Etienne Ackermann, 12/16/2015
The data can be downloaded from the CRCNS (Collaborative Research in Computational Neuroscience) website, and the hc-3 data set in particular.
Here I will do a very quick and rough place field visualization to see which cells show place preferences. In particular, we limit the spikes to only those where the animal was running at some minimum velocity (3 cm/s), and then we further restrict place cells to be those with some minimum maximum firing rate (2 Hz) and a maximum mean firing rate (4 Hz).
WARNING: We do not know what the sampling frequency is that's associated with the .whl trajectory file. We can assume that the entire experiment was logged in the .whl file, and that a uniform sampling interval was used, so that we can determine the sampling frequency by taking the number of samples in the .whl file, and dividing by the experiment duration. We should check to see that several of the .whl-experiment pairs give us the same sampling frequency...
CONCLUSION: It seems like the .whl files were logged at 60 Hz, which is a common sampling rate for video cameras, so at least it seems plausible.
In [184]:
import numpy as np
import pandas as pd
import seaborn as sns
from matplotlib import pyplot as plt
from pandas import Series, DataFrame
%matplotlib inline
# read trajectory:
try:
df1whl = pd.read_table( 'C://Etienne//Dropbox//neoReader//Data//gor01-6-7//2006-6-7_11-26-53_lin1//2006-6-7_11-26-53.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
df2whl = pd.read_table( 'C://Etienne//Dropbox//neoReader//Data//gor01-6-7//2006-6-7_16-40-19_lin2//2006-6-7_16-40-19.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
except:
print( "Cannot load files in C:/...; trying Unix location instead.")
try:
#df1whl = pd.read_table( '/home/etienne/Dropbox/neoReader/Data/gor01-6-7/2006-6-7_11-26-53_lin1/2006-6-7_11-26-53.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
df2whl = pd.read_table( '/home/etienne/Dropbox/neoReader/Data/gor01-6-7/2006-6-7_16-40-19_lin2/2006-6-7_16-40-19.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
#df1whl = pd.read_table( '/home/etienne/Dropbox/neoReader/Data/gor01-6-12/2006-6-12_15-55-31_lin1/2006-6-12_15-55-31.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
#df2whl = pd.read_table( '/home/etienne/Dropbox/neoReader/Data/gor01-6-12/2006-6-12_16-53-46_lin2/2006-6-12_16-53-46.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
#df1whl = pd.read_table( '/home/etienne/Dropbox/neoReader/Data/gor01-6-13/2006-6-13_14-42-6_lin1/2006-6-13_14-42-6.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
#df2whl = pd.read_table( '/home/etienne/Dropbox/neoReader/Data/gor01-6-13/2006-6-13_15-22-3_lin2/2006-6-13_15-22-3.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
except:
print( "Cannot load files in Unix location; trying Mac location instead.")
try:
df1whl = pd.read_table( '/Users/etienne/Dropbox/neoReader/Data/gor01-6-7/2006-6-7_11-26-53_lin1/2006-6-7_11-26-53.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
df2whl = pd.read_table( '/Users/etienne/Dropbox/neoReader/Data/gor01-6-7/2006-6-7_16-40-19_lin2/2006-6-7_16-40-19.whl',sep='\t', skiprows=0, names=['x1', 'y1', 'x2', 'y2'] )
except:
print( "Unexpected error:", sys.exc_info()[0] )
raise
else:
print( "Data loaded successfully." )
else:
print( "Data loaded successfully." )
else:
print( "Data loaded successfully." )
# plot trajectory:
sns.set(rc={'figure.figsize': (8, 4),'lines.linewidth': 1, 'font.size': 16, 'axes.labelsize': 14, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
palette = sns.color_palette()
plt.plot( df2whl['x1'], df2whl['y1'], linewidth=2, color='lightgray');
plt.plot( df2whl['x2'], df2whl['y2'], linewidth=2, color='lightgray');
plt.plot( (df2whl['x1'] + df2whl['x2'])/2, (df2whl['y1'] + df2whl['y2'])/2, linewidth=1, color='k' );
In [185]:
sns.set(rc={'figure.figsize': (16, 4),'lines.linewidth': 1.5, 'font.size': 16, 'axes.labelsize': 14, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
f, ( ax1 ) = plt.subplots(1,1)
ax1.plot(np.linspace(0,len(df2whl.index)/60,len(df2whl.index)),df2whl['x1'], linewidth=2, color='lightgray' )
ax1.plot(np.linspace(0,len(df2whl.index)/60,len(df2whl.index)),df2whl['x2'], linewidth=2, color='lightgray' )
ax1.plot(np.linspace(0,len(df2whl.index)/60,len(df2whl.index)),(df2whl['x1'] + df2whl['x2'])/2, linewidth=1, color='k' )
#ax1.set_xlim([0,2500])
ax1.set_xlabel('time (s)')
ax1.set_ylabel('position along x-axis')
#saveFigure("figures/x-pos vs time.pdf")
Out[185]:
In [186]:
# specify session parameters
# this can either be read from the meta data, or extracted from the file structure, or in this case, hard-coded.
fs = 32552
base_filename1 = '/home/etienne/Dropbox/neoReader/Data/gor01-6-7/2006-6-7_11-26-53_lin1/2006-6-7_11-26-53'
base_filename2 = '/home/etienne/Dropbox/neoReader/Data/gor01-6-7/2006-6-7_16-40-19_lin2/2006-6-7_16-40-19'
num_electrodes = 12
for ele in np.arange(num_electrodes):
dt1a = pd.read_table( base_filename1 + '.clu.' + str(ele + 1), skiprows=1, names='u' )
dt1b = pd.read_table( base_filename1 + '.res.' + str(ele + 1), header=None, names='t' )
dt2a = pd.read_table( base_filename2 + '.clu.' + str(ele + 1), skiprows=1, names='u' )
dt2b = pd.read_table( base_filename2 + '.res.' + str(ele + 1), header=None, names='t' )
ls1a = list(dt1a['u'])
ls1b = list(dt1b['t'])
ls2a = list(dt2a['u'])
ls2b = list(dt2b['t'])
d1 = {'clu' + str( ele + 1 ): Series(ls1a, index=ls1b)}
d2 = {'clu' + str( ele + 1 ): Series(ls2a, index=ls2b)}
if ele == 0:
df1 = DataFrame(d1)
df2 = DataFrame(d2)
else:
df1 = df1.append(DataFrame(d1))
df2 = df2.append(DataFrame(d2))
# determine experiment durations:
exp_duration1 = df1.index[-1]/fs # seconds
exp_duration2 = df2.index[-1]/fs # seconds
print("LinearOne lasted {0:2.2f} minutes, sampling at {1} Hz".format(exp_duration1/60, fs))
print("LinearTwo lasted {0:2.2f} minutes, sampling at {1} Hz".format(exp_duration2/60, fs))
print("LinearOne had {0} position estimates, so that the position sampling frequency is approx {1:2.2f} Hz".format(df1whl.index[-1],df1whl.index[-1]/exp_duration1 ))
print("LinearTwo had {0} position estimates, so that the position sampling frequency is approx {1:2.2f} Hz".format(df2whl.index[-1],df2whl.index[-1]/exp_duration2 ))
...
I have checked a small random sampling of other experiments, and they seem to agree with the 60 Hz sampling rate, so this is what I will use.
Consequently, I do not know where the missing data are for LinearOne---at the beginning, or the end? Or spread throughout?
In estimating place fields, I will only use LinearTwo for now...
In [187]:
import pickle
#with open('../../Data/st_array1rn.pickle', 'rb') as f:
# st_array1 = pickle.load(f)
with open('../../Data/st_array2rn.pickle', 'rb') as f:
st_array2 = pickle.load(f)
In [188]:
import sys
sys.path.insert(0, '../')
import numpy as np
import pandas as pd
import pickle
import seaborn as sns
#import yahmm as ym
from matplotlib import pyplot as plt
from pandas import Series, DataFrame
from efunctions import * # load my helper functions
%matplotlib inline
from scipy.signal import butter, lfilter, filtfilt
def butter_bandpass(lowcut, highcut, fs, order=5):
nyq = 0.5 * fs
low = lowcut / nyq
high = highcut / nyq
b, a = butter(order, [low, high], btype='band')
return b, a
def butter_bandpass_filter(data, lowcut, highcut, fs, order=5):
b, a = butter_bandpass(lowcut, highcut, fs, order=order)
y = lfilter(b, a, data)
return y
def butter_lowpass(cutoff, fs, order=5):
nyq = 0.5 * fs
normal_cutoff = cutoff / nyq
b, a = butter(order, normal_cutoff, btype='low', analog=False)
return b, a
def butter_lowpass_filtfilt(data, cutoff, fs, order=5):
b, a = butter_lowpass(cutoff, fs, order=order)
#y = lfilter(b, a, data)
y = filtfilt(b, a, data, padlen=150)
return y
def rms(x):
return np.sqrt(np.mean(x**2))
In [189]:
# speed as a function of time...
centerx = (np.array(df2whl['x1']) + np.array(df2whl['x2']))/2
centery = (np.array(df2whl['y1']) + np.array(df2whl['y2']))/2
dx = np.ediff1d(centerx,to_begin=0)
dy = np.ediff1d(centery,to_begin=0)
dvdt = np.sqrt(np.square(dx) + np.square(dy))*60 # cm per second
t0 = 0
tend = len(dvdt)/60 # end in seconds
cutoff=1
dvdtlowpass = butter_lowpass_filtfilt(dvdt, cutoff=cutoff, fs=60, order=6)
print('The animal (gor01) ran an average of {0:2.2f} cm/s'.format(dvdt.mean()))
th = 3 #cm/s
runindex = np.where(dvdtlowpass>=th); runindex = runindex[0]
print("The animal ran faster than th = {0:2.1f} cm/s for a total of {1:2.1f} seconds (out of a total of {2:2.1f} seconds).".format(th,len(runindex)/60,len(centerx)/60))
In [190]:
sns.set(rc={'figure.figsize': (15, 4),'lines.linewidth': 3, 'font.size': 18, 'axes.labelsize': 16, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
f, (ax1, ax2) = plt.subplots(1,2)
ax1.plot(np.arange(0,len(dvdt))/60,dvdt,alpha=1,color='lightgray',linewidth=2)
ax1.plot(np.arange(0,len(dvdt))/60,dvdtlowpass, alpha=1,color='k',linewidth=1)
ax1.set_xlabel('time (seconds)')
ax1.set_ylabel('instantaneous velocity (cm/s)')
ax1.legend(['unfiltered', str(cutoff) + ' Hz lowpass filtfilt'])
ax1.set_xlim([0,2500])
ax2.plot(np.arange(0,len(dvdt))/60,dvdt,alpha=1,color='lightgray',linewidth=2)
ax2.plot(np.arange(0,len(dvdt))/60,dvdtlowpass, alpha=1,color='k',linewidth=1)
ax2.set_xlabel('time (seconds)')
ax2.set_ylabel('instantaneous velocity (cm/s)')
ax2.legend(['unfiltered', str(cutoff) + ' Hz lowpass filtfilt'])
ax2.set_xlim([30,70])
Out[190]:
In [ ]:
# extract spikes only corresponding to those time bins where the animal was above threshold:
# idea: bin all spikes in bins corresponding to 60 Hz bins, and then only keep those with indices stored in itemindex
In [229]:
def list_of_spk_time_arrays_to_spk_counts_arrays(st_array_extern, ds=0, fs=0 ):
"""
st_array: list of ndarrays containing spike times (in sample numbers!)
ds: delta sample number; integer value of samples per time bin
fs: sampling frequency
argument logic: if only st_array is passed, use default ds; if ds is passed, use as is and ignore fs; if ds and fs are passed, use ds as time in seconds
returns a (numBins x numCell) array with spike counts
"""
st_array = st_array_extern
if fs == 0:
if ds == 0:
ds = 1000 # assume default interval size
else: # sampling frequency was passed, so interpret ds as time-interval, and convert accordingly:
if ds == 0:
ds = 1000 # assume default interval size
else:
ds = round(ds*fs)
# determine number of units:
num_units = len(st_array)
#columns = np.arange(0,num_units)
#df = DataFrame(columns=columns)
maxtime = 0
for uu in np.arange(num_units):
try:
maxtime = max(st_array[uu].max(), maxtime)
except:
maxtime = maxtime
# create list of intervals:
intlist = np.arange(0,maxtime,ds)
num_bins = len(intlist)
spks_bin = np.zeros((num_bins,num_units))
print("binning data into {0} x {1:2.1f} ms temporal bins...".format(num_bins, ds*1000/fs))
for uu in np.arange(num_units):
# count number of spikes in an interval:
spks_bin[:,uu] = np.histogram(st_array[uu], bins=num_bins, density=False, range=(0,maxtime))[0]
#spk_count_list.append([x&y for (x,y) in zip(st_array[uu]>ii, st_array[uu] < ii+ds)].count(True))
#st_array[uu] = st_array[uu][st_array[uu]>ii+ds]
#if df.empty:
# df = DataFrame([spk_count_list], columns=columns)
#else:
# df = df.append(DataFrame([spk_count_list], columns=columns),ignore_index=True)
return spks_bin
spk_counts2 = list_of_spk_time_arrays_to_spk_counts_arrays(st_array2, ds=0.016666667, fs=32552)
#spk_counts2 = spk_counts2[round(len(spk_counts2)/2):] # form place fields using only 2nd half of data
#spk_counts2 = spk_counts2[:round(len(spk_counts2)/2)] # form place fields using only 1st half of data
runindex = runindex[np.where(runindex<len(spk_counts2))[0]]; # runindexnew = runindexnew[0]
In [230]:
# get bins of spk counts that correspond to where the animal was running above threshold:
run_spks_bin = spk_counts2[runindex,:]
num_bins = 200 # position bins for place fields
x0 = 0
xl = 100
num_units = len(st_array2)
data = np.array(df2whl['x1'][runindex].tolist())
bins = np.linspace(x0,xl,num_bins)
digitized = np.digitize(data, bins) # bin numbers
bin_cnt = [len(data[digitized == i]) for i in range(1, len(bins))]
bin_time = [b/60 for b in bin_cnt] # convert to seconds spent in bin
pfbincenters = bins[:-1] + np.diff(bins)/2
pf2spk_cnt = np.zeros((num_bins,num_units))
closest_bins = np.digitize(data,bins)
for cnt, bb in enumerate(closest_bins):
pf2spk_cnt[bb,:] += run_spks_bin[cnt,:]
pf2 = []
pfsmooth = []
minth = 0.05 # min threshold for backgrnd spking actvy
for uu in np.arange(0,num_units):
pf2.append([b/max(c,1) for (b,c) in zip(pf2spk_cnt[:,uu],bin_time)])
pfsmooth.append(butter_lowpass_filtfilt(pf2[uu], cutoff=15, fs=200, order=4))
pfsmooth = np.array(pfsmooth)
pfsmooth[pfsmooth<minth] = minth
In [231]:
# throw away cells that look like interneurons, or cells that are inactive throughout the entire experiment:
meanfiringrates = pfsmooth.mean(axis=1)
maxfiringrates = pfsmooth.max(axis=1)
max_meanfiringrate = 4 # Hz
min_maxfiringrate = 2 # Hz
pindex = np.where((meanfiringrates<=max_meanfiringrate) & (maxfiringrates>min_maxfiringrate)); pindex = pindex[0]
print("{0} out of {1} cells passed the criteria to be place cells...".format(len(pindex),len(meanfiringrates)))
# order remaining cells by peak hight along the track
peaklocations = pfsmooth.argmax(axis=1)
peakorder = peaklocations[pindex].argsort()
# visualize place fields
In [232]:
sns.set(rc={'figure.figsize': (15, 4),'lines.linewidth': 3, 'font.size': 18, 'axes.labelsize': 16, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
f, ( (ax1, ax2), (ax3, ax4) ) = plt.subplots(2,2)
ax1.plot(meanfiringrates,linewidth=2,color='lightgray')
ax1.plot(maxfiringrates,linewidth=1,color='k')
ax1.legend(['mean firing rate','max firing rate'])
ax1.set_title('mean and max firing rates of all cells')
ax2.plot(meanfiringrates[pindex],linewidth=2,color='lightgray')
ax2.plot(maxfiringrates[pindex],linewidth=1,color='k')
ax2.legend(['mean firing rate','max firing rate'])
ax2.set_title('mean and max firing rates of place cells')
cell_list = [3,7,11,13,14,27,45]
#cell_list = [3,37,68]
#cell_list = [11]
cell_list = pindex
for uu in cell_list:
ax3.plot(bins[1:], pf2[uu], linewidth=2, color='lightgray')
for uu in cell_list:
ax3.plot(bins[1:], pfsmooth[uu], linewidth=1, color='k')
plt.subplots_adjust(hspace=0.40)
#ax3.set_title("place fields in LinearTwo",fontsize=14)
ax1.set_ylabel("firing rate (Hz)")
ax2.set_ylabel("firing rate (Hz)")
ax3.set_ylabel("firing rate (Hz)")
ax3.set_xlim([0,100])
ax3.set_title('Place fields of place cells')
Out[232]:
In [234]:
sns.set(rc={'figure.figsize': (4,8),'lines.linewidth': 3, 'font.size': 18, 'axes.labelsize': 16, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
f, axes = plt.subplots(len(pindex), sharex=True, sharey=True)
plt.subplots_adjust(hspace=0.100)
for ii,pp in enumerate(pindex[peakorder]):
axes[ii].plot(bins[1:], pfsmooth[pp],linewidth=1,color='k')
axes[ii].fill_between(bins[1:], 0, pfsmooth[pp], color='gray')
axes[ii].set_xticks([])
axes[ii].set_yticks([])
axes[ii].spines['top'].set_visible(False)
axes[ii].spines['right'].set_visible(False)
axes[ii].spines['bottom'].set_visible(False)
axes[ii].spines['left'].set_visible(False)
axes[-1].set_xticks([10,50,90])
axes[-1].set_xlabel('position along track [cm]')
f.suptitle('Place fields ordered by peak location along track')
Out[234]:
"Place fields. Position was linearized and binned into 2.5 cm bins. Directional place fields were calculated as the number of spikes fired in a particular position bin and running direction divided by the time spent in that bin, smoothed with a Gaussian kernel with a s.d. of 5 cm, and identified when the peak firing rate of the pyramidal cell along the position bins was no less than 1 Hz. The place field size was defined as the total area of position bins where the firing rates were no less than 1 Hz." -- Silva, D., Feng, T., & Foster, D. J. (2015). Trajectory events across hippocampal place cells require previous experience. Nature neuroscience, 18(12), 1772-1779.
In [ ]:
tau = 0.25 # sec (decoding time window)
tbin = 0.25 # sec (decoding time step/resolution)
bins_per_window = round(tau/tbin)
spk_counts2_supersampled = list_of_spk_time_arrays_to_spk_counts_arrays(st_array2, ds=tbin, fs=32552)
In [ ]:
# need to resample running velocity, or come up with a better alternative?
time_axis = np.arange(0,len(dvdt))/60 # in seconds
running_vel_supersampled = np.interp(np.arange(0,len(spk_counts2_supersampled))*tbin,time_axis,dvdtlowpass)
truepos_supersampled = np.interp(np.arange(0,len(spk_counts2_supersampled))*tbin,time_axis,centerx)
print('The animal (gor01) ran an average of {0:2.2f} cm/s'.format(running_vel_supersampled.mean()))
th = 3 #cm/s
runindex_supersampled = np.where(running_vel_supersampled>=th); runindex_supersampled = runindex_supersampled[0]
print("The animal ran faster than th = {0:2.1f} cm/s for a total of {1:2.1f} seconds (out of a total of {2:2.1f} seconds).".format(th,len(runindex_supersampled)*tbin,len(centerx)/60))
In [ ]:
spk_counts2_supersampled_run = spk_counts2_supersampled[runindex_supersampled]
truepos_supersampled_run = truepos_supersampled[runindex_supersampled]
In [ ]:
sns.set(rc={'figure.figsize': (16,4),'lines.linewidth': 3, 'font.size': 18, 'axes.labelsize': 16, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
plt.plot(np.arange(0,len(spk_counts2_supersampled))*tbin,truepos_supersampled, linewidth=2, color='lightgray' )
plt.plot(runindex_supersampled*tbin,truepos_supersampled_run,marker='o', linestyle='None', markersize=2, color='k')
plt.legend(['true pos', 'true pos run'])
Here we assume all positions are equally likely, and we use
$$P(\mathbf{x}|\mathbf{n}) = c(\tau,\mathbf{n}) P(\mathbf{x}) \left( \prod_{i=1}^C f_i(\mathbf{x})^{n_i} \right) \exp \left(-\tau \sum_{i=1}^C f_i(\mathbf{x}) \right) $$to find the distribution at each time point. In particular, we take $\tau=20$ ms, and we advance our decoding window in 5 ms steps.
In [ ]:
# problem with approach!!! Discontinuities exist in run segments, so that smoothing can average temporally discontinuous segments!
# solution: first get code working on ALL data (not just run data). However, SWR events can still throw off estimates...
x = bins # spatial bins **could resample smoothed place fields onto new spatial grid as well, if we want to make it more flexible
#n C x 1 changes every time step
#fi C x 1 never changes
#f C x nbins never changes
trange=1
P = np.zeros((num_bins-1,trange))
dec_errors = []
f = pfsmooth[pindex,:]
dec_pos = np.zeros((len(runindex_supersampled),1))
for tt in np.arange(0,len(runindex_supersampled)-bins_per_window): #len(spk_counts2_5ms_run)-4):
#tt+=1 # time index
n = spk_counts2_supersampled_run[tt:tt+bins_per_window,pindex].sum(axis=0)
nn = np.tile(n,(num_bins-1,1)).T
if nn.max() == 0:
# print('No spikes in window, so cannot decode position!')
P = P
else:
P = np.exp((np.log((f)**(nn))).sum(axis=0) - tau*f.sum(axis=0))
P = P/P.sum() # normaization not strictly necessary
est_pos = P.argmax()
#print("estimated position: {0:2.1f} cm; actual position: {1:2.1f} cm".format(bins[est_pos],truepos_5ms_run[tt]))
#print("decoding error: {0:2.1f} cm". format(np.abs(bins[est_pos] -truepos_5ms_run[tt])))
dec_errors.append(np.abs(bins[est_pos] -truepos_supersampled_run[tt+round(bins_per_window/2)]))
dec_pos[tt] = bins[P.argmax()]
print("average decoding error: {0:2.1f} cm".format(np.array(dec_errors).mean()))
In [ ]:
sns.set(rc={'figure.figsize': (16,4),'lines.linewidth': 3, 'font.size': 18, 'axes.labelsize': 16, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
plt.plot(runindex_supersampled[0:500]*tbin,dec_pos[0:500],color='lightgray', marker='o', markersize=5,linewidth=1)
plt.plot(runindex_supersampled[0:500]*tbin,truepos_supersampled_run[0:500],linewidth=1,color='k', marker='o', markersize=3,linestyle='None')
plt.legend(['estimated','true'])
plt.xlabel('time [s]')
In [ ]:
dec_pos[5:6]
In [ ]:
#tt=4000
tt=220
tt+=1
n = spk_counts2_5ms_run[tt:tt+4,pindex].sum(axis=0)
nn = np.tile(n,(num_bins-1,1)).T
if nn.max() == 0:
print('No spikes in window, so cannot decode position!')
P = P
else:
P = np.exp((np.log((f)**nn)).sum(axis=0) - tau*f.sum(axis=0))
P = P/P.sum() # normaization not strictly necessary
est_pos = P.argmax()
print("estimated position: {0:2.1f} cm; actual position: {1:2.1f} cm".format(bins[est_pos],truepos_5ms_run[tt]))
print("decoding error: {0:2.1f} cm". format(np.abs(bins[est_pos] -truepos_5ms_run[tt])))
dec_errors.append(np.abs(bins[est_pos] -truepos_5ms_run[tt]))
dec_pos[tt] = bins[P.argmax()]
plt.plot(bins[0:-1],P)
In [ ]:
n[peakorder]
In [ ]:
sns.set(rc={'figure.figsize': (16,4),'lines.linewidth': 3, 'font.size': 18, 'axes.labelsize': 16, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
plt.plot(np.diff(runindex_supersampled))
In [ ]:
nums = runindex_supersampled
run_ends = np.where(np.diff(nums)-1)[0] + 1
sseq_lengths = np.diff(np.hstack((0, run_ends, nums.size)))
np.diff(np.hstack((0, run_ends, nums.size))).max()
In [ ]:
run_ends
In [ ]:
sseq_lengths[sseq_lengths<bins_per_window]
In [ ]:
len(runindex_supersampled)
In [13]:
T = np.array([3,4,5,6,7,8]) # temporal indices for a particular candidate sequence
P = np.array([0.3,0.8,0.5,0.6,0.7,0.5]) # positions or position indices for a particular sequence
prob = np.array([0.3,0.04,0.1,0.1,0.7,0.2]) # probabilities of [peak] decoded positions for seq
In [14]:
def mXprob(X,prob):
den = prob.sum()
num = (prob*X).sum()
return num/den
def covXYprob(X,Y,prob):
den = prob.sum()
num = (prob*(X - mXprob(X,prob))*(Y - mXprob(Y,prob))).sum()
return num/den
def corrXYprob(X,Y,prob):
den = np.sqrt(covXYprob(X,X,prob)*covXYprob(Y,Y,prob))
num = covXYprob(X,Y,prob)
return num/den
In [15]:
corrXYprob(T,P,prob)
Out[15]:
In [206]:
# note that here we re-sample placefields simply with linear interpolation. A more 'accurate' approach might be to compute the mean firing rate within each new bin...
def resample_placefields(pfsmooth, s_bin, pfbincenters, x0,xl):
newx = np.arange(x0,xl,s_bin) + s_bin/2
ss_pfsmooth = np.zeros((pfsmooth.shape[0],len(newx)))
for cc in np.arange(0,pfsmooth.shape[0]):
ss_pfsmooth[cc,:] = np.interp(newx,pfbincenters,pfsmooth[cc,:])
return ss_pfsmooth, newx
def resample_velocity(velocity, t_bin, tvel, t0,tend):
newt = np.arange(t0,tend,t_bin) + t_bin/2
newvel = np.zeros((1,len(newt)))
newvel = np.interp(newt,tvel,velocity)
return newvel, newt
In [214]:
# need to be able to get place fielda in arbitrary [spatial] resolution
# need to be able to get spikes in arbitrary [temporal] resolution
# need to be able to get running velocity in arbitrary [temporal] resolution
s_bin = 0.5 # cm of spatial bins
ss_pfsmooth, ss_pfbincenters = resample_placefields(pfsmooth, s_bin, pfbincenters, x0, xl)#super-sampled or sub-sampled smoothed place fields
t_bin = 0.25 # sec; temporal resolution for binning spikes
ss_spk_counts2 = list_of_spk_time_arrays_to_spk_counts_arrays(st_array2, ds=t_bin, fs=32552)
# WARNING!! This hack only works for evaluating first half/portion of the data, because the position, velocity, etc. are not automatically changed...
#ss_spk_counts2 = ss_spk_counts2[:round(len(ss_spk_counts2)/2)] # 1st half of data
#ss_spk_counts2 = ss_spk_counts2[round(len(ss_spk_counts2)/2):] # 2nd half of data
time_axis = np.arange(0,len(dvdt))/60
ss_velocity, ss_tvel = resample_velocity(velocity=dvdtlowpass,t_bin=t_bin,tvel=time_axis,t0=0,tend=tend)
ss_truepos = np.interp(np.arange(0,len(ss_spk_counts2))*t_bin,time_axis,centerx)
print('The animal (gor01) ran an average of {0:2.2f} cm/s'.format(ss_velocity.mean()))
th = 3 #cm/s
ss_runindex = np.where(ss_velocity>=th); ss_runindex = ss_runindex[0]
ss_runindex = ss_runindex[np.where(ss_runindex<len(ss_spk_counts2))[0]]; # runindexnew = runindexnew[0]
print("The animal ran faster than th = {0:2.1f} cm/s for a total of {1:2.1f} seconds (out of a total of {2:2.1f} seconds).".format(th,len(ss_runindex)*t_bin,len(centerx)/60))
tau = 0.25 # sec (decoding time window)
bins_per_window = round(tau/t_bin)
print("Decoding with {0} x {1} ms bins per window, into one of {2} spatial bins with size {3} cm each...".format(bins_per_window,t_bin*1000,len(ss_pfbincenters),s_bin))
In [208]:
cc=3
sns.set(rc={'figure.figsize': (16,4),'lines.linewidth': 3, 'font.size': 18, 'axes.labelsize': 16, 'legend.fontsize': 12, 'ytick.labelsize': 12, 'xtick.labelsize': 12 })
sns.set_style("white")
plt.bar(pfbincenters,pfsmooth[cc,:],color='lightgray')
plt.bar(ss_pfbincenters,ss_pfsmooth[cc,:],color='k')
plt.legend(['original','sampled'])
Out[208]:
In [215]:
# problem with approach!!! Discontinuities exist in run segments, so that smoothing can average temporally discontinuous segments!
# solution: first get code working on ALL data (not just run data). However, SWR events can still throw off estimates...
ss_spk_counts2_run = ss_spk_counts2[ss_runindex]
ss_truepos_run = ss_truepos[ss_runindex]
x = ss_pfbincenters # spatial bins **could resample smoothed place fields onto new spatial grid as well, if we want to make it more flexible
#n C x 1 changes every time step
#fi C x 1 never changes
#f C x nbins never changes
trange=1
P = np.zeros((len(ss_pfbincenters),trange))
dec_errors = []
f = ss_pfsmooth[pindex,:]
dec_pos = np.zeros((len(ss_runindex),1))
for tt in np.arange(0,len(ss_runindex)-bins_per_window): #len(spk_counts2_5ms_run)-4):
#tt+=1 # time index
n = ss_spk_counts2_run[tt:tt+bins_per_window,pindex].sum(axis=0)
nn = np.tile(n,(len(ss_pfbincenters),1)).T
if nn.max() == 0:
#print('No spikes in window, so cannot decode position!')
P = P
else:
P = np.exp((np.log((f)**(nn))).sum(axis=0) - tau*f.sum(axis=0))
P = P/P.sum() # normalization not strictly necessary
est_pos = P.argmax()
#print("estimated position: {0:2.1f} cm; actual position: {1:2.1f} cm".format(bins[est_pos],truepos_5ms_run[tt]))
#print("decoding error: {0:2.1f} cm". format(np.abs(bins[est_pos] -truepos_5ms_run[tt])))
dec_errors.append(np.abs(x[est_pos] -ss_truepos_run[tt+round(bins_per_window/2)]))
dec_errors.append(np.abs(x[est_pos] -ss_truepos_run[tt+0]))
dec_pos[tt] = x[P.argmax()]
print("average decoding error: {0:2.1f} cm".format(np.array(dec_errors).mean()))
In [199]:
plt.plot(dec_pos[0:500],linewidth=1,color='lightgray',marker='o')
plt.plot(ss_truepos_run[round(bins_per_window/2):500+round(bins_per_window/2)],linewidth=1,color='k')
Out[199]:
In [216]:
plt.plot(dec_pos[0:500],linewidth=1,color='lightgray',marker='o')
plt.plot(ss_truepos_run[round(bins_per_window/2):500+round(bins_per_window/2)],linewidth=1,color='k')
Out[216]:
In [211]:
plt.plot(dec_pos[:1000],linewidth=1,color='lightgray',marker='o')
plt.plot(ss_truepos_run[round(bins_per_window/2):1000-round(bins_per_window/2)],linewidth=1,color='k')
Out[211]:
In [217]:
plt.plot(dec_pos[:1000],linewidth=1,color='lightgray',marker='o')
plt.plot(ss_truepos_run[round(bins_per_window/2):1000-round(bins_per_window/2)],linewidth=1,color='k')
Out[217]:
In [141]:
plt.plot(dec_pos[-500:],linewidth=1,color='lightgray',marker='o')
plt.plot(ss_truepos_run[-500-round(bins_per_window/2):],linewidth=1,color='k')
Out[141]:
In [213]:
plt.plot(dec_pos[-500:],linewidth=1,color='lightgray',marker='o')
plt.plot(ss_truepos_run[-500-0*round(bins_per_window/2):],linewidth=1,color='k')
Out[213]:
In [218]:
plt.plot(dec_pos[-500:],linewidth=1,color='lightgray',marker='o')
plt.plot(ss_truepos_run[-500-0*round(bins_per_window/2):],linewidth=1,color='k')
Out[218]:
In [ ]:
# step 1. identify SWR sequences: in time bins, or in sampling time? Probably sampling time, followed by binning...
# only keep sequences that meet criteria, namely length 100--500 ms
# step 2. decode w normalized rate tuning curves using the 5-20 ms sliding window approach...
# Q. What to do about detection on the edges? I can decode T/5-3 positions in a sequence of length T ms
# this is equivalent to 17--97 position estimates for 100--500 ms sequences