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added all my stuff

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This commit is contained in:
Jan Benda
2014-11-12 18:39:02 +01:00
parent 0fdcf2f82e
commit 350ee7ca2b
160 changed files with 5869 additions and 253 deletions
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10
pointprocesses/code/colorednoisepdf.m Normal file
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function pcn = colorednoisepdf( x, misi, epsilon, tau )
% returns the ISI pdf for PIF with colored noise drive
% x: the input ISI
% misis: the mean isi
% epsilon: a parameter
% tau: the correlation time of the noise
gamma1 = x/tau+exp(-x/tau)-1.0;
gamma2 = 1.0-exp(-x/tau);
pcn=exp(-(x-misi).^2./(4.0*epsilon*tau.^2.*gamma1)).*(((misi-x).*gamma2+2*gamma1*tau).^2./(2*gamma1*tau^2)-epsilon*(gamma2.^2-2*gamma1.*exp(-x/tau))) ./ (2*tau*sqrt(4*pi*epsilon*gamma1.^3));
end

24
pointprocesses/code/colorednoisepdfisifit.m Normal file
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% misi = 0.02;
% epsilon = 1.0;
% tau = 0.1;
x=0:0.002:0.1;
% pcn = colorednoisepdf( x, misi, epsilon, tau )+10.0*randn( size( x ) );
% plot( x, pcn );
spikes = lifouspikes( 10, 15, 50.0, 1.0, 1.0 );
isivec = isis( spikes );
misi = mean( isivec );
1.0/misi
isibins = 0:0.0005:0.1;
[ n, c ] = hist( isivec, isibins );
n = n / sum(n)/(isibins(2)-isibins(1));
bar( c, n );
beta0 = [ 1.0, 0.01 ];
b = nlinfit(c(1:end-2), n(1:end-2), @(b,x)(colorednoisepdf(x, misi, b(1), b(2))), beta0)
pcn = colorednoisepdf( x, misi, b(1), b(2) );
hold on
plot( x, pcn, 'r', 'LineWidth', 3 );
hold off

38
pointprocesses/code/counthist.m Normal file
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function [ counts, bins ] = counthist( spikes, w )
% computes count histogram and compare them with Poisson distribution
% spikes: a cell array of vectors of spike times
% w: observation window duration for computing the counts
% collect spike counts:
tmax = spikes{1}(end);
n = [];
r = [];
for k = 1:length(spikes)
for tk = 0:w:tmax-w
nn = sum( ( spikes{k} >= tk ) & ( spikes{k} < tk+w ) );
%nn = length( find( ( spikes{k} >= tk ) & ( spikes{k} < tk+w ) ) );
n = [ n nn ];
end
rate = (length(spikes{k})-1)/(spikes{k}(end) - spikes{k}(1));
r = [ r rate ];
end
% histogram of spike counts:
maxn = max( n );
[counts, bins ] = hist( n, 0:1:maxn+1 );
counts = counts / sum( counts );
if nargout == 0
bar( bins, counts );
hold on;
% Poisson distribution:
rate = mean( r );
x = 0:1:20;
l = rate*w;
y = l.^x.*exp(-l)./factorial(x);
plot( x, y, 'r', 'LineWidth', 3 );
xlim( [ 0 20 ] );
hold off;
xlabel( 'counts k' );
ylabel( 'P(k)' );
end
end

39
pointprocesses/code/fano.m Normal file
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function fano( spikes )
% computes fano factor as a function of window size
% spikes: a cell array of vectors of spike times
tmax = spikes{1}(end);
windows = 0.01:0.05:0.01*tmax;
mc = windows;
vc = windows;
ff = windows;
fs = windows;
for j = 1:length(windows)
w = windows( j );
% collect counts:
n = [];
for k = 1:length(spikes)
for tk = 0:w:tmax-w
nn = sum( ( spikes{k} >= tk ) & ( spikes{k} < tk+w ) );
%nn = length( find( ( spikes{k} >= tk ) & ( spikes{k} < tk+w ) ) );
n = [ n nn ];
end
end
% statistics for current window:
mc(j) = mean( n );
vc(j) = var( n );
ff(j) = vc( j )/mc( j );
fs(j) = sqrt(vc( j )/mc( j ));
end
subplot( 1, 2, 1 );
scatter( mc, vc, 'filled' );
xlabel( 'Mean count' );
ylabel( 'Count variance' );
subplot( 1, 2, 2 );
scatter( 1000.0*windows, fs, 'filled' );
xlabel( 'Window W [ms]' );
ylabel( 'Fano factor' );
end

5
pointprocesses/code/inversegauss.m Normal file
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function y = inversegauss( x, m, d )
% returns the inverse Gauss density with mean isi m and diffusion
% coefficent d
y = exp(-(x-m).^2./(4.0*d.*x.*m.^2.0))./sqrt(4.0*pi*d.*x.^3.0);
end

28
pointprocesses/code/inversegaussplot.m Normal file
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f = figure;
subplot( 1, 2, 1 );
dx=0.0001;
x = dx:dx:0.5;
hold all
m = 0.02;
for d = [ 0.1 1 10 50 200 ]
plot( 1000.0*x, inversegauss( x, m, d ), 'LineWidth', 3, 'DisplayName', sprintf( 'D=%.1f', d ) );
end
title( sprintf( 'm=%g ms', 1000.0*m ) )
xlim( [ 0 50 ] );
xlabel( 'ISI [ms]' );
ylabel( 'p(ISI)' );
legend( '-DynamicLegend' );
hold off;
subplot( 1, 2, 2 );
hold all;
d = 5.0;
for m = [ 0.005 0.01 0.02 0.05 ]
plot( 1000.0*x, inversegauss( x, m, d ), 'LineWidth', 3, 'DisplayName', sprintf( 'm=%g ms', 1000.0*m ) );
end
title( sprintf( 'D=%g Hz', d ) )
xlim( [ 0 50 ] )
xlabel( 'ISI [ms]' );
ylabel( 'p(ISI)' );
legend( '-DynamicLegend' )
hold off

32
pointprocesses/code/isihist.m Normal file
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function isihist( isis, binwidth )
% plot histogram of isis
% isis: vector of interspike intervals
% binwidth: optional width to be used for the isi bins
if nargin < 2
nperbin = 200; % average number of data points per bin
bins = length( isis )/nperbin; % number of bins
binwidth = max( isis )/bins;
if binwidth < 5e-4 % half a millisecond
binwidth = 5e-4;
end
end
bins = 0.5*binwidth:binwidth:max(isis);
% histogram:
[ nelements, centers ] = hist( isis, bins );
% normalization (integral = 1):
nelements = nelements / sum( nelements ) / binwidth;
% plot:
bar( 1000.0*centers, nelements );
xlabel( 'ISI [ms]' )
ylabel( 'p(ISI) [1/s]')
% annotation:
misi = mean( isis );
sdisi = std( isis );
disi = sdisi^2.0/2.0/misi^3;
text( 0.5, 0.6, sprintf( 'mean=%.1f ms', 1000.0*misi ), 'Units', 'normalized' )
text( 0.5, 0.5, sprintf( 'std=%.1f ms', 1000.0*sdisi ), 'Units', 'normalized' )
text( 0.5, 0.4, sprintf( 'CV=%.2f', sdisi/misi ), 'Units', 'normalized' )
%text( 0.5, 0.3, sprintf( 'D=%.1f Hz', disi ), 'Units', 'normalized' )
end

24
pointprocesses/code/isireturnmap.m Normal file
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function isireturnmap( isis, lag2 )
% plot return maps for lag 1 and lag lag2
clf;
subplot( 1, 2, 1 );
lag = 1;
scatter( 1000.0*isis(1:end-lag)', 1000.0*isis(1+lag:end)', 'b', 'filled', 'MarkerEdgeColor', 'white' );
xlabel( 'ISI T_i [ms]' );
ylabel( 'ISI T_{i+1} [ms]' );
maxisi = max( isis );
maxy = ceil(maxisi/10)*10.0;
xlim( [0 1.5*maxy ])
ylim( [0 maxy ])
subplot( 1, 2, 2 );
lag = lag2;
scatter( 1000.0*isis(1:end-lag)', 1000.0*isis(1+lag:end)', 'b', 'filled', 'MarkerEdgeColor', 'white' );
xlabel( 'ISI T_i [ms]' );
ylabel( 'ISI T_{i+2} [ms]' );
xlim( [0 1.5*maxy ])
ylim( [0 maxy ])
end

15
pointprocesses/code/isis.m Normal file
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function isivec = isis( spikes )
% returns a single list of isis computed from all trials in spikes
% spikes: a cell array of vectors of spike times
isivec = [];
for k = 1:length(spikes)
difftimes = diff( spikes{k} );
if ( size( difftimes, 1 ) == 1 )
isivec = [ isivec difftimes ];
elseif ( size( difftimes, 2 ) == 1 )
isivec = [ isivec difftimes' ];
end
end
end

26
pointprocesses/code/isiserialcorr.m Normal file
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function isicorr = isiserialcorr( isis, maxlag )
% serial correlation of isis
% isis: vector of interspike intervals
% maxlag: the maximum lag
lags = 0:maxlag;
isicorr = zeros( size( lags ) );
for k = 1:length(lags)
lag = lags(k);
if length( isis ) > lag+10
cc = corrcoef( [ isis(1:end-lag)', isis(1+lag:end)' ] );
isicorr(k) = cc( 1, 2 );
end
end
if nargout == 0
% plot:
plot( lags, isicorr, '-b' );
hold on;
scatter( lags, isicorr, 100.0, 'b', 'filled' );
hold off;
xlabel( 'Lag k' )
ylabel( '\rho_k')
end
end

53
pointprocesses/code/lifadaptspikes.m Normal file
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function spikes = lifadaptspikes( trials, input, tmaxdt, D, tauadapt, adaptincr )
% Generate spike times of a leaky integrate-and-fire neuron
% with an adaptation current
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmaxdt: in case of a single value stimulus the duration of a trial
% in case of a vector as a stimulus the time step
% D: the strength of additive white noise
% tauadapt: adaptation time constant
% adaptincr: adaptation strength
tau = 0.01;
if nargin < 4
D = 1e0;
end
if nargin < 5
tauadapt = 0.1;
end
if nargin < 6
adaptincr = 1.0;
end
vreset = 0.0;
vthresh = 10.0;
dt = 1e-4;
if max( size( input ) ) == 1
input = input * ones( ceil( tmaxdt/dt ), 1 );
else
dt = tmaxdt;
end
spikes = cell( trials, 1 );
for k=1:trials
times = [];
j = 1;
v = vreset;
a = 0.0;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
v = v + ( - v - a + noise(i) + input(i))*dt/tau;
a = a + ( - a )*dt/tauadapt;
if v >= vthresh
v = vreset;
a = a + adaptincr/tauadapt;
spiketime = i*dt;
if spiketime > 4.0*tauadapt
times(j) = spiketime - 4.0*tauadapt;
j = j + 1;
end
end
end
spikes{k} = times;
end
end

51
pointprocesses/code/lifboltzmanspikes.m Normal file
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function spikes = lifboltzmanspikes( trials, input, tmaxdt, D, imax, ithresh, slope )
% Generate spike times of a leaky integrate-and-fire neuron
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmaxdt: in case of a single value stimulus the duration of a trial
% in case of a vector as a stimulus the time step
% D: the strength of additive white noise
% imax: maximum output of boltzman
% ithresh: threshold of boltzman input
% slope: slope factor of boltzman input
tau = 0.01;
if nargin < 4
D = 1e0;
end
if nargin < 5
imax = 20;
end
if nargin < 6
ithresh = 10;
end
if nargin < 7
slope = 1;
end
vreset = 0.0;
vthresh = 10.0;
dt = 1e-4;
if length( input ) == 1
input = input * ones( ceil( tmaxdt/dt ), 1 );
else
dt = tmaxdt;
end
inb = imax./(1.0+exp(-slope.*(input - ithresh)));
spikes = cell( trials, 1 );
for k=1:trials
times = [];
j = 1;
v = vreset;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
v = v + ( - v + noise(i) + inb(i))*dt/tau;
if v >= vthresh
v = vreset;
times(j) = i*dt;
j = j + 1;
end
end
spikes{k} = times;
end
end

23
pointprocesses/code/liffano.m Normal file
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input = 65.0; % lifadapt 100Hz
%input = 8.0; % lifadapt 10Hz
%input = 15.7; % lif 100Hz
%input = 8.3; % lif 10Hz
trials = 10;
tmax = 100.0;
Dnoise = 0.1;
Dounoise = 5e1;
outau = 10.0;
adapttau = 0.1;
adaptincr = 5.0;
%spikes = lifouadaptspikes( trials, input, 1.0, Dnoise, Dounoise, outau, adapttau, adaptincr );
%spikeraster( spikes );
%return;
% generate spikes:
%spikes = lifspikes( trials, input, tmax, noise );
spikes = lifouspikes( trials, input, tmax, Dounoise, outau );
%spikes = lifadaptspikes( trials, input, tmax, Dnoise, adapttau, adaptincr );
%spikes = lifouadaptspikes( trials, input, tmax, Dnoise, Dounoise, outau, adapttau, adaptincr );
fano( spikes );

36
pointprocesses/code/lifficurves.m Normal file
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% lif:
noises = [ 1e-5 1e-4 1e-3 1e-2 1e-1 ];
inputs = 0:0.1:20;
duration = 50.0;
% pif:
% noises = [ 1e-1 1 1e1 1e2 1e3 ];
% inputs = -5:0.1:10;
% duration = 100.0;
f = figure;
hold all;
for noise = noises
fprintf( 'noise=%.0e\n', noise );
rates = [];
for input = inputs
spikes = lifspikes( 10, input, duration, noise );
% spikes = pifspikes( 50, input, duration, noise );
nspikes = 0;
for k = 1:length( spikes )
nspikes = nspikes + length( spikes{k} );
end
rate = nspikes/duration/length( spikes );
%fprintf( 'I=%g N=%d rate=%g\n', input, length( spikes ), rate )
rates = [ rates rate ];
end
plot( inputs, rates, 'LineWidth', 2, 'DisplayName', sprintf( 'D=%.0e', noise ) );
end
xlabel( 'Input' );
xlim( [ inputs(1) inputs(end) ] )
ylabel( 'Firing rate [Hz]' );
%title( 'Leaky integrate-and-fire' )
title( 'Perfect integrate-and-fire' )
legend( '-DynamicLegend', 'Location', 'NorthWest' )
hold off

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pointprocesses/code/lifinputdiscriminationslope.m Normal file
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%input = 15.7; % lif 100Hz
%input = 8.3; % lif 10Hz
trials = 10;
tmax = 50.0;
Dnoise = 1.0;
imax = 25.0;
ithresh = 10.0;
slope=0.2;
% inputs = 0:2:30;
% rates = zeros( size( inputs ) );
% for j = 1:length( inputs )
% input = inputs(j);
% spikes = lifboltzmanspikes( trials, input, tmax, Dnoise, imax, ithresh, slope );
% nspikes = 0;
% for k = 1:length( spikes )
% nspikes = nspikes + length( spikes{k} );
% end
% rate = nspikes/tmax/length( spikes );
% rates(j) = rate;
% end
% plot( inputs, rates );
% grid on;
% return
input = 10.0; % 80 Hz
window = 0.2;
slopes = 0.1:0.1:2.0;
pmax = zeros( size( slopes) );
for j = 1:length( slopes )
slope = slopes( j );
spikes = lifboltzmanspikes( trials, input, tmax, Dnoise, imax, ithresh, slope );
[ n1, bins1 ] = counthist( spikes, w );
spikes = lifboltzmanspikes( trials, input+1.0, tmax, Dnoise, imax, ithresh, slope );
[ n2, bins2 ] = counthist( spikes, w );
subplot( 2, 1, 1 );
bar( bins1, n1, 'b' );
hold on;
bar( bins2, n2, 'r' );
hold off;
subplot( 2, 1, 2 );
bmax = max( [ length( bins1 ), length( bins2 ) ] );
decision1 = zeros( bmax, 1 );
decision2 = zeros( bmax, 1 );
cs1 = ones( bmax, 1 );
cs1(1:length(n1)) = cumsum( n1 );
cs2 = ones( bmax, 1 );
cs2(1:length(n2)) = cumsum( n2 );
cbins = 0:1:bmax-1;
plot( cbins, cs1, 'b' );
hold on;
plot( cbins, cs2, 'r' );
plot( cbins, cs1-cs2, 'g' );
hold off;
pause( 0.1 );
pmax(j) = max( cs1-cs2 );
end
clf;
subplot( 1, 1, 1 );
plot( slopes, pmax );

51
pointprocesses/code/lifinputdiscriminationtime.m Normal file
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input = 65.0; % lifadapt 100Hz
%input = 8.0; % lifadapt 10Hz
%input = 15.7; % lif 100Hz
%input = 8.3; % lif 10Hz
trials = 10;
tmax = 50.0;
Dnoise = 0.1;
Dounoise = 5e1;
outau = 10.0;
adapttau = 0.2;
adaptincr = 0.5;
windows = 0.05:0.05:1.0;
pmax = zeros( size( windows ) );
for j = 1:length( windows )
w = windows( j );
spikes = lifadaptspikes( trials, input, tmax, Dnoise, adapttau, adaptincr );
%spikes = lifouspikes( trials, input, tmax, Dounoise, outau);
[ n1, bins1 ] = counthist( spikes, w );
spikes = lifadaptspikes( trials, input+10.0, tmax, Dnoise, adapttau, adaptincr );
%spikes = lifouspikes( trials, input+10.0, tmax, Dounoise, outau );
[ n2, bins2 ] = counthist( spikes, w );
subplot( 2, 1, 1 );
bar( bins1, n1, 'b' );
hold on;
bar( bins2, n2, 'r' );
hold off;
subplot( 2, 1, 2 );
bmax = max( [ length( bins1 ), length( bins2 ) ] );
decision1 = zeros( bmax, 1 );
decision2 = zeros( bmax, 1 );
cs1 = ones( bmax, 1 );
cs1(1:length(n1)) = cumsum( n1 );
cs2 = ones( bmax, 1 );
cs2(1:length(n2)) = cumsum( n2 );
cbins = 0:1:bmax-1;
plot( cbins, cs1, 'b' );
hold on;
plot( cbins, cs2, 'r' );
plot( cbins, cs1-cs2, 'g' );
hold off;
pause( 0.1 );
pmax(j) = max( cs1-cs2 );
end
clf;
subplot( 1, 1, 1 );
plot( windows, pmax );

35
pointprocesses/code/lifisih.m Normal file
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%input = 65.0; % lifadapt 100Hz
%input = 8.0; % lifadapt 10Hz
input = 15.7; % lif 100Hz
%input = 8.3; % lif 10Hz
trials = 10;
tmax = 100.0;
noise = 1e-1;
adapttau = 0.1;
adaptincr = 5.0;
% generate spikes:
spikes = lifspikes( trials, input, tmax, noise );
%spikes = lifadaptspikes( trials, input, tmax, noise, adapttau, adaptincr );
% interspike intervals:
isivec = isis( spikes );
% histogram
f = figure( 1 );
isihist( isivec, 10e-4 );
hold on
% theoretical density:
misi = mean( isivec );
disi = var( isivec )/2.0/misi^3;
xmax = 3.0*misi;
x = 0:0.0001:xmax;
plot( 1000.0*x, inversegauss( x, misi, disi ), 'r', 'LineWidth', 3 );
% plot details:
title( sprintf( 'LIF, input=%g, nisi=%d', input, length( isivec ) ) )
xlim( [ 0.0 1000.0*xmax ] )
legend( 'data', 'inverse Gaussian' )
hold off
% serial correlations:
f = figure( 2 );
isiserialcorr( isivec, 10 );

63
pointprocesses/code/lifisistats.m Normal file
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inputs = 0:0.1:20; % lif
inputs = 0:0.1:10; % pif
avisi = [];
sdisi = [];
cvisi = [];
dcisi = [];
for input = inputs
input
% spikes = lifspikes( 100, input, 100.0, 1e-2 );
spikes = pifspikes( 100, input, 100.0, 1e-1 );
isivec = isis( spikes );
if length( isivec ) <= 1
av = Inf;
sd = NaN;
cv = NaN;
dc = NaN;
else
av = mean( isivec );
sd = std( isivec );
if av > 0.0
cv = sd/av;
dc = sd^2.0/2.0/av^3;
else
cv = NaN;
dc = NaN;
end
end
avisi = [ avisi av ];
sdisi = [ sdisi sd ];
cvisi = [ cvisi cv ];
dcisi = [ dcisi dc ];
end
f = figure;
subplot( 2, 2, 1 );
plot( inputs, 1.0./avisi, '-b', 'LineWidth', 3 );
xlabel( 'Input' );
xlim( [ inputs(1) inputs(end) ] )
title( 'Mean rate [Hz]' );
subplot( 2, 2, 2 );
plot( inputs, 1000.0*avisi, '-b', 'LineWidth', 3 );
hold on;
plot( inputs, 1000.0*sdisi, '-c', 'LineWidth', 3 );
hold off;
xlabel( 'Input' );
xlim( [ inputs(1) inputs(end) ] )
ylim( [ 0 1000 ] )
title( 'ISI [ms]' );
legend( 's.d. ISI', 'mean ISI' );
subplot( 2, 2, 3 );
plot( inputs, cvisi, '-b', 'LineWidth', 3 );
xlabel( 'Input' );
xlim( [ inputs(1) inputs(end) ] )
title( 'CV' );
subplot( 2, 2, 4 );
plot( inputs, dcisi, '-b', 'LineWidth', 3 );
xlabel( 'Input' );
xlim( [ inputs(1) inputs(end) ] )
title( 'D [Hz]' );

64
pointprocesses/code/lifouadaptspikes.m Normal file
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function spikes = lifouadaptspikes( trials, input, tmaxdt, D, Dou, outau, tauadapt, adaptincr )
% Generate spike times of a leaky integrate-and-fire neuron
% with colored noise and an adaptation current
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmaxdt: in case of a single value stimulus the duration of a trial
% in case of a vector as a stimulus the time step
% D: the strength of additive noise
% Dou: the strength of additive colored noise
% outau: time constant of the colored noise
% tauadapt: adaptation time constant
% adaptincr: adaptation strength
tau = 0.01;
if nargin < 4
D = 1e0;
end
if nargin < 5
Dou = 1e0;
end
if nargin < 6
outau = 1.0;
end
if nargin < 7
tauadapt = 0.1;
end
if nargin < 8
adaptincr = 1.0;
end
vreset = 0.0;
vthresh = 10.0;
dt = 1e-4;
if max( size( input ) ) == 1
input = input * ones( ceil( tmaxdt/dt ), 1 );
else
dt = tmaxdt;
end
spikes = cell( trials, 1 );
for k=1:trials
times = [];
j = 1;
v = vreset;
n = 0.0;
a = 0.0;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
noiseou = sqrt(2.0*Dou)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
n = n + ( - n + noiseou(i))*dt/outau;
v = v + ( - v - a + noise(i) + n + input(i))*dt/tau;
a = a + ( - a )*dt/tauadapt;
if v >= vthresh
v = vreset;
a = a + adaptincr;
spiketime = i*dt;
if spiketime > 4.0*tauadapt
times(j) = spiketime - 4.0*tauadapt;
j = j + 1;
end
end
end
spikes{k} = times;
end
end

44
pointprocesses/code/lifouspikes.m Normal file
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function spikes = lifouspikes( trials, input, tmaxdt, D, outau )
% Generate spike times of a leaky integrate-and-fire neuron
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmaxdt: in case of a single value stimulus the duration of a trial
% in case of a vector as a stimulus the time step
% D: the strength of additive white noise
% outau: time constant of the colored noise
tau = 0.01;
if nargin < 4
D = 1e0;
end
if nargin < 5
outau = 1.0;
end
vreset = 0.0;
vthresh = 10.0;
dt = 1e-4;
if length( input ) == 1
input = input * ones( ceil( tmaxdt/dt ), 1 );
else
dt = tmaxdt;
end
spikes = cell( trials, 1 );
for k=1:trials
times = [];
j = 1;
n = 0.0;
v = vreset;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
n = n + ( - n + noise(i))*dt/outau;
v = v + ( - v + n + input(i))*dt/tau;
if v >= vthresh
v = vreset;
times(j) = i*dt;
j = j + 1;
end
end
spikes{k} = times;
end
end

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pointprocesses/code/lifrateisicorr.m Normal file
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% relation between firing rate and serieller correlation
input = 65.0; % lifadapt 100Hz
%input = 8.0; % lifadapt 10Hz
trials = 10;
tmax = 50.0;
noise = 1e-5;
adapttau = 0.1;
adaptincr = 0.5;
clf;
for adapttau = 0.01:0.02:0.2
inputs = 1:5:120;
iscs = zeros( size( inputs ) );
rates = zeros( size( inputs ) );
for k = 1:length(inputs)
input = inputs(k);
% generate spikes:
spikes = lifadaptspikes( trials, input, tmax, noise, adapttau, adaptincr );
isivec = isis( spikes );
isc = isiserialcorr( isivec, 10 );
iscs(k) = isc(2);
rates(k) = 1.0/mean( isivec );
end
subplot( 2, 1, 1 );
hold on;
plot( inputs, rates );
hold off;
subplot( 2, 1, 2 );
hold on;
plot( rates, iscs );
hold off;
end

38
pointprocesses/code/lifspikes.m Normal file
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function spikes = lifspikes( trials, input, tmaxdt, D )
% Generate spike times of a leaky integrate-and-fire neuron
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmaxdt: in case of a single value stimulus the duration of a trial
% in case of a vector as a stimulus the time step
% D: the strength of additive white noise
tau = 0.01;
if nargin < 4
D = 1e0;
end
vreset = 0.0;
vthresh = 10.0;
dt = 1e-4;
if length( input ) == 1
input = input * ones( ceil( tmaxdt/dt ), 1 );
else
dt = tmaxdt;
end
spikes = cell( trials, 1 );
for k=1:trials
times = [];
j = 1;
v = vreset;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
v = v + ( - v + noise(i) + input(i))*dt/tau;
if v >= vthresh
v = vreset;
times(j) = i*dt;
j = j + 1;
end
end
spikes{k} = times;
end
end

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pointprocesses/code/pifouspikes.m Normal file
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function spikes = pifouspikes( trials, input, tmaxdt, D, outau )
% Generate spike times of a perfect integrate-and-fire neuron
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmaxdt: in case of a single value stimulus the duration of a trial
% in case of a vector as a stimulus the time step
% D: the strength of additive white noise
% outau: time constant of the colored noise
tau = 0.01;
if nargin < 4
D = 1e0;
end
if nargin < 5
outau = 1.0;
end
vreset = 0.0;
vthresh = 10.0;
dt = 1e-4;
if length( input ) == 1
input = input * ones( ceil( tmaxdt/dt ), 1 );
else
dt = tmaxdt;
end
spikes = cell( trials, 1 );
for k=1:trials
times = [];
j = 1;
n = 0.0;
v = vreset;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
n = n + ( - n + noise(i))*dt/outau;
v = v + ( n + input(i))*dt/tau;
if v >= vthresh
v = vreset;
times(j) = i*dt;
j = j + 1;
end
end
spikes{k} = times;
end
end

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pointprocesses/code/pifspikes.m Normal file
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function spikes = pifspikes( trials, input, tmaxdt, D )
% Generate spike times of a perfect integrate-and-fire neuron
% trials: the number of trials to be generated
% input: the stimulus either as a single value or as a vector
% tmaxdt: in case of a single value stimulus the duration of a trial
% in case of a vector as a stimulus the time step
% D: the strength of additive white noise
tau = 0.01;
if nargin < 4
D = 1e-1;
end
vreset = 0.0;
vthresh = 10.0;
dt = 1e-4;
if length( input ) == 1
input = input * ones( ceil( tmaxdt/dt ), 1 );
else
dt = tmaxdt;
end
spikes = cell( trials, 1 );
for k=1:trials
times = [];
j = 1;
v = vreset;
noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
for i=1:length( noise )
v = v + ( noise(i) + input(i))*dt/tau;
if v >= vthresh
v = vreset;
times(j) = i*dt;
j = j + 1;
end
end
spikes{k} = times;
end
end

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pointprocesses/code/poissonisih.m Normal file
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rate = 100.0;
trials = 50;
tmax = 100.0;
% generate spikes:
spikes = poissonspikes( trials, rate, tmax );
% interspike intervals:
isivec = isis( spikes );
% histogram
f = figure( 1 );
isihist( isivec );
hold on
% theoretical density:
xmax = 5.0/rate;
x = 0:0.0001:xmax;
y = rate*exp(-rate*x);
plot( 1000.0*x, y, 'r', 'LineWidth', 3 );
% plot details:
title( sprintf( 'Poisson spike trains, rate=%g Hz, nisi=%d', rate, length( isivec ) ) )
xlim( [ 0.0 1000.0*xmax ] )
ylim( [ 0.0 1.1*rate ] )
legend( 'data', 'poisson' )
hold off
% serial correlations:
f = figure( 2 );
isiserialcorr( isivec, 10 );

46
pointprocesses/code/poissonisistats.m Normal file
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rates = 1:1:100;
avisi = [];
sdisi = [];
cvisi = [];
for rate = rates
spikes = poissonspikes( 10, rate, 100.0 );
isivec = isis( spikes );
av = mean( isivec );
sd = std( isivec );
cv = sd/av;
avisi = [ avisi av ];
sdisi = [ sdisi sd ];
cvisi = [ cvisi cv ];
end
f = figure;
subplot( 1, 3, 1 );
scatter( rates, 1000.0*avisi, 'b', 'filled' );
hold on;
plot( rates, 1000.0./rates, 'r' );
hold off;
xlabel( 'Rate \lambda [Hz]' );
ylim( [ 0 1000 ] );
title( 'Mean ISI [ms]' );
legend( 'simulation', 'theory 1/\lambda' );
subplot( 1, 3, 2 );
scatter( rates, 1000.0*sdisi, 'b', 'filled' );
hold on;
plot( rates, 1000.0./rates, 'r' );
hold off;
xlabel( 'Rate \lambda [Hz]' );
ylim( [ 0 1000 ] )
title( 'Standard deviation ISI [ms]' );
legend( 'simulation', 'theory 1/\lambda' );
subplot( 1, 3, 3 );
scatter( rates, cvisi, 'b', 'filled' );
hold on;
plot( rates, ones( size( rates ) ), 'r' );
hold off;
xlabel( 'Rate \lambda [Hz]' );
ylim( [ 0 2 ] )
title( 'CV' );
legend( 'simulation', 'theory' );

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pointprocesses/code/poissonspikes.m Normal file
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function spikes = poissonspikes( trials, rate, tmax )
% Generate spike times of a homogeneous poisson process
% trials: number of trials that should be generated
% rate: the rate of the Poisson process in Hertz
% tmax: the duration of each trial in seconds
% returns a cell array of vectors of spike times
dt = 3.33e-5;
p = rate*dt; % probability of event per bin of width dt
% make sure p is small enough:
if p > 0.1
p = 0.1
dt = p/rate;
end
spikes = cell( trials, 1 );
for k=1:trials
x = rand( 1, round(tmax/dt) ); % uniform random numbers for each bin
spikes{k} = find( x < p ) * dt;
end
end

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pointprocesses/code/savefigpdf.m Normal file
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function savefigpdf( fig, name, width, height )
% Saves figure fig in pdf file name.pdf with appropriately set page size
% and fonts
% default width:
if nargin < 3
width = 11.7;
end
% default height:
if nargin < 4
height = 9.0;
end
% paper:
set( fig, 'PaperUnits', 'centimeters' );
set( fig, 'PaperSize', [width height] );
set( fig, 'PaperPosition', [0.0 0.0 width height] );
set( fig, 'Color', 'white')
% font:
set( findall( fig, 'type', 'axes' ), 'FontSize', 12 )
set( findall( fig, 'type', 'text' ), 'FontSize', 12 )
% save:
saveas( fig, name, 'pdf' )
end

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pointprocesses/code/spikeraster.m Normal file
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function spikeraster( spikes )
% Display a spike raster of the spike times given in spikes.
% spikes: a cell array of vectors of spike times
ntrials = length(spikes);
for k = 1:ntrials
times = 1000.0*spikes{k}; % conversion to ms
for i = 1:length( times )
line([times(i) times(i)],[k-0.4 k+0.4], 'Color', 'k' );
end
end
xlabel( 'Time [ms]' );
ylabel( 'Trials');
ylim( [ 0.3 ntrials+0.7 ] )
end