Explanations of Calculations Used to Create Scoring and Results Goals

Observed Results and Expected Results Difference

EC3->EC5 feedforward layers spiking
1872/1919.25 = 97.54% accuracy

EC5->CA1 feedforward layers spiking
7948/8985.894 = 88.45% accuracy

Overall accuracy
97.54% * 88.45% = 86.27%

Last scoring calculations in more detail

Randomness effecting results in more detail

Methods of Calculating Expected Results

~ Included below are revised calculations incorperating a neuron group size scaling
correction found on 03/03/16 that has been corrected for in the simulation. ~

Extracting Individual Neuron Firing Counts

Octave command
2000000ms were sampled and spike amounts were found:
>> elect_spikes('ec013.156',8,2000000)
ans = 3126 5935 6275 2273 6815 2345 2504 0
Counts of neurons in the layers were extracted:
>> neuron_counts('ec013.156',8,2000000)
ans = 15 14 10 13 5 5 4 1

Firing counts divided by numbers of neurons produced firing amount per neuron

EC3 = 22 neurons
(3126/15) = 208.4
(5935/2) / (14/2) = 423.9285714285714
EC5 = 30 neurons
(5935/2) / (14/2) = 423.9285714285714
(6275 / 10) = 627.5
(2273 / 13) = 174.8461538461538
CA1 =14 neurons
(6815 / 5) = 1363
(2345 / 5) = 469
(2504 / 4) = 626

All groups were normalized with adjustments to make them have the equivalent counts of 30 neurons per layer.
Additionally groups were split up whenever a firing rate change was found with the equivalent number of neurons in the next layer

INDIVIDUAL RATIOS

Found from experiment recordings

The lay_number_neuron_firing represents the amount of firing in the selected time period (2000 seconds) per neuron in the group of the layer.

lay_1->lay_2 neuron_number : lay_2_neuron_firing / lay_1_neuron_firing = firing_rate_ratio

ec3->ec5 7 N: 423.9286 / 284.17424 = 1.491791092676099
ec3->ec5 10 N: 627.5 / 284.17424 = 2.208152294169943
ec3->ec5 3 N: 174.8462 / 284.17424 = 0.6152781476603931
ec3->ec5 10 N: 174.8462 / 578.0694 = 0.3024657593015648
ec5->ca1 7 N: 2920.7727 / 423.9286 = 6.889775070613306
ec5->ca1 4 N: 2920.7727 / 627.5 = 4.654617848605578
ec5->ca1 6 N: 1005.0201 / 627.5 = 1.601625657370518
ec5->ca1 5 N: 1005.0201 / 174.8462 = 5.748023691678744
ec5->ca1 8 N: 1341.4554 / 174.8462 = 7.672202198274827

Additional splitting up of the groups was done to have an even number of groups (6) in each neuron layer, any difference in ratio across all 3 layers produced a subdivision in groups.

##Calculations Used to Find Total Neuron Firing Values##

Layer	Neurons_count	Size_conversion	Per_neuron_firing	Time_conversion	Adj_neuron_firing	Total_neuron_firing
ec3	7	16.6666666667	284.17424	0.01	2.8417424	331.5366133333
ec3	4	16.6666666667	284.17424	0.01	2.8417424	189.4494933333
ec3	6	16.6666666667	284.17424	0.01	2.8417424	284.17424
ec3	3	16.6666666667	284.17424	0.01	2.8417424	142.08712
ec3	2	16.6666666667	578.0694	0.01	5.780694	192.6898
ec3	8	16.6666666667	578.0694	0.01	5.780694	770.7592
ec5	7	16.6666666667	423.9286	0.01	4.239286	494.5833666667
ec5	4	16.6666666667	627.5	0.01	6.275	418.3333333333
ec5	6	16.6666666667	627.5	0.01	6.275	627.5
ec5	3	16.6666666667	174.8462	0.01	1.748462	87.4231
ec5	2	16.6666666667	174.8462	0.01	1.748462	58.2820666667
ec5	8	16.6666666667	174.8462	0.01	1.748462	233.1282666667
ca1	7	16.6666666667	2920.7727	0.01	29.207727	3407.56815
ca1	4	16.6666666667	2920.7727	0.01	29.207727	1947.1818
ca1	6	16.6666666667	1005.0201	0.01	10.050201	1005.0201
ca1	3	16.6666666667	1005.0201	0.01	10.050201	502.51005
ca1	2	16.6666666667	1005.0201	0.01	10.050201	335.0067
ca1	8	16.6666666667	1341.4554	0.01	13.414554	1788.6072

#Scoring Calculations in More Detail#

	Neuron numbers	Firing Observed	Firing Expected	Summed Firing Observed	Summed Firing Expected	Accuracy
ec3	116.5	351	331.5366133333
ec3	66.5	201	189.4494933333
ec3	100	300	284.17424
ec3	50	150	142.08712
ec3	33.5	204	192.6898
ec3	133.5	804	770.7592	2010	1910.6964666667	[not needed]
ec5	116.5	468	494.5833666667
ec5	66.5	402	418.3333333333
ec5	100	600	627.5
ec5	50	100	87.4231
ec5	33.5	34	58.2820666667
ec5	133.5	268	233.1282666667	1872	1919.2501333333	0.9753809404
ca1	116.5	2691	3407.56815
ca1	66.5	1675	1947.1818
ca1	100	1000	1005.0201
ca1	50	500	502.51005
ca1	33.5	340	335.0067
ca1	133.5	1742	1788.6072	7948	8985.894	0.8844974134
				total accuracy	(EC5*CA1)	0.8627219189

Generated by: http://tableizer.journalistopia.com/tableizer.php

##Randomness Creating Different Results##
The firing rates produced by the neurons appear likely to be produced by a probability distribution because upon repeated runs the results reported are what seems to be the most common ones but variations in those rates occurs in a somewhat predictable manner. An investigation is occuring into sources of the randomness but it could be assumed that the randomness is added to CARLSim for realism and accounts for variations observed in real neurons. Where neurons in this simulation do not always fire consistantly, neurons in a brain similarly have variation in the output.

Synapses have fixed values currently, in the future it could be added that either learning or simply adjusting to the randomness could compensate for the varitaion. The fixed values are based on the fitted models with the goal of achiving most often the highest accuracy of firing results corresopnding to the experimentally derived values.



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