Handling of underscores in code filenames. Added code to pointprocesses.
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27
header.tex
27
header.tex
@ -10,6 +10,9 @@
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\newcommand{\tr}[2]{#2} % de
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\usepackage[ngerman]{babel}
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%%%% encoding %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[T1]{fontenc}
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%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[left=25mm,right=25mm,top=20mm,bottom=30mm]{geometry}
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\usepackage{pslatex} % nice font for pdf file
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@ -216,24 +219,34 @@
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% Innerhalb der exercise Umgebung ist enumerate umdefiniert, um (a), (b), (c), .. zu erzeugen.
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\usepackage{ifthen}
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\usepackage{mdframed}
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\usepackage{xstring}
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\newcommand{\codepath}{}
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\DeclareFloatingEnvironment[
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fileext=loe,
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listname={\tr{Exercises}{\"Ubungen}},
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name={\tr{Exercise}{\"Ubung}},
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placement=t
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]{exercisef}
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\newcounter{maxexercise}
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\setcounter{maxexercise}{10000} % show listings up to exercise maxexercise
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\newcounter{exercise}[chapter]
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\renewcommand{\theexercise}{\arabic{exercise}}
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\newcommand{\codepath}{}
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\newenvironment{exercise}[2]%
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{\newcommand{\exercisesource}{#1}%
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\newcommand{\exercisefile}{\protect\StrSubstitute{#1}{_}{\_}}%
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\newcommand{\exerciseoutput}{#2}%
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\setlength{\fboxsep}{2mm}%
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\newcommand{\saveenumi}{\theenumi}\renewcommand{\labelenumi}{(\alph{enumi})}%
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\stepcounter{exercise}%
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\captionsetup{singlelinecheck=off,hypcap=false,labelfont={large,sf,it,bf},font={large,sf,it,bf},skip={0.5ex}}
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\begin{mdframed}[linewidth=0pt,backgroundcolor=exerciseback]%
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\noindent\textbf{\tr{Exercise}{\"Ubung} \thechapter.\theexercise:}\newline}%
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\captionof{exercisef}[\exercisefile]{}%
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\captionsetup{font={normal,sf,it}}%
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}%
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{\ifthenelse{\equal{\exercisesource}{}}{}%
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{\ifthenelse{\value{exercise}>\value{maxexercise}}{}%
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{\lstinputlisting[belowskip=0pt]{\codepath\exercisesource}%
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{\addtocounter{lstlisting}{-1}%
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\lstinputlisting[belowskip=0pt,aboveskip=1ex,nolol=true,title={\textbf{Listing:} \exercisefile}]{\codepath\exercisesource}%
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\ifthenelse{\equal{\exerciseoutput}{}}{}%
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{\addtocounter{lstlisting}{-1}\lstinputlisting[language={},title={\textbf{\tr{Output}{Ausgabe}:}},nolol=true,belowskip=0pt]{\codepath\exerciseoutput}}}}%
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{\addtocounter{lstlisting}{-1}%
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\lstinputlisting[language={},title={\textbf{\tr{Output}{Ausgabe}:}},nolol=true,belowskip=0pt]{\codepath\exerciseoutput}}}}%
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\end{mdframed}%
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\renewcommand{\theenumi}{\saveenumi}}
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@ -1,9 +1,13 @@
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function [counts, bins] = counthist(spikes, w)
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% computes count histogram and compare them with Poisson distribution
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% computes count histogram and compare with Poisson distribution
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%
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% [counts, bins] = counthist(spikes, w)
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%
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% Arguments:
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% spikes: a cell array of vectors of spike times in seconds
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% w: observation window duration in seconds for computing the counts
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%
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% Returns:
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% counts: the histogram of counts normalized to probabilities
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% bins: the bin centers for the histogram
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@ -27,11 +31,14 @@ function [counts, bins] = counthist(spikes, w)
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rate = (length(times)-1)/(times(end) - times(1));
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r = [ r rate ];
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end
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% histogram of spike counts:
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maxn = max( n );
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[counts, bins ] = hist( n, 0:1:maxn+10 );
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% normalize to probabilities:
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counts = counts / sum( counts );
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% plot:
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if nargout == 0
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bar( bins, counts );
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hold on;
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29
pointprocesses/code/isi_hist.m
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29
pointprocesses/code/isi_hist.m
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@ -0,0 +1,29 @@
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function [pdf, centers] = isi_hist(isis, binwidth)
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% Compute normalized histogram of interspike intervals.
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%
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% [pdf, centers] = isi_hist(isis, binwidth)
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%
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% Arguments:
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% isis: vector of interspike intervals in seconds
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% binwidth: optional width in seconds to be used for the isi bins
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%
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% Returns:
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% pdf: vector with probability density of interspike intervals in Hz
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% centers: vector with corresponding centers of interspikeintervalls in seconds
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if nargin < 2
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% compute good binwidth:
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nperbin = 200; % average number of data points per bin
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bins = length( isis )/nperbin; % number of bins
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binwidth = max( isis )/bins;
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if binwidth < 5e-4 % half a millisecond
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binwidth = 5e-4;
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end
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end
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bins = 0.5*binwidth:binwidth:max(isis);
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% histogram data:
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[ nelements, centers ] = hist(isis, bins);
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% normalization (integral = 1):
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pdf = nelements / sum(nelements) / binwidth;
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end
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@ -1,34 +0,0 @@
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function isihist( isis, binwidth )
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% plot histogram of interspike intervals
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%
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% isihist(isis, binwidth)
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% isis: vector of interspike intervals in seconds
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% binwidth: optional width in seconds to be used for the isi bins
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if nargin < 2
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nperbin = 200; % average number of data points per bin
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bins = length( isis )/nperbin; % number of bins
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binwidth = max( isis )/bins;
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if binwidth < 5e-4 % half a millisecond
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binwidth = 5e-4;
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end
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end
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bins = 0.5*binwidth:binwidth:max(isis);
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% histogram:
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[ nelements, centers ] = hist( isis, bins );
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% normalization (integral = 1):
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nelements = nelements / sum( nelements ) / binwidth;
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% plot:
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bar( 1000.0*centers, nelements );
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xlabel( 'ISI [ms]' )
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ylabel( 'p(ISI) [1/s]')
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% annotation:
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misi = mean( isis );
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sdisi = std( isis );
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disi = sdisi^2.0/2.0/misi^3;
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text( 0.95, 0.8, sprintf( 'mean=%.1f ms', 1000.0*misi ), 'Units', 'normalized', 'HorizontalAlignment', 'right' )
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text( 0.95, 0.7, sprintf( 'std=%.1f ms', 1000.0*sdisi ), 'Units', 'normalized', 'HorizontalAlignment', 'right' )
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text( 0.95, 0.6, sprintf( 'CV=%.2f', sdisi/misi ), 'Units', 'normalized', 'HorizontalAlignment', 'right' )
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%text( 0.5, 0.3, sprintf( 'D=%.1f Hz', disi ), 'Units', 'normalized' )
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end
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@ -2,8 +2,12 @@ function isicorr = isiserialcorr( isis, maxlag )
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% serial correlation of interspike intervals
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%
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% isicorr = isiserialcorr(isis, maxlag)
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%
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% Arguments:
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% isis: vector of interspike intervals in seconds
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% maxlag: the maximum lag in seconds
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%
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% Returns:
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% isicorr: vector with the serial correlations for lag 0 to maxlag
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lags = 0:maxlag;
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@ -11,7 +15,7 @@ function isicorr = isiserialcorr( isis, maxlag )
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for k = 1:length(lags)
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lag = lags(k);
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if length( isis ) > lag+10 % ensure "enough" data
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% DANGER: the arguments to corr must be column vectors!
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% NOTE: the arguments to corr must be column vectors!
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% We insure this in the isis() function that generats the isis.
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isicorr(k) = corr( isis(1:end-lag), isis(lag+1:end) );
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end
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28
pointprocesses/code/plot_isi_hist.m
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28
pointprocesses/code/plot_isi_hist.m
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@ -0,0 +1,28 @@
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function plot_isi_hist(isis, binwidth)
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% Plot and annotate histogram of interspike intervals.
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%
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% isihist(isis, binwidth)
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%
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% Arguments:
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% isis: vector of interspike intervals in seconds
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% binwidth: optional width in seconds to be used for the isi bins
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if nargin < 2
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[pdf, centers] = isi_hist(isis);
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else
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[pdf, centers] = isi_hist(isis, binwidth);
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end
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bar(1000.0*centers, nelements); % milliseconds on x-axis
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xlabel('ISI [ms]')
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ylabel('p(ISI) [1/s]')
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% annotation:
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misi = mean(isis);
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sdisi = std(isis);
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disi = sdisi^2.0/2.0/misi^3;
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text(0.95, 0.8, sprintf('mean=%.1f ms', 1000.0*misi), 'Units', 'normalized', 'HorizontalAlignment', 'right')
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text(0.95, 0.7, sprintf('std=%.1f ms', 1000.0*sdisi), 'Units', 'normalized', 'HorizontalAlignment', 'right')
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text(0.95, 0.6, sprintf('CV=%.2f', sdisi/misi), 'Units', 'normalized', 'HorizontalAlignment', 'right')
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%text(0.5, 0.3, sprintf('D=%.1f Hz', disi), 'Units', 'normalized')
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end
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@ -1,10 +1,14 @@
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function spikes = poissonspikes(trials, rate, tmax)
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% Generate spike times of a homogeneous poisson process
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% Generate spike times of a homogeneous poisson process.
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%
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% spikes = poissonspikes(trials, rate, tmax)
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%
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% Arguments:
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% trials: number of trials that should be generated
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% rate: the rate of the Poisson process in Hertz
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% tmax: the duration of each trial in seconds
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%
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% Returns:
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% spikes: a cell array of vectors of spike times in seconds
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dt = 3.33e-5;
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@ -16,7 +20,8 @@ function spikes = poissonspikes( trials, rate, tmax )
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end
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spikes = cell(trials, 1);
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for k=1:trials
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x = rand(round(tmax/dt), 1); % uniform random numbers for each bin
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% uniform random numbers for each bin:
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x = rand(round(tmax/dt), 1);
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spikes{k} = find(x < p) * dt;
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end
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end
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@ -11,7 +11,7 @@ all: pdf slides thumbs
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# script:
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pdf : $(BASENAME)-chapter.pdf
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$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex $(GPTTEXFILES) $(PYPDFFILES)
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$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex ../../header.tex $(GPTTEXFILES) $(PYPDFFILES)
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CHAPTER=$$(( $$(sed -n -e '/contentsline {chapter}/{s/.*numberline {\([0123456789]*\)}.*/\1/; p}' $(BASENAME).aux) - 1 )); \
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PAGE=$$(sed -n -e '/contentsline {chapter}/{s/.*numberline {.*}.*}{\(.*\)}{chapter.*/\1/; p}' $(BASENAME).aux); \
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sed -i -e "s/setcounter{page}{.*}/setcounter{page}{$$PAGE}/; s/setcounter{chapter}{.*}/setcounter{chapter}{$$CHAPTER}/" $(BASENAME)-chapter.tex
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@ -54,7 +54,7 @@ erzeugt. Zum Beispiel:
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\begin{figure}[t]
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\texpicture{pointprocessscetch}
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\titlecaption{\label{pointprocessscetchfig} Statistik von
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Punktprozessesen.}{Ein Punktprozess ist eine Abfolge von
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Punktprozessen.}{Ein Punktprozess ist eine Abfolge von
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Zeitpunkten $t_i$ die auch durch die Intervalle $T_i=t_{i+1}-t_i$
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oder die Anzahl der Ereignisse $n_i$ beschrieben werden kann. }
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\end{figure}
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@ -89,7 +89,7 @@ kann mit den \"ublichen Gr\"o{\ss}en beschrieben werden.
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\end{figure}
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\begin{exercise}{isis.m}{}
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Schreibe eine Funktion, die aus mehreren trials von Spiketrains die
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Schreibe eine Funktion \code{isis()}, die aus mehreren trials von Spiketrains die
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Interspikeintervalle bestimmt und diese in einem Vektor
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zur\"uckgibt. Jeder trial der Spiketrains ist ein Vektor mit den
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Spikezeiten gegeben in Sekunden als Element in einem \codeterm{cell-array}.
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@ -110,11 +110,18 @@ kann mit den \"ublichen Gr\"o{\ss}en beschrieben werden.
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\frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$.
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\end{itemize}
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\begin{exercise}{isihist.m}{}
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Schreibe eine Funktion, die einen Vektor mit Interspikeintervallen
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entgegennimmt und daraus ein Histogramm der Interspikeintervalle
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plottet. Das Histogramm soll zus\"atzlich mit Mittelwert,
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Standardabweichung und Korrelationskoeffizient der
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\begin{exercise}{isi_hist.m}{}
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Schreibe eine Funktion \code{isi\_hist()}, die einen Vektor mit Interspikeintervallen
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entgegennimmt und daraus ein normalisiertes Histogramm der Interspikeintervalle
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berechnet.
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\end{exercise}
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\begin{exercise}{plot_isi_hist.m}{}
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Schreibe eine Funktion, die die Histogrammdaten der Funktion
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\code{isi\_hist()} entgegennimmt, um das Histogramm zu plotten. Im
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Plot sollen die Interspikeintervalle in Millisekunden aufgetragen
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werden. Das Histogramm soll zus\"atzlich mit Mittelwert,
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Standardabweichung und Variationskoeffizient der
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Interspikeintervalle annotiert werden.
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\end{exercise}
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@ -141,6 +148,11 @@ zwischen aufeinander folgenden Intervallen getrennt durch \enterm{lag} $k$:
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aufgetragen (\figref{returnmapfig}). $\rho_0=1$ (Korrelation jedes
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Intervalls mit sich selber).
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\begin{exercise}{isiserialcorr.m}{}
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Schreibe eine Funktion \code{isiserialcorr()}, die einen Vektor mit Interspikeintervallen
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entgegennimmt und daraus die seriellen Korrelationen berechnet und plottet.
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\end{exercise}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Z\"ahlstatistik}
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@ -180,6 +192,15 @@ Zeit, \determ{Feuerrate}) gemessen in Hertz
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% \titlecaption{\label{fanofig}Fano factor.}{}
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% \end{figure}
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\begin{exercise}{counthist.m}{}
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Schreibe eine Funktion \code{counthist()}, die aus mehreren trials
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von Spiketrains die Verteilung der Anzahl der Spikes in Fenstern
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einer der Funktion \"ubergegebenen Breite bestimmt, das Histogramm
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plottet und zur\"uckgibt. Jeder trial der Spiketrains ist ein Vektor
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mit den Spikezeiten gegeben in Sekunden als Element in einem
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\codeterm{cell-array}.
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\end{exercise}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Homogener Poisson Prozess}
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@ -211,7 +232,7 @@ Zeit ab: $\lambda = \lambda(t)$.
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zweier Poissonprozesse.}{}
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\end{figure}
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Der homogne Poissonprozess hat folgende Eigenschaften:
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Der homogene Poissonprozess hat folgende Eigenschaften:
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\begin{itemize}
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\item Die Intervalle $T$ sind exponentiell verteilt: $p(T) = \lambda e^{-\lambda T}$ (\figref{hompoissonisihfig}).
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\item Das mittlere Intervall ist $\mu_{ISI} = \frac{1}{\lambda}$ .
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@ -233,6 +254,12 @@ Der homogne Poissonprozess hat folgende Eigenschaften:
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\titlecaption{\label{hompoissoncountfig}Z\"ahlstatistik von Poisson Spikes.}{}
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\end{figure}
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\begin{exercise}{poissonspikes.m}{}
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Schreibe eine Funktion \code{poissonspikes()}, die die Spikezeiten
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eines homogenen Poisson-Prozesses mit gegebener Rate in Hertz f\"ur
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eine Anzahl von trials gegebener maximaler L\"ange in Sekunden in
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einem \codeterm{cell-array} zur\"uckgibt.
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\end{exercise}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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@ -13,6 +13,7 @@
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\tableofcontents
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\listoffigures
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\lstlistoflistings
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\listofexercisefs
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\listofiboxfs
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%\listofimportantfs
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