassman-Hopf Gebras'), (9644, 'Clifford algebras: Applications to mathematics, physics, and engineering'), (9645, 'Progress in Mathematical Physics'), (9646, 'Birkhäuser'), (9647, 'http://arxiv.org/abs/math-ph/0208018'), (9648, 'arXiv:math-ph/0208018'), (9649, '2002-08-13 2002-08-13'), (9650, 'arXiv: math-ph/0208018'), (9651, '2014-08-30 01:35:46'), (9652, "In the traditional approaches to Clifford algebras, the Clifford product is evaluated by recursive application of the product of a one-vector (span of the generators) on homogeneous i.e. sums of decomposable (Grassmann), multivectors and later extended by bilinearity. The Hestenesian 'dot' product, extending the one-vector scalar product, is even worse having exceptions for scalars and the need for applying grade operators at various times. Moreover, the multivector grade is not a generic Clifford algebra concept. The situation becomes even worse in geometric applications if a meet, join or contractions have to be calculated. Starting from a naturally graded Grassmann Hopf gebra, we derive general formulae for the products: meet and join, comeet and cojoin, left/right contraction, left/right cocontraction, Clifford and co-Clifford products. All these product formulae are valid for any grade and any inhomogeneous multivector factors in Clifford algebras of any bilinear form, including non-symmetric and degenerated forms. We derive the three well known Chevalley formulae as a specialization of our approach and will display co-Chevalley formulae. The Rota--Stein cliffordization is shown to be the generalization of Chevalley deformation. Our product formulae are based on invariant theory and are not tied to representations/matrices and are highly computationally effective. The method is applicable to symplectic Clifford algebras too."), (9653, 'http://arxiv.org/abs/1409.1800'), (9654, 'http://www.arxiv.org/pdf/math-ph/0208018.pdf'), (9655, 'arXiv:math-ph/0208018 PDF'), (9656, 'http://arxiv.org/abs/math/0011263'), (9657, 'arXiv:math/0011263'), (9658, '2000-11-30 2000-11-30'), (9659, 'arXiv: math/0011263'), (9660, '2014-08-30 01:36:07'), (9661, 'A Clifford algebra Cl(V,\\eta\\in V^*\\otimes V^*) jointly with a Clifford cogebra Cl(V,\\xi\\in V\\otimes V) is said to be a Clifford biconvolution Cl(\\eta,\\xi). We show that a Clifford biconvolution for dim_R Cl=4 does possess an antipode iff det(id-\\xi\\circ\\eta)\\neq 0. An antipodal Clifford biconvolution is said to be a Clifford Hopf gebra. We study the Clifford Hopf gebra and examples of antipode less Clifford bigebras including the Grassmann case.'), (9662, 'Clifford Hopf gebra for two-dimensional space'), (9663, 'http://www.arxiv.org/pdf/math/0011263.pdf'), (9664, 'arXiv:math/0011263 PDF'), (9665, 'Grade-free product formulae from Grassmann-Hopf gebras'), (9666, 'http://arxiv.org/abs/gr-qc/0011015'), (9667, 'arXiv:gr-qc/0011015'), (9668, '2000-11-04 2000-11-04'), (9669, 'arXiv: gr-qc/0011015'), (9670, '2014-08-30 01:38:23'), (9671, "We give a critical analysis of projective relativity theory. Examining Kaluza's own intention and the following development by Klein, Jordan, Pauli, Thiry, Ludwig and others, we conclude that projective relativity was abused in its own terms. Much more in the case of newer higher dimensional Kaluza--Klein theories with non-Abelian gauge groups. Reviewing the projective formulation of the Jordan isomorphy theorem yields some hints how one can proceed in a different direction. We can interpret the condition R5_{\\mu\\nu}=0 not as a field equation in a 5-dimensional Riemannian space, e.g. as vacuum Einstein-Hilbert equation, but can (or should) interpret it as a geometrical object, a null-quadric. Projective aspects of quantum (field) theory are discussed under this viewpoint."), (9672, 'Projective Relativity: Present Status and Outlook'), (9673, 'Projective Relativity'), (9674, 'http://www.arxiv.org/pdf/gr-qc/0011015.pdf'), (9675, 'arXiv:gr-qc/0011015 PDF'), (9676, 'arXiv:1409.1800 [gr-qc, physics:hep-th, physics:math-ph]'), (9677, '2014-09-05 2014-09-05'), (9678, 'arXiv: 1409.1800'), (9679, '2014-09-11 10:35:10'), (9680, 'In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups, symplectic geometry on the space of gravitational connections and geometric quantization via K\\"ahler structures. On the physical side, null infinity provides a natural home to study gravitational radiation and its structure leads to several interesting effects such as an infinite dimensional enlargement of the Poincar\\\'e group, geometrical expressions of energy and momentum carried by gravitational waves, emergence of non-trivial `vacuum configurations\' and an unforeseen interplay between infrared properties of the quantum gravitational field and the enlargement of the asymptotic symmetry group. The goal of this article is to present a succinct summary of this subtle and beautiful interplay.'), (9681, 'Geometry and Physics of Null Infinity'), (9682, 'http://www.arxiv.org/pdf/1409.1800.pdf'), (9683, 'arXiv:1409.1800 PDF'), (9684, 'http://arxiv.org/abs/1409.3546'), (9685, 'arXiv:1409.3546 [gr-qc]'), (9686, '2014-09-11 2014-09-11'), (9687, 'arXiv: 1409.3546'), (9688, '2014-09-12 22:03:37'), (9689, 'This paper is motivated by the need to improve the post-Newtonian (PN) amplitude accuracy of waveforms for gravitational waves generated by inspiralling compact binaries, both for use in data analysis and in the comparison between post-Newtonian approximations and numerical relativity computations. It presents: (i) the non-linear couplings between multipole moments of general post-Newtonian matter sources up to order 3.5PN, including all contributions from tails, tails-of-tails and the non-linear memory effect; and (ii) the source mass-type octupole moment of (non-spinning) compact binaries up to order 3PN, which permits to complete the expressions of the octupole modes (3,3) and (3,1) of the gravitational waveform to order 3.5PN. At this occasion we reconfirm by means of independent calculations our earlier results concerning the source mass-type quadrupole moment to order 3PN. Related discussions on factorized resummed waveforms and the occurence of logarithmic contributions to high order are also included.'), (9690, 'Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order'), (9691, 'http://www.arxiv.org/pdf/1409.3546.pdf'), (9692, 'arXiv:1409.3546 PDF'), (9693, 102), (9694, '1340-1363'), (9695, '0018-9219'), (9696, '2014-09-00 Sept 2014'), (9697, '10.1109/JPROC.2014.2339299'), (9698, 'Geometric Algebra for Electrical and Electronic Engineers'), (9699, '06876131.pdf'), (9700, 'Nat Phys'), (9701, '10.1038/nphys2011'), (9702, '2014-09-13 11:12:51'), (9703, 'Geometric intuition'), (9704, 'http://www.nature.com.proxy.library.cornell.edu/nphys/journal/v7/n6/pdf/nphys2011.pdf'), (9705, 'http://www.jstor.org.proxy.library.cornell.edu/stable/2323537'), (9706, 'Copyright © 1983 Mathematical Association of America'), (9707, 90), (9708, '697-701'), (9709, '0002-9890'), (9710, '1983-12-01 December 1, 1983'), (9711, '10.2307/2323537'), (9712, '2014-09-14 09:58:39'), (9713, 'Cross Products of Vectors in Higher Dimensional Euclidean Spaces'), (9714, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2323537.pdf?acceptTC=true'), (9715, 'http://arxiv.org/abs/1409.4431'), (9716, 'arXiv:1409.4431 [gr-qc]'), (9717, '2014-09-15 2014-09-15'), (9718, '37–44'), (9719, '2014-09-17 22:37:53'), (9720, 'Gravitational waves from precessing black-hole binaries exhibit features that are absent in nonprecessing systems. The most prominent of these is a parity-violating asymmetry that beams energy and linear momentum preferentially along or opposite to the orbital angular momentum, leading to recoil of the binary. The asymmetry will appear as amplitude and phase modulations at the orbital frequency. For strongly precessing systems, it accounts for at least 3% amplitude modulation for binaries in the sensitivity band of ground-based gravitational-wave detectors, and can exceed 50% for massive systems. Such asymmetric features are also clearly visible when the waves are decomposed into modes of spin-weighted spherical harmonics, and are inherent in the waves themselves---rather than resulting from residual eccentricity in numerical simulations, or from mode-mixing due to precession. In particular, there is generically no instantaneous frame for which the mode decomposition will have any symmetry. We introduce a method to simplify the expressions for waveforms given in analytical relativity, which can be used to combine existing high-order waveforms for nonprecessing systems with expressions for the precessing contributions, leading to improved accuracy and a unified treatment of precessing and nonprecessing binaries. Using this method, it is possible to clarify the nature and the origins of the asymmetries and show the effects of asymmetry on recoils more clearly. We present post-Newtonian (PN) expressions for the waveform modes that include these terms, complete to the relative 2PN level in spin (proportional to $v^4/c^4$ times a certain combination of the spins). Comparing the results of those expressions to numerical results, we find good qualitative agreement. We also demonstrate how these expressions can be used to efficiently calculate waveforms for gravitational-wave astronomy.'), (9721, 'Gravitational-wave modes from precessing black-hole binaries'), (9722, 'http://www.arxiv.org/pdf/1409.4431.pdf'), (9723, 'arXiv:1409.4431 PDF'), (9724, '610-647'), (9725, 'Introduction to Clifford Algebra'), (9726, 'http://www.av8n.com/physics/clifford-intro.htm'), (9727, '2014-09-19'), (9728, 'crgeo.pdf'), (9729, 'http://people.reed.edu/~jerry/311/crgeo.pdf'), (9730, '2008-07-01 2008/07/01'), (9731, '10.1007/s10701-008-9223-3'), (9732, 'arXiv:1411.0674 [astro-ph, physics:gr-qc]'), (9733, 'In 1960–1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons. The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his calculus by developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent. A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms.'), (9734, 'The Foundations of Quantum Mechanics and the Evolution of the Cartan-Kähler Calculus'), (9735, 'arXiv:1410.2130 [astro-ph, physics:gr-qc, physics:hep-th]'), (9736, '2014-10-01 14:15:47'), (9737, '2014-10-08 2014-10-08'), (9738, 'Foundations.pdf'), (9739, 'http://arxiv.org/abs/1205.4657'), (9740, 'arXiv:1205.4657 [math]'), (9741, '2012-05-18 2012-05-18'), (9742, 'arXiv: 1205.4657'), (9743, '2014-10-01 14:16:47'), (9744, 'A very small amount of K\\"ahler algebra (i.e. Clifford algebra of differential forms) in the real plane makes x + ydxdy emerge as a factor between the differentials of the Cartesian and polar coordinates, largely replacing the concept of complex variable. The integration on closed curves of closed 1-forms on multiply connected regions takes us directly to a real plane version of the theorem of residues. One need not resort to anything like differentiation and integration with respect to x + ydxdy. It is a matter of algebra and integration of periodic functions. We then derive Cauchy\'s integral formulas, including the ones for the derivatives. Additional complex variable theory of general interest for phyicists is then trivial. The approach is consistent with the Weierstrass point of view: power series expansions, even if explicit expressions are not needed. By design, this approach cannot replace integrations that yield complex results. These can be obtained with an approach based on the Cauchy point of view, where the Cauchy-Riemann conditions come first and the theorem of residues comes last.'), (9745, 'Real Version of Calculus of Complex Variable (I): Weierstrass Point of View'), (9746, 'Real Version of Calculus of Complex Variable (I)'), (9747, 'http://www.arxiv.org/pdf/1205.4657.pdf'), (9748, 'arXiv:1205.4657 PDF'), (9749, 'http://arxiv.org/abs/1205.4256'), (9750, 'arXiv:1205.4256 [math]'), (9751, 'arXiv: 1205.4256'), (9752, '2014-10-01 14:16:54'), (9753, 'As was the case in a previous paper, the differential form x+ydxdy plays the role that the variable z plays in the standard calculus of complex variable. The role of holomorphic functions will now be played by strict harmonic differential forms in the Kaehler algebra of the real plane. These differential forms satisfy the Cauchy-Riemann relations. No new concept of differentiation is needed, and yet this approach parallels standard Cauchy theory, but more simply. The power series and theorem of residues belong here at the end, unlike in the previous paper.'), (9754, "Real Version of Calculus of Complex Variable (II): Cauchy's Point of View"), (9755, 'Real Version of Calculus of Complex Variable (II)'), (9756, 'http://www.arxiv.org/pdf/1205.4256.pdf'), (9757, 'arXiv:1205.4256 PDF'), (9758, 'http://link.springer.com/article/10.1007/s00006-008-0112-9'), (9759, '993-1006'), (9760, '10.1007/s00006-008-0112-9'), (9761, '2014-10-01 14:17:02'), (9762, 'In 1960-1962, Kähler produced a generalization of Cartan’s calculus of differential forms which he claimed to be a common language for relativity and quantum mechanics. It revolves around the “Kähler-Dirac (KD) equation”, which plays a role in this calculus comparable to that of the equations of structure in geometry. Its reach is such that the input differential form needed to solve the relativistic hydrogen atom is just a very simple one among the possible inputs. We show how Cartan’s methods allow one to simplify or ignore many of Kähler’s cumbersome formulas. We interpret the three series of indices in the components of this calculus and show a promising connection between the structure of its solutions to problems with symmetries and Schmeikal’s algebraic representation of low energy quarks.'), (9763, 'New Perspectives on the Kähler Calculus and Wave Functions'), (9764, 'arXiv: 1410.2130'), (9765, 'art%3A10.1007%2Fs00006-008-0112-9.pdf'), (9766, 'http://link.springer.com/article/10.1007/s00006-014-0452-6'), (9767, '817-847'), (9768, '2014-09-01 2014/09/01'), (9769, '10.1007/s00006-014-0452-6'), (9770, '2014-10-01 18:25:24'), (9771, 'We first recall using the Clifford bundle formalism (CBF) of differential forms and the theory of extensors acting on \ue22fℓ{\\mathcal{C}\\ell} (M, g) (the Clifford bundle of differential forms) the formulation of the intrinsic geometry of a differential manifold M equipped with a metric field g of signature (p, q) and an arbitrary metric compatible connection ∇{\\nabla} introducing the torsion (2−1)-extensor field τ{\\tau} , the curvature (2 − 2) extensor field ℜ{\\Re} and (once fixing a gauge) the connection (1−2)-extensor ω{\\omega} and the Ricci operator ∂⋀∂{\\partial \\bigwedge \\partial} (where ∂{\\partial} is the Dirac operator acting on sections of \ue22fℓ(M,g){\\mathcal{C}\\ell(M, g)} ) which plays an important role in this paper. Next, using the CBF we give a thoughtful presentation the Riemann or the Lorentzian geometry of an orientable submanifold M (dim M = m) living in a manifold M̊ (such that M̊ ≃ℝn{\\simeq \\mathbb{R}^n} is equipped with a semi- Riemannian metric g̊ with signature (p̊, q̊) and p̊+q̊ = n and its Levi- Civita connection D̊) and where there is defined a metric g = i*g̊, where i:M→{i : M \\rightarrow} M̊ is the inclusion map. We prove several equivalent forms for the curvature operator ℜ{\\Re} of M. Moreover we show a very important result, namely that the Ricci operator of M is the (negative) square of the shape operator S of M (object obtained by applying the restriction on M of the Dirac operator ∂̊ of \ue22fℓ{\\mathcal{C}\\ell} (M̊, g̊) to the projection operator P). Also we disclose the relationship between the (1−2)-extensor ω{\\omega} and the shape biform \ue23f{\\mathcal{S}} (an object related to S). The results obtained are used to give a mathematical formulation to Clifford’s theory of matter. It is hoped that our presentation will be useful for differential geometers and theoretical physicists interested, e.g., in string and brane theories and relativity theory by divulging, improving and expanding very important and so far unfortunately largely ignored results appearing in reference [13].'), (9772, 'A Clifford Bundle Approach to the Differential Geometry of Branes'), (9773, '2014-10-09 15:27:10'), (9774, 'art%3A10.1007%2Fs00006-014-0452-6.pdf'), (9775, 'http://link.springer.com/article/10.1007/s00006-014-0459-z'), (9776, '713-736'), (9777, '10.1007/s00006-014-0459-z'), (9778, '2014-10-01 18:27:15'), (9779, 'In this paper we combine methods from projective geometry, Klein’s model, and Clifford algebra. We develop a Clifford algebra whose Pin group is a double cover of the group of regular projective transformations. The Clifford algebra we use is constructed as homogeneous model for the five-dimensional real projective space ℙ5(ℝ){\\mathbb {P}^5 (\\mathbb{R})} where Klein’s quadric M42{M^4_2} defines the quadratic form. We discuss all entities that can be represented naturally in this homogeneous Clifford algebra model. Projective automorphisms of Klein’s quadric induce projective transformations of ℙ3(ℝ){\\mathbb {P}^3 (\\mathbb{R})} and vice versa. Cayley-Klein geometries can be represented by Clifford algebras, where the group of Cayley-Klein isometries is given by the Pin group of the corresponding Clifford algebra. Therefore, we examine the versor group and study the correspondence between versors and regular projective transformations represented as 4 × 4 matrices. Furthermore, we give methods to compute a versor corresponding to a given projective transformation.'), (9780, 'A Clifford Algebraic Approach to Line Geometry'), (9781, 'This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric\'s importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the "miraculous" nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.'), (9782, 'http://link.springer.com/article/10.1007/s00006-014-0446-4'), (9783, '849-874'), (9784, '10.1007/s00006-014-0446-4'), (9785, '2014-10-01 18:27:24'), (9786, 'Supergroups are defined in the framework of ℤ2{\\mathbb{Z}_2} 2-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex and real supergroups are defined by Brauer-Wall groups related with the modulo 2 and modulo 8 periodicities of the complex and real Clifford algebras. Particle (fermionic and bosonic) representations of a universal covering (spinor group Spin +(1, 3)) of the proper orthochronous Lorentz group are constructed via the Clifford algebra formalism. Complex and real supergroups are defined on the representation system of Spin +(1, 3). It is shown that a cyclic (modulo 2) structure of the complex supergroup is equivalent to a supersymmetric action, that is, it converts fermionic representations into bosonic representations and vice versa. The cyclic action of the real supergroup leads to a much more high-graded symmetry related with the modulo 8 periodicity of the real Clifford algebras. This symmetry acts on the system of real representations of Spin +(1, 3).'), (9787, 'Cyclic Structures of Cliffordian Supergroups and Particle Representations of Spin+(1, 3)'), (9788, 'The Kerr Metric'), (9789, 'art%3A10.1007%2Fs00006-014-0446-4.pdf'), (9790, 'art%3A10.1007%2Fs00006-014-0459-z.pdf'), (9791, 'World Scientific Publishing Company'), (9792, 9789814566391), (9793, '2014-04-18 April 18, 2014'), (9794, 'This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative — almost like a story being told — that does not impede sophistication and deep results. It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter. In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose. Readership: Physicists and mathematicians working on differential geometry.'), (9795, 'Differential Geometry for Physicists and Mathematicians: Moving Frames and Differential Forms: From Euclid Past Riemann'), (9796, 'Differential Geometry for Physicists and Mathematicians'), (9797, 312), (9798, 'http://www.amazon.com/Differential-Geometry-Physicists-Mathematicians-Riemann/dp/981456639X/ref=sr_1_1?s=books&ie=UTF8&qid=1398325103&sr=1-1&keywords=Differential+Geometry+for+Physicists+and+Mathematicians'), (9799, '2014-10-01 20:12:18'), (9800, 'Amazon.com Link'), (9801, 'http://iopscience.iop.org/1742-6596/256/1/012026'), (9802, 256), (9803, '012026'), (9804, '2010-11-01 2010-11-01'), (9805, '10.1088/1742-6596/256/1/012026'), (9806, '2014-10-01 22:18:57'), (9807, "SciNet, one of seven regional HPC consortia operating under the Compute Canada umbrella, runs Canada's first and third fastest computers (as of June 2010) in a state-of-the-art, highly energy-efficient datacentre with a Power Usage Effectiveness (PUE) design-point of 1.16. Power efficiency, computational bang for the buck and system capability for a handful of flagship science projects were important criteria in choosing the nature of the computers and the data centre itself. Here we outline some of the lessons learned in putting together the systems and the data centre that hosts Canada's fastest computer to date."), (9808, 'SciNet: Lessons Learned from Building a Power-efficient Top-20 System and Data Centre'), (9809, 'SciNet'), (9810, 'http://iopscience.iop.org/1742-6596/256/1/012026/pdf/1742-6596_256_1_012026.pdf'), (9811, '978-1-4503-1638-5'), (9812, '2014-10-02 01:26:03'), (9813, 'http://iopscience.iop.org/0264-9381/30/7/075017/pdf/0264-9381_30_7_075017.pdf'), (9814, 'bibtex: Marsat2013'), (9815, '2014-10-02 03:25:25'), (9816, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.84.124002'), (9817, 'Berlin'), (9818, '10.1145/2365934.2365942'), (9819, '2014-10-27 04:15:13'), (9820, 'Comparing Post-Newtonian and Numerical-Relativity Precession Dynamics'), (9821, 'A typical recommender setting is based on two kinds of relations: similarity between users (or between objects) and the taste of users towards certain objects. In environments such as online dating websites, these two relations are difficult to separate, as the users can be similar to each other, but also have preferences towards other users, i.e., rate other users. In this paper, we present a novel and unified way to model this duality of the relations by using split-complex numbers, a number system related to the complex numbers that is used in mathematics, physics and other fields. We show that this unified representation is capable of modeling both notions of relations between users in a joint expression and apply it for recommending potential partners. In experiments with the Czech dating website Libimseti.cz we show that our modeling approach leads to an improvement over baseline recommendation methods in this scenario.'), (9822, 'bibtex: Schmidt2011'), (9823, 'bibtex: Schutz1986'), (9824, 'arXiv:1303.7412 [gr-qc] \nbibtex: Bohe2013'), (9825, 'bibtex: Bohe2013a'), (9826, 'arXiv: 1409.4431 \nbibtex: Boyle2014'), (9827, 'bibtex: Boyle2009'), (9828, 'bibtex: Boyle2011'), (9829, 'bibtex: Boyle2009a'), (9830, 'bibtex: Boyle2013'), (9831, 'bibtex: Buonanno2003'), (9832, 'bibtex: Doran2003'), (9833, 'bibtex: Duistermaat2000'), (9834, 'bibtex: Huynh2009'), (9835, 'bibtex: Lehner2007'), (9836, 'bibtex: Loken2010'), (9837, 'bibtex: Moakher2002'), (9838, 'bibtex: Mroue2013'), (9839, 'bibtex: OShaughnessy2011a'), (9840, 'not yet published \nbibtex: Ossokine2014'), (9841, 'bibtex: Perwass2009'), (9842, 'bibtex: Taylor2013'), (9843, 'We review the applications of geometric algebra in electromag- netism, gravitation and multiparticle quantum systems. We discuss a gauge the- ory formulation of gravity and its implementation in geometric algebra, and apply this to the fermion bound state problem in a black hole background. We show that a discrete energy spectrum arises in an analogous way to the hydrogen atom. A geometric algebra approach to multiparticle quantum systems is given in terms of the multiparticle spacetime algebra. This is applied to quantum information processing, multiparticle wave equations and to conformal geometry. The appli- cation to conformal geometry highlight some surprising links between relativistic quantum theory, twistor theory and de Sitter spaces.'), (9844, 'http://arxiv.org/abs/math-ph/0604048'), (9845, 'arXiv:math-ph/0604048'), (9846, '2006-04-20 2006-04-20'), (9847, 'arXiv: math-ph/0604048'), (9848, '2014-10-06 16:39:46'), (9849, 'Events in Minkowski space-time can be obtained from the intersection of two twistors with no helicity. These can be represented within the geometric (Clifford) algebra formalism, in a particular conformal space that is constructed from a quantum system of two particles. The realisation takes place in the multiparticle space-time algebra. This representation allows us to identify an event with the wave-function for a non-charged Klein-Gordon particle. A more general point can also be obtained, if the space is complexified and the twistors have non-zero helicity. In this case, such a point is no longer an event, but it can be identified with the wave-function for a charged Klein-Gordon particle. Other spaces of cosmological relevance can also be constructed using the 2-particle representation of the conformal space, as is the case for de Sitter and anti-de Sitter spaces. Furthermore, we show that Friedmann-Robertson-Walker spaces, with and without big bang, are fully described through two twistors, which are expressed within our formalism in terms of entities belonging to quantum mechanics: the Dirac matrix $\\gamma_0$, a massless maximally entangled state and its complex conjugate.'), (9850, 'Events and cosmological spaces through twistors in the geometric (Clifford) algebra formalism'), (9851, 'http://www.arxiv.org/pdf/math-ph/0604048.pdf'), (9852, 'arXiv:math-ph/0604048 PDF'), (9853, 'http://www.arxiv.org/pdf/1410.2130.pdf'), (9854, 'arXiv:1410.2130 PDF'), (9855, 'Online Dating Recommender Systems: The Split-complex Number Approach'), (9856, 'Proceedings of the 4th ACM RecSys Workshop on Recommender Systems and the Social Web'), (9857, 'CRC Press'), (9858, 9780849378744), (9859, 'Online Dating Recommender Systems'), (9860, 'This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.'), (9861, 'Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem'), (9862, 'Invariance Theory'), (9863, 'Hestenes - 2002 - New foundations for classical mechanics.djvu'), (9864, 'http://arxiv.org/abs/1403.7698'), (9865, 'arXiv:1403.7698 [cs]'), (9866, 'http://pages.uoregon.edu/gilkey/dirPDF/InvarianceTheory1Ed.pdf'), (9867, 'InvarianceTheory1Ed.pdf'), (9868, '1996 electronic reprint'), (9869, 'http://www.jstor.org/stable/2369379'), (9870, 'Ann Arbor, MI'), (9871, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/34/8/10.1063/1.530050'), (9872, '3642-3669'), (9873, '1993-08-01 1993/08/01'), (9874, '10.1063/1.530050'), (9875, '2014-10-11 18:17:30'), (9876, 'It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie group can be represented as a spin group. Thus, the computational power of geometric algebra is available to simplify the analysis and applications of Lie groups and Lie algebras. The spin version of the general linear group is thoroughly analyzed, and an invariant method for constructing real spin representations of other classical groups is developed. Moreover, it is demonstrated that every linear transformation can be represented as a monomial of vectors in geometric algebra.'), (9877, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/34/8/1.530050.pdf?itemId=/content/aip/journal/jmp/34/8/10.1063/1.530050&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (9878, 'http://arxiv.org/abs/1410.2781'), (9879, 'arXiv:1410.2781 [gr-qc, physics:physics]'), (9880, '2014-09-01 2014-09-01'), (9881, 'arXiv: 1410.2781'), (9882, '2014-10-13 14:58:41'), (9883, 'It is taken into account that not the Ricci tensor ${R_{il}}$ (Einstein equation), but the Riemann tensor ${R_{iklm}}$ provides the most general description of the space geometry. If ${{R_{il}}=0}$ (the space empty with matter, but it can be occupied by gravitational waves) then ${{R_{iklm}}={C_{iklm}}} $ . The tensor ${C_{iklm}}$ is the Weyl tensor, which disappears by conversion:${{R_{il}}={g^{km}}{R_{iklm}}}$ and we lose all information about the space structure, which is described by ${C_{iklm}}$ .The symmetry of ${R_{il}}$ provides the existents of gravitational waves with the spin s=2. We show that ${C_{iklm}}$ describes gravitational waves with s=1. Such gravitational waves can be created in inhomogeneous media, where the selected directions are determined by derivates of the energy-momentum tensor ${T^m}_{i,k}$ of matter. It is taken into account that gravitation is described not only by the metric tensor $g^{ik} = (1/2)(\\gamma^i \\gamma^k + \\gamma^k \\gamma^i)$, but also by the anti-symmetric tensor $\\sigma^{ik} = (i/2)({\\gamma^i}{\\gamma^k} - {\\gamma^k}{\\gamma^i})$, where ${\\gamma^k}(x)$ are Clifford matrices. We show that the tensor ${K_{ik}} = (1/4){\\sigma^{lm}} {R_{iklm}}$, is the anty-simmetric analog to the Ricci tensor. The ${K_{lm}}$ describes various kinds of space metrics, not described by the Ricci tensor. It includes the Weyl tensor ${C_{iklm}}$, because $\\sigma^{lm} {C_{lmik}}$ is not zero.'), (9884, 'The Riemann Geometry of Space and Gravitational Waves With The Spin $s=1$'), (9885, 'http://www.arxiv.org/pdf/1410.2781.pdf'), (9886, 'arXiv:1410.2781 PDF'), (9887, 'http://iopscience.iop.org/1742-6596/538/1/012010'), (9888, 538), (9889, '012010'), (9890, '2014-10-10 2014-10-10'), (9891, '10.1088/1742-6596/538/1/012010'), (9892, '2014-10-20 14:48:21'), (9893, 'It is still a great riddle to me why Wolfgang Pauli and P.A.M. Dirac had not fully grasped the meaning of their own mathematical constructions. They invented magnificent, fantastic and very important mathematical features of modern physics, but they only delivered half of the interpretations of their own inventions. Of course, Pauli matrices and Dirac matrices represent operators, which Pauli and Dirac discussed in length. But this is only part of the true meaning behind them, as the non-commutative ideas of Grassmann, Clifford, Hamilton and Cartan allow a second, very far reaching interpretation of Pauli and Dirac matrices. An introduction to this alternative interpretation will be discussed. Some applications of this view on Pauli and Dirac matrices are given, e.g. a geometric algebra picture of the plane wave solution of the Maxwell equation, a geometric algebra picture of special relativity, a toy model of SU(3) symmetry, and some only very preliminary thoughts about a possible geometric meaning of quantum mechanics.'), (9894, 'An Introduction to Geometric Algebra with some Preliminary Thoughts on the Geometric Meaning of Quantum Mechanics'), (9895, 'http://iopscience.iop.org/1742-6596/538/1/012010/pdf/1742-6596_538_1_012010.pdf'), (9896, 'http://link.springer.com/article/10.1007/s00006-009-0184-1'), (9897, '673-686'), (9898, '2009-12-01 2009/12/01'), (9899, '10.1007/s00006-009-0184-1'), (9900, '2014-10-20 15:13:56'), (9901, 'This is a short review of the algebraic properties of Clifford algebras and spinors. Their use in the description of fundamental physics (elementary particles) is also summarized.'), (9902, 'Clifford Algebras, Spinors and Fundamental Interactions: Twenty Years After'), (9903, 'Clifford Algebras, Spinors and Fundamental Interactions'), (9904, 'p37-kunegis.pdf'), (9905, 'art%3A10.1007%2Fs00006-009-0184-1.pdf'), (9906, 'http://link.springer.com/article/10.1007/s00006-009-0197-9'), (9907, '819-834'), (9908, '10.1007/s00006-009-0197-9'), (9909, '2014-10-20 15:15:42'), (9910, 'The main objective of this lecture is to discuss the proper place for Clifford’s geometric algebra in the mathematical curriculum at all levels.'), (9911, 'Clifford Algebra and the Didactics of Mathematics'), (9912, 'http://arxiv.org/abs/math-ph/0603037'), (9913, 'art%3A10.1007%2Fs00006-009-0197-9.pdf'), (9914, 'http://link.springer.com/article/10.1007/s00006-009-0194-z'), (9915, '793-817'), (9916, '10.1007/s00006-009-0194-z'), (9917, '2014-10-20 15:16:36'), (9918, 'A unipotent isometry is said to be a reflection. In 1937 Élie Cartan proved that every isometry can be expressed as a composition of reflections. The Lie subalgebra of bivectors inside a Clifford algebra generate isometries without the Grassmann exponential. The main result is the coordinate-free and basis-free construction of two isometries from a simple bivector. Hestenes introduced in 1966 a rotor in a Spin group as a square root of the Clifford product of two vectors. We compare a rotor from reflections, with a rotor from a simple bivector. This result generalizes the Lorentz transformations considered by Pertti Lounesto in 1997.'), (9919, 'Isometry from Reflections Versus Isometry from Bivector'), (9920, 'arXiv:math-ph/0603037'), (9921, 'art%3A10.1007%2Fs00006-009-0194-z.pdf'), (9922, '2006-03-13 2006-03-13'), (9923, 'arXiv: math-ph/0603037'), (9924, '2014-10-27 17:51:20'), (9925, 'In previous work by two of the present authors, twistors were re-interpreted as 4-d spinors with a position dependence within the formalism of geometric (Clifford) algebra. Here we extend that approach and justify the nature of the position dependence. We deduce the spinor representation of the restricted conformal group in geometric algebra, and use it to show that the position dependence is the result of the action of the translation operator in the conformal space on the 4-d spinor. We obtain the geometrical description of twistors through the conformal geometric algebra, and derive the Robinson congruence. This verifies our formalism. Furthermore, we show that this novel approach brings considerable simplifications to the twistor formalism, and new advantages. We map the twistor to the 6-d conformal space, and derive the simplest geometrical description of the twistor as an observable of a relativistic quantum system. The new 6-d twistor takes the r\\^ole of the state for that system. In our new interpretation of twistors as 4-d spinors, we therefore only need to apply the machinery already known from quantum mechanics in the geometric algebra formalism, in order to recover the physical and geometrical properties of 1-valence twistors.'), (9926, 'A representation of twistors within geometric (Clifford) algebra'), (9927, 'http://www.arxiv.org/pdf/math-ph/0603037.pdf'), (9928, 'arXiv:math-ph/0603037 PDF'), (9929, 'http://iopscience.iop.org/0305-4470/36/25/305'), (9930, 6963), (9931, '2003-06-27 2003-06-27'), (9932, '10.1088/0305-4470/36/25/305'), (9933, '2014-10-27 18:22:59'), (9934, 'The Kustaanheimo–Stiefel (KS) transformation maps the non-linear and singular equations of motion of the three-dimensional Kepler problem to the linear and regular equations of a four-dimensional harmonic oscillator. It is used extensively in studies of the perturbed Kepler problem in celestial mechanics and atomic physics. In contrast to the conventional matrix-based approach, the formulation of the KS-transformation in the language of geometric Clifford algebra offers the advantages of a clearer geometrical interpretation and greater computational simplicity. It is demonstrated that the geometric algebra formalism can readily be used to derive a Lagrangian and Hamiltonian description of the KS dynamics in arbitrary static electromagnetic fields.'), (9935, 'The Kustaanheimo–Stiefel transformation in geometric algebra'), (9936, '350-358'), (9937, 'JPA_v36_p6963.pdf'), (9938, 'http://arxiv.org/abs/1410.6687'), (9939, 'arXiv:1410.6687 [gr-qc]'), (9940, '2014-10-24 2014-10-24'), (9941, 'arXiv: 1410.6687'), (9942, '2014-10-28 15:53:35'), (9943, 'Gravitational-wave parameter estimation is only as good as the theory the waveform generation models are based upon. It is therefore crucial to test General Relativity (GR) once data becomes available. Many previous works, such as studies connected with the ppE framework by Yunes and Pretorius, rely on the stationary phase approximation (SPA) to model deviations from GR in the frequency domain. As Fast Fourier Transform algorithms have become considerably faster and in order to circumvent possible problems with the SPA, we test GR with corrected time domain waveforms instead of SPA waveforms. Since a considerable amount of work has been done already in the field using SPA waveforms, we establish a connection between leading-order-corrected waveforms in time and frequency domain, concentrating on phase-only corrected terms. In a Markov Chain Monte Carlo study, whose results are preliminary and will only be available later, we will assess the ability of the eLISA detector to measure deviations from GR for signals coming from supermassive black hole inspirals using these corrected waveforms.'), (9944, 'A Time Domain Waveform for Testing General Relativity'), (9945, 'http://www.arxiv.org/pdf/1410.6687.pdf'), (9946, 'arXiv:1410.6687 PDF'), (9947, 'American Journal of Mathematics'), (9948, '0002-9327'), (9949, '1878-01-01 January 1, 1878'), (9950, '10.2307/2369379'), (9951, '2014-10-29 12:20:07'), (9952, "Applications of Grassmann's Extensive Algebra"), (9953, 'http://www.jstor.org/stable/pdfplus/2369379.pdf?acceptTC=true'), (9954, 'http://scitation.aip.org/content/aapt/journal/ajp/61/6/10.1119/1.17202'), (9955, '505-513'), (9956, '1993-06-01 1993/06/01'), (9957, '10.1119/1.17202'), (9958, '2014-10-29 18:13:16'), (9959, 'scitation.aip.org'), (9960, 'A tutorial of geometric calculus is presented as a continuation of the development of geometric algebra in a previous paper. The geometric derivative is defined in a natural way that maintains the close correspondence between geometric algebra and the algebra of real numbers. The use of geometric calculus in physics is illustrated by expressing some basic results of electrodynamics.'), (9961, 'An introduction to geometric calculus and its application to electrodynamics'), (9962, 'http://scitation.aip.org/deliver/fulltext/aapt/journal/ajp/61/6/1.17202.pdf?itemId=/content/aapt/journal/ajp/61/6/10.1119/1.17202&mimeType=pdf&containerItemId=content/aapt/journal/ajp'), (9963, 'http://scripts.iucr.org.proxy.library.cornell.edu/cgi-bin/paper?S0108767306017478'), (9964, '491-504'), (9965, '10.1119/1.17201'), (9966, 'Acta Crystallographica Section A Foundations of Crystallography'), (9967, 'This paper presents a tutorial of geometric algebra, a very useful but generally unappreciated extension of vector algebra. The emphasis is on physical interpretation of the algebra and motives for developing this extension, and not on mathematical rigor. The description of rotations is developed and compared with descriptions using vector and matrix algebra. The use of geometric algebra in physics is illustrated by solving an elementary problem in classical mechanics, the motion of a freely spinning axially symmetric rigid body.'), (9968, 'An introduction to geometric algebra with an application in rigid body mechanics'), (9969, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aapt/journal/ajp/61/6/10.1119/1.17201'), (9970, '2014-10-29 18:57:39'), (9971, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aapt/journal/ajp/61/6/1.17201.pdf?itemId=/content/aapt/journal/ajp/61/6/10.1119/1.17201&mimeType=pdf&containerItemId=content/aapt/journal/ajp'), (9972, 'http://arxiv.org/abs/1410.7775'), (9973, 'arXiv:1410.7775 [astro-ph, physics:gr-qc]'), (9974, '2014-10-28 2014-10-28'), (9975, 'arXiv: 1410.7775'), (9976, '2014-10-30 18:09:03'), (9977, 'We present a method of calculating the strong-field gravitational lensing caused by many analytic and numerical spacetimes. We use this procedure to calculate the distortion caused by isolated black holes and by numerically evolved black hole binaries. We produce both demonstrative images illustrating details of the spatial distortion and realistic images of collections of stars taking both lensing amplification and redshift into account. On large scales the lensing from inspiraling binaries resembles that of single black holes, but on small scales the resulting images show complex and in some cases self-similar structure across different angular scales.'), (9978, 'What would a binary black hole merger look like?'), (9979, 'http://www.arxiv.org/pdf/1410.7775.pdf'), (9980, 'arXiv:1410.7775 PDF'), (9981, 'http://link.springer.com/article/10.1007/s00006-014-0513-x'), (9982, '1-33'), (9983, '2014-10-31 2014/10/31'), (9984, '10.1007/s00006-014-0513-x'), (9985, '2014-10-30 19:24:32'), (9986, 'We present a generalization of the spinor and twistor geometry for (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler–Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors are defined as solutions of generalized twistor equations determined by spin connections and frames adapted to nonlinear connection structures. We show that the constructions for local twistors can be globalized using nonholonomic deformations with “auxiliary” metric compatible connections completely determined by the metric structure and/or the Finsler fundamental function. We explain how to perform such an approach in the Einstein gravity theory formulated in Finsler like variables with conventional nonholonomic 2+2 splitting.'), (9987, 'Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications'), (9988, '2014-11-03 2014-11-03'), (9989, 'art%3A10.1007%2Fs00006-014-0513-x.pdf'), (9990, 'arXiv: 1411.0674'), (9991, '2014-11-06 03:26:24'), (9992, 'Binary black holes (BBHs) on quasicircular orbits are fully characterized by their total mass $M$, mass ratio $q$, spins $\\mathbf{S}_1$ and $\\mathbf{S}_2$, and orbital angular momentum $\\mathbf{L}$. When the binary separation $r \\gg GM/c^2$, the precession timescale is much shorter than the radiation-reaction time on which $L = |\\mathbf{L}|$ decreases due to gravitational-wave (GW) emission. We use conservation of the total angular momentum $\\mathbf{J} = \\mathbf{L} + \\mathbf{S}_1 + \\mathbf{S}_2$ (with magnitude $J$) and the projected effective spin $\\xi \\equiv M^{-2} [(1+q) \\mathbf{S}_1 + (1+q^{-1})\\mathbf{S}_2] \\cdot \\hat{\\mathbf{L}}$ on the precession time to derive an effective potential for BBH spin precession. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a period $\\tau(L, J, \\xi)$ the angular momenta return to their initial relative orientations and precess about $\\mathbf{J}$ by an angle $\\alpha(L, J, \\xi)$. We classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. Our new solutions constitute fundamental progress in our understanding of BBH spin precession and also have important astrophysical applications. We derive a precession-averaged evolution equation $dJ/dL$ that can be numerically integrated on the radiation-reaction time, allowing us to statistically track BBH spins from formation to merger far more efficiently than was possible with previous orbit-averaged precession equations. This will greatly help us predict the signatures of BBH formation in the GWs emitted near merger and the distributions of final spins and gravitational recoils. The solutions may also help efforts to model and interpret GWs from generic BBH mergers.'), (9993, 'Effective potentials and morphological transitions for binary black-hole spin precession'), (9994, 'http://www.arxiv.org/pdf/1411.0674.pdf'), (9995, 'arXiv:1411.0674 PDF'), (9996, '2014-03-30 2014-03-30'), (9997, 'arXiv: 1403.7698'), (9998, '2014-11-11 03:27:13'), (9999, "Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods in three dimensions for the Helmholtz, Laplace and related equations, if rotation-based decomposition of translation operators are used. In these and related problems related to representation of functions on a sphere via spherical harmonic expansions computation of the rotation coefficients of large degree $n$ (of the order of thousands and more) may be necessary. Existing algorithms for their computation, based on recursions, are usually unstable, and do not extend to $n$. We develop a new recursion and study its behavior for large degrees, via computational and asymptotic analyses. Stability of this recursion was studied based on a novel application of the Courant-Friedrichs-Lewy condition and the von Neumann method for stability of finite-difference schemes for solution of PDEs. A recursive algorithm of minimal complexity $O\\left(n^{2}\\right)$ for degree $n$ and FFT-based algorithms of complexity $O\\left(n^{2}\\log n\\right) $ suitable for computation of rotation coefficients of large degrees are proposed, studied numerically, and cross-validated. It is shown that the latter algorithm can be used for $n\\lesssim 10^{3}$ in double precision, while the former algorithm was tested for large $n$ (up to $10^{4}$ in our experiments) and demonstrated better performance and accuracy compared to the FFT-based algorithm."), (10000, 'Recursive computation of spherical harmonic rotation coefficients of large degree'), (10001, 'http://www.arxiv.org/pdf/1403.7698.pdf'), (10002, 'arXiv:1403.7698 PDF'), (10003, '1st edition'), (10004, 9780471164333), (10005, '1991-01-08 January 8, 1991'), (10006, 'This didactically unrivalled textbook and timeless reference by Nobel Prize Laureate Claude Cohen-Tannoudji separates essential underlying principles of quantum mechanics from specific applications and practical examples and deals with each of them in a different section. Chapters emphasize principles; complementary sections supply applications. The book provides a qualitative introduction to quantum mechanical ideas; a systematic, complete and elaborate presentation of all the mathematical tools and postulates needed, including a discussion of their physical content and applications. The book is recommended on a regular basis by lecturers of undergraduate courses.'), (10007, '0108-7673'), (10008, 914), (10009, 'http://www.livingreviews.org/lrr-2014-2'), (10010, 'bibtex: lrr-2014-2'), (10011, 'Quantum Mechanics'), (10012, 'Quantum Mechanics - Vol 1 - Cohen-Tannoudji.pdf'), (10013, 'Quantum Mechanics - Vol 2 - Cohen-Tannoudji.pdf'), (10014, 'http://arxiv.org/abs/1411.4547'), (10015, 'arXiv:1411.4547 [astro-ph, physics:gr-qc, physics:physics]'), (10016, '2014-11-17 2014-11-17'), (10017, 'arXiv: 1411.4547'), (10018, '2014-11-18 20:01:57'), (10019, 'The Advanced LIGO gravitational wave detectors are second generation instruments designed and built for the two LIGO observatories in Hanford, WA and Livingston, LA. The two instruments are identical in design, and are specialized versions of a Michelson interferometer with 4 km long arms. As in initial LIGO, Fabry-Perot cavities are used in the arms to increase the interaction time with a gravitational wave, and power recycling is used to increase the effective laser power. Signal recycling has been added in Advanced LIGO to improve the frequency response. In the most sensitive frequency region around 100 Hz, the design strain sensitivity is a factor of 10 better than initial LIGO. In addition, the low frequency end of the sensitivity band is moved from 40 Hz down to 10 Hz. All interferometer components have been replaced with improved technologies to achieve this sensitivity gain. Much better seismic isolation and test mass suspensions are responsible for the gains at lower frequencies. Higher laser power, larger test masses and improved mirror coatings lead to the improved sensitivity at mid- and high- frequencies. Data collecting runs with these new instruments are planned to begin in mid-2015.'), (10020, 'http://www.arxiv.org/pdf/1411.4547.pdf'), (10021, 'arXiv:1411.4547 PDF'), (10022, 'http://arxiv.org/abs/1411.4118'), (10023, 'arXiv:1411.4118 [gr-qc]'), (10024, '2014-11-15 2014-11-15'), (10025, 'arXiv: 1411.4118'), (10026, '2014-11-18 22:51:41'), (10027, 'We investigate cubic-in-spin effects for inspiralling compact objects binaries, both in the dynamics and the energy flux emitted in gravitational waves, at the leading post-Newtonian order. We use a Lagrangian formalism to implement finite-size effects, and extend it at cubic order in the spins, which corresponds to the octupolar order in a multipolar decomposition. This formalism allows us to derive the equation of motion, equations of precession for the spin, and stress-energy tensor of each body in covariant form, and admits a formal generalization to any multipolar order. For spin-induced multipoles, i.e. in the case where the rotation of the compact object is sole responsible for the additional multipole moments, we find a unique structure for the octupolar moment representing cubic-in-spin effects. We apply these results to compute the associated effects in the dynamics of compact binary systems, and deduce the corresponding terms in the energy loss rate due to gravitational waves. These effects enter at the third-and-a-half post-Newtonian order, and can be important for binaries involving rapidly spinning black holes. We provide simplified results for spin-aligned, circular orbits, and discuss the quantitative importance of the new contributions.'), (10028, 'Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries'), (10029, 'http://www.arxiv.org/pdf/1411.4118.pdf'), (10030, 'arXiv:1411.4118 PDF'), (10031, 'http://www.sciencedirect.com/science/article/pii/S0166128097001851'), (10032, 419), (10033, '19-27'), (10034, 'Journal of Molecular Structure: THEOCHEM'), (10035, '0166-1280'), (10036, '1997-12-08 December 8, 1997'), (10037, '10.1016/S0166-1280(97)00185-1'), (10038, '2014-11-20 21:54:02'), (10039, 'Rotation matrices (or Wigner D functions) are the matrix representations of the rotation operators in the basis of spherical harmonics. They are the key entities in the generation of symmetry-adapted functions by means of projection operators. Although their expression in terms of ordinary (complex) spherical harmonics and Euler rotation angles is well known, an alternative representation using real spherical harmonics is desirable. The aim of this contribution is to obtain a general algorithm to compute the representation matrix of any point-group symmetry operation in the basis of the real spherical harmonics, paying attention to the use of recurrence relationships that allow the treatment of functions with high angular momenta.'), (10040, 'Evaluation of the rotation matrices in the basis of real spherical harmonics'), (10041, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0166128097001851/pdfft?md5=3620e20879ce94043826776e81780f47&pid=1-s2.0-S0166128097001851-main.pdf'), (10042, 'Singapore ; Teaneck, NJ, USA'), (10043, 'World Scientific Pub'), (10044, 9971501074), (10045, 'QC793.3.A5 V3713 1988'), (10046, 'newcatalog.library.cornell.edu'), (10047, 'Quantum theory of angular momentum: irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols'), (10048, 'Quantum theory of angular momentum'), (10049, 514), (10050, '2002 edition'), (10051, 'Dordrecht ; Boston'), (10052, 9780792358664), (10053, '1999-07-31 July 31, 1999'), (10054, 'A course in angular momentum techniques is essential for quantitative study of problems in atomic physics, molecular physics, nuclear physics and solid state physics. This book has grown out of such a course given to the students of the M. Sc. and M. Phil. degree courses at the University of Madras. An elementary knowledge of quantum mechanics is an essential pre-requisite to undertake this course but no knowledge of group theory is assumed on the part of the readers. Although the subject matter has group-theoretic origin, special efforts have been made to avoid the gro- theoretical language but place emphasis on the algebraic formalism dev- oped by Racah (1942a, 1942b, 1943, 1951). How far I am successful in this project is left to the discerning reader to judge. After the publication of the two classic books, one by Rose and the other by Edmonds on this subject in the year 1957, the application of angular momentum techniques to solve physical problems has become so common that it is found desirable to organize a separate course on this subject to the students of physics. It is to cater to the needs of such students and research workers that this book is written. A large number of questions and problems given at the end of each chapter will enable the reader to have a clearer understanding of the subject.'), (10055, 'Angular Momentum Techniques in Quantum Mechanics'), (10056, 242), (10057, 'http://arxiv.org/abs/1501.00918'), (10058, 'arXiv:1501.00918 [gr-qc]'), (10059, 'Angular Momentum Techniques in Quantum Mechanics - Devanathan V..djvu'), (10060, 'http://link.aps.org/doi/10.1103/PhysRevE.57.7274'), (10061, '7274-7277'), (10062, 'Physical Review E'), (10063, '1998-06-01 June 1, 1998'), (10064, 'Phys. Rev. E'), (10065, '10.1103/PhysRevE.57.7274'), (10066, '2014-11-22 16:55:36'), (10067, 'We present a highly accurate, ab initio recursive algorithm for evaluating the Wigner 3j and 6j symbols. Our method makes use of two-term, nonlinear recurrence relations that are obtained from the standard three-term recurrence relations satisfied by these quantities. The use of two-term recurrence relations eliminates the need for rescaling of iterates to control numerical overflows and thereby simplifies the widely used recursive algorithm of Schulten and Gordon.'), (10068, 'Simplified recursive algorithm for Wigner 3j and 6j symbols'), (10069, 'http://journals.aps.org.proxy.library.cornell.edu/pre/pdf/10.1103/PhysRevE.57.7274'), (10070, '2006-07-01 2006-07-01'), (10071, '2014-11-29 05:13:58'), (10072, 'Calculation of spherical harmonics and Wigner <i>d</i> functions by FFT. Applications to fast rotational matching in molecular replacement and implementation into <i>AMoRe</i>'), (10073, 'http://link.springer.com/article/10.1007/BF01090814'), (10074, '383-396'), (10075, 'Journal of Geodesy'), (10076, '0949-7714, 1432-1394'), (10077, '1996-07-01 1996/07/01'), (10078, '10.1007/BF01090814'), (10079, '2014-11-29 05:14:32'), (10080, 'The relation between D- and d-functions, spherical harmonic functions and Legendre functions is reviewed. Dmatrices and irreducible representations of the rotation group O(3) and SU(2) group are briefly reviewed. Two new recursive methods for calculations of D-matrices are presented. Legendre functions are evaluated as part of this scheme. Vector spherical harmonics in the form af generalized spherical harmonics are also included as well as derivatives of the spherical harmonics. The special dmatrices evaluated for argument equal toπ/2 offer a simple method of calculating the Fourier coefficients of Legendre functions, derivatives of Legendre functions and vector spherical harmonics. Summation of a Legendre series or a full synthesis on the unit sphere of a field can then be performed by transforming the spherical harmonic coefficients to Fourier coefficients and making the summation by an inverse FFT (Fast Fourier Transform). The procedure is general and can also be applied to evaluate derivatives of a field and components of vector and tensor fields.'), (10081, 'Fourier transform summation of Legendre series and D-functions'), (10082, 'Boyle et al - 2009 - Comparison of high-accuracy numerical simulations .pdf'), (10083, 'cc5006.pdf'), (10084, 'http://link.springer.com/article/10.1023/A%3A1022458904447'), (10085, '83-93'), (10086, 'Foundations of Physics Letters'), (10087, 'Investigations in physics'), (10088, '3d print., with corrections'), (10089, 'Princeton, N.J'), (10090, 'Princeton University Press'), (10091, '0691079129'), (10092, 'QC793.3.A5 E35 1974'), (10093, 'Angular momentum in quantum mechanics'), (10094, 146), (10095, 'http://scitation.aip.org/content/aapt/journal/ajp/37/5/10.1119/1.1975665'), (10096, '531-536'), (10097, '1969-05-01 1969/05/01'), (10098, '10.1119/1.1975665'), (10099, '2014-12-03 17:10:27'), (10100, 'The wide variety of conventions in use concerning rotation operators can be confusing to the student who is beginning a serious study of the quantum theory of angular momentum. These conventions are discussed and compared, and the relation between active and passive rotations is examined. Using these results, a useful formula is derived which connects the reduced matrix element of a tensor operator with quantities that are measured relative to a rotating reference frame.'), (10101, 'Rotation Operators'), (10102, 'http://scitation.aip.org/deliver/fulltext/aapt/journal/ajp/37/5/1.1975665.pdf?itemId=/content/aapt/journal/ajp/37/5/10.1119/1.1975665&mimeType=pdf&containerItemId=content/aapt/journal/ajp'), (10103, 'http://link.aps.org/doi/10.1103/PhysRevD.87.044022'), (10104, '044022'), (10105, '2013-02-08 February 8, 2013'), (10106, '10.1103/PhysRevD.87.044022'), (10107, '2014-12-03 23:05:38'), (10108, 'We calculate the linear vacuum perturbations of a Kerr black hole surrounded by a slowly varying external spacetime to third order in the ratio of the black-hole mass to the radius of curvature of the external spacetime. This expansion applies to two relevant physical scenarios: (i) a small Kerr black hole immersed in the gravitational field of a much larger external black hole, and (ii) a Kerr black hole moving slowly around another external black hole of comparable mass. This small-hole/slow-motion approximation allows us to parametrize the perturbation through slowly varying, time-dependent electric and magnetic tidal tensors, which then enable us to separate the Teukolsky equation and compute the Newman-Penrose scalar analytically to third order in our expansion parameter. We obtain generic expressions for the mass and angular momentum flux through the perturbed black hole horizon, as well as the rate of change of the horizon surface area, in terms of certain invariants constructed from the electric and magnetic tidal tensors. We conclude by applying these results to the second scenario described above.'), (10109, 'Tidal heating and torquing of a Kerr black hole to next-to-leading order in the tidal coupling'), (10110, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.044022'), (10111, 'http://arxiv.org/abs/1412.2046'), (10112, 'arXiv:1412.2046 [gr-qc]'), (10113, '2014-12-05 2014-12-05'), (10114, 'arXiv: 1412.2046'), (10115, '2014-12-08 18:26:37'), (10116, 'We present a tensorial relative of the familiar affine connection and argue that it should be regarded as the gravitational field tensor. Remarkably, the Lagrangian density expressed in terms of this tensor has a simple form, which depends only on the metric and its first derivatives and, moreover, is a true scalar quantity. The geodesic equation, moreover, shows that our tensor plays a role that is strongly reminiscent of the gravitational field in Newtonian mechanics and this, together with other evidence, which we present, leads us to identify it as the gravitational field tensor. We calculate the gravitational field tensor for the Schwarzschild metric. We suggest some of the advantages to be gained from applying our tensor to the study of gravitational waves.'), (10117, 'Gravitational Field Tensor'), (10118, 'http://www.arxiv.org/pdf/1412.2046.pdf'), (10119, 'arXiv:1412.2046 PDF'), (10120, 'http://iopscience.iop.org/0264-9381/31/11/115004'), (10121, 115004), (10122, '2014-06-07 2014-06-07'), (10123, '10.1088/0264-9381/31/11/115004'), (10124, '2014-12-09 16:44:31'), (10125, 'The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave (GW) astrophysics communities. The purpose of NINJA is to study the ability to detect GWs emitted from merging binary black holes (BBH) and recover their parameters with next-generation GW observatories. We report here on the results of the second NINJA project, NINJA-2, which employs 60 complete BBH hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. In a ‘blind injection challenge’ similar to that conducted in recent Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo science runs, we added seven hybrid waveforms to two months of data recoloured to predictions of Advanced LIGO (aLIGO) and Advanced Virgo (AdV) sensitivity curves during their first observing runs. The resulting data was analysed by GW detection algorithms and 6 of the waveforms were recovered with false alarm rates smaller than 1 in a thousand years. Parameter-estimation algorithms were run on each of these waveforms to explore the ability to constrain the masses, component angular momenta and sky position of these waveforms. We find that the strong degeneracy between the mass ratio and the BHs’ angular momenta will make it difficult to precisely estimate these parameters with aLIGO and AdV. We also perform a large-scale Monte Carlo study to assess the ability to recover each of the 60 hybrid waveforms with early aLIGO and AdV sensitivity curves. Our results predict that early aLIGO and AdV will have a volume-weighted average sensitive distance of 300 Mpc (1 Gpc) for 10M⊙ + 10M⊙ (50M⊙ + 50M⊙) BBH coalescences. We demonstrate that neglecting the component angular momenta in the waveform models used in matched-filtering will result in a reduction in sensitivity for systems with large component angular momenta. This reduction is estimated to be up to ∼15% for 50M⊙ + 50M⊙ BBH coalescences with almost maximal angular momenta aligned with the orbit when using early aLIGO and AdV sensitivity curves.'), (10126, 'The NINJA-2 project: detecting and characterizing gravitational waveforms modelled using numerical binary black hole simulations'), (10127, 'The NINJA-2 project'), (10128, '10.12942/lrr-2014-2'), (10129, '0264-9381_31_11_115004.pdf'), (10130, 'http://arxiv.org/abs/1412.3082'), (10131, 'arXiv:1412.3082 [astro-ph, physics:cond-mat, physics:math-ph, physics:physics]'), (10132, '2014-12-09 2014-12-09'), (10133, 'arXiv: 1412.3082'), (10134, '2014-12-10 05:35:21'), (10135, "We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial value formulation of physical problems and allows for time-irreversible processes, such as dissipation, to be included at the level of the action. In this formalism, the equations of motion are generated by extremizing a nonconservative action $\\mathcal{S}$, which is a functional of a doubled set of degrees of freedom. The corresponding nonconservative Lagrangian contains a potential $K$ which generates nonconservative forces and interactions. Such a nonconservative potential can arise in several ways, including from an open system interacting with inaccessible degrees of freedom or from integrating out or coarse-graining a subset of variables in closed systems. We generalize Noether's theorem to show how Noether currents are modified and no longer conserved when $K$ is non-vanishing. Consequently, the nonconservative aspects of a physical system are derived solely from $K$. We show how to use the formalism with examples of nonconservative actions for discrete systems including forced damped harmonic oscillators, radiation reaction on an accelerated charge, and RLC circuits. We present examples for nonconservative classical field theories. Our approach naturally allows for irreversible thermodynamic processes to be included in an unconstrained variational principle. We present the nonconservative action for a Navier-Stokes fluid including the effects of viscous dissipation and heat diffusion, as well as an action that generates the Maxwell model for viscoelastic materials, which can be easily generalized to more realistic rheological models. We show that the nonconservative action can be derived as the classical limit of a more complete quantum theory."), (10136, 'The principle of stationary nonconservative action for classical mechanics and field theories'), (10137, 'http://www.arxiv.org/pdf/1412.3082.pdf'), (10138, 'arXiv:1412.3082 PDF'), (10139, 'lrr-2014-2Color.pdf'), (10140, '2015-01-05 2015-01-05'), (10141, 'arXiv: 1501.00918'), (10142, '2015-01-07 19:03:13'), (10143, 'Gravitational waveforms which describe the inspiral, merger and ringdown of coalescing binaries are usually constructed by synthesising information from perturbative descriptions, in particular post-Newtonian theory and black-hole perturbation theory, with numerical solutions of the full Einstein equations. In this paper we discuss the "glueing" of numerical and post-Newtonian waveforms to produce hybrid waveforms which include subdominant spherical harmonics ("higher order modes"), and focus in particular on the process of consistently aligning the waveforms, which requires a comparison of both descriptions and a discussion of their imprecisions. We restrict to the non-precessing case, and illustrate the process using numerical waveforms of up to mass ratio $q=18$ produced with the BAM code, and publicly available waveforms from the SXS catalogue. The results also suggest new ways of analysing finite radius errors in numerical simulations.'), (10144, 'Comparison of subdominant gravitational wave harmonics between post-Newtonian and numerical relativity calculations and construction of multi-mode hybrids'), (10145, 'http://www.arxiv.org/pdf/1501.00918.pdf'), (10146, 'arXiv:1501.00918 PDF'), (10147, '0894-9875, 1572-9524'), (10148, 'Found Phys Lett'), (10149, '10.1023/A:1022458904447'), (10150, '2015-01-18 19:32:13'), (10151, 'Einstein equations describing gravitational fields are expressed as a compact exterior system of spinor-valued forms. It is pointed out that Clifford algebra-valued differential forms provide a natural formalism for Einstein gravitational fields. Finally we try to express these equations in a real spacetime.'), (10152, 'Einstein field equations in spinor formalism: a clifford-algebra approach'), (10153, 'Einstein field equations in spinor formalism'), (10154, 'http://arxiv.org/abs/1501.06878'), (10155, 'art%3A10.1023%2FA%3A1022458904447.pdf'), (10156, 'Applied Geometric Algebra'), (10157, 'László Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976.\n\nOver the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza\'s attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems.\n\nThe lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, \'77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.'), (10158, 'http://ocw.mit.edu/resources/res-8-001-applied-geometric-algebra-spring-2009/index.htm'), (10159, '2015-01-21'), (10160, 'http://www.jstor.org.proxy.library.cornell.edu/stable/1969203'), (10161, 'MIT OpenCourseWare'), (10162, 'MITRES_8_001_lec_complete.pdf'), (10163, '2015-01-22'), (10164, 'arXiv:1501.06878 [gr-qc]'), (10165, '2015-01-27 2015-01-27'), (10166, 'arXiv: 1501.06878'), (10167, '2015-01-28 15:19:41'), (10168, 'We present a space--time model of the collision of two homogeneous, plane impulsive gravitational waves (each having a delta function profile) propagating in a vacuum before collision and for which the post collision space--time has constant curvature. The profiles of the incoming waves are $k\\,\\delta(u)$ and $l\\,\\delta(v)$ where $k, l$ are real constants and $u=0, v=0$ are intersecting null hypersurfaces. The cosmological constant $\\Lambda$ in the post collision region of the space--time is given by $\\Lambda=-6\\,k\\,l$. In this sense this model collision provides a mechanism for generating a cosmological constant and therefore may be relevant to the theoretical description of dark energy.'), (10169, 'Colliding Impulsive Gravitational Waves and a Cosmological Constant'), (10170, 'http://www.arxiv.org/pdf/1501.06878.pdf'), (10171, 'arXiv:1501.06878 PDF'), (10172, 'http://arxiv.org/abs/1501.07096'), (10173, 'arXiv:1501.07096 [gr-qc]'), (10174, '2015-01-28 2015-01-28'), (10175, 'arXiv: 1501.07096'), (10176, '2015-01-29 17:52:18'), (10177, "We compute the instantaneous contributions to the spherical harmonic modes of gravitational waveforms from compact binary systems in general orbits up to the third post-Newtonian order. We further extend these results for compact binaries in quasi-elliptical orbits using the 3PN quasi-Keplerian representation of the conserved dynamics of compact binaries in eccentric orbits. Using the multipolar post-Minkowskian formalism, starting from the different mass and current type multipole moments, we compute the spin weighted spherical harmonic decomposition of the instantaneous part of the gravitational waveform. These are terms which are functions of the retarded time and do not depend on the history of the binary evolution. Together with the hereditary part, which depends on the binary's dynamical history, these waveforms form the basis for construction of accurate templates for the detection of gravitational wave signals from binaries moving in quasi-elliptical orbits."), (10178, 'The third post-Newtonian gravitational waveforms for compact binary systems in general orbits: instantaneous terms'), (10179, 'The third post-Newtonian gravitational waveforms for compact binary systems in general orbits'), (10180, 'http://www.arxiv.org/pdf/1501.07096.pdf'), (10181, 'arXiv:1501.07096 PDF'), (10182, 'http://arxiv.org/abs/1501.07274'), (10183, 'arXiv:1501.07274 [astro-ph, physics:gr-qc, physics:hep-ph, physics:hep-th]'), (10184, 'arXiv: 1501.07274'), (10185, '2015-01-30 14:27:02'), (10186, "One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most (if not all) of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime."), (10187, 'Testing General Relativity with Present and Future Astrophysical Observations'), (10188, 'http://www.arxiv.org/pdf/1501.07274.pdf'), (10189, 'arXiv:1501.07274 PDF'), (10190, '1 edition'), (10191, 805), (10192, 9780521795401), (10193, '2001-12-03 December 3, 2001'), (10194, 'In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.'), (10195, 'Algebraic Topology'), (10196, 556), (10197, 'http://arxiv.org/abs/1106.3197'), (10198, 'arXiv:1106.3197 [math-ph, physics:physics]'), (10199, 'AT.pdf'), (10200, 'http://link.springer.com/article/10.1007/BF00761722'), (10201, '281-287'), (10202, '1987-03-01 1987-03-01'), (10203, '10.1007/BF00761722'), (10204, '2015-02-12 18:49:20'), (10205, 'A simple statement and derivation of the quadrupole radiation formula for selfgravitating systems is presented. The primary physical ingredient is the existence of a Newtonian limit for general relativity based upon a family of outgoing null cones, supplemented by a weak asymptotic flatness condition. This eliminates extraneous incoming gravitational waves that would otherwise obscure the physical meaning of the quadrupole formula.'), (10206, 'The quadrupole radiation formula'), (10207, 'Copyright © 1945 Annals of Mathematics'), (10208, 'art%3A10.1007%2FBF00761722.pdf'), (10209, 'http://link.aps.org/doi/10.1103/PhysRev.150.1039'), (10210, '1039-1053'), (10211, '1966-10-28 October 28, 1966'), (10212, '10.1103/PhysRev.150.1039'), (10213, '2015-02-12 18:52:08'), (10214, 'We generalize the Bondi-Sachs treatment of the initial-value problem using null coordinate systems. This treatment is applicable in both finite and asymptotic regions of space whose sources are bounded by a finite world tube. Using the conformal techniques developed by Penrose, we rederive the results of Bondi and co-workers and of Sachs in conformal-space language. Definitions of asymptotic symmetry "linkages" are developed which offer an invariant way of labeling the properties of finite regions of space, e.g., energy and momentum. These linkages form a representation of the Bondi-Metzner-Sachs asymptotic symmetry group.'), (10215, 'Gravitational Fields in Finite and Conformal Bondi Frames'), (10216, 'http://journals.aps.org.proxy.library.cornell.edu/pr/pdf/10.1103/PhysRev.150.1039'), (10217, 'http://arxiv.org/abs/1412.1803'), (10218, 'arXiv:1412.1803 [gr-qc]'), (10219, '2014-12-04 2014-12-04'), (10220, 'arXiv: 1412.1803'), (10221, '2015-02-12 19:16:15'), (10222, 'Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass $m$ and spin $S$ exceeding the Bowen-York limit of $S/m^2=0.93$. We present improved methods that enable us to simulate merging, nearly extremal black holes more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole coalescence, where the larger black hole has $S/m^2=0.99$. We also use these methods to simulate a non-precessing binary black hole coalescence, where both black holes have $S/m^2=0.994$, nearly reaching the Novikov-Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; we compare the evolution of the black-hole masses and spins with analytic predictions; and we explore the effect of increasing spin magnitude on the orbital dynamics (the so-called "orbital hangup" effect).'), (10223, 'Improved methods for simulating nearly extremal binary black holes'), (10224, 'http://www.arxiv.org/pdf/1412.1803.pdf'), (10225, 'arXiv:1412.1803 PDF'), (10226, 'Second Series'), (10227, '674-684'), (10228, '1945-10-01 October 1, 1945'), (10229, '10.2307/1969203'), (10230, '2015-02-12 20:53:44'), (10231, 'On the Curvatura Integra in a Riemannian Manifold'), (10232, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/1969203.pdf?acceptTC=true'), (10233, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/36/6/10.1063/1.531015'), (10234, '3094-3105'), (10235, '1995-06-01 1995/06/01'), (10236, '10.1063/1.531015'), (10237, '2015-02-13 05:57:03'), (10238, 'For Riemannian manifolds with boundary, the well‐known Gauss–Bonnet–Chern theorem gives an integral formula for the Euler characteristic of the manifold. Here we extend a proof by Avez to show that there is a similar result for manifolds with boundary endowed with a pseudo–Riemannian metric of arbitrary signature. In the case when the metric is Lorentzian there are some applications to general relativity. The generalized Gauss–Bonnet–Chern theorem also provides a formula for the gravitational kink.'), (10239, 'The generalized Gauss–Bonnet–Chern theorem'), (10240, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/36/6/1.531015.pdf;jsessionid=332dku1kmodmr.x-aip-live-02?itemId=/content/aip/journal/jmp/36/6/10.1063/1.531015&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10241, 'http://arxiv.org/abs/1405.7613'), (10242, 'arXiv:1405.7613 [math]'), (10243, '2014-05-29 2014-05-29'), (10244, 'arXiv: 1405.7613'), (10245, '2015-02-13 06:18:27'), (10246, 'We derive the Chern-Gauss-Bonnet Theorem for manifolds with smooth non-degenerate boundary in the pseudo-Riemannian context from the corresponding result in the Riemannian setting by examining the Euler-Lagrange equations associated to the Pfaffian of a complex "metric" on the tangent space and then applying analytic continuation.'), (10247, 'A proof of the Chern-Gauss-Bonnet theorem for indefinite signature metrics using analytic continuation'), (10248, 'http://iopscience.iop.org/0264-9381/14/4/013'), (10249, 977), (10250, 'http://www.sciencedirect.com/science/article/pii/S0393044014002393'), (10251, '88-93'), (10252, '2015-02-00 February 2015'), (10253, '10.1016/j.geomphys.2014.11.006'), (10254, 'http://arxiv.org/abs/1503.00718'), (10255, 'We use analytic continuation to derive the Euler–Lagrange equations associated to the Pfaffian in indefinite signature ( p , q ) directly from the corresponding result in the Riemannian setting. We also use analytic continuation to derive the Chern–Gauss–Bonnet theorem for pseudo-Riemannian manifolds with boundary directly from the corresponding result in the Riemannian setting. Complex metrics on the tangent bundle play a crucial role in our analysis and we obtain a version of the Chern–Gauss–Bonnet theorem in this setting for certain complex metrics.'), (10256, 'Analytic continuation, the Chern–Gauss–Bonnet theorem, and the Euler–Lagrange equations in Lovelock theory for indefinite signature metrics'), (10257, 'http://link.aps.org/doi/10.1103/PhysRevD.87.084004'), (10258, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044014002393/pdfft?md5=cb1b2b869131c4f24f12b16752096672&pid=1-s2.0-S0393044014002393-main.pdf'), (10259, '1st ed. 1982. Corr. 3rd printing 1995 edition'), (10260, 9780387906133), (10261, '1995-04-21 April 21, 1995'), (10262, 'Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.'), (10263, 'Differential Forms in Algebraic Topology'), (10264, 338), (10265, 'arXiv:1503.00718 [astro-ph, physics:gr-qc]'), (10266, '2015-03-02 2015-03-02'), (10267, 'BottAndTu.pdf'), (10268, '1997-04-01 1997-04-01'), (10269, '10.1088/0264-9381/14/4/013'), (10270, '2015-02-19 15:15:05'), (10271, 'We present a finite difference version of the eth formalism, which allows use of tensor fields in spherical coordinates in a manner which avoids polar singularities. The method employs two overlapping stereographic coordinate patches, with interpolations between the patches in the regions of overlap. It provides a new and effective computational tool for dealing with a wide variety of systems in which spherical coordinates are natural, such as the generation of radiation from an isolated source. We test the formalism with the evolution of waves in three spatial dimensions and the calculation of the curvature scalar of arbitrarily curved geometries on topologically spherical manifolds. The formalism is applied to the solution of the Robinson - Trautman equation and reveals some new features of gravitational waveforms in the nonlinear regime.'), (10272, 'The eth formalism in numerical relativity'), (10273, '10.1063/1.4825543'), (10274, '2015-04-06 17:50:00'), (10275, '11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013'), (10276, 'As it will turn out in this paper, the recent hype about most of the Clifford Fourier transforms is not thoroughly worth the pain. Almost every one that has a real application is separable and these transforms can be decomposed into a sum of real valued transforms with constant multivecor factors. This fact makes their interpretation, their analysis, and their implementation almost trivial.'), (10277, 'Demystification of the geometric Fourier transforms'), (10278, 'AIP Conference Proceedings'), (10279, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/proceeding/aipcp/1558/10.1063/1.4825543/1.4825543.pdf?itemId=/content/aip/proceeding/aipcp/10.1063/1.4825543&mimeType=pdf&containerItemId=content/aip/proceeding/aipcp'), (10280, 'http://link.aps.org/doi/10.1103/PhysRevD.87.084035'), (10281, 'http://arxiv.org/abs/1502.06987'), (10282, 'arXiv:1502.06987 [gr-qc]'), (10283, '2015-02-24 2015-02-24'), (10284, 'arXiv: 1502.06987'), (10285, '2015-03-01 19:10:04'), (10286, 'We present gauge invariant spectral Cauchy characteristic extraction. We compare gravitational waveforms extracted from a head-on black hole merger simulated in two different gauges by two different codes. We show rapid convergence, demonstrating both gauge invariance of the extraction algorithm and consistency between the legacy Pitt null code and the much faster Spectral Einstein Code (SpEC).'), (10287, 'Gauge Invariant Spectral Cauchy Characteristic Extraction'), (10288, 'http://www.arxiv.org/pdf/1502.06987.pdf'), (10289, 'arXiv:1502.06987 PDF'), (10290, 'http://arxiv.org/abs/1502.07758'), (10291, 'arXiv:1502.07758 [astro-ph, physics:gr-qc, physics:physics]'), (10292, '2015-02-26 2015-02-26'), (10293, 'arXiv: 1502.07758'), (10294, '2015-03-02 04:19:27'), (10295, "Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. In this paper, we construct an accurate and fast-to-evaluate surrogate model for numerical relativity (NR) waveforms from non-spinning binary black hole coalescences with mass ratios from $1$ to $10$ and durations corresponding to about $15$ orbits before merger. Our surrogate, which is built using reduced order modeling techniques, is distinct from traditional modeling efforts. We find that the full multi-mode surrogate model agrees with waveforms generated by NR to within the numerical error of the NR code. In particular, we show that our modeling strategy produces surrogates which can correctly predict NR waveforms that were {\\em not} used for the surrogate's training. For all practical purposes, then, the surrogate waveform model is equivalent to the high-accuracy, large-scale simulation waveform but can be evaluated in a millisecond to a second depending on the number of output modes and the sampling rate. Our model includes all spherical-harmonic ${}_{-2}Y_{\\ell m}$ waveform modes that can be resolved by the NR code up to $\\ell=8$, including modes that are typically difficult to model with other approaches. We assess the model's uncertainty, which could be useful in parameter estimation studies seeking to incorporate model error. We anticipate NR surrogate models to be useful for rapid NR waveform generation in multiple-query applications like parameter estimation, template bank construction, and testing the fidelity of other waveform models."), (10296, 'Fast and accurate prediction of numerical relativity waveforms from binary black hole mergers using surrogate models'), (10297, 'http://www.arxiv.org/pdf/1502.07758.pdf'), (10298, 'arXiv:1502.07758 PDF'), (10299, 'http://astrophysics.physics.fsu.edu/~huffenbe/research/spinsfast/index.html'), (10300, '2015-03-05 13:17:14'), (10301, 'http://link.aps.org/doi/10.1103/PhysRevLett.69.1719'), (10302, '1719-1721'), (10303, '1992-09-21 September 21, 1992'), (10304, '10.1103/PhysRevLett.69.1719'), (10305, '2015-03-05 14:02:00'), (10306, 'We show that if a change of spatial topology is mediated by a spacetime with an everywhere-non-singular metric of Lorentzian signature which admits a spinor structure, then the Kervaire semicharacteristic of the boundary plus the kink number of the Lorentzian metric on the boundary must vanish modulo 2. The kink number is a measure of how many times the light cone tips over on the boundary. It vanishes if the boundary is everywhere spacelike. This result gives a generalization of a previous selection rule: The number of wormholes plus the number of kinks created during a topology change is conserved modulo 2.'), (10307, 'Kinks and topology change'), (10308, 'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.69.1719'), (10309, 'http://www.sciencedirect.com/science/article/pii/S0393044008000569'), (10310, '1137-1147'), (10311, '2008-09-00 September 2008'), (10312, '10.1016/j.geomphys.2008.03.011'), (10313, '2015-03-05 14:32:33'), (10314, 'Compact pseudo-Riemannian manifolds that have parallel Weyl tensor without being conformally flat or locally symmetric are known to exist in infinitely many dimensions greater than 4. We prove some general topological properties of such manifolds, namely, vanishing of the Euler characteristic and real Pontryagin classes, and infiniteness of the fundamental group. We also show that, in the Lorentzian case, each of them is at least 5-dimensional and admits a two-fold cover which is a bundle over the circle.'), (10315, 'On compact manifolds admitting indefinite metrics with parallel Weyl tensor'), (10316, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044008000569/pdfft?md5=2b988d22550ac01c5229fe3af064bff9&pid=1-s2.0-S0393044008000569-main.pdf'), (10317, 'http://link.springer.com/article/10.1023/A%3A1006545621874'), (10318, '299-316'), (10319, 'Acta Mathematica Hungarica'), (10320, '0236-5294, 1588-2632'), (10321, '1997-06-01 1997-06-01'), (10322, '10.1023/A:1006545621874'), (10323, '2015-03-05 14:33:50'), (10324, 'Pseudo-Chern Classes and Opposite Chern Classes of Indefinite Almost Hermitian Manifolds'), (10325, '2014-03-19 Wednesday, March 19, 2014'), (10326, 'art%3A10.1023%2FA%3A1006545621874.pdf'), (10327, 'http://www.ams.org/mathscinet-getitem?mr=0169199'), (10328, '191–197 (1963)'), (10329, 'Revista de la Unión Matemática Argentina'), (10330, '0041-6932'), (10331, '1963-00-00 1963'), (10332, '2011-06-16 2011-06-16'), (10333, 'Rev. Un. Mat. Argentina'), (10334, '2015-03-05 15:32:52'), (10335, 'AMS MathSciNet'), (10336, 'Formule de Gauss-Bonnet-Chern en métrique de signature quelconque'), (10337, 'arXiv: 1106.3197'), (10338, 'p191-197.pdf'), (10339, 'MR: 0169199; http://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol21; http://inmabb.criba.edu.ar/revuma/pdf/v21n4/p191-197.pdf'), (10340, '2015-03-05 18:32:39'), (10341, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0040938364900035/pdf?md5=f55e052338189ca79550217063b0aedf&pid=1-s2.0-0040938364900035-main.pdf'), (10342, 'Vector Bundles and K-Theory'), (10343, '2.1'), (10344, '2009-05-00 May 2009'), (10345, 'VB.pdf'), (10346, '2015-03-12 02:44:51'), (10347, 'Structural insight'), (10348, 'Structural insight: The great vectors-versus-quaternions debate'), (10349, '10.1103/PhysRevD.87.084004'), (10350, '2015-03-12 02:45:35'), (10351, 'http://www.ams.org/bull/2002-39-02/S0273-0979-01-00934-X/'), (10352, '145-205'), (10353, '0273-0979, 1088-9485'), (10354, '10.1090/S0273-0979-01-00934-X'), (10355, '2015-03-12 15:45:00'), (10356, 'The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.'), (10357, 'The octonions'), (10358, 'http://www.ams.org/bull/2002-39-02/S0273-0979-01-00934-X/S0273-0979-01-00934-X.pdf'), (10359, 'http://www.ams.org/bull/2005-42-02/S0273-0979-05-01052-9/'), (10360, '213-213'), (10361, '10.1090/S0273-0979-05-01052-9'), (10362, '2015-03-12 15:45:18'), (10363, 'Errata for “The Octonions”'), (10364, 'http://www.ams.org/bull/2005-42-02/S0273-0979-05-01052-9/S0273-0979-05-01052-9.pdf'), (10365, 'http://link.aps.org/doi/10.1103/RevModPhys.51.591'), (10366, 51), (10367, '591-648'), (10368, '1979-07-01 July 1, 1979'), (10369, '10.1103/RevModPhys.51.591'), (10370, '2015-03-12 16:26:45'), (10371, 'Aspects of the theory of homotopy groups are described in a mathematical style closer to that of condensed matter physics than that of topology. The aim is to make more readily accessible to physicists the recent applications of homotopy theory to the study of defects in ordered media. Although many physical examples are woven into the development of the subject, the focus is on mathematical pedagogy rather than on a systematic review of applications.'), (10372, 'The topological theory of defects in ordered media'), (10373, 'RevModPhys.51.591.pdf'), (10374, 'http://www.jstor.org.proxy.library.cornell.edu/stable/1970240'), (10375, 'Copyright © 1961 Annals of Mathematics'), (10376, '407-413'), (10377, '1961-09-01 September 1, 1961'), (10378, '10.2307/1970240'), (10379, '2015-03-12 17:07:05'), (10380, 'On the Homotopy Groups of the Classical Groups'), (10381, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/1970240.pdf?acceptTC=true'), (10382, 'http://projecteuclid.org.proxy.library.cornell.edu/euclid.pjm/1102992189'), (10383, '197-204'), (10384, 'Pacific Journal of Mathematics'), (10385, '0030-8730'), (10386, 'MR: MR0213470\nZbl: 0178.02802'), (10387, 'Pacific J. Math.'), (10388, '2015-03-12 18:55:37'), (10389, 'Project Euclid'), (10390, 'Project Euclid - mathematics and statistics online'), (10391, 'Local isomorphism of compact connected Lie groups.'), (10392, '2015-03-17 02:09:39'), (10393, 'euclid.pjm.1102992189.pdf'), (10394, 'Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-seven-year-old "Introduction to Majorana masses" by P.D. Mannheim and includes historical notes and biographical data on past participants in the story.'), (10395, 'http://www.arxiv.org/pdf/1106.3197.pdf'), (10396, 'arXiv:1106.3197 PDF'), (10397, 'https://sites.google.com/site/grassmannalgebra/thegrassmannalgebrabook'), (10398, '2015-03-17 02:28:48'), (10399, 'This is the companion site for the book Grassmann Algebra: Exploring extended vector algebra with Mathematica and for the Mathematica-based software package GrassmannAlgebra'), (10400, 'The Grassmann Algebra Book - Grassmann Algebra'), (10401, 'GrassmannAlgebraBook.pdf'), (10402, 'bibtex: Gilkey2015'), (10403, 'arXiv: 1503.00718'), (10404, '2015-03-20 23:28:22'), (10405, "We derive an analytical expression for extracting the gravitational waveforms at null infinity using the Weyl scalar $\\psi_4$ measured at a finite radius. Our expression is based on a series solution in orders of 1/r to the equations for gravitational perturbations about a spinning black hole. We compute this expression to order $1/r^2$ and include the spin parameter $a$ of the Kerr background. We test the accuracy of this extraction procedure by measuring the waveform for a merging black-hole binary at ten different extraction radii (in the range r/M=75-190) and for three different resolutions in the convergence regime. We find that the extraction formula provides a set of values for the radiated energy and momenta that at finite extraction radii converges towards the expected values with increasing resolution, which is not the case for the `raw' waveform at finite radius. We also examine the phase and amplitude errors in the waveform as a function of observer location and again observe the benefits of using our extraction formula. The leading corrections to the phase are ${\\cal O}(1/r)$ and to the amplitude are ${\\cal O}(1/r^2)$. This method provides a simple and practical way of estimating the waveform at infinity, and may be especially useful for scenarios such as well separated binaries, where the radiation zone is far from the sources, that would otherwise require extended simulation grids in order to extrapolate the `raw' waveform to infinity. Thus this method saves important computational resources and provides an estimate of errors."), (10406, 'Perturbative extraction of gravitational waveforms generated with Numerical Relativity'), (10407, 'http://www.arxiv.org/pdf/1503.00718.pdf'), (10408, 'arXiv:1503.00718 PDF'), (10409, 'http://www.ams.org/bull/2009-46-02/S0273-0979-09-01249-X/'), (10410, '255-308'), (10411, '10.1090/S0273-0979-09-01249-X'), (10412, '2015-03-22 15:36:51'), (10413, 'Topology and data'), (10414, 'http://www.ams.org/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf'), (10415, 'http://arxiv.org/abs/1503.07536'), (10416, 'arXiv:1503.07536 [astro-ph, physics:gr-qc]'), (10417, '2015-03-25 2015-03-25'), (10418, 'arXiv: 1503.07536'), (10419, '2015-03-27 15:18:01'), (10420, 'We revisit the modeling of the properties of the black-hole remnant resulting the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 126 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of the analysis, we chose configurations that have one of the black holes spinning, with dimensionless spin alpha=0.8, at different angles with respect to the orbital angular momentum, and the other non-spinning. In addition to evolving families of binaries with different spin-inclination angles, we also evolved binaries with mass ratios as small as q=1/6. We use the resulting empirical formulas to predict the probabilities of black hole mergers leading to a given recoil velocity, total radiated gravitational energy, and final black hole spin.'), (10421, 'Recoils from unequal-mass, precessing black-hole binaries: The Intermediate Mass Ratio Regime'), (10422, 'Recoils from unequal-mass, precessing black-hole binaries'), (10423, 'http://www.arxiv.org/pdf/1503.07536.pdf'), (10424, 'arXiv:1503.07536 PDF'), (10425, '2013-04-12 April 12, 2013'), (10426, '10.1103/PhysRevD.87.084035'), (10427, '2015-04-07 03:47:13'), (10428, 'We improve the effective-one-body (EOB) description of nonspinning coalescing black-hole binaries by incorporating several recent analytical advances, notably: (i) logarithmic contributions to the conservative dynamics; (ii) resummed horizon-absorption contribution to the orbital angular momentum loss; and (iii) a specific radial component of the radiation-reaction force implied by consistency with the azimuthal one. We then complete this analytically improved EOB model by comparing it to accurate numerical-relativity (NR) simulations performed by the Caltech-Cornell-CITA group for mass ratios q=(1,2,3,4,6). In particular, the comparison to NR data allows us to determine with high accuracy (∼10−4) the value of the main EOB radial potential: A(u;ν), where u=GM/(Rc2) is the interbody gravitational potential and ν=q/(q+1)2 is the symmetric mass ratio. We introduce a new technique for extracting from NR data an intrinsic measure of the phase evolution [Qω(ω) diagnostics]. Aligning the NR-completed EOB quadrupolar waveform and the NR one at low frequencies, we find that they keep agreeing (in phase and amplitude) within the NR uncertainties throughout the evolution for all mass ratios considered. We also find good agreement for several subdominant multipoles without having to introduce and tune any extra parameters.'), (10429, 'Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion'), (10430, '2015-04-13 00:54:00'), (10431, '2015-04-07 03:47:27'), (10432, 'Optimal extraction of information from gravitational-wave observations of binary black-hole coalescences requires detailed knowledge of the waveforms. Current approaches for representing waveform information are based on spin-weighted spherical harmonic decomposition. Higher-order harmonic modes carrying a few percent of the total power output near merger can supply information critical to determining intrinsic and extrinsic parameters of the binary. One obstacle to constructing a full multimode template of merger waveforms is the apparently complicated behavior of some of these modes; instead of settling down to a simple quasinormal frequency with decaying amplitude, some |m|≠ℓ modes show periodic bumps characteristic of mode mixing. We analyze the strongest of these modes—the anomalous (3, 2) harmonic mode—measured in a set of binary black-hole merger waveform simulations, and show that to leading order, they are due to a mismatch between the spherical harmonic basis used for extraction in 3D numerical relativity simulations, and the spheroidal harmonics adapted to the perturbation theory of Kerr black holes. Other causes of mode mixing arising from gauge ambiguities and physical properties of the quasinormal ringdown modes are also considered and found to be small for the waveforms studied here.'), (10433, 'PhysRevD.87.084035.pdf'), (10434, 'arXiv: 1311.5854'), (10435, '2015-04-07 07:16:39'), (10436, 'arXiv:1311.5854 PDF'), (10437, 'Decoding mode mixing in black-hole merger ringdown'), (10438, 'http://link.aps.org/doi/10.1103/PhysRevD.49.883'), (10439, 'PhysRevD.87.084004.pdf'), (10440, 'http://link.aps.org/doi/10.1103/PhysRevD.90.065019'), (10441, '065019'), (10442, '2014-09-16 September 16, 2014'), (10443, '10.1103/PhysRevD.90.065019'), (10444, '2015-04-15 14:10:29'), (10445, 'Massive fields can exist in long-lived configurations around black holes. We examine how the gravitational wave signal of a perturbed black hole is affected by such “dirtiness” within linear theory. As a concrete example, we consider the gravitational radiation emitted by the infall of a massive scalar field into a Schwarzschild black hole. Whereas part of the scalar field is absorbed/scattered by the black hole and triggers gravitational wave emission, another part lingers in long-lived quasibound states. Solving numerically the Teukolsky master equation for gravitational perturbations coupled to the massive Klein-Gordon equation, we find a characteristic gravitational wave signal, composed by a quasinormal ringing followed by a late time tail. In contrast to “clean” black holes, however, the late time tail contains small amplitude wiggles with the frequency of the dominating quasibound state. Additionally, an observer dependent beating pattern may also be seen. These features were already observed in fully nonlinear studies; our analysis shows they are present at linear level, and, since it reduces to a 1+1 dimensional numerical problem, allows for cleaner numerical data. Moreover, we discuss the power law of the tail and that it only becomes universal sufficiently far away from the dirty black hole. The wiggly tails, by constrast, are a generic feature that may be used as a smoking gun for the presence of massive fields around black holes, either as a linear cloud or as fully nonlinear hair.'), (10446, 'Wiggly tails: A gravitational wave signature of massive fields around black holes'), (10447, 'Wiggly tails'), (10448, '883-889'), (10449, 'PhysRevD.90.065019.pdf'), (10450, 'http://link.aps.org/doi/10.1103/PhysRevD.5.2419'), (10451, '2419-2438'), (10452, '1972-05-15 May 15, 1972'), (10453, '10.1103/PhysRevD.5.2419'), (10454, 'arXiv:1007.2481 [gr-qc, physics:math-ph]'), (10455, 'When a nearly spherical star gravitationally collapses through its event horizon, it cannot leave behind a static gravitational field with nonspherical perturbations. The dynamics of these perturbations during collapse is studied with a scalar-field analog. Computations in comoving coordinates show that the field neither vanishes nor becomes singular as the star falls inside its gravitational radius. The scalar field on the surface of the star must vary as a1+a2exp(−t2M) due to time dilation. An analysis is presented of the evolution of the exterior scalar field, based on a simple wave equation containing a space-time-curvature-induced potential barrier. This barrier is shown to be impenetrable to zero-frequency waves and thus a1, the final value of the field on the surface of the star, is not manifested in the exterior; the exterior field vanishes. The detailed nature of the falloff of the field depends on backscattering off the potential. It is shown that an initially static l pole dies out as t−(2l+2). If there is no initial l pole but one develops during the collapse it must fall off as t−(2l+3). Wave equations with curvature-induced potential barriers have been derived by Regge and Wheeler and by Zerilli for gravitational perturbations. With these equations the analysis of gravitational perturbations is precisely the same as for the scalar ones. In particular, gravitational multipole perturbations (with l≥2) fall off at large t as t−(2l+2) or t−(2l+3), depending on initial conditions. (In an accompanying paper it is shown that this result applies as well to the radiatable multipoles of a zero-rest-mass field of any integer spin.)'), (10456, 'Nonspherical Perturbations of Relativistic Gravitational Collapse. I. Scalar and Gravitational Perturbations'), (10457, '1994-01-15 January 15, 1994'), (10458, '2015-04-15 14:14:56'), (10459, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.5.2419'), (10460, 'http://link.aps.org/doi/10.1103/PhysRevD.84.084012'), (10461, '084012'), (10462, '2011-10-06 October 6, 2011'), (10463, '10.1103/PhysRevD.84.084012'), (10464, 'arXiv: 1007.2481'), (10465, 'We discuss a new ringdown frequency mode for vacuum perturbations of the Kerr black hole. We evolve initial data for the vacuum radial Teukolsky equation using a near horizon approximation and find a frequency mode analogous to that found in a recent study of radiation generated by a plunging particle close to the Kerr horizon. We discuss our results in the context of that study. We also explore the utility of this mode by fitting a numerical waveform with a combination of the usual quasinormal modes and the new oscillation frequency.'), (10466, 'New generic ringdown frequencies at the birth of a Kerr black hole'), (10467, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.84.084012'), (10468, '2015-04-15 16:40:22'), (10469, 'http://link.springer.com/article/10.1140/epjp/i2012-12067-1'), (10470, 127), (10471, '1-52'), (10472, 'The European Physical Journal Plus'), (10473, '2190-5444'), (10474, '2012-06-22 2012/06/22'), (10475, 'Eur. Phys. J. Plus'), (10476, '10.1140/epjp/i2012-12067-1'), (10477, '2015-04-15 18:14:13'), (10478, 'Black holes (BHs) have many faces. Within the gauge/string duality they provide useful insights on strongly coupled quantum field theories and on quantum gravity. Furthermore, probing the strong curvature regime of any gravity theory, BHs carry the imprint of possible strong curvature corrections to General Relativity. Finally, beside their unique theoretical properties, compelling experimental evidence suggests that astrophysical BHs are very common objects in the universe. Here we discuss some applications of BH perturbation theory in various contexts. As applications in theoretical physics, we study perturbations of dilatonic BHs in Einstein-Maxwell theory and the holographic properties of the dual field theory via the Anti de Sitter/Condensed Matter duality. As applications in astrophysics, we discuss how the characteristic oscillations of BHs in string-inspired theories of gravity can provide observable signatures of deviations from Einstein’s theory. We study two well-motivated effective theories: Dynamical Chern-Simons gravity and Einstein-Dilatonic-Gauss-Bonnet gravity. We conclude by discussing the BH paradigm. Motivated by the lack of a definitive answer on the existence of astrophysical BHs, we study some viable alternatives, generically called “BH mimickers”. We focus on two representative cases: static thin-shell gravastars and superspinars, discussing their stability, gravitational-wave signature and viability as astrophysical objects.'), (10479, 'Applications of black hole perturbation theory'), (10480, '10.1103/PhysRevD.49.883'), (10481, 'art%3A10.1140%2Fepjp%2Fi2012-12067-1.pdf'), (10482, 'http://link.aps.org/doi/10.1103/PhysRevD.89.102006'), (10483, 102006), (10484, '2014-05-27 May 27, 2014'), (10485, '10.1103/PhysRevD.89.102006'), (10486, '2015-04-15 18:23:06'), (10487, 'We report results from a search for gravitational waves produced by perturbed intermediate mass black holes (IMBH) in data collected by LIGO and Virgo between 2005 and 2010. The search was sensitive to astrophysical sources that produced damped sinusoid gravitational wave signals, also known as ringdowns, with frequency 50≤f0/Hz≤2000 and decay timescale 0.0001≲τ/s≲0.1 characteristic of those produced in mergers of IMBH pairs. No significant gravitational wave candidate was detected. We report upper limits on the astrophysical coalescence rates of IMBHs with total binary mass 50≤M/M⊙≤450 and component mass ratios of either 1:1 or 4:1. For systems with total mass 100≤M/M⊙≤150, we report a 90% confidence upper limit on the rate of binary IMBH mergers with nonspinning and equal mass components of 6.9×10−8 Mpc−3 yr−1. We also report a rate upper limit for ringdown waveforms from perturbed IMBHs, radiating 1% of their mass as gravitational waves in the fundamental, ℓ=m=2, oscillation mode, that is nearly three orders of magnitude more stringent than previous results.'), (10488, 'Search for gravitational wave ringdowns from perturbed intermediate mass black holes in LIGO-Virgo data from 2005\\char21{}2010'), (10489, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.102006'), (10490, 'http://link.aps.org/doi/10.1103/PhysRevD.88.064045'), (10491, '064045'), (10492, '2013-09-23 September 23, 2013'), (10493, '10.1103/PhysRevD.88.064045'), (10494, '2015-04-15 18:23:15'), (10495, 'Since black holes can be formed through widely varying processes, the horizon structure is highly complicated in the dynamical phase. Nonetheless, as numerical simulations show, the final state appears to be universal, well described by the Kerr geometry. How are all these large and widely varying deviations from the Kerr horizon washed out? To investigate this issue, we introduce a well-suited notion of horizon multipole moments and equations governing their dynamics, thereby providing a coordinate- and slicing-independent framework to investigate the approach to equilibrium. In particular, our flux formulas for multipoles can be used as analytical checks on numerical simulations and, in turn, the simulations could be used to fathom possible universalities in the way black holes approach their final equilibrium.'), (10496, 'Dynamical black holes: Approach to the final state'), (10497, 'Dynamical black holes'), (10498, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.064045'), (10499, 'http://iopscience.iop.org/0264-9381/30/1/015010'), (10500, '015010'), (10501, '2013-01-07 2013-01-07'), (10502, '10.1088/0264-9381/30/1/015010'), (10503, '2015-04-15 18:23:34'), (10504, 'A new numerical method is introduced to study the problem of time evolution of generic nonlinear dynamical systems in four-dimensional spacetimes. It is assumed that the time level surfaces are foliated by a one-parameter family of codimension-2 compact surfaces with no boundary and which are conformal to a Riemannian manifold . The method is based on the use of a multipole expansion determined uniquely by the induced metric structure on . The approach is fully spectral—i.e. it avoids pointwise evaluations of the basic variables—in the angular directions. Instead, Gaunt coefficients as matrix elements are used to evaluate multilinear expressions. The dynamics in the complementary 1+1 Lorentzian spacetime is followed by making use of a fourth-order finite differencing scheme. In handling the pertinent 1+1 transverse degrees of freedom, the techniques of adaptive mesh refinement (AMR) is also applied. In checking the reliability and effectiveness of the introduced new method, the evolution of a massless scalar field on a fixed Kerr spacetime is investigated. In particular, the angular distribution of the evolving field in superradiant scattering is studied. The primary aim was to check the validity of some of the recent arguments claiming that the Penrose process, or its field theoretical correspondence—superradiance—does play a crucial role in jet formation in black hole spacetimes while matter accretes onto the central object. Our findings appear to be contrary to these claims as the angular dependence of superradiant scattering of massless scalar fields does not show any preference of the axis of rotation. In addition, the characteristic properties of superradiance in the case of a massless scalar field were also investigated. Contrary to the general expectations, we found that by an incident wave packet, which had been tuned to be maximally superradiant, the acquired extra energy in the scattering process must be less than 0.1% of the energy sent in. It was found that instead of the occurrence of an anticipated scale of energy extraction from black hole, the to be superradiant part of the incident wave packet fails to reach the ergoregion; rather it suffers a nearly perfect reflection which appears to be an interesting phenomenon.'), (10505, 'On the use of multipole expansion in time evolution of nonlinear dynamical systems and some surprises related to superradiance'), (10506, '2015-04-16 16:43:58'), (10507, '0264-9381_30_1_015010.pdf'), (10508, 'http://arxiv.org/abs/1502.06120'), (10509, 'arXiv:1502.06120 [gr-qc, physics:hep-th]'), (10510, '2015-02-21 2015-02-21'), (10511, 'arXiv: 1502.06120'), (10512, '2015-04-15 18:26:17'), (10513, "The conventional gravitational memory effect is a relative displacement in the position of two detectors induced by radiative energy flux. We find a new type of gravitational `spin memory' in which beams on clockwise and counterclockwise orbits acquire a relative delay induced by radiative angular momentum flux. It has recently been shown that the displacement memory formula is a Fourier transform in time of Weinberg's soft graviton theorem. Here we see that the spin memory formula is a Fourier transform in time of the recently-discovered subleading soft graviton theorem."), (10514, 'New Gravitational Memories'), (10515, 'http://www.arxiv.org/pdf/1502.06120.pdf'), (10516, 'arXiv:1502.06120 PDF'), (10517, 'http://link.aps.org/doi/10.1103/PhysRevD.83.044039'), (10518, '044039'), (10519, '2011-02-22 February 22, 2011'), (10520, '10.1103/PhysRevD.83.044039'), (10521, '2015-04-16 05:15:19'), (10522, 'The computation of the gravitational radiation emitted by a particle falling into a Schwarzschild black hole is a classic problem that was already studied in the 1970s. Here we present a detailed numerical analysis of the case of radial infall starting at infinity with no initial velocity. We compute the radiated waveforms, spectra, and energies for multipoles up to l=6, improving significantly on the numerical accuracy of existing results. This is done by integrating the Zerilli equation in the frequency domain using the Green’s function method. The resulting wave exhibits a “ring-down” phase whose dominant contribution is a superposition of the quasinormal modes of the black hole. The numerical accuracy allows us to recover the frequencies of these modes through a fit of that part of the wave. Comparing with direct computations of the quasinormal modes, we reach a ∼10−4 to ∼10−2 accuracy for the first two overtones of each multipole. Our numerical accuracy also allows us to display the power-law tail that the wave develops after the ring-down has been exponentially cut off. The amplitude of this contribution is ∼102 to ∼103 times smaller than the typical scale of the wave.'), (10523, 'Gravitational radiation from radial infall of a particle into a Schwarzschild black hole: A numerical study of the spectra, quasinormal modes, and power-law tails'), (10524, 'Gravitational radiation from radial infall of a particle into a Schwarzschild black hole'), (10525, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.83.044039'), (10526, 'http://link.aps.org/doi/10.1103/PhysRevD.69.104006'), (10527, '2004-05-12 May 12, 2004'), (10528, '10.1103/PhysRevD.69.104006'), (10529, '2015-04-16 05:21:11'), (10530, 'We investigate the behavior of a dynamical scalar field on a fixed Kerr background in Kerr-Schild coordinates using a (3+1)-dimensional spectral evolution code, and we measure the power-law tail decay that occurs at late times. We compare evolutions of initial data proportional to f(r)Y𝓁m(θ,φ), where Y𝓁m is a spherical harmonic and (r,θ,φ) are Kerr-Schild coordinates, to that of initial data proportional to f(rBL)Y𝓁m(θBL,φ), where (rBL,θBL) are Boyer-Lindquist coordinates. We find that although these two cases are initially almost identical, the evolution can be quite different at intermediate times; however, at late times the power-law decay rates are equal.'), (10531, '3D simulations of linearized scalar fields in Kerr spacetime'), (10532, 'We study the power-law tails in the evolution of massless fields around a fixed background geometry corresponding to a black hole. We give analytical arguments for their existence at scri+, at the future horizon, and at future timelike infinity. We confirm their existence with numerical integrations of the curved spacetime wave equation on the background of a Schwarzschild and a Reissner-Nordström black hole. These results are relevant to studies of mass inflation and the instability of Cauchy horizons. The analytic arguments also suggest the behavior of the full nonlinear dynamics, which we study numerically in a companion paper.'), (10533, '2015-04-16 05:21:38'), (10534, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.69.104006'), (10535, 'http://www.cambridge.org/us/academic/subjects/physics/cosmology-relativity-and-gravitation/black-hole-uniqueness-theorems'), (10536, '2015-04-16 14:13:20'), (10537, 'This timely review provides a self-contained introduction to the mathematical theory of stationary black holes and a self-consistent exposition of the corresponding uniqueness theorems. The opening chapters examine the general properties of space-times ad'), (10538, 'Black Hole Uniqueness Theorems'), (10539, 'Cambridge, UK'), (10540, 'http://iopscience.iop.org/0264-9381/25/10/105022'), (10541, 105022), (10542, '2008-05-21 2008-05-21'), (10543, '10.1088/0264-9381/25/10/105022'), (10544, '2015-04-16 14:15:19'), (10545, 'We investigate the late-time behavior of a scalar field on a fixed Kerr background using a 2 + 1 dimensional pseudo-spectral evolution code. We compare evolutions of pure axisymmetric multipoles in both Kerr–Schild and Boyer–Lindquist coordinates. We find that the late-time power-law decay rate depends upon the slicing of the background, confirming previous theoretical predictions for those decay rates. The accuracy of the numerical evolutions is sufficient to decide unambiguously between competing claims in the literature.'), (10546, 'High accuracy simulations of Kerr tails: coordinate dependence and higher multipoles'), (10547, 'High accuracy simulations of Kerr tails'), (10548, 'Late-time behavior of stellar collapse and explosions. I. Linearized perturbations'), (10549, '0264-9381_25_10_105022.pdf'), (10550, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.49.883'), (10551, 'http://link.aps.org/doi/10.1103/PhysRevD.49.890'), (10552, '890-899'), (10553, '10.1103/PhysRevD.49.890'), (10554, '2015-04-16 16:44:20'), (10555, 'We compare the predictions of linearized theory for the radiation produced in the collapse of a spherically symmetric scalar field with a full numerical integration of the Einstein equations. We find power-law tails and quasinormal ringing remarkably similar to predictions of linearized theory even in cases where nonlinearities are crucial. We also show that power-law tails develop even when the collapsing scalar field fails to produce a black hole.'), (10556, 'Late-time behavior of stellar collapse and explosions. II. Nonlinear evolution'), (10557, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.49.890'), (10558, 'http://link.aps.org/doi/10.1103/PhysRevD.34.384'), (10559, '384-408'), (10560, '1986-07-15 July 15, 1986'), (10561, '10.1103/PhysRevD.34.384'), (10562, '2015-05-27 13:19:25'), (10563, 'The radiative Green’s function for the one-dimensional wave equation with the Regge-Wheeler and Zerilli potentials is formally constructed from recently developed analytic representations for generalized spheroidal wave functions, and decomposed into a convergent sum over quasinormal modes, an integral around a branch cut in the frequency domain, and a high-frequency remnant of the free-space propagator. This paper discusses the contribution to the time response made by the quasinormal modes and, at very late times, by the branch-cut integral. The initial-value problem is considered for source fields with both compact and extended radial dependences, and the problem of the formal divergence of the integrals of extended sources over quasinormal-mode wave functions is solved. The branch-cut integral produces a weak late-time radiative power-law decay tail that will characterize the astrophysically observed radiation spectrum for times subsequent to the exponential decay of the quasinormal ringing, when (ct-r*)≫2MG/c2 and (ct-r*)/r*≪1. This radiative decay tail is shown to diminish to Price’s nonradiative tail in the final limit ct/r*≫1. The method is applied to a characteristic-value problem used to model the gravitational collapse of massive stars, and to the small-body radial in-fall problem. The analysis presented is generalizable, through the Newman-Penrose formalism and Teukolsky’s equations, to obtain the radiative Green’s function for perturbations to the Kerr geometry.'), (10564, 'Spectral decomposition of the perturbation response of the Schwarzschild geometry'), (10565, 'arXiv:1007.2481 PDF'), (10566, '2015-04-16 16:55:41'), (10567, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.34.384'), (10568, 'http://link.aps.org/doi/10.1103/PhysRevD.38.725'), (10569, '725-725'), (10570, '1988-07-15 July 15, 1988'), (10571, '10.1103/PhysRevD.38.725'), (10572, '2015-04-16 16:55:52'), (10573, 'DOI:'), (10574, 'Erratum: spectral decomposition of the perturbation response of the schwarzschild geometry'), (10575, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.38.725'), (10576, 'http://link.aps.org/doi/10.1103/PhysRevD.52.2118'), (10577, '2118-2132'), (10578, '1995-08-15 August 15, 1995'), (10579, '10.1103/PhysRevD.52.2118'), (10580, '2015-05-27 13:19:28'), (10581, 'It is well known that the dominant late time behavior of waves propagating on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic treatment of the tail phenomenon for a broad class of models via a Green’s function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Green’s function G̃(ω) along the -Imω axis, generalizing the Schwarzschild result. (ii) The ω dependence of the cut is determined by the asymptotic but not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a star as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case with a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and the time dependence of the tail for a broad class of models are obtained analytically. (v) The analytical results are in perfect agreement with numerical calculations.'), (10582, 'Wave propagation in gravitational systems: Late time behavior'), (10583, 'Wave propagation in gravitational systems'), (10584, 'http://www.jstor.org.proxy.library.cornell.edu/stable/2373586'), (10585, '2015-04-16 16:57:39'), (10586, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.52.2118'), (10587, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/32/12/10.1063/1.529456'), (10588, 32), (10589, '3423-3426'), (10590, '1991-12-01 1991/12/01'), (10591, '10.1063/1.529456'), (10592, '2015-04-16 17:39:08'), (10593, 'The global behavior of light cone cuts at null infinity, i.e., the intersection of light cones of interior point, with null infinity, is investigated. In particular, it is shown that the topological structure of these cuts, for the case of an asymptotically flat space‐time, is very simple. The nature of the light cone cuts singularities is also analyzed. Generically, only two different types of singularities occur and their local description is given.'), (10594, 'Global aspects of light cone cuts'), (10595, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/32/12/1.529456.pdf?itemId=/content/aip/journal/jmp/32/12/10.1063/1.529456&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10596, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/40/5/10.1063/1.533077'), (10597, '2483-2493'), (10598, '1999-05-01 1999/05/01'), (10599, '10.1063/1.533077'), (10600, '2015-04-16 17:40:45'), (10601, 'It is shown that the main variable Z of the null surface formulation of GR is the generating family of a constrained Lagrange submanifold that lives on the energy surface H=0 and that its level surfaces Z= const yield Legendre submanifolds on that energy surface. Thus, the singularity structure of past null cones with apex at I + is obtained by studying the projection map of the Legendre submanifolds to the configuration space. The behavior of the coordinate system defined by the variable Z at the caustic points is analyzed. It is shown that a single function Z(x a ,ζ,ζ̄) cannot generate the conformal structure of an asymptotically flat space–time that satisfies the generic and weak energy condition.'), (10602, 'Null cones from I+ and Legendre submanifolds'), (10603, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/40/5/1.533077.pdf?itemId=/content/aip/journal/jmp/40/5/10.1063/1.533077&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10604, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/40/2/10.1063/1.532705'), (10605, '1041-1056'), (10606, '1999-02-01 1999/02/01'), (10607, '10.1063/1.532705'), (10608, '2015-04-16 17:41:14'), (10609, 'In an arbitrary Lorentzian manifold we provide a description for the construction of null surfaces and their associated singularities, via solutions of the Eikonal equation. In particular, we study the singularities of the past light-cones from points on null infinity, the future light-cones from arbitrary interior points and the intersection of these with null infinity and unifying relationships between the different singularities. The starting point for this work is the assumption of a known family of solutions to the Eikonal equation. The work is based on the standard theory of singularities of smooth maps by Arnold and his colleagues. Though the work is intended to stand on its own, it can be thought of as being closely related to the recently developed null surface reformulation of GR.'), (10610, 'The Eikonal equation in asymptotically flat space–times'), (10611, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/40/2/1.532705.pdf?itemId=/content/aip/journal/jmp/40/2/10.1063/1.532705&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10612, 'http://iopscience.iop.org/0264-9381/23/2/014'), (10613, 497), (10614, '2006-01-21 2006-01-21'), (10615, '10.1088/0264-9381/23/2/014'), (10616, '2015-04-16 18:22:43'), (10617, 'We show how to define and go from the spin-s spherical harmonics to the tensorial spin-s harmonics. These quantities, which are functions on the sphere taking values as Euclidean tensors, turn out to be extremely useful for many calculations in general relativity. In the calculations, products of these functions, with their needed decompositions which are given here, often arise naturally.'), (10618, 'Tensorial spin-s harmonics'), (10619, 'Copyright © 1974 The Johns Hopkins University Press'), (10620, '0264-9381_23_2_014.pdf'), (10621, 'http://pldml.icm.edu.pl/mathbwn/element/bwmeta1.element.bwnjournal-article-fmv25i1p35bwm'), (10622, '427-440'), (10623, 'Fundamenta Mathematicae'), (10624, '0016-2736'), (10625, '1935-00-00 1935'), (10626, '2015-04-20 14:13:13'), (10627, 'pldml.icm.edu.pl'), (10628, 'DE'), (10629, 'Über die Abbildungen von Sphären auf Sphäre niedrigerer Dimension'), (10630, 'fm25135.pdf'), (10631, '156-206'), (10632, '1974-04-01 April 1, 1974'), (10633, '10.2307/2373586'), (10634, '2015-05-01 17:59:12'), (10635, '2015-05-27 13:30:13'), (10636, 'https://molecularmusings.wordpress.com/2013/05/24/a-faster-quaternion-vector-multiplication/'), (10637, '2015-04-20 17:55:24'), (10638, "Today's post is only a small gem I accidentally came across while I was looking for something entirely different: a faster method of multiplying a quaternion by a vector. I use quaternion-vector mu..."), (10639, 'Molecular Musings'), (10640, 'A faster quaternion-vector multiplication'), (10641, 'http://www.sciencedirect.com/science/article/pii/0020019075900368'), (10642, '177-179'), (10643, 'Information Processing Letters'), (10644, '0020-0190'), (10645, '1975-07-00 July 1975'), (10646, '10.1016/0020-0190(75)90036-8'), (10647, '2015-04-20 17:55:34'), (10648, 'On the complexity of quaternion multiplication'), (10649, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0020019075900368/pdf?md5=9c5accabcf472ac59c8d5c721e38d8b4&pid=1-s2.0-0020019075900368-main.pdf'), (10650, 'http://www.sciencedirect.com/science/article/pii/0041555377901872'), (10651, '221-222'), (10652, 'USSR Computational Mathematics and Mathematical Physics'), (10653, '0041-5553'), (10654, '10.1016/0041-5553(77)90187-2'), (10655, '2015-04-20 17:55:48'), (10656, 'An algorithm is given for the multiplication of two quaternions, requiring 8 actual multiplications to be performed (disregarding multiplications by absolute constants).'), (10657, 'An algorithm for the multiplication of two quaternions'), (10658, 'http://link.springer.com/article/10.1007/s00006-014-0466-0'), (10659, '2014-06-10 2014/06/10'), (10660, '10.1007/s00006-014-0466-0'), (10661, '2015-04-20 18:00:56'), (10662, 'In this paper we introduce an efficient algorithm for the multiplication of Pauli numbers. The direct multiplication of two Pauli numbers requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how to compute a product of the Pauli numbers with 24 conventional multiplications, 8 multiplications by 1/2 and 56 real additions.'), (10663, 'An Algorithm for Fast Multiplication of Pauli Numbers'), (10664, 'http://link.springer.com/content/pdf/10.1007%2Fs00006-014-0466-0.pdf'), (10665, 'http://www.sciencedirect.com/science/article/pii/002001909090153O'), (10666, '267-272'), (10667, '1990-12-01 December 1, 1990'), (10668, '10.1016/0020-0190(90)90153-O'), (10669, '2015-04-20 18:02:22'), (10670, 'Nonstandard transformations over matrices allow the derivation of different, optimal algorithms in digital signal processing.'), (10671, 'On the synthesis of fast algorithms for signal processing'), (10672, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/002001909090153O/pdf?md5=b0e42479c932f998290775e68bc0c2ab&pid=1-s2.0-002001909090153O-main.pdf'), (10673, 'http://www.sciencedirect.com/science/article/pii/002001909290009K'), (10674, '161-164'), (10675, '1992-09-14 September 14, 1992'), (10676, '10.1016/0020-0190(92)90009-K'), (10677, '2015-04-20 18:07:22'), (10678, 'We present two efficient algorithms for the multiplication of the so-called reduced biquaternions. The proposed algorithms may be used for the realization of digital filters with hypercomplex coefficients.'), (10679, 'On the multiplication of reduced biquaternions and applications'), (10680, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/002001909290009K/pdf?md5=4772c0eab4faefef45f163e84854652e&pid=1-s2.0-002001909290009K-main.pdf'), (10681, '2 edition'), (10682, 'Singapore ; River Edge, N.J'), (10683, 'World Scientific Pub Co Inc'), (10684, 9789810235628), (10685, '1999-06-00 June 1999'), (10686, 'Amazon'), (10687, 'These lecture notes are the content of an introductory course on modern, co-ordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course, "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory. This edition of the text contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made. The volume is divided into four parts. The first provides an introduction to general topology, the second covers introductory co-ordinate-free differential geometry, the third examines geometrical aspects of the theory of Lie groups and Lie group actions on manifolds, and the fourth provides an introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view - some geometrical, others more algebraic.'), (10688, 'Modern Differential Geometry for Physicists'), (10689, 289), (10690, 'Clifford Algebras and Spinor Norms Over a Commutative Ring'), (10691, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2373586.pdf?acceptTC=true'), (10692, 'Isham, Chris - Modern Differential Geometry for Physicists(306s)(T).djvu'), (10693, 'Wiley-Interscience'), (10694, 9780471157335), (10695, '1996-02-22 February 22, 1996'), (10696, "This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques."), (10697, 'Foundations of Differential Geometry, Vol.1'), (10698, 'http://www.jstor.org.proxy.library.cornell.edu/stable/2653243'), (10699, 'Copyright © 1998 Society for Industrial and Applied Mathematics'), (10700, 'Kobayashi.Nomizu.-.Foundations.of.Differential.Geometry.Vol.1.djvu'), (10701, 'Volume 2 edition'), (10702, 9780471157328), (10703, 'Foundations of Differential Geometry, Vol. 2'), (10704, 488), (10705, '703-705'), (10706, 'SIAM Review'), (10707, 'Kobayashi.Nomizu.-.Foundations.of.Differential.Geometry.Vol.2.djvu'), (10708, 'Matrix elements of irreducible representations of the Lorentz group are calculated on the basis of complex angular momentum. It is shown that Laplace–Beltrami operators, defined on this basis, give rise to Fuchsian differential equations. An explicit form of the matrix elements of the Lorentz group has been found via the addition theorem for generalized spherical functions. Different expressions of the matrix elements are given in terms of hypergeometric functions both for finite-dimensional and unitary representations of the principal and supplementary series of the Lorentz group.'), (10709, 9780817649074), (10710, '2009-09-01 2009-09-01'), (10711, 'Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of PoincarA(c), de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions. a oeThis book is a well-informed and detailed analysis of the problems and development of algebraic topology, from PoincarA(c) and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it!a (MathSciNet) a oe[The author] traces the development of algebraic and differential topology from the innovative work by PoincarA(c) at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields.a ] The details are interwoven with the narrative in a very pleasant fashion.a ] [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders.a (Zentralblatt MATH)'), (10712, 'A History of Algebraic and Differential Topology, 1900 - 1960'), (10713, 666), (10714, '0036-1445'), (10715, '1998-09-01 September 1, 1998'), (10716, 'http://www.jstor.org.proxy.library.cornell.edu/stable/2320587'), (10717, 'Copyright © 1979 Mathematical Association of America'), (10718, '571-574'), (10719, '1979-08-01 August 1, 1979'), (10720, '10.2307/2320587'), (10721, '2015-04-21 04:09:55'), (10722, 'A Proof of the Hairy Ball Theorem'), (10723, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2320587.pdf?acceptTC=true'), (10724, 'Providence, RI'), (10725, 'http://link.springer.com/chapter/10.1007/978-3-662-02781-3_22'), (10726, '©1993 Springer-Verlag Berlin Heidelberg'), (10727, 'The Collected Works of Eugene Paul Wigner'), (10728, '334-389'), (10729, '978-3-642-08154-5, 978-3-662-02781-3'), (10730, '2015-04-22 23:07:04'), (10731, 'A / 1'), (10732, 'It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally represented by wave functions3 in such a way that φ and constant multiples of φ represent the same physical state. It is possible, therefore, to normalize the wave function, i.e., to multiply it by a constant factor such that its scalar product with itself becomes 1. Then, only a constant factor of modulus 1, the so-called phase, will be left undetermined in the wave function. The linear character of the wave function is called the superposition principle. The square of the modulus of the unitary scalar product (ψ, φ) of two normalized wave functions ψ and φ is called the transition probability from the state ψ into φ or conversely. This is supposed to give the probability that an experiment performed on a system in the state φ, to see whether or not the state is ψ gives the result that it is ψ. If there are two or more different experiments to decide this (e.g., essentially the same experiment, performed at different times) they are all supposed to give the same result, i.e., the transition probability has an invariant physical sense.'), (10733, '2015-05-27 14:04:17'), (10734, 'bok%3A978-3-662-02781-3.pdf'), (10735, 'http://link.springer.com/article/10.1007/BF03155711'), (10736, '175-185'), (10737, 'Acta Physica Hungarica'), (10738, '0231-4428'), (10739, '1985-12-01 1985-12-01'), (10740, '10.1007/BF03155711'), (10741, '2015-04-22 23:26:43'), (10742, "By means of suitable coordinate systems spherical functions of the Lorentz group are derived on the double-sheeted, single-sheeted hyperboloids and similarly on the light cone. These form complete orthonormal sets of functions on each hyperboloid as well as on the light cone and transform according to the principal series of unitary representations of the Lorentz group. The spherical functions are given in a basis defined by the two-dimensional momentum (N 1+M 2,N 2 −M 1) of horospheric translations where N and M denote the generators of Lorentz transformations and spatial rotations. It is known that the upper sheet of the double-sheeted hyperboloid is a homogeneous space even under the subgroup (α0βα−1)\\left( {\\begin{array}{*{20}c} \\alpha & \\beta \\\\ 0 & {\\alpha ^{ - 1} } \\\\ \\end{array} } \\right) ∈ SL(2, C). As 'a consequence of this the spherical functions have rather simple transformation properties under the Lorentz group."), (10743, 'Spherical functions of the Lorentz group on the hyperboloids'), (10744, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/6/10.1063/1.1705341'), (10745, 'art%3A10.1007%2FBF03155711.pdf'), (10746, 'http://link.springer.com/article/10.1007/BF03157011'), (10747, '3-14'), (10748, 'Acta Physica Academiae Scientiarum Hungaricae'), (10749, '0001-6705'), (10750, '1975-05-01 1975-05-01'), (10751, 'Acta Physica'), (10752, '10.1007/BF03157011'), (10753, '2015-04-23 03:10:00'), (10754, 'Representations of theSL(2,C) groups are reduced with respect to the horospheric subgroup (10β1)\\left( {\\begin{array}{*{20}c} 1 \\\\ 0 \\\\ \\end{array} \\begin{array}{*{20}c} \\beta \\\\ 1 \\\\ \\end{array} } \\right) isomorphic to the translation group in two dimensions. The matrix elements of unitary representations of the principal and supplementary series are derived in a basis defined by a two-dimensional momentum corresponding to the above subgroup. Matrix elements of unitary representations expressed in this basis assume a simpler form than in any other basis considered so far. The two-dimensional momentum introduced proves to be essentially identical with the impact parameter.'), (10755, 'Horospheric basis of the SL(2, C) group'), (10756, '1252-1265'), (10757, 'art%3A10.1007%2FBF03157011.pdf'), (10758, 'http://link.springer.com/article/10.1007/BF01038301'), (10759, '867-876'), (10760, 'Theoretical and Mathematical Physics'), (10761, '0040-5779, 1573-9333'), (10762, '1970-09-01 1970-09-01'), (10763, 'Theor Math Phys'), (10764, '10.1007/BF01038301'), (10765, '2015-04-23 03:28:09'), (10766, 'Representations of the Lorentz group and generalization of helicity states'), (10767, '1967-06-01 1967/06/01'), (10768, 'art%3A10.1007%2FBF01038301.pdf'), (10769, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/10/1/10.1063/1.1664752'), (10770, '21-29'), (10771, '1969-01-01 1969/01/01'), (10772, '10.1063/1.1664752'), (10773, '2015-04-23 03:30:23'), (10774, 'Starting from the functional representation of Gel'fand and Naimark, the unitary irreducible representations of SL(2, C) are described in a basis of the subgroup E(2)⊗D , where E(2)⊗D is the subgroup of all 2 × 2 matrices of the form ( α 0 γ δ ) , αδ=1 . Physically, this is the subgroup into which SL(2, C) degenerates at infinite momentum and may be thought of as the 2‐dimensional Euclidean group together with its dilations. Advantages to using the E(2)⊗D basis are: (1) It is convenient to calculate form factors; (2) the generators of E(2)⊗D are represented either multiplicatively or by first‐order differential operators and are independent of the values of the SL(2, C) Casimir operators; (3) the principal and supplementary series of SL(2, C) are treated on the same footing and, in particular, have the same inner product; and (4) the transformation coefficients to the usual angular‐momentum basis are related to Bessel functions. The E(2)⊗D is used to compute explicitly the finite matrix elements of an arbitrary Lorentz transformation and to investigate the structure of vector operators in unitary representation of SL(2, C).'), (10775, 'Unitary Representations of SL(2, C) in an E(2) Basis'), (10776, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/10/1/1.1664752.pdf?itemId=/content/aip/journal/jmp/10/1/10.1063/1.1664752&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10777, 'http://link.aps.org/doi/10.1103/PhysRevLett.40.203'), (10778, '203-206'), (10779, '1978-01-23 January 23, 1978'), (10780, '10.1103/PhysRevLett.40.203'), (10781, 'In this note an elementary method of calculating any power of a given matrix is described. The method is quite similar to that presented by I. E. Leonard [SIAM Rev., 38 (1996), pp. 507-512].'), (10782, 'An example is given of a space-time which satisfies the conditions for asymptotic region is not "as large" as that of Minkowski space-time.'), (10783, 'Asymptotically Simple Does Not Imply Asymptotically Minkowskian'), (10784, 'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.40.203'), (10785, '2015-04-24 17:33:06'), (10786, 'The Power of a Matrix'), (10787, '©2007 Springer Science+Business Media, LLC'), (10788, 'Universitext'), (10789, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2653243.pdf?acceptTC=true'), (10790, 'Wick Rotation as a reason for choosing Cl_{1,3} over Cl_{3,1}'), (10791, '978-0-387-26040-2, 978-0-387-28929-8'), (10792, '2015-04-27 19:11:24'), (10796, '10.1063/1.1705341'), (10797, 'Lie Groups: An Approach through Invariants and Representations'), (10798, 'http://link.springer.com/book/10.1007%2F978-0-387-28929-8'), (10799, 'bok%3A978-0-387-28929-8.pdf'), (10800, '2015-05-01 18:00:15'), (10801, 'The unitary irreducible representations of the group SL(2C) belonging to the principal series restricted to the subgroup SU(1, 1) are decomposed into a direct integral of unitary irreducible representations of SU(1, 1). The matrix elements of the unitary operator which performs the decomposition are given explicitly and used to obtain a relation between the matrix elements of the unitary irreducible representations of the groups SL(2C) and SU(1, 1). Similar identities between the matrix elements of nonunitary representations of these groups are obtained by means of analytic continuation. The relevance of these results to the theory of complex angular momentum and of high energy nearly forwardscattering is pointed out.'), (10802, 'Decomposition of the Unitary Irreducible Representations of the Group SL(2C) Restricted to the Subgroup SU(1, 1)'), (10803, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/6/1.1705341.pdf?itemId=/content/aip/journal/jmp/8/6/10.1063/1.1705341&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10804, 9780821886526), (10805, '1978-00-00 1978'), (10806, 'Special Functions and the Theory of Group Representations'), (10807, 628), (10808, 'https://books.google.com/books?id=08hPoGgSQFIC'), (10809, '2015-05-01 19:16:29'), (10810, 'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/415/4/3227'), (10811, 415), (10812, '3227-3236'), (10813, '2011-08-21 08/21/2011'), (10814, '10.1111/j.1365-2966.2011.18934.x'), (10815, '2015-05-04 12:58:08'), (10816, 'It is well known that our motion with respect to the cosmic microwave background (CMB) rest frame introduces a large dipolar CMB anisotropy, with an amplitude ∝β=v/c∼ 10−3. In addition it should lead to a small breaking of statistical isotropy which becomes most notable at higher multipoles. In principle this could be used to determine our velocity with respect to the CMB rest frame using high angular resolution data from Planck, without directly relying on the amplitude and direction of the CMB dipole, allowing us to constrain cosmological models in which the cosmic dipole arises partly from large-scale isocurvature perturbations instead of being fully motion-induced. Here, we derive simple recursion relations that allow precise computation of the motion-induced coupling between different spherical harmonic coefficients. Although the lowest order approximations for the coupling kernel can be deficient by factors of 2–5 at multipoles l∼ 1000–3000, using our results for the aberration kernel we explicitly confirm that for a statistical detection of the aberration effect only first-order terms in β matter. However, the expressions given here are not restricted to β∼ 10−3, but can be used at much higher velocities. We demonstrate the robustness of these formulae, illustrating the dependence of the kernel on β, as well as the spherical harmonic indices l and m.'), (10817, 'Fast and accurate computation of the aberration kernel for the cosmic microwave background sky'), (10818, 'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/415/4/3227.full.pdf'), (10819, 'http://link.aps.org/doi/10.1103/PhysRevD.89.123504'), (10820, 123504), (10821, '2014-06-05 June 5, 2014'), (10822, '10.1103/PhysRevD.89.123504'), (10823, '2015-05-04 13:01:53'), (10824, 'Aberration kernels describe how harmonic-space multipole coefficients of cosmic microwave background (CMB) observables transform under Lorentz boosts of the reference frame. For spin-weighted CMB observables, transforming like the CMB temperature (i.e., Doppler weight d=1), we show that the aberration kernels are the matrix elements of a unitary boost operator in harmonic space. Algebraic properties of the rotation and boost generators then give simple, exact recursion relations that allow us to raise or lower the multipole quantum numbers ℓ and m and the spin weight s. Further recursion relations express kernels of other Doppler weights d≠1 in terms of the d=1 kernels. From those we show that on the full sky, to all orders in β=v/c, E- and B-mode polarization observables do not mix under aberration if and only if d=1. The new relations, fully nonlinear in the boost velocity β, form the basis of a practical recursive algorithm to accurately compute any aberration kernel. In addition, we develop a second, fast algorithm in which aberration kernels are obtained using a set of ordinary differential equations. This system can also be approximately solved at small scales, providing simple asymptotic formulas for the aberration kernels. The results of this work will be useful for further studying the effect of aberration on future CMB temperature and polarization analysis and might provide a basis for relativistic radiative transfer schemes.'), (10825, 'New operator approach to the CMB aberration kernels in harmonic space'), (10826, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.123504'), (10827, 'Chandrasekhar S. The mathematical theory of black holes.djvu'), (10828, 'http://iopscience.iop.org/1475-7516/2012/02/026'), (10829, 2012), (10830, '026'), (10831, 'Journal of Cosmology and Astroparticle Physics'), (10832, '1475-7516'), (10833, '2012-02-01 2012-02-01'), (10834, 'J. Cosmol. Astropart. Phys.'), (10835, '10.1088/1475-7516/2012/02/026'), (10836, '2015-05-04 17:45:59'), (10837, 'It was recently shown that our peculiar velocity β with respect to the CMB induces mixing among multipoles and off-diagonal correlations at all scales which can be used as a measurement of β, which is independent of the standard measurement using the CMB temperature dipole. The proposed techniques rely however on a perturbative expansion which breaks down for ℓ1/β ≈ 800. Here we propose a technique which consists of deboosting the CMB temperature in the time-ordered data and show that it extends the validity of the perturbation analysis multipoles up to ℓ ~ 10000. We also obtain accurate fitting functions for the mixing between multipoles valid in a full non-linear treatment. Finally we forecast the achievable precision with which these correlations can be measured in a number of current and future CMB missions. We show that Planck could measure the velocity with a precision of around 60 km/s, ACTPol in 4 years around 40 km/s, while proposed future experiments could further shrink this error bar by over a factor of around 2.'), (10838, "Measuring our peculiar velocity by ``pre-deboosting'' the CMB"), (10840, '1475-7516_2012_02_026.pdf'), (10841, 'http://iopscience.iop.org/0004-637X/624/1/7'), (10842, '2005-05-01 2005-05-01'), (10843, '10.1086/428936'), (10844, '2015-05-04 17:46:46'), (10845, "Recent studies have found the earth's peculiar velocity to be significant in microwave-background-based tests for compact cosmic topology, and modifications to these tests have been proposed. Tests of non-Gaussianity, weak-lensing analysis, and new tests using improved cosmic microwave background (CMB) data will also be sensitive to peculiar velocity. We propose here to simplify matters by showing how to construct a deaberrated CMB map to which any test requiring a Hubble flow view point can be applied without further complication. In a similar manner, deaberration can also be applied to object surveys used, for example, in topological searches and matter distribution analysis. In particular, we have produced a revised list of objects with z > 1.0 using the NASA/IPAC Extragalactic Database."), (10846, 'Peculiar Velocity and Deaberration of the Sky'), (10847, 'http://iopscience.iop.org/0004-637X/624/1/7/pdf/0004-637X_624_1_7.pdf'), (10848, 'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/432/3/2208'), (10849, 432), (10850, '2208-2215'), (10851, '2013-07-01 07/01/2013'), (10852, '10.1093/mnras/stt577'), (10853, '2015-05-04 17:47:05'), (10854, "The effect of our Galaxy's motion through the cosmic microwave background (CMB) rest frame, which aberrates and Doppler shifts incoming photons measured by current CMB experiments, has been shown to produce mode mixing in the multipole space temperature coefficients. However, multipole space determinations are subject to many difficulties, and a real-space analysis can provide a straightforward alternative. In this work we describe a numerical method for removing Lorentz-boost effects from real-space temperature maps. We show that to deboost a map so that one can accurately extract the temperature power spectrum requires calculating the boost kernel at a finer pixelization than one might naively expect. In idealized cases that allow for easy comparison to analytic results, we have confirmed that there is indeed mode mixing among the spherical harmonic coefficients of the temperature. We find that using a boost kernel calculated at Nside = 8192 leads to a 1 per cent bias in the binned boosted power spectrum at ℓ ∼ 2000, while individual Cℓs exhibit ∼5 per cent fluctuations around the binned average. However, this bias is dominated by pixelization effects and not the aberration and Doppler shift of CMB photons that causes the fluctuations. Performing analysis on maps with Galactic cuts does not induce any additional error in the boosted, binned power spectra over the full sky analysis. For multipoles that are free of resolution effects, there is no detectable deviation between the binned boosted and unboosted spectra. This result arises because the power spectrum is a slowly varying function of ℓ and does not show that, in general, Lorentz boosts can be neglected for other cosmological quantities such as polarization maps or higher point functions."), (10855, 'Real-space approach to cosmic microwave background deboosting'), (10856, 'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/432/3/2208.full.pdf'), (10857, 'http://arxiv.org/abs/1009.4937'), (10858, 'arXiv:1009.4937 [astro-ph]'), (10859, 'arXiv: 1009.4937'), (10860, '2015-05-04 17:57:18'), (10861, "The largest fluctuation in the observed CMB temperature field is the dipole, its origin being usually attributed to the Doppler Effect - the Earth's velocity with respect to the CMB rest frame. The lowest order boost correction to temperature multipolar coefficients appears only as a second order correction in the temperature power spectrum, $C_{\\ell}$. Since v/c - 10-3, this effect can be safely ignored when estimating cosmological parameters [4-7]. However, by cutting our galaxy from the CMB sky we induce large-angle anisotropies in the data. In this case, the corrections to the cut-sky $C_{\\ell}$s show up already at first order in the boost parameter. In this paper we investigate this issue and argue that this effect might turn out to be important when reconstructing the power spectrum from the cut-sky data."), (10862, 'Effects of a Cut, Lorentz-Boosted sky on the Angular Power Spectrum'), (10863, 'http://www.arxiv.org/pdf/1009.4937.pdf'), (10864, 'arXiv:1009.4937 PDF'), (10865, 'http://link.aps.org/doi/10.1103/PhysRevD.65.103001'), (10866, 103001), (10867, '2002-04-23 April 23, 2002'), (10868, '10.1103/PhysRevD.65.103001'), (10869, '2015-05-04 17:59:17'), (10870, 'We investigate the impact of peculiar velocity effects due to the motion of the solar system relative to the cosmic microwave background (CMB) on high resolution CMB experiments. It is well known that on the largest angular scales the combined effects of Doppler shifts and aberration are important; the lowest Legendre multipoles of total intensity receive power from the large CMB monopole in transforming from the CMB frame. On small angular scales aberration dominates and is shown here to lead to significant distortions of the total intensity and polarization multipoles in transforming from the rest frame of the CMB to the frame of the solar system. We provide convenient analytic results for the distortions as series expansions in the relative velocity of the two frames, but at the highest resolutions a numerical quadrature is required. Although many of the high resolution multipoles themselves are severely distorted by the frame transformations, we show that their statistical properties distort by only an insignificant amount. Therefore, the cosmological parameter estimation is insensitive to the transformation from the CMB frame (where theoretical predictions are calculated) to the rest frame of the experiment.'), (10871, 'Peculiar velocity effects in high-resolution microwave background experiments'), (10873, '2015-05-04 17:59:31'), (10874, 'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.65.103001'), (10875, '2015-05-04 17:59:43'), (10876, 'http://iopscience.iop.org/1475-7516/2011/07/027'), (10877, 2011), (10878, '07'), (10879, '027'), (10880, '2011-07-01 2011-07-01'), (10881, '10.1088/1475-7516/2011/07/027'), (10882, '2015-05-04 18:04:35'), (10883, 'Our peculiar velocity with respect to the CMB rest frame is known to induce a large dipole in the CMB. However, the motion of an observer has also the effect of distorting the anisotropies at all scales, as shown by Challinor and Van Leeuwen (2002), due to aberration and Doppler effects. We propose to measure independently our local motion by using off-diagonal two-point correlation functions for high multipoles. We study the observability of the signal for temperature and polarization anisotropies. We point out that Planck can measure the velocity β with an error of about 30% and the direction with an error of about 20°. This method constitutes a cross-check, which can be useful to verify that our CMB dipole is due mainly to our velocity or to disentangle the velocity from other possible intrinsic sources. Although in this paper we focus on our peculiar velocity, a similar effect would result also from other intrinsic vectorial distortion of the CMB which would induce a dipolar lensing. Measuring the off-diagonal correlation terms is therefore a test for a preferred direction on the CMB sky.'), (10884, 'Measuring our peculiar velocity on the CMB with high-multipole off-diagonal correlations'), (10886, '1475-7516_2011_07_027.pdf'), (10887, 'A note on the matrix elements of a unitary representation of the homogeneous Lorentz group'), (10888, 'Arkiv för fysik'), (10889, '465--469'), (10891, '1967-01-18 January 18, 1967'), (10892, '20150505103938789.pdf'), (10893, 'On the matrix elements of a unitary representation of the homogeneous Lorentz group'), (10894, '467--483'), (10896, '1965-07-29 July 29, 1965'), (10897, '20150505103822960.pdf'), (10898, 'http://arxiv.org/abs/hep-th/0611263'), (10899, 'arXiv:hep-th/0611263'), (10900, '2006-11-24 2006-11-24'), (10901, 'arXiv: hep-th/0611263'), (10902, '2015-05-06 16:57:45'), (10903, 'An extensive group-theoretical treatment of linear relativistic wave equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes. To start with, the one-to-one correspondence between linear relativistic wave equations and unitary representations of the isometry group is reviewed. In turn, the method of induced representations reduces the problem of classifying the representations of the Poincare group ISO(D-1,1) to the classication of the representations of the stability subgroups only. Therefore, an exhaustive treatment of the two most important classes of unitary irreducible representations, corresponding to massive and massless particles (the latter class decomposing in turn into the ``helicity\'\' and the "infinite-spin" representations) may be performed via the well-known representation theory of the orthogonal groups O(n) (with D-4<n<D). Finally, covariant wave equations are given for each unitary irreducible representation of the Poincare group with non-negative mass-squared. Tachyonic representations are also examined. All these steps are covered in many details and with examples. The present notes also include a self-contained review of the representation theory of the general linear and (in)homogeneous orthogonal groups in terms of Young diagrams.'), (10904, 'The unitary representations of the Poincare group in any spacetime dimension'), (10905, 'http://www.arxiv.org/pdf/hep-th/0611263.pdf'), (10906, 'arXiv:hep-th/0611263 PDF'), (10907, 'http://www.emis.de/journals/SIGMA/2014/084/'), (10908, 'Symmetry, Integrability and Geometry: Methods and Applications'), (10909, 18150659), (10910, '2014-08-12 2014-08-12'), (10911, '10.3842/SIGMA.2014.084'), (10912, '2015-05-06 16:58:01'), (10913, 'A Compact Formula for Rotations as Spin Matrix Polynomials'), (10914, 'sigma14-084.pdf'), (10915, 'https://en.wikipedia.org/w/index.php?title=Stirling_number&oldid=647550498'), (10916, 'Creative Commons Attribution-ShareAlike License'), (10917, '2015-02-17 2015-02-17T13:50:15Z'), (10918, 'Page Version ID: 647550498'), (10919, '2015-05-08 03:30:51'), (10920, 'Wikipedia'), (10921, 'Wikipedia, the free encyclopedia'), (10922, 'In mathematics, Stirling numbers arise in a variety of analytic and combinatorics problems. They are named after James Stirling, who introduced them in the 18th century. Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second kind.'), (10923, 'Stirling number'), (10924, 'http://www.sciencedirect.com/science/article/pii/0024379594002459'), (10925, 'Honoring J.J.Seidel'), (10926, '226–228'), (10927, '57-72'), (10928, 'Linear Algebra and its Applications'), (10929, '0024-3795'), (10930, '1995-09-00 September 1995'), (10931, '10.1016/0024-3795(94)00245-9'), (10932, '2015-05-08 03:32:51'), (10933, "Extending earlier work of R. Donaghey and P. J. Cameron, we investigate some canonical “eigen-sequences” associated with transformations of integer sequences. Several known sequences appear in a new setting: for instance, the sequences (such as 1, 3, 11, 49, 257, 1531, …) studied by T. Tsuzuku, H. O. Foulkes, and A. Kerber in connection with multiply transitive groups are eigen-sequences for the binomial transform. Many interesting new sequences also arise, such as 1, 1, 2, 26, 152, 1144, ..., which shifts one place left when transformed by the Stirling numbers of the second kind, and whose exponential generating function satisfies A'(x) = A(ex − 1) + 1."), (10934, 'Some canonical sequences of integers'), (10935, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0024379594002459/pdf?md5=f94b22554f46ce7988eeb86e822bc4cf&pid=1-s2.0-0024379594002459-main.pdf'), (10936, 'http://arxiv.org/abs/math/0106123'), (10937, 'arXiv:math/0106123'), (10938, '2001-06-14 2001-06-14'), (10939, 'arXiv: math/0106123'), (10940, '2015-05-08 03:43:40'), (10941, "Exponentiating the hypergeometric series gives a recursion relation for integer sequences which are generalizations of conventional Bell numbers. The corresponding associated Stirling numbers of the second kind are also generated and investigated. For the lowest order generalisation, one can give a combinatorial interpretation of these 'Bell' numbers, and of some Stirling numbers associated with them. We also consider these analogues of Bell numbers in the case of restricted partitions."), (10942, 'Extended Bell and Stirling numbers from hypergeometric exponentiation'), (10943, 'http://www.arxiv.org/pdf/math/0106123.pdf'), (10944, 'arXiv:math/0106123 PDF'), (10945, 'http://dlmf.nist.gov/26.8#E8'), (10946, '2015-05-08 19:38:14'), (10947, 'DLMF: §26.8 Set Partitions: Stirling Numbers'), (10948, '2015-05-08 19:38:16'), (10949, 'http://dlmf.nist.gov/'), (10950, 'Online companion to Olver:2010:NHMF \nbibtex: NIST:DLMF \nbibtex[key=relaxDLMF]'), (10951, 'NIST Digital Library of Mathematical Functions'), (10952, 'Print companion to NIST:DLMF \nbibtex: Olver:2010:NHMF'), (10953, 'NIST Handbook of Mathematical Functions'), (10954, 'https://slehar.wordpress.com/2014/03/18/clifford-algebra-a-visual-introduction/'), (10955, '2015-05-14 15:20:59'), (10956, 'Clifford Algebra, a.k.a. Geometric Algebra, is a most extraordinary synergistic confluence of a diverse range of specialized mathematical fields,\xa0each with its own methods and formalisms, all of wh...'), (10957, 'slehar'), (10958, 'Clifford Algebra: A visual introduction'), (10959, 'Clifford Algebra'), (10960, 'http://www.sciencedirect.com/science/article/pii/S0003491603000629'), (10961, 307), (10962, '90-131'), (10963, '2003-09-00 September 2003'), (10964, '10.1016/S0003-4916(03)00062-9'), (10965, '2015-05-17 01:43:02'), (10966, 'For a two-surface B tending to an infinite-radius round sphere at spatial infinity, we consider the Brown–York boundary integral HB belonging to the energy sector of the gravitational Hamiltonian. Assuming that the lapse function behaves as N∼1 in the limit, we find agreement between HB and the total Arnowitt–Deser–Misner energy, an agreement first noted by Braden, Brown, Whiting, and York. However, we argue that the Arnowitt–Deser–Misner mass-aspect differs from a gauge invariant mass-aspect by a pure divergence on the unit sphere. We also examine the boundary integral HB corresponding to the Hamiltonian generator of an asymptotic boost, in which case the lapse N∼xk grows like one of the asymptotically Cartesian coordinate functions. Such a two-surface integral defines the kth component of the center of mass for (the initial data belonging to) a Cauchy surface Σ bounded by B. In the large-radius limit, we find agreement between HB and an integral introduced by Beig and ó Murchadha as an improvement upon the center-of-mass integral first written down by Regge and Teitelboim. Although both HB and the Beig–ó Murchadha integral are naively divergent, they are in fact finite modulo the Hamiltonian constraint. Furthermore, we examine the relationship between HB and a certain two-surface integral which is linear in the spacetime Riemann curvature tensor. Similar integrals featuring the curvature appear in works by Ashtekar and Hansen, Penrose, Goldberg, and Hayward. Within the canonical 3+1 formalism, we define gravitational energy and center of mass as certain moments of Riemann curvature.'), (10967, 'Center of mass integral in canonical general relativity'), (10968, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0003491603000629/pdfft?md5=dcc8f906fde1035b0317d55cfe84cc4a&pid=1-s2.0-S0003491603000629-main.pdf'), (10969, 'http://arxiv.org/abs/1505.04621'), (10970, 'arXiv:1505.04621 [gr-qc]'), (10971, '2015-05-18 2015-05-18'), (10972, 'arXiv: 1505.04621'), (10973, '2015-05-20 12:31:37'), (10974, 'Advanced LIGO and Advanced Virgo are expected to make the first direct detections of gravitational waves (GW) in the next several years. Possible types of GW emission include short-duration bursts, signals from the coalescence of compact binaries consisting of neutron stars or black holes, continuous radiation from fast-spinning neutron stars, and stochastic background radiation of a primordial nature or resulting from the superposition of a large number of individually unresolvable sources. We describe the different approaches that have been developed to search for these different types of signals. In this paper we focus on the GW detection methods themselves; multi-messenger searches as well as further science enabled by detections are dealt with in separate contributions to this volume.'), (10975, 'Gravitational wave searches with Advanced LIGO and Advanced Virgo'), (10976, 'http://www.arxiv.org/pdf/1505.04621.pdf'), (10977, 'arXiv:1505.04621 PDF'), (10978, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/19/4/10.1063/1.523750'), (10979, '874-877'), (10980, '1978-04-01 1978/04/01'), (10981, '10.1063/1.523750'), (10982, '2015-05-21 13:44:58'), (10983, 'We exhibit the complexified spin and conformally weighted functions as sections of holomorphic line bundles over P 1(C) ×P 1(C). As an example of a nontrivial bundle, we discuss the complex null cone in some detail.'), (10984, 'Complex line bundles in relativity'), (10985, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/19/4/1.523750.pdf?itemId=/content/aip/journal/jmp/19/4/10.1063/1.523750&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10986, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/11/11/10.1063/1.1665105'), (10987, '1970-11-01 1970/11/01'), (10988, '10.1063/1.1665105'), (10989, '2015-05-21 13:45:38'), (10990, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/11/11/1.1665105.pdf?itemId=/content/aip/journal/jmp/11/11/10.1063/1.1665105&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10991, 'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/11/10.1063/1.1705144'), (10992, '2221-2222'), (10993, '1967-11-01 1967/11/01'), (10994, '10.1063/1.1705144'), (10995, '2015-05-21 14:24:25'), (10996, 'The spin‐weighted functions introduced recently are shown to be eigenfunctions of the total angular momentum for appropriately defined geometric objects on the sphere, namely the Pensov objects.'), (10997, 'Geometric Theory of the Spin‐Weighted Functions'), (10998, 'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/11/1.1705144.pdf?itemId=/content/aip/journal/jmp/8/11/10.1063/1.1705144&mimeType=pdf&containerItemId=content/aip/journal/jmp'), (10999, 'http://journals.cambridge.org/article_S0305004100049884'), (11000, '275–282'), (11001, '1469-8064'), (11002, '1971-09-00 September 1971'), (11003, '10.1017/S0305004100049884'), (11004, '2015-05-21 16:00:31'), (11005, 'A class of objects, sometimes known as weighted tensors, are investigated. Their relation to a Lie group acting as a transform group on a manifold is analysed. An equivalence relation between weighted tensors is established along with a method for their generation. Several examples are given.'), (11006, 'Weighted tensors and Lie groups'), (11007, 'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?type=1&fid=2070768&jid=PSP&volumeId=70&issueId=02&aid=2070760&bodyId=&membershipNumber=&societyETOCSession=&toPdf=true'), (11008, 'http://arxiv.org/abs/0907.0995'), (11009, 'arXiv:0907.0995 [math]'), (11010, 'arXiv: 0907.0995'), (11011, '2015-05-22 02:09:58'), (11012, 'Essentials of sheaves are briefly presented, followed by related comments on presheaves, bundles, manifolds and singularities, aiming to point to their differences not only in their different formal mathematical structures, but also in the very purposes for which they were introduced in the first place.'), (11013, 'Brief Notes on Sheaves Theory'), (11014, 'http://www.arxiv.org/pdf/0907.0995.pdf'), (11015, 'arXiv:0907.0995 PDF'), (11016, 'http://arxiv.org/abs/1505.05213'), (11017, 'arXiv:1505.05213 [gr-qc]'), (11018, '2015-05-19 2015-05-19'), (11019, 'arXiv: 1505.05213'), (11020, '2015-05-22 13:57:12'), (11021, "General relativity explains gravitational radiation from binary black hole or neutron star mergers, from core-collapse supernovae and even from the inflation period in cosmology. These waves exhibit a unique effect called memory or Christodoulou effect, which in a detector like LIGO or LISA shows as a permanent displacement of test masses and in radio telescopes like NANOGrav as a change in the frequency of pulsars' pulses. It was shown that electromagnetic fields and neutrino radiation enlarge the memory. Recently it has been understood that the two types of memory addressed in the literature as `linear' and `nonlinear' are in fact two different phenomena. The former is due to fields that do not and the latter is due to fields that do reach null infinity."), (11022, 'Gravitational Waves and Their Memory in General Relativity'), (11023, 'http://www.arxiv.org/pdf/1505.05213.pdf'), (11024, 'arXiv:1505.05213 PDF'), (11025, 'http://www.jstor.org.proxy.library.cornell.edu/stable/2372398'), (11026, 'Copyright © 1954 The Johns Hopkins University Press'), (11027, '33-65'), (11028, '1954-01-01 January 1, 1954'), (11029, '10.2307/2372398'), (11030, '2015-05-25 22:32:43'), (11031, 'Invariant Affine Connections on Homogeneous Spaces'), (11032, 'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2372398.pdf?acceptTC=true'), (11033, 'http://arxiv.org/abs/0712.1320'), (11034, 'arXiv:0712.1320 [math]'), (11035, '2007-12-09 2007-12-09'), (11036, 'arXiv: 0712.1320'), (11037, '2015-05-25 22:50:20'), (11038, "This expository paper, aimed at the reader without much background in set theory or logic, gives an overview of Cohen's proof (via forcing) of the independence of the continuum hypothesis. It emphasizes the broad outlines and the intuitive motivation while omitting most of the proofs. The reader must of course consult standard textbooks for the missing details, but this article provides a map of the forest so that the beginner will not get lost while forging through the trees."), (11039, "A beginner's guide to forcing"), (11040, 'http://www.arxiv.org/pdf/0712.1320.pdf'), (11041, 'arXiv:0712.1320 PDF'), (11042, 'of Ann. Math. Stud'), (11043, "Introduction I have committed | the sin of falsely proving Poincare's Conjecture. But that was in another country; and besides, until now no one has known about it. Now, in hope of deterring others from making similar mistakes, I shall describe my mistaken proof. Who knows but that somehow a small change, a new interpretation, and this line of proof may be rectied! In the back of my mind when I conceived my proof was this theorem. Theorem 0. (For n 6= 2). Let f : M ! K be a map of a connected orientable n-manifold into an n-complex, and let C 1 , : : : , C k be some of the n-simplexes of K such that the degree of f on each C i is zero (that is, the homology map induced by f , Hn"), (11044, 'How Not To Prove The Poincaré Conjecture'), (11045, 'http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.32.3404&rep=rep1&type=pdf'), (11046, '2015-05-25 22:50:31'), (11047, 'http://rsta.royalsocietypublishing.org/content/308/1505/523'), (11048, 1505), (11049, '523-615'), (11050, 'Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences'), (11051, '1364-503X, 1471-2962'), (11052, '1983-03-17 1983/03/17'), (11053, '10.1098/rsta.1983.0017'), (11054, '2015-05-25 22:53:17'), (11055, 'rsta.royalsocietypublishing.org.proxy.library.cornell.edu'), (11056, "The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a `perfect' functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail."), (11057, 'The Yang-Mills Equations over Riemann Surfaces'), (11059, '523.full.pdf'), (11060, 'http://projecteuclid.org/euclid.bams/1183533964'), (11061, '1972-09-00 1972-09'), (11062, 'MR: MR0522147\nZbl: 0271.01005'), (11063, '2015-05-25 22:54:48'), (11064, 'EN'), (11066, '2015-05-25 22:58:07'), (11068, 'euclid.bams.1183533964.pdf'), (11069, 'http://arxiv.org/abs/math/9404236'), (11070, 'arXiv:math/9404236'), (11071, '1994-03-31 1994-03-31'), (11072, 'arXiv: math/9404236'), (11073, '2015-05-25 22:59:07'), (11074, 'In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.'), (11075, 'On proof and progress in mathematics'), (11076, 'http://www.arxiv.org/pdf/math/9404236.pdf'), (11077, 'arXiv:math/9404236 PDF'), (11078, '379-423'), (11079, 'Bell System Technical Journal, The'), (11080, '0005-8580'), (11081, '1948-07-00 July 1948'), (11082, '10.1002/j.1538-7305.1948.tb01338.x'), (11083, 'IEEE Xplore'), (11084, 'The recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important papers of Nyquist1 and Hartley2 on this subject. In the present paper we will extend the theory to include a number of new factors, in particular the effect of noise in the channel, and the savings possible due to the statistical structure of the original message and due to the nature of the final destination of the information.'), (11085, 'A mathematical theory of communication'), (11086, 'http://ieeexplore.ieee.org/ielx7/6731005/6773023/06773024.pdf?tp=&arnumber=6773024&isnumber=6773023'), (11087, '2015-05-25 23:00:17'), (11088, 'IEEE Xplore Full Text PDF'), (11089, 'Halmos-How-To-Write.pdf'), (11090, 'How to write mathematics')]
I can run a query to select the values corresponding to URLs, and only show those URLs containing 'proxy':
In [9]:
[url[0]
for url in cur.execute("SELECT value FROM itemDataValues WHERE valueID IN (SELECT valueID FROM itemData where fieldID=1)").fetchall()
if 'proxy' in url[0]]
Out[9]:
['http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v78/e124020',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000012124020000001&idtype=cvips&prog=normal',
'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v78/e044039',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2009.15427.x/abstract;jsessionid=BF1B9266CFD6F052747D05BB4714066C.d03t04',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000004044039000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/proceeding/aipcp/10.1063/1.4825543',
'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v79/e084011',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000079000008084011000001&idtype=cvips&prog=normal',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/26/6/065008/',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/26/6/065008/cqg9_6_065008.pdf',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000010104020000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000076000012124038000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000075000002024006000001&idtype=cvips&prog=normal',
'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v79/e084025',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2009.15427.x/full',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000079000008084025000001&idtype=cvips&prog=normal',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/26/11/114008/',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/26/11/114008/cqg9_11_114008.pdf',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/25/10/105006/',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/25/10/105006/cqg8_10_105006.pdf',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000077000004044020000001&idtype=cvips&prog=normal',
'http://www.nature.com.proxy.library.cornell.edu/nphys/journal/v7/n6/full/nphys2011.html',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=SMJMAP000010000004000768000001&idtype=cvips&prog=normal',
'http://www.iop.org.proxy.library.cornell.edu/EJ/article/0264-9381/24/12/S22/cqg7_12_s22.pdf',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRL/v95/i12/e121101',
'http://iopscience.iop.org.proxy.library.cornell.edu/1538-4357/661/2/L147',
'http://www.jstor.org.clsproxy.library.caltech.edu/stable/37878',
'http://www.jstor.org.clsproxy.library.caltech.edu/stable/pdfplus/37878.pdf',
'http://iopscience.iop.org.proxy.library.cornell.edu/1538-4357/661/2/L147/pdf/1538-4357_661_2_L147.pdf',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/599/2/1254/',
'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v82/i4/p3069_1',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/25/16/165003/cqg8_16_165003.pdf',
'http://link.aip.org.clsproxy.library.caltech.edu/link/?JMP/42/2203/1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i6/e064003',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000042000005002203000001&idtype=cvips&prog=normal',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/24/12/S06/',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/24/12/S06/pdf/0264-9381_24_12_S06.pdf',
'http://rspb.royalsocietypublishing.org.clsproxy.library.caltech.edu/content/276/1674/3835.abstract',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRD/v10/i6/p1701_1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000026000005001030000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000007000005000863000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000008000011002155000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000045000002000173000001&idtype=cvips&prog=normal',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2315883.pdf',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRD/v10/i6/p1736_1',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6WB1-4DDR40K-SY-1&_cdi=6697&_user=492137&_orig=search&_coverDate=06%2F30%2F1960&_sk=999899997&view=c&wchp=dGLzVlz-zSkzS&md5=c43354e46d2de8756cfa153dd2a9350c&ie=/sdarticle.pdf',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRL/v29/i16/p1114_1',
'http://articles.adsabs.harvard.edu.proxy.library.cornell.edu/cgi-bin/nph-iarticle_query?1973ApJ...185..635T&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000080000012124045000001&idtype=cvips&prog=normal',
'http://www.springerlink.com.proxy.library.cornell.edu/content/x2h84m0286018747/fulltext.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v54/i8/p4813_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v49/i6/p2658_1',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/27/8/084020',
'http://www.iop.org.proxy.library.cornell.edu/EJ/article/2041-8205/711/2/L138/apjl_711_2_138.pdf',
'http://www.springerlink.com.proxy.library.cornell.edu/content/q0641644m2132200/',
'http://www.springerlink.com.proxy.library.cornell.edu/content/rr6lw3j81638m34k/',
'http://www.springerlink.com.proxy.library.cornell.edu/content/u4p4882856l67mp8/',
'http://www.springerlink.com.proxy.library.cornell.edu/content/t43118767q08351k/',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104034',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v75/i4/e049903',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104033',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i2/e024003',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i10/e104023',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e089901',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i6/e062005',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v65/i4/e044029',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i8/e084016',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i6/e064004',
'http://iopscience.iop.org.proxy.library.cornell.edu/0305-4470/10/11/011',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084041',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i6/e064015',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v59/i8/e084006',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.63.044023',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i4/e044023',
'http://www.springerlink.com.proxy.library.cornell.edu/content/gw6257261r015077/',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6TVK-46G8PC0-15-1&_cdi=5537&_user=492137&_pii=016727899090019L&_origin=search&_coverDate=05%2F31%2F1990&_sk=999569998&view=c&wchp=dGLbVzW-zSkWb&md5=e0fb768f76ee1483a273048d17c6c2b3&ie=/sdarticle.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6TVM-46MDCD1-X8-2&_cdi=5538&_user=492137&_pii=0375960190900923&_origin=search&_coverDate=11%2F12%2F1990&_sk=998499994&view=c&wchp=dGLbVtb-zSkzk&md5=d39aabb1981f2d249de4dc195f55e0ae&ie=/sdarticle.pdf',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.73.064030',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v73/i6/e064030',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.62.124022',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i12/e124022',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.83.024006',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i2/e024006',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.78.044004',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i4/e044004',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.67.064028',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i6/e064028',
'http://www.springerlink.com.proxy.library.cornell.edu/content/g33336t216w7094n/',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/26/16/163001',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.76.064028',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i6/e064028',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.78.024009',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i2/e024009',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.62.084011',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i8/e084011',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.64.124013',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i12/e124013',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.76.104049',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i10/e104049',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.67.024016',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i2/e024016',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.57.885',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v57/i2/p885_1',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/725/2/1918',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/725/2/1918/pdf/0004-637X_725_2_1918.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i8/e084036',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v59/i12/e124016',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v73/i12/e124006',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v77/i2/e024043',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v80/i10/e104025',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v77/i2/e026004',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v75/i12/e123003',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v53/i6/p3033_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i12/e124031',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v31/i8/p1815_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v60/i10/e104054',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/abs/10.1080/08927028908031380',
'http://iopscience.iop.org.proxy.library.cornell.edu/0143-0807/5/3/008',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i4/e044024',
'http://iopscience.iop.org.proxy.library.cornell.edu/0305-4470/9/6/010;jsessionid=299AED68BAF264E81DA887573DC6A0AC.c3',
'http://www.springerlink.com.proxy.library.cornell.edu/content/j640q10u51044755/',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/27/8/084004',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i10/e104020',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v87/i23/e231101',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v25/i22/p1596_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v49/i12/p6274_1',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/26/15/153001/pdf/0264-9381_26_15_153001.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i6/e064018',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i8/e084010',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v61/i6/e067503',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i6/e064005',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/606/2/819/',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/668/2/806',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i8/e083501',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i2/e023517',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v71/i10/e103521',
'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v25/i3/p714_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v42/i8/p2585_1',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/693/1/383',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v82/i10/e104029',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v37/i2/p318_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i4/e044057',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2010.17913.x/abstract',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1111/j.1365-2966.2010.17913.x/asset/j.1365-2966.2010.17913.x.pdf?v=1&t=gu74y41g&s=3605a70584189e906e7df58ad56a14ad11a16cdb',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272507&_user=492137&_pii=S0003491604000053&_check=y&_origin=&_coverDate=30-Jun-2004&view=c&wchp=dGLbVBA-zSkzS&md5=ce6ca86c96435434b5dbeb5d6875455d/1-s2.0-S0003491604000053-main.pdf',
'http://www.springerlink.com.proxy.library.cornell.edu/content/jt63m68488j71814/',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i12/e124002',
'http://physicstoday.org.proxy.library.cornell.edu/resource/1/phtoad/v64/i11/p49_s1#figref_f1',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PR/v108/i4/p1063_1',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1046/j.1365-8711.1999.02703.x/abstract',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1046/j.1365-8711.1999.02703.x/asset/j.1365-8711.1999.02703.x.pdf?v=1&t=guyi4qk8&s=6f5e152f902d8a3150bb29a1b78d65af7f5ef11d',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271074&_user=492137&_pii=S0140673601481931&_check=y&_origin=&_coverDate=22-Jun-1907&view=c&wchp=dGLzVlt-zSkzS&md5=197ceaa203d791ad76809cba3d27252a/1-s2.0-S0140673601481931-main.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v82/i4/e044025',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i8/e084016',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i12/e124011',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272570&_user=492137&_pii=S0021999107003816&_check=y&_origin=article&_zone=toolbar&_coverDate=10-Dec-2007&view=c&originContentFamily=serial&wchp=dGLzVlB-zSkzS&md5=ff78787591d337e95d27ffcb70811224/1-s2.0-S0021999107003816-main.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2347791.pdf?acceptTC=true',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v81/i6/p1150_1',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v15/i6/p231_1',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v6/i6/p902_s1?isAuthorized=no',
'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/6/902/1/pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v69/i10/e104017',
'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?type=1&fid=2117060&jid=PSP&volumeId=55&issueId=01&aid=2049244&bodyId=&membershipNumber=&societyETOCSession=',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271610&_user=492137&_pii=0771050X75900340&_check=y&_origin=article&_zone=toolbar&_coverDate=30-Sep-1975&view=c&originContentFamily=serial&wchp=dGLbVlB-zSkzk&md5=34d7bc40d7dbe28acc37eec6d7025133/1-s2.0-0771050X75900340-main.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i4/e042003',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i8/e082002',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i8/e084027',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2004.08028.x/abstract;jsessionid=F0398C0343139ED8366977DB4F5358DA.d01t03?systemMessage=Wiley+Online+Library+will+be+disrupted+on+26+May+from+10%3A00-12%3A00+BST+%2805%3A00-07%3A00+EDT%29+for+essential+maintenance',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1111/j.1365-2966.2004.08028.x/asset/j.1365-2966.2004.08028.x.pdf?v=1&t=h2j4rop7&s=eb918feabcf6216ac3c9a6805ae1d2db408d1909',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v52/i6/pR3159_1',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v393/n6681/abs/393139a0.html',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v393/n6681/pdf/393139a0.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v70/i12/e124020',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i10/e104002',
'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/14/874/1/pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v14/i7/p874_s1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i6/e064041',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v19/i7/p1542_s1?isAuthorized=no',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v3/i5/p891_s1?isAuthorized=no',
'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/3/891/1/pdf',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PR/v128/i6/p2851_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i4/e041502',
'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/19/1542/1/pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v55/i4/p1977_1',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v15/i10/p1768_s1',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v15/i10/p1778_s1',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v3/i3/p566_s1?isAuthorized=yes',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v2/i3/p290_s1?isAuthorized=yes',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v21/i8/p2245_s1?isAuthorized=yes',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v27/i5/p1398_s1?isAuthorized=yes',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i4/e044023',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v39/i12/p6631_s1?isAuthorized=yes',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v40/i11/p6126_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000040000011006126000001&idtype=cvips&doi=10.1063/1.533081&prog=normal',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v22/i4/p803_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000022000004000803000001&idtype=cvips&doi=10.1063/1.524987&prog=normal',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v80/i23/p5052_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i8/e084001',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271541&_user=492137&_pii=0375960187901447&_check=y&_origin=article&_zone=toolbar&_coverDate=23-Nov-1987&view=c&originContentFamily=serial&wchp=dGLbVlt-zSkzS&md5=064818a1d52f3c3e5b76d112d830f98c&pid=1-s2.0-0375960187901447-main.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i8/e084027',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v56/i12/pR7498_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i12/e124040',
'http://www.springerlink.com.proxy.library.cornell.edu/content/k712q7283161g221/abstract/',
'http://www.springerlink.com.proxy.library.cornell.edu/content/k712q7283161g221/fulltext.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i2/e024011',
'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v29/i4/p547_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i8/e084017',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i4/e041501',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104006',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1002/3527608958.ch14/summary',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i2/e024009',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i6/e064020',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i12/e124002',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v107/i19/e191104',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i10/e104045',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084001',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v8/i2/p345_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000008000002000345000001&idtype=cvips&doi=10.1063/1.1705200&prog=normal',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271950&_user=492137&_pii=0034487777900477&_check=y&_origin=article&_zone=toolbar&_coverDate=1977--31&view=c&originContentFamily=serial&wchp=dGLbVlV-zSkzS&md5=2dd3759c5bcfea2ffaa8c9c4c3c84d04&pid=1-s2.0-0034487777900477-main.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs00006-008-0083-x',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272507&_user=492137&_pii=S0003491604002209&_check=y&_origin=article&_zone=toolbar&_coverDate=2005--30&view=c&originContentFamily=serial&wchp=dGLzVlV-zSkWb&md5=0aaf6c3702d07fcdefa2cdbb5ec411a7&pid=1-s2.0-S0003491604002209-main.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i10/e104063',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF00668831',
'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/388/1795/457.full.pdf',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/10867651.1998.10487493',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i4/e044009',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/30/5/055007/pdf/0264-9381_30_5_055007.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F11403913_64.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000072000001000092000001&idtype=cvips&doi=10.1119/1.1621029&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000060000009000788000001&idtype=cvips&doi=10.1119/1.17060&prog=normal',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i10/e104006',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs10714-010-1110-5.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i8/e081503',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF03161249.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1968551.pdf?acceptTC=true',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v117/n2945/pdf/117514a0.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2689497.pdf?acceptTC=true',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/400/3/1366',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/400/3/1366.full.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i6/e064039',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_1.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_3.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_4.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_2.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_5.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_6.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_7.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_8.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_9.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_10.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_11.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_12.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/bfm%3A978-0-8176-8283-5%2F1.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/bbm%3A978-0-8176-8283-5%2F1.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v11/i11/p3145_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000011000011003145000001&idtype=cvips&doi=10.1063/1.1665105&prog=normal',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/17/21/304/pdf/q02104.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v61/i8/e084027',
'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/354/1679/379.full.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v23/i12/p2410_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000023000012002410000001&idtype=cvips&doi=10.1063/1.525283&prog=normal',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v22/i9/p1837_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000022000009001837000001&idtype=cvips&doi=10.1063/1.525155&prog=normal',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271541&_user=492137&_pii=S0375960198007683&_check=y&_origin=article&_zone=toolbar&_coverDate=21-Dec-1998&view=c&originContentFamily=serial&wchp=dGLbVlS-zSkWA&md5=3a04da43cad499721ea71ef5e39145bd&pid=1-s2.0-S0375960198007683-main.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v9/i6/p861_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000009000006000861000001&idtype=cvips&doi=10.1063/1.1664652&prog=normal',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v10/i2/p66_1',
'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/376/1767/585.full.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF00669365.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v47/i12/p123504_s1',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1968929.pdf?acceptTC=true',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v43/n1118/pdf/043511c0.pdf',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v44/n1126/pdf/044079b0.pdf',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v47/n1220/pdf/047463a0.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000047000012123504000001&idtype=cvips&doi=10.1063/1.2375037&prog=normal',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v48/n1242/pdf/048364b0.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v13/i11/p1837_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000013000011001837000001&idtype=cvips&doi=10.1063/1.1665917&prog=normal',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1023%2FA%3A1024498001488.pdf',
'http://www.worldscientific.com.proxy.library.cornell.edu/doi/abs/10.1142/S0129055X01000922?prevSearch=%28pin+group%29+and+%5BContrib%3A+berg%5D&searchHistoryKey=',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01078610.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v23/i4/p484_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000023000004000484000001&idtype=cvips&doi=10.1063/1.525405&prog=normal',
'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/287/1411/532.full.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1969129.pdf?acceptTC=true',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01336904.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01883677.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i6/e064010',
'http://download.springer.com.proxy.library.cornell.edu/static/pdf/131/bok%253A978-0-387-48101-2.pdf?auth66=1381075251_22a09d75eab2741b7d73f98882aedfd0&ext=.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-3-0348-0603-9.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i4/e043016',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/28/17/175001/pdf/0264-9381_28_17_175001.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i12/e124014',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i4/e043017',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084045',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/ebook.jsf?bid=CBO9780511790904',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A005;jsessionid=DAD056502B05D010D438DDC4ADEB5B46?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A006?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A007?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A008?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A186?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A274?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A025?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A042?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A299?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A300?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1023%2FA%3A1007901028047.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/54/5/10.1063/1.4802878;jsessionid=8g6q1gphp8flm.x-aip-live-01',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/54/5/1.4802878.pdf?itemId=/content/aip/journal/jmp/54/5/10.1063/1.4802878&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://www.ams.org.proxy.library.cornell.edu/bull/1972-78-05/S0002-9904-1972-12971-9/S0002-9904-1972-12971-9.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/33/1/10.1063/1.529955',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/33/1/1.529955.pdf?itemId=/content/aip/journal/jmp/33/1/10.1063/1.529955&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aapt/journal/ajp/70/9/10.1119/1.1475326',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aapt/journal/ajp/70/9/1.1475326.pdf?itemId=/content/aapt/journal/ajp/70/9/10.1119/1.1475326&mimeType=pdf&containerItemId=content/aapt/journal/ajp',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs10714-009-0781-2.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/4/10.1063/1.1705280',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/4/1.1705280.pdf?itemId=/content/aip/journal/jmp/8/4/10.1063/1.1705280&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/4/10.1063/1.1705279',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/4/1.1705279.pdf?itemId=/content/aip/journal/jmp/8/4/10.1063/1.1705279&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01883781.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0165168496000710/pdf?md5=b84de43000e46dff6ec45d40a51b9291&pid=1-s2.0-0165168496000710-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0550321306007632/pdfft?md5=e4142bfb37613c0921b3828f96b5a8db&pid=1-s2.0-S0550321306007632-main.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/3219300.pdf?acceptTC=true',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v60/i16/p1599_1',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v60/i25/p2704_1',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444808646139',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444908646257',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444908646169',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786445008646598',
'http://download.springer.com.proxy.library.cornell.edu/static/pdf/316/bok%253A978-3-7643-7791-5.pdf?auth66=1389996833_f53e4819b8806cb562774f3eabbf6b15&ext=.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084025',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044002001213/pdfft?md5=00beb14dc52536f62e26332c24c0f2ba&pid=1-s2.0-S0393044002001213-main.pdf',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.59.124022',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/10/7/10.1063/1.1664958',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/10/7/1.1664958.pdf?itemId=/content/aip/journal/jmp/10/7/10.1063/1.1664958&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://epubs.siam.org.proxy.library.cornell.edu/doi/abs/10.1137/S0895479801383877',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.111.241104',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.124010',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2949580.pdf?acceptTC=true',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.98.231102',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.98.231101',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.80.044010',
'http://epubs.siam.org.proxy.library.cornell.edu/doi/abs/10.1137/S1064827503422932',
'http://epubs.siam.org.proxy.library.cornell.edu/doi/pdf/10.1137/S1064827503422932',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.77.124047',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.76.061502',
'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?pageCode=100101&type=1&fid=5048576&jid=GMJ&volumeId=26&issueId=02&aid=5048568&fromPage=online',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.024010',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.83.084002',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.76.082001',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.122002',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0965997811001177/pdfft?md5=479e8e81ed5935d037f657dea4cd4120&pid=1-s2.0-S0965997811001177-main.pdf',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1107/S0108767306017478/abstract',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.062001',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.084008',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.70.104016',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.86.084020',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.105.111103',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.104003',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/6/9/10.1063/1.1704788',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/6/9/1.1704788.pdf;jsessionid=63gk0bka4s2l3.x-aip-live-06?itemId=/content/aip/journal/jmp/6/9/10.1063/1.1704788&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://www.nature.com.proxy.library.cornell.edu/nphys/journal/v7/n6/pdf/nphys2011.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2323537',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2323537.pdf?acceptTC=true',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.84.124002',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/34/8/10.1063/1.530050',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/34/8/1.530050.pdf?itemId=/content/aip/journal/jmp/34/8/10.1063/1.530050&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scripts.iucr.org.proxy.library.cornell.edu/cgi-bin/paper?S0108767306017478',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aapt/journal/ajp/61/6/10.1119/1.17201',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aapt/journal/ajp/61/6/1.17201.pdf?itemId=/content/aapt/journal/ajp/61/6/10.1119/1.17201&mimeType=pdf&containerItemId=content/aapt/journal/ajp',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0166128097001851/pdfft?md5=3620e20879ce94043826776e81780f47&pid=1-s2.0-S0166128097001851-main.pdf',
'http://journals.aps.org.proxy.library.cornell.edu/pre/pdf/10.1103/PhysRevE.57.7274',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.044022',
'http://www.jstor.org.proxy.library.cornell.edu/stable/1969203',
'http://journals.aps.org.proxy.library.cornell.edu/pr/pdf/10.1103/PhysRev.150.1039',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/1969203.pdf?acceptTC=true',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/36/6/10.1063/1.531015',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/36/6/1.531015.pdf;jsessionid=332dku1kmodmr.x-aip-live-02?itemId=/content/aip/journal/jmp/36/6/10.1063/1.531015&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044014002393/pdfft?md5=cb1b2b869131c4f24f12b16752096672&pid=1-s2.0-S0393044014002393-main.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/proceeding/aipcp/1558/10.1063/1.4825543/1.4825543.pdf?itemId=/content/aip/proceeding/aipcp/10.1063/1.4825543&mimeType=pdf&containerItemId=content/aip/proceeding/aipcp',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.69.1719',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044008000569/pdfft?md5=2b988d22550ac01c5229fe3af064bff9&pid=1-s2.0-S0393044008000569-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0040938364900035/pdf?md5=f55e052338189ca79550217063b0aedf&pid=1-s2.0-0040938364900035-main.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/1970240',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/1970240.pdf?acceptTC=true',
'http://projecteuclid.org.proxy.library.cornell.edu/euclid.pjm/1102992189',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.5.2419',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.84.084012',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.102006',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.064045',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.83.044039',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.69.104006',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.49.883',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.49.890',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.34.384',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.38.725',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2373586',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.52.2118',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/32/12/10.1063/1.529456',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/32/12/1.529456.pdf?itemId=/content/aip/journal/jmp/32/12/10.1063/1.529456&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/40/5/10.1063/1.533077',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/40/5/1.533077.pdf?itemId=/content/aip/journal/jmp/40/5/10.1063/1.533077&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/40/2/10.1063/1.532705',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/40/2/1.532705.pdf?itemId=/content/aip/journal/jmp/40/2/10.1063/1.532705&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0020019075900368/pdf?md5=9c5accabcf472ac59c8d5c721e38d8b4&pid=1-s2.0-0020019075900368-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/002001909090153O/pdf?md5=b0e42479c932f998290775e68bc0c2ab&pid=1-s2.0-002001909090153O-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/002001909290009K/pdf?md5=4772c0eab4faefef45f163e84854652e&pid=1-s2.0-002001909290009K-main.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2373586.pdf?acceptTC=true',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2653243',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2320587',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2320587.pdf?acceptTC=true',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/6/10.1063/1.1705341',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/10/1/10.1063/1.1664752',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/10/1/1.1664752.pdf?itemId=/content/aip/journal/jmp/10/1/10.1063/1.1664752&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.40.203',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2653243.pdf?acceptTC=true',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/6/1.1705341.pdf?itemId=/content/aip/journal/jmp/8/6/10.1063/1.1705341&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/415/4/3227',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/415/4/3227.full.pdf',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.123504',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/432/3/2208',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/432/3/2208.full.pdf',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.65.103001',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0024379594002459/pdf?md5=f94b22554f46ce7988eeb86e822bc4cf&pid=1-s2.0-0024379594002459-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0003491603000629/pdfft?md5=dcc8f906fde1035b0317d55cfe84cc4a&pid=1-s2.0-S0003491603000629-main.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/19/4/10.1063/1.523750',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/19/4/1.523750.pdf?itemId=/content/aip/journal/jmp/19/4/10.1063/1.523750&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/11/11/10.1063/1.1665105',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/11/11/1.1665105.pdf?itemId=/content/aip/journal/jmp/11/11/10.1063/1.1665105&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/11/10.1063/1.1705144',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/11/1.1705144.pdf?itemId=/content/aip/journal/jmp/8/11/10.1063/1.1705144&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?type=1&fid=2070768&jid=PSP&volumeId=70&issueId=02&aid=2070760&bodyId=&membershipNumber=&societyETOCSession=&toPdf=true',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2372398',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2372398.pdf?acceptTC=true']
In [10]:
len(_)
Out[10]:
434
Here's another way to do the same thing, doing that string match just within SQL:
In [11]:
[url[0]
for url in cur.execute("SELECT value FROM itemDataValues "
"WHERE valueID IN (SELECT valueID FROM itemData where fieldID=1) and value LIKE '%proxy%'").fetchall()]
Out[11]:
['http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v78/e124020',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000012124020000001&idtype=cvips&prog=normal',
'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v78/e044039',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2009.15427.x/abstract;jsessionid=BF1B9266CFD6F052747D05BB4714066C.d03t04',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000004044039000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/proceeding/aipcp/10.1063/1.4825543',
'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v79/e084011',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000079000008084011000001&idtype=cvips&prog=normal',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/26/6/065008/',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/26/6/065008/cqg9_6_065008.pdf',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000078000010104020000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000076000012124038000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000075000002024006000001&idtype=cvips&prog=normal',
'http://link.aps.org.clsproxy.library.caltech.edu/abstract/PRD/v79/e084025',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2009.15427.x/full',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000079000008084025000001&idtype=cvips&prog=normal',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/26/11/114008/',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/26/11/114008/cqg9_11_114008.pdf',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/abstract/0264-9381/25/10/105006/',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/25/10/105006/cqg8_10_105006.pdf',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000077000004044020000001&idtype=cvips&prog=normal',
'http://www.nature.com.proxy.library.cornell.edu/nphys/journal/v7/n6/full/nphys2011.html',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=SMJMAP000010000004000768000001&idtype=cvips&prog=normal',
'http://www.iop.org.proxy.library.cornell.edu/EJ/article/0264-9381/24/12/S22/cqg7_12_s22.pdf',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRL/v95/i12/e121101',
'http://iopscience.iop.org.proxy.library.cornell.edu/1538-4357/661/2/L147',
'http://www.jstor.org.clsproxy.library.caltech.edu/stable/37878',
'http://www.jstor.org.clsproxy.library.caltech.edu/stable/pdfplus/37878.pdf',
'http://iopscience.iop.org.proxy.library.cornell.edu/1538-4357/661/2/L147/pdf/1538-4357_661_2_L147.pdf',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/599/2/1254/',
'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v82/i4/p3069_1',
'http://www.iop.org.clsproxy.library.caltech.edu/EJ/article/0264-9381/25/16/165003/cqg8_16_165003.pdf',
'http://link.aip.org.clsproxy.library.caltech.edu/link/?JMP/42/2203/1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i6/e064003',
'http://scitation.aip.org.clsproxy.library.caltech.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000042000005002203000001&idtype=cvips&prog=normal',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/24/12/S06/',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/24/12/S06/pdf/0264-9381_24_12_S06.pdf',
'http://rspb.royalsocietypublishing.org.clsproxy.library.caltech.edu/content/276/1674/3835.abstract',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRD/v10/i6/p1701_1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000026000005001030000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000007000005000863000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000008000011002155000001&idtype=cvips&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000045000002000173000001&idtype=cvips&prog=normal',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2315883.pdf',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRD/v10/i6/p1736_1',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6WB1-4DDR40K-SY-1&_cdi=6697&_user=492137&_orig=search&_coverDate=06%2F30%2F1960&_sk=999899997&view=c&wchp=dGLzVlz-zSkzS&md5=c43354e46d2de8756cfa153dd2a9350c&ie=/sdarticle.pdf',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PRL/v29/i16/p1114_1',
'http://articles.adsabs.harvard.edu.proxy.library.cornell.edu/cgi-bin/nph-iarticle_query?1973ApJ...185..635T&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRVDAQ000080000012124045000001&idtype=cvips&prog=normal',
'http://www.springerlink.com.proxy.library.cornell.edu/content/x2h84m0286018747/fulltext.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v54/i8/p4813_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v49/i6/p2658_1',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/27/8/084020',
'http://www.iop.org.proxy.library.cornell.edu/EJ/article/2041-8205/711/2/L138/apjl_711_2_138.pdf',
'http://www.springerlink.com.proxy.library.cornell.edu/content/q0641644m2132200/',
'http://www.springerlink.com.proxy.library.cornell.edu/content/rr6lw3j81638m34k/',
'http://www.springerlink.com.proxy.library.cornell.edu/content/u4p4882856l67mp8/',
'http://www.springerlink.com.proxy.library.cornell.edu/content/t43118767q08351k/',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104034',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v75/i4/e049903',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104033',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i2/e024003',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i10/e104023',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e089901',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i6/e062005',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v65/i4/e044029',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i8/e084016',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i6/e064004',
'http://iopscience.iop.org.proxy.library.cornell.edu/0305-4470/10/11/011',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084041',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i6/e064015',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v59/i8/e084006',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.63.044023',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i4/e044023',
'http://www.springerlink.com.proxy.library.cornell.edu/content/gw6257261r015077/',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6TVK-46G8PC0-15-1&_cdi=5537&_user=492137&_pii=016727899090019L&_origin=search&_coverDate=05%2F31%2F1990&_sk=999569998&view=c&wchp=dGLbVzW-zSkWb&md5=e0fb768f76ee1483a273048d17c6c2b3&ie=/sdarticle.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MImg&_imagekey=B6TVM-46MDCD1-X8-2&_cdi=5538&_user=492137&_pii=0375960190900923&_origin=search&_coverDate=11%2F12%2F1990&_sk=998499994&view=c&wchp=dGLbVtb-zSkzk&md5=d39aabb1981f2d249de4dc195f55e0ae&ie=/sdarticle.pdf',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.73.064030',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v73/i6/e064030',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.62.124022',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i12/e124022',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.83.024006',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i2/e024006',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.78.044004',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i4/e044004',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.67.064028',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i6/e064028',
'http://www.springerlink.com.proxy.library.cornell.edu/content/g33336t216w7094n/',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/26/16/163001',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.76.064028',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i6/e064028',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.78.024009',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i2/e024009',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.62.084011',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i8/e084011',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.64.124013',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i12/e124013',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.76.104049',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i10/e104049',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.67.024016',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i2/e024016',
'http://link.aps.org.proxy.library.cornell.edu/doi/10.1103/PhysRevD.57.885',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v57/i2/p885_1',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/725/2/1918',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/725/2/1918/pdf/0004-637X_725_2_1918.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v62/i8/e084036',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v59/i12/e124016',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v73/i12/e124006',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v77/i2/e024043',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v80/i10/e104025',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v77/i2/e026004',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v75/i12/e123003',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v53/i6/p3033_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i12/e124031',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v31/i8/p1815_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v60/i10/e104054',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/abs/10.1080/08927028908031380',
'http://iopscience.iop.org.proxy.library.cornell.edu/0143-0807/5/3/008',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i4/e044024',
'http://iopscience.iop.org.proxy.library.cornell.edu/0305-4470/9/6/010;jsessionid=299AED68BAF264E81DA887573DC6A0AC.c3',
'http://www.springerlink.com.proxy.library.cornell.edu/content/j640q10u51044755/',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/27/8/084004',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v64/i10/e104020',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v87/i23/e231101',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v25/i22/p1596_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v49/i12/p6274_1',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/26/15/153001/pdf/0264-9381_26_15_153001.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i6/e064018',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i8/e084010',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v61/i6/e067503',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i6/e064005',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/606/2/819/',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/668/2/806',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i8/e083501',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i2/e023517',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v71/i10/e103521',
'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v25/i3/p714_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v42/i8/p2585_1',
'http://iopscience.iop.org.proxy.library.cornell.edu/0004-637X/693/1/383',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v82/i10/e104029',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v37/i2/p318_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i4/e044057',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2010.17913.x/abstract',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1111/j.1365-2966.2010.17913.x/asset/j.1365-2966.2010.17913.x.pdf?v=1&t=gu74y41g&s=3605a70584189e906e7df58ad56a14ad11a16cdb',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272507&_user=492137&_pii=S0003491604000053&_check=y&_origin=&_coverDate=30-Jun-2004&view=c&wchp=dGLbVBA-zSkzS&md5=ce6ca86c96435434b5dbeb5d6875455d/1-s2.0-S0003491604000053-main.pdf',
'http://www.springerlink.com.proxy.library.cornell.edu/content/jt63m68488j71814/',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i12/e124002',
'http://physicstoday.org.proxy.library.cornell.edu/resource/1/phtoad/v64/i11/p49_s1#figref_f1',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PR/v108/i4/p1063_1',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1046/j.1365-8711.1999.02703.x/abstract',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1046/j.1365-8711.1999.02703.x/asset/j.1365-8711.1999.02703.x.pdf?v=1&t=guyi4qk8&s=6f5e152f902d8a3150bb29a1b78d65af7f5ef11d',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271074&_user=492137&_pii=S0140673601481931&_check=y&_origin=&_coverDate=22-Jun-1907&view=c&wchp=dGLzVlt-zSkzS&md5=197ceaa203d791ad76809cba3d27252a/1-s2.0-S0140673601481931-main.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v82/i4/e044025',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i8/e084016',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i12/e124011',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272570&_user=492137&_pii=S0021999107003816&_check=y&_origin=article&_zone=toolbar&_coverDate=10-Dec-2007&view=c&originContentFamily=serial&wchp=dGLzVlB-zSkzS&md5=ff78787591d337e95d27ffcb70811224/1-s2.0-S0021999107003816-main.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2347791.pdf?acceptTC=true',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v81/i6/p1150_1',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v15/i6/p231_1',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v6/i6/p902_s1?isAuthorized=no',
'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/6/902/1/pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v69/i10/e104017',
'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?type=1&fid=2117060&jid=PSP&volumeId=55&issueId=01&aid=2049244&bodyId=&membershipNumber=&societyETOCSession=',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271610&_user=492137&_pii=0771050X75900340&_check=y&_origin=article&_zone=toolbar&_coverDate=30-Sep-1975&view=c&originContentFamily=serial&wchp=dGLbVlB-zSkzk&md5=34d7bc40d7dbe28acc37eec6d7025133/1-s2.0-0771050X75900340-main.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i4/e042003',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v67/i8/e082002',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v72/i8/e084027',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1111/j.1365-2966.2004.08028.x/abstract;jsessionid=F0398C0343139ED8366977DB4F5358DA.d01t03?systemMessage=Wiley+Online+Library+will+be+disrupted+on+26+May+from+10%3A00-12%3A00+BST+%2805%3A00-07%3A00+EDT%29+for+essential+maintenance',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/store/10.1111/j.1365-2966.2004.08028.x/asset/j.1365-2966.2004.08028.x.pdf?v=1&t=h2j4rop7&s=eb918feabcf6216ac3c9a6805ae1d2db408d1909',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v52/i6/pR3159_1',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v393/n6681/abs/393139a0.html',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v393/n6681/pdf/393139a0.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v70/i12/e124020',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v63/i10/e104002',
'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/14/874/1/pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v14/i7/p874_s1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i6/e064041',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v19/i7/p1542_s1?isAuthorized=no',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v3/i5/p891_s1?isAuthorized=no',
'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/3/891/1/pdf',
'http://prola.aps.org.proxy.library.cornell.edu/pdf/PR/v128/i6/p2851_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i4/e041502',
'http://link.aip.org.proxy.library.cornell.edu/link/?JMAPAQ/19/1542/1/pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v55/i4/p1977_1',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v15/i10/p1768_s1',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v15/i10/p1778_s1',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v3/i3/p566_s1?isAuthorized=yes',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v2/i3/p290_s1?isAuthorized=yes',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v21/i8/p2245_s1?isAuthorized=yes',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v27/i5/p1398_s1?isAuthorized=yes',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v83/i4/e044023',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v39/i12/p6631_s1?isAuthorized=yes',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v40/i11/p6126_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000040000011006126000001&idtype=cvips&doi=10.1063/1.533081&prog=normal',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v22/i4/p803_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000022000004000803000001&idtype=cvips&doi=10.1063/1.524987&prog=normal',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v80/i23/p5052_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i8/e084001',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271541&_user=492137&_pii=0375960187901447&_check=y&_origin=article&_zone=toolbar&_coverDate=23-Nov-1987&view=c&originContentFamily=serial&wchp=dGLbVlt-zSkzS&md5=064818a1d52f3c3e5b76d112d830f98c&pid=1-s2.0-0375960187901447-main.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v78/i8/e084027',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v56/i12/pR7498_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i12/e124040',
'http://www.springerlink.com.proxy.library.cornell.edu/content/k712q7283161g221/abstract/',
'http://www.springerlink.com.proxy.library.cornell.edu/content/k712q7283161g221/fulltext.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i2/e024011',
'http://rmp.aps.org.proxy.library.cornell.edu/pdf/RMP/v29/i4/p547_1',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i8/e084017',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v76/i4/e041501',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v74/i10/e104006',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1002/3527608958.ch14/summary',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i2/e024009',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i6/e064020',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v84/i12/e124002',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v107/i19/e191104',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i10/e104045',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084001',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v8/i2/p345_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000008000002000345000001&idtype=cvips&doi=10.1063/1.1705200&prog=normal',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271950&_user=492137&_pii=0034487777900477&_check=y&_origin=article&_zone=toolbar&_coverDate=1977--31&view=c&originContentFamily=serial&wchp=dGLbVlV-zSkzS&md5=2dd3759c5bcfea2ffaa8c9c4c3c84d04&pid=1-s2.0-0034487777900477-main.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs00006-008-0083-x',
'http://pdn.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=272507&_user=492137&_pii=S0003491604002209&_check=y&_origin=article&_zone=toolbar&_coverDate=2005--30&view=c&originContentFamily=serial&wchp=dGLzVlV-zSkWb&md5=0aaf6c3702d07fcdefa2cdbb5ec411a7&pid=1-s2.0-S0003491604002209-main.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v86/i10/e104063',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF00668831',
'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/388/1795/457.full.pdf',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/10867651.1998.10487493',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i4/e044009',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/30/5/055007/pdf/0264-9381_30_5_055007.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F11403913_64.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000072000001000092000001&idtype=cvips&doi=10.1119/1.1621029&prog=normal',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000060000009000788000001&idtype=cvips&doi=10.1119/1.17060&prog=normal',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i10/e104006',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs10714-010-1110-5.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v87/i8/e081503',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF03161249.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1968551.pdf?acceptTC=true',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v117/n2945/pdf/117514a0.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2689497.pdf?acceptTC=true',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/400/3/1366',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/400/3/1366.full.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i6/e064039',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_1.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_3.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_4.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_2.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_5.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_6.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_7.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_8.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_9.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_10.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_11.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-0-8176-8283-5_12.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/bfm%3A978-0-8176-8283-5%2F1.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/bbm%3A978-0-8176-8283-5%2F1.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v11/i11/p3145_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000011000011003145000001&idtype=cvips&doi=10.1063/1.1665105&prog=normal',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/17/21/304/pdf/q02104.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v61/i8/e084027',
'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/354/1679/379.full.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v23/i12/p2410_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000023000012002410000001&idtype=cvips&doi=10.1063/1.525283&prog=normal',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v22/i9/p1837_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000022000009001837000001&idtype=cvips&doi=10.1063/1.525155&prog=normal',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science?_ob=MiamiImageURL&_cid=271541&_user=492137&_pii=S0375960198007683&_check=y&_origin=article&_zone=toolbar&_coverDate=21-Dec-1998&view=c&originContentFamily=serial&wchp=dGLbVlS-zSkWA&md5=3a04da43cad499721ea71ef5e39145bd&pid=1-s2.0-S0375960198007683-main.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v9/i6/p861_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000009000006000861000001&idtype=cvips&doi=10.1063/1.1664652&prog=normal',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v10/i2/p66_1',
'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/376/1767/585.full.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF00669365.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v47/i12/p123504_s1',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1968929.pdf?acceptTC=true',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v43/n1118/pdf/043511c0.pdf',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v44/n1126/pdf/044079b0.pdf',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v47/n1220/pdf/047463a0.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000047000012123504000001&idtype=cvips&doi=10.1063/1.2375037&prog=normal',
'http://www.nature.com.proxy.library.cornell.edu/nature/journal/v48/n1242/pdf/048364b0.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v13/i11/p1837_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000013000011001837000001&idtype=cvips&doi=10.1063/1.1665917&prog=normal',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1023%2FA%3A1024498001488.pdf',
'http://www.worldscientific.com.proxy.library.cornell.edu/doi/abs/10.1142/S0129055X01000922?prevSearch=%28pin+group%29+and+%5BContrib%3A+berg%5D&searchHistoryKey=',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01078610.pdf',
'http://jmp.aip.org.proxy.library.cornell.edu/resource/1/jmapaq/v23/i4/p484_s1',
'http://scitation.aip.org.proxy.library.cornell.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JMAPAQ000023000004000484000001&idtype=cvips&doi=10.1063/1.525405&prog=normal',
'http://rspa.royalsocietypublishing.org.proxy.library.cornell.edu/content/287/1411/532.full.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/1969129.pdf?acceptTC=true',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01336904.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01883677.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v85/i6/e064010',
'http://download.springer.com.proxy.library.cornell.edu/static/pdf/131/bok%253A978-0-387-48101-2.pdf?auth66=1381075251_22a09d75eab2741b7d73f98882aedfd0&ext=.pdf',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2F978-3-0348-0603-9.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i4/e043016',
'http://iopscience.iop.org.proxy.library.cornell.edu/0264-9381/28/17/175001/pdf/0264-9381_28_17_175001.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i12/e124014',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v79/i4/e043017',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084045',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/ebook.jsf?bid=CBO9780511790904',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A005;jsessionid=DAD056502B05D010D438DDC4ADEB5B46?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A006?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A007?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A008?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A186?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A274?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A025?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A042?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A299?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://ebooks.cambridge.org.proxy.library.cornell.edu/open_pdf/CBO9780511790904A300?pubCode=CUP&urlPrefix=cambridge&productCode=cbo',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1023%2FA%3A1007901028047.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/54/5/10.1063/1.4802878;jsessionid=8g6q1gphp8flm.x-aip-live-01',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/54/5/1.4802878.pdf?itemId=/content/aip/journal/jmp/54/5/10.1063/1.4802878&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://www.ams.org.proxy.library.cornell.edu/bull/1972-78-05/S0002-9904-1972-12971-9/S0002-9904-1972-12971-9.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/33/1/10.1063/1.529955',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/33/1/1.529955.pdf?itemId=/content/aip/journal/jmp/33/1/10.1063/1.529955&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aapt/journal/ajp/70/9/10.1119/1.1475326',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aapt/journal/ajp/70/9/1.1475326.pdf?itemId=/content/aapt/journal/ajp/70/9/10.1119/1.1475326&mimeType=pdf&containerItemId=content/aapt/journal/ajp',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2Fs10714-009-0781-2.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/4/10.1063/1.1705280',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/4/1.1705280.pdf?itemId=/content/aip/journal/jmp/8/4/10.1063/1.1705280&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/4/10.1063/1.1705279',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/4/1.1705279.pdf?itemId=/content/aip/journal/jmp/8/4/10.1063/1.1705279&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://link.springer.com.proxy.library.cornell.edu/content/pdf/10.1007%2FBF01883781.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0165168496000710/pdf?md5=b84de43000e46dff6ec45d40a51b9291&pid=1-s2.0-0165168496000710-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0550321306007632/pdfft?md5=e4142bfb37613c0921b3828f96b5a8db&pid=1-s2.0-S0550321306007632-main.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/3219300.pdf?acceptTC=true',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v60/i16/p1599_1',
'http://prl.aps.org.proxy.library.cornell.edu/pdf/PRL/v60/i25/p2704_1',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444808646139',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444908646257',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786444908646169',
'http://www.tandfonline.com.proxy.library.cornell.edu/doi/pdf/10.1080/14786445008646598',
'http://download.springer.com.proxy.library.cornell.edu/static/pdf/316/bok%253A978-3-7643-7791-5.pdf?auth66=1389996833_f53e4819b8806cb562774f3eabbf6b15&ext=.pdf',
'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v81/i8/e084025',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044002001213/pdfft?md5=00beb14dc52536f62e26332c24c0f2ba&pid=1-s2.0-S0393044002001213-main.pdf',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.59.124022',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/10/7/10.1063/1.1664958',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/10/7/1.1664958.pdf?itemId=/content/aip/journal/jmp/10/7/10.1063/1.1664958&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://epubs.siam.org.proxy.library.cornell.edu/doi/abs/10.1137/S0895479801383877',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.111.241104',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.124010',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2949580.pdf?acceptTC=true',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.98.231102',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.98.231101',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.80.044010',
'http://epubs.siam.org.proxy.library.cornell.edu/doi/abs/10.1137/S1064827503422932',
'http://epubs.siam.org.proxy.library.cornell.edu/doi/pdf/10.1137/S1064827503422932',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.77.124047',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.76.061502',
'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?pageCode=100101&type=1&fid=5048576&jid=GMJ&volumeId=26&issueId=02&aid=5048568&fromPage=online',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.024010',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.83.084002',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.76.082001',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.122002',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0965997811001177/pdfft?md5=479e8e81ed5935d037f657dea4cd4120&pid=1-s2.0-S0965997811001177-main.pdf',
'http://onlinelibrary.wiley.com.proxy.library.cornell.edu/doi/10.1107/S0108767306017478/abstract',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.062001',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.084008',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.70.104016',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.86.084020',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.105.111103',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.104003',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/6/9/10.1063/1.1704788',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/6/9/1.1704788.pdf;jsessionid=63gk0bka4s2l3.x-aip-live-06?itemId=/content/aip/journal/jmp/6/9/10.1063/1.1704788&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://www.nature.com.proxy.library.cornell.edu/nphys/journal/v7/n6/pdf/nphys2011.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2323537',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/2323537.pdf?acceptTC=true',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.84.124002',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/34/8/10.1063/1.530050',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/34/8/1.530050.pdf?itemId=/content/aip/journal/jmp/34/8/10.1063/1.530050&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scripts.iucr.org.proxy.library.cornell.edu/cgi-bin/paper?S0108767306017478',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aapt/journal/ajp/61/6/10.1119/1.17201',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aapt/journal/ajp/61/6/1.17201.pdf?itemId=/content/aapt/journal/ajp/61/6/10.1119/1.17201&mimeType=pdf&containerItemId=content/aapt/journal/ajp',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0166128097001851/pdfft?md5=3620e20879ce94043826776e81780f47&pid=1-s2.0-S0166128097001851-main.pdf',
'http://journals.aps.org.proxy.library.cornell.edu/pre/pdf/10.1103/PhysRevE.57.7274',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.87.044022',
'http://www.jstor.org.proxy.library.cornell.edu/stable/1969203',
'http://journals.aps.org.proxy.library.cornell.edu/pr/pdf/10.1103/PhysRev.150.1039',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/1969203.pdf?acceptTC=true',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/36/6/10.1063/1.531015',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/36/6/1.531015.pdf;jsessionid=332dku1kmodmr.x-aip-live-02?itemId=/content/aip/journal/jmp/36/6/10.1063/1.531015&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044014002393/pdfft?md5=cb1b2b869131c4f24f12b16752096672&pid=1-s2.0-S0393044014002393-main.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/proceeding/aipcp/1558/10.1063/1.4825543/1.4825543.pdf?itemId=/content/aip/proceeding/aipcp/10.1063/1.4825543&mimeType=pdf&containerItemId=content/aip/proceeding/aipcp',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.69.1719',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0393044008000569/pdfft?md5=2b988d22550ac01c5229fe3af064bff9&pid=1-s2.0-S0393044008000569-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0040938364900035/pdf?md5=f55e052338189ca79550217063b0aedf&pid=1-s2.0-0040938364900035-main.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/1970240',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/1970240.pdf?acceptTC=true',
'http://projecteuclid.org.proxy.library.cornell.edu/euclid.pjm/1102992189',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.5.2419',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.84.084012',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.102006',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.88.064045',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.83.044039',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.69.104006',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.49.883',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.49.890',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.34.384',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.38.725',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2373586',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.52.2118',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/32/12/10.1063/1.529456',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/32/12/1.529456.pdf?itemId=/content/aip/journal/jmp/32/12/10.1063/1.529456&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/40/5/10.1063/1.533077',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/40/5/1.533077.pdf?itemId=/content/aip/journal/jmp/40/5/10.1063/1.533077&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/40/2/10.1063/1.532705',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/40/2/1.532705.pdf?itemId=/content/aip/journal/jmp/40/2/10.1063/1.532705&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0020019075900368/pdf?md5=9c5accabcf472ac59c8d5c721e38d8b4&pid=1-s2.0-0020019075900368-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/002001909090153O/pdf?md5=b0e42479c932f998290775e68bc0c2ab&pid=1-s2.0-002001909090153O-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/002001909290009K/pdf?md5=4772c0eab4faefef45f163e84854652e&pid=1-s2.0-002001909290009K-main.pdf',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2373586.pdf?acceptTC=true',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2653243',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2320587',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2320587.pdf?acceptTC=true',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/6/10.1063/1.1705341',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/10/1/10.1063/1.1664752',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/10/1/1.1664752.pdf?itemId=/content/aip/journal/jmp/10/1/10.1063/1.1664752&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://journals.aps.org.proxy.library.cornell.edu/prl/pdf/10.1103/PhysRevLett.40.203',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2653243.pdf?acceptTC=true',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/6/1.1705341.pdf?itemId=/content/aip/journal/jmp/8/6/10.1063/1.1705341&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/415/4/3227',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/415/4/3227.full.pdf',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.89.123504',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/432/3/2208',
'http://mnras.oxfordjournals.org.proxy.library.cornell.edu/content/432/3/2208.full.pdf',
'http://journals.aps.org.proxy.library.cornell.edu/prd/pdf/10.1103/PhysRevD.65.103001',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0024379594002459/pdf?md5=f94b22554f46ce7988eeb86e822bc4cf&pid=1-s2.0-0024379594002459-main.pdf',
'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/S0003491603000629/pdfft?md5=dcc8f906fde1035b0317d55cfe84cc4a&pid=1-s2.0-S0003491603000629-main.pdf',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/19/4/10.1063/1.523750',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/19/4/1.523750.pdf?itemId=/content/aip/journal/jmp/19/4/10.1063/1.523750&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/11/11/10.1063/1.1665105',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/11/11/1.1665105.pdf?itemId=/content/aip/journal/jmp/11/11/10.1063/1.1665105&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://scitation.aip.org.proxy.library.cornell.edu/content/aip/journal/jmp/8/11/10.1063/1.1705144',
'http://scitation.aip.org.proxy.library.cornell.edu/deliver/fulltext/aip/journal/jmp/8/11/1.1705144.pdf?itemId=/content/aip/journal/jmp/8/11/10.1063/1.1705144&mimeType=pdf&containerItemId=content/aip/journal/jmp',
'http://journals.cambridge.org.proxy.library.cornell.edu/action/displayFulltext?type=1&fid=2070768&jid=PSP&volumeId=70&issueId=02&aid=2070760&bodyId=&membershipNumber=&societyETOCSession=&toPdf=true',
'http://www.jstor.org.proxy.library.cornell.edu/stable/2372398',
'http://www.jstor.org.proxy.library.cornell.edu/stable/pdfplus/10.2307/2372398.pdf?acceptTC=true']
In [12]:
len(_)
Out[12]:
434
Now I'll try to update the table to replace those strings:
In [13]:
cur.execute("UPDATE itemDataValues SET value = replace( replace( value, '.proxy.library.cornell.edu', '' ), '.clsproxy.library.caltech.edu', '')"
"WHERE (valueID IN (SELECT valueID FROM itemData where fieldID=1) and value LIKE '%proxy%')")
---------------------------------------------------------------------------
IntegrityError Traceback (most recent call last)
<ipython-input-13-6a3ad13b83d3> in <module>()
----> 1 cur.execute("UPDATE itemDataValues SET value = replace( replace( value, '.proxy.library.cornell.edu', '' ), '.clsproxy.library.caltech.edu', '')"
2 "WHERE (valueID IN (SELECT valueID FROM itemData where fieldID=1) and value LIKE '%proxy%')")
IntegrityError: UNIQUE constraint failed: itemDataValues.value
The itemDataValues table did indeed insist that the value field should be unique. But I don't really understand why there should be clashes. Maybe I got the same paper at Caltech and Cornell, via the respective proxies. I'll try going through them individually. (This is presumably slower than pure SQL, but there shouldn't be so many that it'll be a problem.)
In [14]:
itemDataValues = cur.execute("SELECT * FROM itemDataValues "
"WHERE valueID IN (SELECT valueID FROM itemData where fieldID=1) and value LIKE '%proxy%'").fetchall()
for valueID, value in itemDataValues:
new_value = value.replace('.proxy.library.cornell.edu', '' ).replace('.clsproxy.library.caltech.edu', '')
#print(valueID, value, '\n ', new_value); sys.stdout.flush()
try:
cur.execute("UPDATE itemDataValues SET value = '{0}'".format(new_value)
+ "WHERE valueID = {0}".format(valueID))
except sqlite3.IntegrityError:
print(cur.execute("SELECT * from itemDataValues WHERE value LIKE '%{0}%' OR value LIKE '%{1}%'".format(value, new_value)).fetchall())
print("")
[(1347, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v49/i6/p2658_1'), (2448, 'http://prd.aps.org/pdf/PRD/v49/i6/p2658_1')]
[(3349, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v58/i12/e124031'), (4002, 'http://prd.aps.org/pdf/PRD/v58/i12/e124031')]
[(4800, 'http://prd.aps.org/pdf/PRD/v82/i4/e044025'), (4803, 'http://prd.aps.org.proxy.library.cornell.edu/pdf/PRD/v82/i4/e044025')]
[(8824, 'http://www.sciencedirect.com/science/article/pii/0040938364900035/pdf?md5=f55e052338189ca79550217063b0aedf&pid=1-s2.0-0040938364900035-main.pdf'), (10341, 'http://www.sciencedirect.com.proxy.library.cornell.edu/science/article/pii/0040938364900035/pdf?md5=f55e052338189ca79550217063b0aedf&pid=1-s2.0-0040938364900035-main.pdf')]
These all appear to be double-PDFs, presumably from Duplicate Items that I've merged. I'll just go through and delete them all, and run this notebook again...
In [15]:
if con:
con.commit()
con.close()
Now, I'm too scared to actually add this as an executable statement to this notebook, but the following command will also need to be executed
cp zotero.sqlite /Users/boyle/Library/Application\ Support/Firefox/Profiles/l1i89wc9.default/zotero/zotero.sqlite
In [ ]:
Content source: moble/PaperInfrastructure
Similar notebooks: