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[pointprocesses] moved exercise codes to exercise folder

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Jan Benda 2021-01-19 00:10:39 +01:00
parent 2bc8119e2e
commit 84b14d72ac
20 changed files with 341 additions and 81 deletions
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25
pointprocesses/code/counts.m Normal file
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function n = counts(spikes, w)
% Count spikes in time windows.
%
% Arguments:
% spikes: a cell array of vectors of spike times in seconds
% w: duration of window in seconds for computing the counts
%
% Returns:
% n: vector with spike counts
tmax = spikes{1}(end);
n = [];
for k = 1:length(spikes)
times = spikes{k};
% alternative 1: count the number of spikes in each window:
% for tk = 0:w:tmax-w
% nn = sum((times >= tk) & (times < tk+w));
% % nn = length(find((times >= tk) & (times < tk+w)));
% n = [n, nn];
% end
% alternative 2: use the hist() function to do that!
tbins = 0.5*w:w:tmax-0.5*w;
nn = hist(times, tbins);
n = [n, nn];
end
end

2
pointprocesses/code/plotcounthist.m
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@ -1,4 +1,4 @@
function counthist(spikes, w)
function plotcounthist(spikes, w)
% Plot histogram of spike counts.
%
% Arguments:

30
pointprocesses/code/spikecounts.m
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@ -1,30 +0,0 @@
function counts = spikecounts(spikes, w)
% Compute vector of spike counts.
%
% counts = spikecounts(spikes, w)
%
% Arguments:
% spikes: a cell array of vectors of spike times in seconds
% w: observation window duration in seconds for computing the counts
%
% Returns:
% counts: vector of spike counts
% collect spike counts:
tmax = spikes{1}(end);
counts = [];
for k = 1:length(spikes)
times = spikes{k};
% method 1: count the number of spikes in each window:
% for tk = 0:w:tmax-w
% nn = sum((times >= tk) & (times < tk+w));
% %nn = length(times((times >= tk) & (times < tk+w)));
% %nn = length(find((times >= tk) & (times < tk+w)));
% counts = [counts nn];
% end
% method 2: use the hist() function to do that!
tbins = 0.5*w:w:tmax-0.5*w;
nn = hist(times, tbins);
counts = [counts nn];
end
end

17
pointprocesses/code/spikecountshists.m
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@ -1,17 +0,0 @@
w = 0.1;
bins = 0.0:1.0:10.0;
counts{1} = spikecounts(poissonspikes, w);
counts{2} = spikecounts(pifouspikes, w);
counts{3} = spikecounts(lifadaptspikes, w);
titles = {'Poisson', 'PIF OU', 'LIF adapt'};
for k = 1:3
subplot(1, 3, k);
[h, b] = hist(counts{k}, bins);
bar(b, h/sum(h));
title(titles{k})
xlabel('Spike count');
xlim([-0.5, 8.5]);
ylim([0.0 0.8]);
end
savefigpdf(gcf, 'spikecountshists.pdf', 20, 7);

25
pointprocesses/exercises/counts.m Normal file
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function n = counts(spikes, w)
% Count spikes in time windows.
%
% Arguments:
% spikes: a cell array of vectors of spike times in seconds
% w: duration of window in seconds for computing the counts
%
% Returns:
% n: vector with spike counts
tmax = spikes{1}(end);
n = [];
for k = 1:length(spikes)
times = spikes{k};
% alternative 1: count the number of spikes in each window:
% for tk = 0:w:tmax-w
% nn = sum((times >= tk) & (times < tk+w));
% % nn = length(find((times >= tk) & (times < tk+w)));
% n = [n, nn];
% end
% alternative 2: use the hist() function to do that!
tbins = 0.5*w:w:tmax-0.5*w;
nn = hist(times, tbins);
n = [n, nn];
end
end

32
pointprocesses/exercises/fanoplot.m Normal file
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function fanoplot(spikes, titles)
% Plots fano factor as a function of window size.
%
% Arguments:
% spikes: a cell array of vectors of spike times
% titles: string that is used as a title for the plots
windows = logspace(-3.0, -0.5, 100);
mc = zeros(1, length(windows));
vc = zeros(1, length(windows));
for j = 1:length(windows)
w = windows(j);
spikecounts = counts(spikes, w);
mc(j) = mean(spikecounts);
vc(j) = var(spikecounts);
end
subplot(1, 2, 1);
scatter(mc, vc, 'filled');
title(titles);
xlabel('Mean count');
ylabel('Count variance');
subplot(1, 2, 2);
scatter(1000.0*windows, vc ./ mc, 'filled');
title(titles);
xlabel('Window [ms]');
ylabel('Fano factor');
xlim(1000.0*[windows(1) windows(end)])
ylim([0.0 1.1]);
set(gca, 'XScale', 'log');
end

9
pointprocesses/exercises/fanoplots.m Normal file
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spikes{1} = poissonspikes;
spikes{2} = pifouspikes;
spikes{3} = lifadaptspikes;
idents = {'poisson', 'pifou', 'lifadapt'};
for k = 1:3
figure(k)
fanoplot(spikes{k}, titles{k});
savefigpdf(gcf, sprintf('fanoplots%s.pdf', idents{k}), 20, 7);
end

29
pointprocesses/exercises/isihist.m Normal file
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function [pdf, centers] = isihist(isis, binwidth)
% Compute normalized histogram of interspike intervals.
%
% [pdf, centers] = isihist(isis, binwidth)
%
% Arguments:
% isis: vector of interspike intervals in seconds
% binwidth: optional width in seconds to be used for the isi bins
%
% Returns:
% pdf: vector with pdf of interspike intervals in Hertz
% centers: vector with centers of interspikeintervalls in seconds
if nargin < 2
% compute good binwidth:
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 data:
[nelements, centers] = hist(isis, bins);
% normalization (integral = 1):
pdf = nelements / sum(nelements) / binwidth;
end

16
pointprocesses/exercises/isis.m Normal file
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function isivec = isis(spikes)
% returns a single list of isis computed from all trials in spikes
%
% Arguments:
% spikes: a cell array of vectors of spike times in seconds
%
% Returns:
% isivec: a column vector with all the interspike intervals
isivec = [];
for k = 1:length(spikes)
difftimes = diff(spikes{k});
% difftimes(:) ensures a column vector
% regardless of the type of vector in spikes{k}
isivec = [isivec; difftimes(:)];
end
end

21
pointprocesses/exercises/isiserialcorr.m Normal file
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@ -0,0 +1,21 @@
function [isicorr, lags] = isiserialcorr(isivec, maxlag)
% serial correlation of interspike intervals
%
% Arguments:
% isivec: vector of interspike intervals in seconds
% maxlag: the maximum lag
%
% Returns:
% isicorr: vector with the serial correlations for lag 0 to maxlag
% lags: vector with the lags corresponding to isicorr
lags = 0:maxlag;
isicorr = zeros(size(lags));
for k = 1:length(lags)
lag = lags(k);
if length(isivec) > lag+10 % ensure "enough" data
% NOTE: the arguments to corr must be column vectors!
% We insure this already in the isis() function.
isicorr(k) = corr(isivec(1:end-lag), isivec(lag+1:end));
end
end
end

31
pointprocesses/exercises/plotisihist.m Normal file
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@ -0,0 +1,31 @@
function plotisihist(isis, binwidth)
% Plot and annotate histogram of interspike intervals.
%
% plotisihist(isis, binwidth)
%
% Arguments:
% isis: vector of interspike intervals in seconds
% binwidth: optional width in seconds to be used for the isi bins
% compute normalized histogram:
if nargin < 2
[pdf, centers] = isihist(isis);
else
[pdf, centers] = isihist(isis, binwidth);
end
% plot:
bar(1000.0*centers, pdf); % milliseconds on x-axis
xlabel('ISI [ms]')
ylabel('p(ISI) [1/s]')
% annotation:
misi = mean(isis);
sdisi = std(isis);
text(0.95, 0.8, sprintf('mean=%.1f ms', 1000.0*misi), ...
'Units', 'normalized', 'HorizontalAlignment', 'right')
text(0.95, 0.7, sprintf('std=%.1f ms', 1000.0*sdisi), ...
'Units', 'normalized', 'HorizontalAlignment', 'right')
text(0.95, 0.6, sprintf('CV=%.2f', sdisi/misi), ...
'Units', 'normalized', 'HorizontalAlignment', 'right')
end

0
pointprocesses/code/plotisihs.m → pointprocesses/exercises/plotisihs.m
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14
pointprocesses/exercises/plotisiserialcorr.m Normal file
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function isicorr = plotisiserialcorr(isivec, maxlag)
% plot serial correlation of interspike intervals
%
% Arguments:
% isivec: vector of interspike intervals in seconds
% maxlag: the maximum lag
[isicorr, lags] = isiserialcorr(isivec, maxlag);
plot(lags, isicorr, '-b');
hold on;
scatter(lags, isicorr, 20.0, 'b', 'filled');
hold off;
xlabel('Lag k')
ylabel('\rho_k')
end

12
pointprocesses/exercises/plotpoissonisih.m Normal file
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@ -0,0 +1,12 @@
maxisi = 300.0;
poissonisis = isis(poissonspikes);
rate = 1.0/mean(poissonisis);
plotisihist(poissonisis, 0.001);
tt = linspace(0.0, 0.001*maxisi, 200);
pexp = rate*exp(-tt*rate);
hold on;
plot(1000.0*tt, pexp, 'r')
hold off;
xlim([0, maxisi])
title('Poisson');
savefigpdf(gcf, 'poissonisihist.pdf', 10, 7);

6
pointprocesses/code/plotserialcorr.m → pointprocesses/exercises/plotserialcorr.m
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@ -1,17 +1,17 @@
maxlag = 10;
rrange = [-0.5, 1.05];
subplot(1, 3, 1);
isiserialcorr(poissonisis, maxlag);
plotisiserialcorr(poissonisis, maxlag);
ylim(rrange)
title('Poisson');
subplot(1, 3, 2);
isiserialcorr(pifouisis, maxlag);
plotisiserialcorr(pifouisis, maxlag);
ylim(rrange)
title('PIF OU');
subplot(1, 3, 3);
isiserialcorr(lifadaptisis, maxlag);
plotisiserialcorr(lifadaptisis, maxlag);
ylim(rrange)
title('LIF adapt');
savefigpdf(gcf, 'serialcorr.pdf', 20, 7);

0
pointprocesses/code/plotspikeraster.m → pointprocesses/exercises/plotspikeraster.m
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80
pointprocesses/exercises/pointprocesses-1.tex
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@ -15,6 +15,9 @@
\begin{questions}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\question \qt{Read in chapter 10 on ``Spike-train analysis'' sections 10.1 -- 10.5!}\vspace{-3ex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\question \qt{Statistics of interspike intervals}
Download the files \code{poisson.mat},
@ -61,11 +64,12 @@
of the spike. When appropriate, the function should use milliseconds
for the time axis instead of seconds.
Use this function to plot the first second of the
spike rasters of the three neurons.
Use this function to plot the first second of the spike rasters of
the three neurons. Carefully look at the raster plots. How do the
spike rasters differ between the three neurons?
\begin{solution}
\lstinputlisting{../code/rasterplot.m}
\lstinputlisting{../code/plotspikeraster.m}
\lstinputlisting{rasterplot.m}
\lstinputlisting{plotspikeraster.m}
\mbox{}\\[-3ex]
\colorbox{white}{\includegraphics[width=1\textwidth]{spikeraster}}
\end{solution}
@ -73,7 +77,7 @@
\part Write a function that returns a single vector containing the
interspike intervals of all trials of spike times.
\begin{solution}
\lstinputlisting{../code/isis.m}
\lstinputlisting{isis.m}
\end{solution}
\part Write a function that computes an estimate of the
@ -90,33 +94,51 @@
the standard deviation and the coefficient of variation and
display them in the plot as well.
Use this and the previous functions to compare the
interspike interval statistics of the three neurons.
Use this and the previous functions to compare the interspike
interval statistics of the three neurons. How do the ISI
histograms differ between the three neurons?
\begin{solution}
\lstinputlisting{../code/isihist.m}
\lstinputlisting{../code/plotisihist.m}
\lstinputlisting{../code/plotisihs.m}
\lstinputlisting{isihist.m}
\lstinputlisting{plotisihist.m}
\lstinputlisting{plotisihs.m}
\mbox{}\\[-3ex]
\colorbox{white}{\includegraphics[width=1\textwidth]{isihist}}
\end{solution}
\part Compare the interspike interval histogram of the Poisson
spike train to the expected exponential distribution
\[ p(T) = \lambda e^{-\lambda T} \; .\] of a Poisson process with
firing rate $\lambda$. Estimate the firing rate from the inverse
of the mean interspike interval.
\begin{solution}
\lstinputlisting{plotpoissonisih.m}
%\mbox{}\\[-3ex]
%\colorbox{white}{\includegraphics[width=1\textwidth]{poissonisihist}}
\end{solution}
% XXX Add return map!!! XXX
\part Write a function that computes and plots the serial
correlations of interspike intervals for lags upto
\code{maxlag}. The serial correlations $\rho_k$ for lag $k$ of the
interspike intervals $T_i$ are the correlation coefficients
between interspike intervals $T_i$ and the intervals $T_{i+k}$
that are shifted by lag $k$:
\part Write a function that computes the serial correlations of
interspike intervals for lags up to \code{maxlag}. The serial
correlations $\rho_k$ for lag $k$ of the interspike intervals
$T_i$ are the correlation coefficients between interspike
intervals $T_i$ and the intervals $T_{i+k}$ that are shifted by
lag $k$:
\[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i -
\langle T \rangle) \rangle}{\langle (T_i - \langle T
\rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm
var}(T_i)} = {\rm corr}(T_{i+k}, T_i) \]
Use this function to compare the serial correlations of the
interspike intervals of the three neurons.
Write another function that plots the serial correlations.
Use the functions to compare the serial correlations of the
interspike intervals of the three neurons. What do the serial
correlations mean? How do they relate to what you see in the
raster plots? Do the serial correlations of the Poisson spike
train match the expectations?
\begin{solution}
\lstinputlisting{../code/isiserialcorr.m}
\lstinputlisting{../code/plotserialcorr.m}
\lstinputlisting{isiserialcorr.m}
\lstinputlisting{plotisiserialcorr.m}
\lstinputlisting{plotserialcorr.m}
\colorbox{white}{\includegraphics[width=1\textwidth]{serialcorr}}
\end{solution}
@ -127,16 +149,22 @@
\question \qt{Statistics of spike counts}
Now let's have a look at the statistics of the spike counts.
\begin{parts}
\part Write a function that counts and returns the number of
spikes in windows of a given width $W$.
\part Write a function that counts and returns a vector with the
number of spikes in windows of a given width $W$.
Use this function to generate a properly normalized histogram of
spike counts for the data of the three types of neurons. Use
100\,ms for the window width.
Compare the distributions with the Poisson distribution expected
for a Poisson spike train:
\[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \; , \] where
$\lambda$ is the rate of the spike train that you should estimate
from the data.
\begin{solution}
\lstinputlisting{../code/spikecounts.m}
\lstinputlisting{counts.m}
\newsolutionpage
\lstinputlisting{../code/spikecountshists.m}
\lstinputlisting{spikecounthists.m}
\colorbox{white}{\includegraphics[width=1\textwidth]{spikecountshists}}
\end{solution}
@ -148,9 +176,9 @@
(the mean spike count increases for larger window widths). The
other plot showing the Fano factor as a function of window width.
\begin{solution}
\lstinputlisting{../code/fanoplot.m}
\lstinputlisting{fanoplot.m}
\newsolutionpage
\lstinputlisting{../code/fanoplots.m}
\lstinputlisting{fanoplots.m}
\colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotspoisson}}
\colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotspifou}}
\colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotslifadapt}}

4
pointprocesses/exercises/pointprocesses-2.tex
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@ -103,7 +103,7 @@ f\"ur gen\"ugend kleine $\Delta t$.
soll. Hinweis: es gibt eine \code{matlab} Funktion, die die
Fakult\"at $n!$ berechnet.
\begin{solution}
\lstinputlisting{../code/counthist.m}
\lstinputlisting{counthist.m}
\colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}}
\colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}}
\end{solution}
@ -115,7 +115,7 @@ f\"ur gen\"ugend kleine $\Delta t$.
den Ergebnissen angefertigt werden: (i) Varianz gegen Mittelwert der counts.
(ii) Fano Faktor als Funktion der Fensterbreite.
\begin{solution}
\lstinputlisting{../code/fano.m}
\lstinputlisting{fanoplot.m}
\colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonfano100hz}}
\end{solution}

43
pointprocesses/exercises/rasterplot.m Normal file
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@ -0,0 +1,43 @@
function rasterplot(spikes, tmax)
% Display a spike raster of the spike times given in spikes.
%
% rasterplot(spikes, tmax)
%
% Arguments:
% spikes: a cell array of vectors of spike times in seconds
% tmax: plot spike raster up to tmax seconds
in_msecs = tmax < 1.5
spiketimes = [];
trials = [];
ntrials = length(spikes);
for k = 1:ntrials
times = spikes{k};
times = times(times<tmax);
if in_msecs
times = 1000.0*times; % conversion to ms
end
% (x,y) pairs for start and stop of stroke
% plus nan separating strokes:
spiketimes = [spiketimes, ...
[times(:)'; times(:)'; times(:)'*nan]];
trials = [trials, ...
[ones(1, length(times)) * (k-0.4); ...
ones(1, length(times)) * (k+0.4); ...
ones(1, length(times)) * nan]];
end
% convert matrices into simple vectors of (x,y) pairs:
spiketimes = spiketimes(:);
trials = trials(:);
% plotting this is lightning fast:
plot(spiketimes, trials, 'k')
if in_msecs
xlabel('Time [ms]');
xlim([0.0 1000.0*tmax]);
else
xlabel('Time [s]');
xlim([0.0 tmax]);
end
ylabel('Trials');
ylim([0.3 ntrials+0.7]);
end

22
pointprocesses/exercises/spikecountshists.m Normal file
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@ -0,0 +1,22 @@
w = 0.1;
bins = 0:1:10;
spikecounts{1} = counts(poissonspikes, w);
spikecounts{2} = counts(pifouspikes, w);
spikecounts{3} = counts(lifadaptspikes, w);
titles = {'Poisson', 'PIF OU', 'LIF adapt'};
for k = 1:3
subplot(1, 3, k);
[h, b] = hist(spikecounts{k}, bins);
bar(b, h/sum(h));
mu = mean(spikecounts{k});
ppois = poisspdf(bins, mu);
hold on;
scatter(bins, ppois, 'filled');
hold off;
title(titles{k})
xlabel('Spike count');
xlim([-0.5, 8.5]);
ylim([0.0 0.8]);
end
savefigpdf(gcf, 'spikecountshists.pdf', 20, 7);