added all my stuff

2014-11-12 18:39:02 +01:00
parent 0fdcf2f82e
commit 350ee7ca2b
160 changed files with 5869 additions and 253 deletions
--- a/pointprocesses/code/colorednoisepdf.m
+++ b/pointprocesses/code/colorednoisepdf.m
@@ -0,0 +1,10 @@
+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
--- a/pointprocesses/code/colorednoisepdfisifit.m
+++ b/pointprocesses/code/colorednoisepdfisifit.m
@@ -0,0 +1,24 @@
+% 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
+
--- a/pointprocesses/code/counthist.m
+++ b/pointprocesses/code/counthist.m
@@ -0,0 +1,38 @@
+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
+
--- a/pointprocesses/code/fano.m
+++ b/pointprocesses/code/fano.m
@@ -0,0 +1,39 @@
+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
+
--- a/pointprocesses/code/inversegauss.m
+++ b/pointprocesses/code/inversegauss.m
@@ -0,0 +1,5 @@
+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
--- a/pointprocesses/code/inversegaussplot.m
+++ b/pointprocesses/code/inversegaussplot.m
@@ -0,0 +1,28 @@
+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
--- a/pointprocesses/code/isihist.m
+++ b/pointprocesses/code/isihist.m
@@ -0,0 +1,32 @@
+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
+
--- a/pointprocesses/code/isireturnmap.m
+++ b/pointprocesses/code/isireturnmap.m
@@ -0,0 +1,24 @@
+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
+
--- a/pointprocesses/code/isis.m
+++ b/pointprocesses/code/isis.m
@@ -0,0 +1,15 @@
+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
+
--- a/pointprocesses/code/isiserialcorr.m
+++ b/pointprocesses/code/isiserialcorr.m
@@ -0,0 +1,26 @@
+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
+
--- a/pointprocesses/code/lifadaptspikes.m
+++ b/pointprocesses/code/lifadaptspikes.m
@@ -0,0 +1,53 @@
+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
--- a/pointprocesses/code/lifboltzmanspikes.m
+++ b/pointprocesses/code/lifboltzmanspikes.m
@@ -0,0 +1,51 @@
+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
--- a/pointprocesses/code/liffano.m
+++ b/pointprocesses/code/liffano.m
@@ -0,0 +1,23 @@
+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 );
--- a/pointprocesses/code/lifficurves.m
+++ b/pointprocesses/code/lifficurves.m
@@ -0,0 +1,36 @@
+% 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
+
+
--- a/pointprocesses/code/lifinputdiscriminationslope.m
+++ b/pointprocesses/code/lifinputdiscriminationslope.m
@@ -0,0 +1,65 @@
+%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 );
--- a/pointprocesses/code/lifinputdiscriminationtime.m
+++ b/pointprocesses/code/lifinputdiscriminationtime.m
@@ -0,0 +1,51 @@
+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 );
--- a/pointprocesses/code/lifisih.m
+++ b/pointprocesses/code/lifisih.m
@@ -0,0 +1,35 @@
+%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 );
--- a/pointprocesses/code/lifisistats.m
+++ b/pointprocesses/code/lifisistats.m
@@ -0,0 +1,63 @@
+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]' );
--- a/pointprocesses/code/lifouadaptspikes.m
+++ b/pointprocesses/code/lifouadaptspikes.m
@@ -0,0 +1,64 @@
+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
--- a/pointprocesses/code/lifouspikes.m
+++ b/pointprocesses/code/lifouspikes.m
@@ -0,0 +1,44 @@
+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
--- a/pointprocesses/code/lifrateisicorr.m
+++ b/pointprocesses/code/lifrateisicorr.m
@@ -0,0 +1,34 @@
+% 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
--- a/pointprocesses/code/lifspikes.m
+++ b/pointprocesses/code/lifspikes.m
@@ -0,0 +1,38 @@
+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
--- a/pointprocesses/code/pifouspikes.m
+++ b/pointprocesses/code/pifouspikes.m
@@ -0,0 +1,44 @@
+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
--- a/pointprocesses/code/pifspikes.m
+++ b/pointprocesses/code/pifspikes.m
@@ -0,0 +1,38 @@
+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
--- a/pointprocesses/code/poissonisih.m
+++ b/pointprocesses/code/poissonisih.m
@@ -0,0 +1,27 @@
+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 );
--- a/pointprocesses/code/poissonisistats.m
+++ b/pointprocesses/code/poissonisistats.m
@@ -0,0 +1,46 @@
+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' );
--- a/pointprocesses/code/poissonspikes.m
+++ b/pointprocesses/code/poissonspikes.m
@@ -0,0 +1,20 @@
+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
--- a/pointprocesses/code/raster.pdf
+++ b/pointprocesses/code/raster.pdf
--- a/pointprocesses/code/savefigpdf.m
+++ b/pointprocesses/code/savefigpdf.m
@@ -0,0 +1,28 @@
+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
+
--- a/pointprocesses/code/spikeraster.m
+++ b/pointprocesses/code/spikeraster.m
@@ -0,0 +1,17 @@
+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
+
--- a/pointprocesses/exercises/hompoissonisih.m
+++ b/pointprocesses/exercises/hompoissonisih.m
@@ -0,0 +1,18 @@
+% generate spike times:
+rate = 20.0;
+spikes = hompoissonspikes( 10, rate, 50.0 );
+% isi histogram:
+isivec = isis( spikes );
+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
--- a/pointprocesses/exercises/hompoissonisistats.m
+++ b/pointprocesses/exercises/hompoissonisistats.m
@@ -0,0 +1,46 @@
+rates = 1:1:100;
+avisi = [];
+sdisi = [];
+cvisi = [];
+
+for rate = rates
+    spikes = hompoissonspikes( 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' );
--- a/pointprocesses/exercises/hompoissonspikes.m
+++ b/pointprocesses/exercises/hompoissonspikes.m
@@ -0,0 +1,19 @@
+function spikes = hompoissonspikes( 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;
+    if p > 0.2
+        p = 0.2
+        dt = p/rate;
+    end
+    x = rand( trials, ceil(tmax/dt) );
+    spikes = cell( trials, 1 );
+    for k=1:trials
+        spikes{k} = find( x(k,:) >= 1.0-p ) * dt;
+    end
+end
--- a/pointprocesses/exercises/iafisistats-solutions.pdf
+++ b/pointprocesses/exercises/iafisistats-solutions.pdf
--- a/pointprocesses/exercises/iafisistats.pdf
+++ b/pointprocesses/exercises/iafisistats.pdf
--- a/pointprocesses/exercises/iafisistats.tex
+++ b/pointprocesses/exercises/iafisistats.tex
@@ -0,0 +1,142 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+\usepackage{graphicx}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+
+\firstpageheader{Scientific Computing}{Integrate-and-fire models}{Oct 28, 2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+\shadedsolutions
+
+\usepackage[mediumspace,mediumqspace,Gray]{SIunits}      % \ohm, \micro
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+ captionpos=t,
+ xleftmargin=2em,
+ xrightmargin=1em,
+ aboveskip=10pt,
+ %title=\lstname,
+ title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
+ }
+
+
+\begin{document}
+
+\sffamily
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{questions}
+  \question \textbf{Statistics of integrate-and-fire neurons}
+  For the following use different variants of the leaky integrate-and-fire models provided in \texttt{lifspikes.m}, 
+  \texttt{lifouspikes.m}, and \texttt{lifadaptspikes.m} do generate some spike train data.
+  Use the functions you wrote for the Poisson process to analyze the statistics of the spike trains.
+  \begin{parts}
+    \part Generate a few trials of the two models for two different inputs
+    that result in qualitatively different spike trains and display
+    them in a raster plot. Decide for a noise strength (good values to try are 0.001, 0.01, 0.1, 1).
+    \begin{solution}
+      \begin{lstlisting}
+spikes = pifspikes( 10, 1.0, 0.5, 0.01 );
+%spikes = pifspikes( 10, 10.0, 0.5, 0.01 );
+%spikes = lifspikes( 10, 11.0, 0.5, 0.001 );
+%spikes = lifspikes( 10, 15.0, 0.5, 0.001 );
+spikeraster( spikes )
+      \end{lstlisting}
+      \mbox{}\\[-3ex]
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster02}}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster10}}\\
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster10}}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster15}}
+    \end{solution}
+
+
+    \part The inverse Gaussian describes the interspike interval distribution of a PIF driven with white noise:
+    \[ p(T) = \frac{1}{\sqrt{4\pi D T^3}}\exp\left[-\frac{(T-\langle T \rangle)^2}{4DT\langle T \rangle^2}\right] \]
+    where $\langle T \rangle$ is the mean interspike interval and 
+    \[ D = \frac{\langle(T - \langle T \rangle)^2\rangle}{2 \langle T \rangle^3} \]
+    is the diffusion coefficient (variance of the interspike intervals
+    $T$ divided by two times the mean cubed). Show in two plots how
+    this distribution depends on $\langle T \rangle$ and $D$.
+    \begin{solution}
+      \lstinputlisting{simulations/inversegauss.m}
+      \lstinputlisting{simulations/inversegaussplot.m}
+      \colorbox{white}{\includegraphics[width=0.98\textwidth]{inversegauss}}
+    \end{solution}
+
+    \part Extent your function plotting an interspike interval histogram
+    to also report the diffusion coefficient $D$.
+    \begin{solution}
+      \begin{lstlisting}
+...
+% annotation:
+misi = mean( isis );
+sdisi = std( isis );
+disi = sdisi^2.0/2.0/misi^3;
+text( 0.6, 0.7, sprintf( 'mean=%.1f ms', 1000.0*misi ), 'Units', 'normalized' )
+text( 0.6, 0.6, sprintf( 'std=%.1f ms', 1000.0*sdisi ), 'Units', 'normalized' )
+text( 0.6, 0.5, sprintf( 'CV=%.2f', sdisi/misi ), 'Units', 'normalized' )
+text( 0.6, 0.4, sprintf( 'D=%.1f Hz', disi ), 'Units', 'normalized' )
+...
+      \end{lstlisting}
+    \end{solution}
+
+    \part Compare intersike interval histograms obtained from the LIF and PIF models with the inverse Gaussian.
+    \begin{solution}
+      \lstinputlisting{simulations/lifisih.m}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih01}}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih10}}\\
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih08}}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih16}}
+    \end{solution}
+
+    \part Plot the firing rate (inverse mean interspike interval),
+    mean interspike interval, the corresponding standard deviation,
+    CV, and diffusion coefficient as a function of the input to the LIF
+    and the PIF with noise strength set to 0.01.
+    \begin{solution}
+      \lstinputlisting{simulations/lifisistats.m}
+      Leaky integrate-and-fire:\\
+      \colorbox{white}{\includegraphics[width=0.8\textwidth]{lifisistats}}\\
+      Perfect integrate-and-fire:\\
+      \colorbox{white}{\includegraphics[width=0.8\textwidth]{pifisistats}}
+    \end{solution}
+
+    \part Plot the firing rate as a function of input of the LIF and the PIF for various values
+    of the noise strength.
+    \begin{solution}
+      \lstinputlisting{simulations/lifficurves.m}
+      Leaky integrate-and-fire:\\
+      \colorbox{white}{\includegraphics[width=0.7\textwidth]{lifficurves}}\\
+      Perfect integrate-and-fire:\\
+      \colorbox{white}{\includegraphics[width=0.7\textwidth]{pifficurves}}
+    \end{solution}
+
+    \part Use the functions for computing serial correlations, count statistics and fano factors
+    to further explore the statistics of the integrate-and-fire models!
+
+  \end{parts}
+  
+\end{questions}
+
+
+\end{document}
--- a/pointprocesses/exercises/inversegauss.pdf
+++ b/pointprocesses/exercises/inversegauss.pdf
--- a/pointprocesses/exercises/lifficurves.pdf
+++ b/pointprocesses/exercises/lifficurves.pdf
--- a/pointprocesses/exercises/lifisih08.pdf
+++ b/pointprocesses/exercises/lifisih08.pdf
--- a/pointprocesses/exercises/lifisih16.pdf
+++ b/pointprocesses/exercises/lifisih16.pdf
--- a/pointprocesses/exercises/lifisistats.pdf
+++ b/pointprocesses/exercises/lifisistats.pdf
--- a/pointprocesses/exercises/lifraster10.pdf
+++ b/pointprocesses/exercises/lifraster10.pdf
--- a/pointprocesses/exercises/lifraster15.pdf
+++ b/pointprocesses/exercises/lifraster15.pdf
--- a/pointprocesses/exercises/pifficurves.pdf
+++ b/pointprocesses/exercises/pifficurves.pdf
--- a/pointprocesses/exercises/pifisih01.pdf
+++ b/pointprocesses/exercises/pifisih01.pdf
--- a/pointprocesses/exercises/pifisih10.pdf
+++ b/pointprocesses/exercises/pifisih10.pdf
--- a/pointprocesses/exercises/pifisistats.pdf
+++ b/pointprocesses/exercises/pifisistats.pdf
--- a/pointprocesses/exercises/pifraster02.pdf
+++ b/pointprocesses/exercises/pifraster02.pdf
--- a/pointprocesses/exercises/pifraster10.pdf
+++ b/pointprocesses/exercises/pifraster10.pdf
--- a/pointprocesses/exercises/poisson-solutions.pdf
+++ b/pointprocesses/exercises/poisson-solutions.pdf
--- a/pointprocesses/exercises/poisson.pdf
+++ b/pointprocesses/exercises/poisson.pdf
--- a/pointprocesses/exercises/poisson.tex
+++ b/pointprocesses/exercises/poisson.tex
@@ -0,0 +1,160 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+\usepackage{graphicx}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+
+\firstpageheader{Scientific Computing}{Homogeneous Poisson process}{Oct 27, 2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+\shadedsolutions
+
+\usepackage[mediumspace,mediumqspace,Gray]{SIunits}      % \ohm, \micro
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+ captionpos=t,
+ xleftmargin=2em,
+ xrightmargin=1em,
+ aboveskip=10pt,
+ %title=\lstname,
+ title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
+ }
+
+
+\begin{document}
+
+\sffamily
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{questions}
+  \question \textbf{Homogeneous Poisson process}
+  We use the Poisson process to generate spike trains on which we can test and imrpove some 
+  standard analysis functions.
+
+  A homogeneous Poisson process of rate $\lambda$ (measured in Hertz) is a point process
+  where the probability of an event is independent of time $t$ and independent of previous events.
+  The probability $P$ of an event within a bin of width $\Delta t$ is 
+  \[ P = \lambda \cdot \Delta t \]
+  for sufficiently small $\Delta t$.
+  \begin{parts}
+
+    \part Write a function that generates $n$ homogeneous Poisson spike trains of a given duration $T_{max}$
+    with rate $\lambda$.
+    \begin{solution}
+      \lstinputlisting{hompoissonspikes.m}
+    \end{solution}
+
+    \part Using this function, generate a few trials and display them in a raster plot.
+    \begin{solution}
+      \lstinputlisting{simulations/spikeraster.m}
+      \begin{lstlisting}
+spikes = hompoissonspikes( 10, 100.0, 0.5 );
+spikeraster( spikes )
+      \end{lstlisting}
+      \mbox{}\\[-3ex]
+      \colorbox{white}{\includegraphics[width=0.7\textwidth]{poissonraster100hz}}
+    \end{solution}
+
+    \part Write a function that extracts a single vector of interspike intervals
+    from the spike times returned by the first function.
+    \begin{solution}
+      \lstinputlisting{simulations/isis.m}
+    \end{solution}
+
+    \part Write a function that plots the interspike-interval histogram
+    from a vector of interspike intervals. The function should also
+    compute the mean, the standard deviation, and the CV of the intervals
+    and display the values in the plot.
+    \begin{solution}
+      \lstinputlisting{simulations/isihist.m}
+    \end{solution}
+
+    \part Compute histograms for Poisson spike trains with rate
+    $\lambda=100$\,Hz. Play around with $T_{max}$ and $n$ and the bin width
+    (start with 1\,ms) of the histogram.
+    How many
+    interspike intervals do you approximately need to get a ``nice''
+    histogram? How long do you need to record from the neuron?
+    \begin{solution}
+      About 5000 intervals for 25 bins. This corresponds to a $5000 / 100\,\hertz = 50\,\second$ recording
+      of a neuron firing with 100\,\hertz.
+    \end{solution}
+
+    \part Compare the histogram with the true distribution of intervals $T$ of the Poisson process
+    \[ p(T) = \lambda e^{-\lambda T} \]
+    for various rates $\lambda$.
+    \begin{solution}
+      \lstinputlisting{hompoissonisih.m}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih100hz}}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih20hz}}
+    \end{solution}
+
+    \part What happens if you make the bin width of the histogram smaller than $\Delta t$ 
+    used for generating the Poisson spikes?
+    \begin{solution}
+      The bins between the discretization have zero entries. Therefore
+      the other ones become higher than they should be.
+    \end{solution}
+
+    \part Plot the mean interspike interval, the corresponding standard deviation, and the CV
+    as a function of the rate $\lambda$ of the Poisson process.
+    Compare the simulations with the theoretical expectations for the dependence on $\lambda$.
+    \begin{solution}
+      \lstinputlisting{hompoissonisistats.m}
+      \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonisistats}}
+    \end{solution}
+
+    \part Write a function that computes serial correlations for the interspike intervals
+    for a range of lags.
+    The serial correlations $\rho_k$ at lag $k$ are defined as
+    \[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - \langle T \rangle) \rangle}{\langle (T_i - \langle T \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm var}(T_i)} \]
+    Use this function to show that interspike intervals of Poisson spikes are independent.
+    \begin{solution}
+      \lstinputlisting{simulations/isiserialcorr.m}
+      \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonserial100hz}}
+    \end{solution}
+
+    \part Write a function that generates from spike times 
+    a histogram of spike counts in a count window of given duration $W$.
+    The function should also plot the Poisson distribution
+    \[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \]
+    for the rate $\lambda$ determined from the spike trains.
+    \begin{solution}
+      \lstinputlisting{simulations/counthist.m}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}}
+      \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}}
+    \end{solution}
+
+    \part Write a function that computes mean count, variance of count and the corresponding Fano factor
+    for a range of count window durations. The function should generate tow plots: one plotting
+    the count variance against the mean, the other one the Fano factor as a function of the window duration.
+    \begin{solution}
+      \lstinputlisting{simulations/fano.m}
+      \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonfano100hz}}
+    \end{solution}
+
+  \end{parts}
+  
+\end{questions}
+
+
+\end{document}
--- a/pointprocesses/exercises/poissoncounthistdist100hz100ms.pdf
+++ b/pointprocesses/exercises/poissoncounthistdist100hz100ms.pdf
--- a/pointprocesses/exercises/poissoncounthistdist100hz10ms.pdf
+++ b/pointprocesses/exercises/poissoncounthistdist100hz10ms.pdf
--- a/pointprocesses/exercises/poissonfano100hz.pdf
+++ b/pointprocesses/exercises/poissonfano100hz.pdf
--- a/pointprocesses/exercises/poissonisih100hz.pdf
+++ b/pointprocesses/exercises/poissonisih100hz.pdf
--- a/pointprocesses/exercises/poissonisih20hz.pdf
+++ b/pointprocesses/exercises/poissonisih20hz.pdf
--- a/pointprocesses/exercises/poissonisistats.pdf
+++ b/pointprocesses/exercises/poissonisistats.pdf
--- a/pointprocesses/exercises/poissonraster100hz.pdf
+++ b/pointprocesses/exercises/poissonraster100hz.pdf
--- a/pointprocesses/exercises/poissonserial100hz.pdf
+++ b/pointprocesses/exercises/poissonserial100hz.pdf
--- a/pointprocesses/lecture/Makefile
+++ b/pointprocesses/lecture/Makefile
@@ -0,0 +1,142 @@
+BASENAME=pointprocesses
+
+TEXFILE=$(BASENAME).tex
+DVIFILE=$(BASENAME).dvi
+PSFILE=$(BASENAME).ps
+PDFFILE=$(BASENAME).pdf
+
+FOILSFILE=foils.pdf
+THUMBNAILSFILE=thumbnails.pdf
+
+HTMLBASENAME=$(BASENAME)h
+HTMLTEXFILE=$(BASENAME)h.tex
+HTMLDIR=$(BASENAME)h
+
+GPTFILES=$(wildcard *.gpt)
+GPTTEXFILES=$(GPTFILES:.gpt=.tex)
+
+
+all: ps pdf talk again watchps watchpdf foils thumbs html html1 epsfigs clean cleanup cleanplots help
+.PHONY: epsfigs
+
+
+# thumbnails:
+thumbs: $(THUMBNAILSFILE)
+$(THUMBNAILSFILE): $(TEXFILE) $(GPTTEXFILES)
+	sed -e 's/setboolean{presentation}{true}/setboolean{presentation}{false}/; s/usepackage{crop}/usepackage[frame]{crop}/' $< > thumbsfoils.tex
+	pdflatex thumbsfoils | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex thumbsfoils || true
+	pdfnup --nup 2x4 --no-landscape --paper a4paper --trim "-1cm -1cm -1cm -1cm" --outfile $@ thumbsfoils.pdf '1-19'
+	rm thumbsfoils.*
+
+# transparencies:
+foils: $(FOILSFILE)
+$(FOILSFILE): $(TEXFILE) $(GPTTEXFILES)
+	sed -e 's/setboolean{presentation}{true}/setboolean{presentation}{false}/' $< > tfoils.tex
+	pdflatex tfoils | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex tfoils || true
+	pdfnup --nup 1x2 --orient portrait --trim "-1mm -1mm -1mm -1mm" --frame true --delta "1cm 1cm" --paper a4paper --outfile tfoils2.pdf tfoils.pdf
+	pdfnup --nup 1x1 --orient portrait --trim "-2cm -2cm -2cm -2cm" --paper a4paper --outfile $@ tfoils2.pdf 
+	rm tfoils.* tfoils2.pdf
+
+# talk:
+talk: $(PDFFILE)
+pdf: $(PDFFILE)
+$(PDFFILE): $(TEXFILE) $(GPTTEXFILES)
+	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
+# batchmode (no output, no stop on error)
+# nonstopmode / scrollmode (no stop on error)
+# errorstopmode (stop on error)
+
+
+again :
+	pdflatex $(TEXFILE)
+
+watchpdf :
+	while true; do ! make -q pdf && make pdf; sleep 0.5; done
+
+# html
+html : $(HTMLTEXFILE) $(GPTTEXFILES)
+	rm -f $(HTMLDIR)/*
+	htlatex $<
+	mkdir -p $(HTMLDIR)
+	mv $(HTMLBASENAME).html $(HTMLDIR)
+	mv $(HTMLBASENAME)*.* $(HTMLDIR)
+	mv z*.gif $(HTMLDIR)
+	cd $(HTMLDIR); for i in *.gif; do convert -page +0+0 $$i tmp.gif; mv tmp.gif $$i; done; rmtex $(HTMLBASENAME)
+
+#$(HTMLTEXFILE) : $(TEXFILE) Makefile
+#	sed 's/setboolean{html}{false}/setboolean{html}{true}/; s/\\colorbox{white}{\(.*\)}/\1/g' $< > $@
+
+html1 : $(HTMLTEXFILE) $(GPTTEXFILES)
+	latex2html -dir $(HTMLDIR) -mkdir -subdir -nonavigation -noinfo -image_type png -notransparent -white -split 0 $<
+	sed 's-<I>Date:</I>--' $(HTMLDIR)/$(HTMLDIR).html > tmp.html
+	cp tmp.html $(HTMLDIR)/index.html
+	mv tmp.html $(HTMLDIR)/$(HTMLDIR).html
+
+$(HTMLTEXFILE) : $(TEXFILE)
+	sed '/^%nohtml/,/^%endnohtml/d; s/\\colorbox{white}{\(.*\)}/\1/g' $< > $@
+
+
+# eps of all figures:
+epsfigs:
+	mkdir -p epsfigs; \
+	for i in $(GPTFILES); do \
+	  { sed -n -e '1,/\\begin{document}/p' $(TEXFILE); echo "\texpicture{$${i%%.*}}"; echo "\end{document}"; } > tmp.tex; \
+	  latex tmp.tex; \
+	  dvips tmp.dvi; \
+	  ps2eps tmp.ps; \
+	  mv tmp.eps epsfigs/$${i%%.*}.eps; \
+	  rm tmp.*; \
+	done
+
+
+# plots:
+%.tex: %.gpt whitestyles.gp
+	gnuplot whitestyles.gp $<
+	epstopdf $*.eps
+
+
+clean :
+	rm -f *~
+	rmtex $(BASENAME)
+	rm -f $(GPTTEXFILES)
+
+cleanup :
+	rm -f *~
+	rmtex $(BASENAME)
+	rm -f $(PSFILE) $(PDFFILE) $(FOILSFILE) $(THUMBNAILSFILE)
+	rm -f $(GPTTEXFILES)
+	rm -f -r $(HTMLDIR)
+
+
+cleanplots :
+	sed -n -e '/\\begin{document}/,/\\end{document}/p' $(TEXFILE) | fgrep '\input{' | grep -v '^%' | sed 's/.*input{\(.*\).tex}.*/\1.gpt/' > plot.fls
+	mkdir -p unusedplots
+	for i in *.gp*; do \
+	  grep -q $$i plot.fls || { grep -q $$i $$(<plot.fls) && echo $$i || mv $$i unusedplots; }; \
+	done >> plot.fls
+	for i in $$(<plot.fls); do \
+	  sed "s/\([^'\" ]*\.dat\)/\n\1\n/g;" $$i | fgrep .dat; \
+	done | sort | uniq > dat.fls
+	mkdir -p unuseddata 
+	for i in *.dat; do \
+	  grep -q $$i dat.fls || mv $$i unuseddata; \
+	done
+	rm dat.fls plot.fls
+
+
+help : 
+	@echo -e \
+	"make pdf:    make the pdf file of the talk.\n"\
+	"make foils:  make black&white postscript foils of the talk.\n"\
+	"make thumbs: make color thumbnails of the talk.\n"\
+	"make again: run latex and make the pdf file of the talk,\n"\
+        "            no matter whether you changed the .tex file or not.\n\n"\
+	"make watchpdf:   make the pdf file of the talk\n"\
+        "                 whenever the tex file is modified.\n"\
+	"make html:       make a html version of the paper (in $(HTMLDIR)).\n\n"\
+	"make clean:      remove all intermediate files,\n"\
+        "                 just leave the source files and the final .ps and .pdf files.\n"\
+	"make cleanup:    remove all intermediate files as well as\n"\
+        "                 the final .ps and .pdf files.\n"\
+	"make cleanplots: move all unused .gpt and .dat files\n"\
+        "                 into unusedplots/ and unuseddata/, respectively."
--- a/pointprocesses/lecture/UT_WBMW_Rot_RGB.pdf
+++ b/pointprocesses/lecture/UT_WBMW_Rot_RGB.pdf
--- a/pointprocesses/lecture/beamercolorthemetuebingen.sty
+++ b/pointprocesses/lecture/beamercolorthemetuebingen.sty
@@ -0,0 +1,61 @@
+% Copyright 2007 by Till Tantau
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/licenses/LICENSE for more details.
+
+\usepackage{color} 
+\definecolor{karminrot}{RGB}{165,30,55}
+\definecolor{gold}{RGB}{180,160,105}
+\definecolor{anthrazit}{RGB}{50 ,65 ,75 }
+
+\mode<presentation>
+
+\setbeamercolor*{normal text}{fg=anthrazit,bg=white}
+\setbeamercolor*{alerted text}{fg=anthrazit}
+\setbeamercolor*{example text}{fg=anthrazit}
+\setbeamercolor*{structure}{fg=gold,bg=karminrot}
+
+\providecommand*{\beamer@bftext@only}{%
+  \relax
+  \ifmmode
+    \expandafter\beamer@bftext@warning
+  \else
+    \expandafter\bfseries
+  \fi
+}
+\providecommand*{\beamer@bftext@warning}{%
+  \ClassWarning{beamer}
+    {Cannot use bold for alerted text in math mode}%
+}
+
+\setbeamerfont{alerted text}{series=\beamer@bftext@only}
+
+\setbeamercolor{palette primary}{fg=karminrot,bg=white}
+\setbeamercolor{palette secondary}{fg=gold,bg=white}
+\setbeamercolor{palette tertiary}{fg=anthrazit,bg=white}
+\setbeamercolor{palette quaternary}{fg=black,bg=white}
+
+\setbeamercolor{sidebar}{bg=karminrot!100}
+
+\setbeamercolor{palette sidebar primary}{fg=karminrot}
+\setbeamercolor{palette sidebar secondary}{fg=karminrot}
+\setbeamercolor{palette sidebar tertiary}{fg=karminrot}
+\setbeamercolor{palette sidebar quaternary}{fg=karminrot}
+
+\setbeamercolor{item projected}{fg=black,bg=black!20}
+
+\setbeamercolor*{block body}{}
+\setbeamercolor*{block body alerted}{}
+\setbeamercolor*{block body example}{}
+\setbeamercolor*{block title}{parent=structure}
+\setbeamercolor*{block title alerted}{parent=alerted text}
+\setbeamercolor*{block title example}{parent=example text}
+
+\setbeamercolor*{titlelike}{parent=structure}
+
+\mode
+<all>
--- a/pointprocesses/lecture/lifadaptfano10-100ms.pdf
+++ b/pointprocesses/lecture/lifadaptfano10-100ms.pdf
--- a/pointprocesses/lecture/lifadaptisihdistr08-100ms.pdf
+++ b/pointprocesses/lecture/lifadaptisihdistr08-100ms.pdf
--- a/pointprocesses/lecture/lifadaptisihdistr65-100ms.pdf
+++ b/pointprocesses/lecture/lifadaptisihdistr65-100ms.pdf
--- a/pointprocesses/lecture/lifadaptreturnmap10-100ms.pdf
+++ b/pointprocesses/lecture/lifadaptreturnmap10-100ms.pdf
--- a/pointprocesses/lecture/lifadaptserial10-100ms.pdf
+++ b/pointprocesses/lecture/lifadaptserial10-100ms.pdf
--- a/pointprocesses/lecture/liffano16.pdf
+++ b/pointprocesses/lecture/liffano16.pdf
--- a/pointprocesses/lecture/lifisih16.pdf
+++ b/pointprocesses/lecture/lifisih16.pdf
--- a/pointprocesses/lecture/lifisihdistr08.pdf
+++ b/pointprocesses/lecture/lifisihdistr08.pdf
--- a/pointprocesses/lecture/lifisihdistr16.pdf
+++ b/pointprocesses/lecture/lifisihdistr16.pdf
--- a/pointprocesses/lecture/lifoufano16-100ms.pdf
+++ b/pointprocesses/lecture/lifoufano16-100ms.pdf
--- a/pointprocesses/lecture/lifouisihdistr08-100ms.pdf
+++ b/pointprocesses/lecture/lifouisihdistr08-100ms.pdf
--- a/pointprocesses/lecture/lifouisihdistr16-100ms.pdf
+++ b/pointprocesses/lecture/lifouisihdistr16-100ms.pdf
--- a/pointprocesses/lecture/lifoureturnmap16-100ms.pdf
+++ b/pointprocesses/lecture/lifoureturnmap16-100ms.pdf
--- a/pointprocesses/lecture/lifouserial16-100ms.pdf
+++ b/pointprocesses/lecture/lifouserial16-100ms.pdf
--- a/pointprocesses/lecture/lifraster16.pdf
+++ b/pointprocesses/lecture/lifraster16.pdf
--- a/pointprocesses/lecture/lifreturnmap16.pdf
+++ b/pointprocesses/lecture/lifreturnmap16.pdf
--- a/pointprocesses/lecture/lifserial16.pdf
+++ b/pointprocesses/lecture/lifserial16.pdf
--- a/pointprocesses/lecture/pifisihdistr01.pdf
+++ b/pointprocesses/lecture/pifisihdistr01.pdf
--- a/pointprocesses/lecture/pifisihdistr10.pdf
+++ b/pointprocesses/lecture/pifisihdistr10.pdf
--- a/pointprocesses/lecture/pointprocesses.pdf
+++ b/pointprocesses/lecture/pointprocesses.pdf
--- a/pointprocesses/lecture/pointprocesses.tex
+++ b/pointprocesses/lecture/pointprocesses.tex
@@ -0,0 +1,412 @@
+\documentclass{beamer}
+
+%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title[]{Scientific Computing --- Point Processes}
+\author[]{Jan Benda}
+\institute[]{Neuroethology}
+\date[]{WS 14/15}
+\titlegraphic{\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
+
+%%%%% beamer %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>
+{
+  \usetheme{Singapore}
+  \setbeamercovered{opaque}
+  \usecolortheme{tuebingen}
+  \setbeamertemplate{navigation symbols}{}
+  \usefonttheme{default}
+  \useoutertheme{infolines}
+  % \useoutertheme{miniframes}
+}
+
+%\AtBeginSection[]
+%{
+%  \begin{frame}<beamer>
+%    \begin{center}
+%      \Huge \insertsectionhead
+%    \end{center}
+%  \end{frame}
+%}
+
+\setbeamertemplate{blocks}[rounded][shadow=true]
+\setcounter{tocdepth}{1}
+
+%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage[english]{babel}
+\usepackage{amsmath}
+\usepackage{bm} 
+\usepackage{pslatex}   % nice font for pdf file
+%\usepackage{multimedia}
+
+\usepackage{dsfont}
+\newcommand{\naZ}{\mathds{N}}
+\newcommand{\gaZ}{\mathds{Z}}
+\newcommand{\raZ}{\mathds{Q}}
+\newcommand{\reZ}{\mathds{R}}
+\newcommand{\reZp}{\mathds{R^+}}
+\newcommand{\reZpN}{\mathds{R^+_0}}
+\newcommand{\koZ}{\mathds{C}}
+
+%%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{graphicx}
+\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}}
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ commentstyle=\itshape\color{darkgray},
+ keywordstyle=\color{blue},
+ stringstyle=\color{green},
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+ xleftmargin=1em,
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+ }
+
+ 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document} 
+
+\begin{frame}[plain]
+  \frametitle{}
+  \vspace{-1cm}
+  \titlepage % erzeugt Titelseite
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+  \frametitle{Content}
+  \tableofcontents
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Point processes}
+
+\begin{frame}
+  \frametitle{Point process}
+  \vspace{-3ex}
+  \texpicture{pointprocessscetchA}
+
+  A point process is a stochastic (or random) process that generates a sequence of events
+  at times $\{t_i\}$, $t_i \in \reZ$.
+
+  For each point process there is an underlying continuous-valued
+  process evolving in time. The associated point process occurs when
+  the underlying continuous process crosses a threshold.
+  Examples:
+  \begin{itemize}
+  \item Spikes/heartbeat: generated by the dynamics of the membrane potential of neurons/heart cells.
+  \item Earth quakes: generated by the pressure dynamics between the tectonic plates on either side of a geological fault line.
+  \item Onset of cricket/frogs/birds/... songs: generated by the dynamics of the state of a nervous system.
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Point process}
+  \texpicture{pointprocessscetchB}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Homogeneous Poisson process}
+
+\begin{frame}
+  \frametitle{Homogeneous Poisson process}
+  The probability $p(t)\delta t$ of an event occuring at time $t$
+  is independent of $t$ and independent of any previous event
+  (independent of event history).
+
+  The probability $P$ for an event occuring within a time bin of width $\Delta t$
+  is
+  \[ P=\lambda \cdot \Delta t \]
+  for a Poisson process with rate $\lambda$.
+  \includegraphics[width=1\textwidth]{poissonraster100hz}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Interval statistics}
+
+\begin{frame}
+  \frametitle{Rate}
+  Rate of events $r$ (``spikes per time'') measured in Hertz.
+  \begin{itemize}
+  \item Number of events $N$ per observation time $W$: $r = \frac{N}{W}$
+  \item Without boundary effects: $r = \frac{N-1}{t_N-t_1}$
+  \item Inverse interval: $r = \frac{1}{\mu_{ISI}}$
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{(Interspike) interval statistics}
+  \begin{itemize}
+  \item Histogram $p(T)$ of intervals $T$. Normalized to $\int_0^{\infty} p(T) \; dT = 1$
+  \item Mean interval $\mu_{ISI} = \langle T \rangle = \frac{1}{n}\sum\limits_{i=1}^n T_i$
+  \item Variance of intervals $\sigma_{ISI}^2 = \langle (T - \langle T \rangle)^2 \rangle$\vspace{1ex}
+  \item Coefficient of variation $CV_{ISI} = \frac{\sigma_{ISI}}{\mu_{ISI}}$
+  \item Diffusion coefficient $D_{ISI} = \frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$
+  \vfill
+  \end{itemize}
+  \includegraphics[width=0.45\textwidth]{poissonisih100hz}\hfill
+  \includegraphics[width=0.45\textwidth]{lifisih16}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Interval statistics of homogeneous Poisson process}
+  \begin{itemize}
+  \item Exponential distribution of intervals $T$: $p(T) = \lambda e^{-\lambda T}$
+  \item Mean interval $\mu_{ISI} = \frac{1}{\lambda}$
+  \item Variance of intervals $\sigma_{ISI}^2 = \frac{1}{\lambda^2}$
+  \item Coefficient of variation $CV_{ISI} = 1$
+  \end{itemize}
+  \vfill
+  \includegraphics[width=0.45\textwidth]{poissonisihexp20hz}\hfill
+  \includegraphics[width=0.45\textwidth]{poissonisihexp100hz}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Interval return maps}
+  Scatter plot between succeeding intervals separated by lag $k$.
+  \vfill
+  Poisson process $\lambda=100$\,Hz:
+  \includegraphics[width=1\textwidth]{poissonreturnmap100hz}\hfill
+\end{frame}
+
+\begin{frame}
+  \frametitle{Serial interval correlations}
+  Correlation coefficients between succeeding intervals separated by lag $k$:
+  \[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - \langle T \rangle) \rangle}{\langle (T_i - \langle T \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm var}(T_i)} \]
+  \begin{itemize}
+  \item $\rho_0=1$ (correlation of each interval with itself).
+  \item Poisson process: $\rho_k =0$ for $k>0$ (renewal process!) 
+  \end{itemize}
+  \vfill
+  \includegraphics[width=0.7\textwidth]{poissonserial100hz}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Count statistics}
+
+\begin{frame}
+  \frametitle{Count statistics}
+  Histogram of number of events $N$ (counts) within observation window of duration $W$.
+
+  \vfill
+  \includegraphics[width=0.48\textwidth]{poissoncounthist100hz10ms}\hfill
+  \includegraphics[width=0.48\textwidth]{poissoncounthist100hz100ms}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Count statistics of Poisson process}
+  Poisson distribution:
+  \[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \]
+
+  \vfill
+  \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}\hfill
+  \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Count statistics --- Fano factor}
+  Statistics of number of events $N$ within observation window of duration $W$.
+  \begin{itemize}
+  \item Mean count: $\mu_N = \langle N \rangle$
+  \item Count variance: $\sigma_N^2 = \langle (N - \langle N \rangle)^2 \rangle$
+  \item Fano factor (variance divided by mean): $F = \frac{\sigma_N^2}{\mu_N}$
+  \item Poisson process: $F=1$
+  \end{itemize}
+  \vfill
+  Poisson process $\lambda=100$\,Hz:
+  \includegraphics[width=1\textwidth]{poissonfano100hz}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Integrate-and-fire models}
+
+\begin{frame}
+  \frametitle{Integrate-and-fire models}
+  Leaky integrate-and-fire model (LIF):
+  \[ \tau \frac{dV}{dt} = -V + RI + D\xi \]
+  Whenever membrane potential $V(t)$ crosses the firing threshold $\theta$, a spike is emitted and
+  $V(t)$ is reset to $V_{reset}$.
+  \begin{itemize}
+  \item $\tau$: membrane time constant (typically 10\,ms)
+  \item $R$: input resistance (here 1\,mV (!))
+  \item $D\xi$: additive Gaussian white noise of strength $D$
+  \item $\theta$: firing threshold (here 10\,mV)
+  \item $V_{reset}$: reset potential (here 0\,mV)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Integrate-and-fire models}
+  Discretization with time step $\Delta t$: $V(t) \rightarrow V_i,\;t_i = i \Delta t$.\\
+  Euler integration:
+  \begin{eqnarray*}
+    \frac{dV}{dt} & \approx & \frac{V_{i+1} - V_i}{\Delta t} \\
+    \Rightarrow \quad V_{i+1} & = & V_i + \Delta t \frac{-V_i+RI_i+\sqrt{2D\Delta t}N_i}{\tau}
+  \end{eqnarray*}
+  $N_i$ are normally distributed random numbers (Gaussian with zero mean and unit variance)
+  --- the $\sqrt{\Delta t}$ is for white noise.
+
+  \includegraphics[width=0.82\textwidth]{lifraster16}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Interval statistics of LIF}
+  Interval distribution approaches Inverse Gaussian for large $I$:
+  \[ p(T) = \frac{1}{\sqrt{4\pi D T^3}}\exp\left[-\frac{(T-\langle T \rangle)^2}{4DT\langle T \rangle^2}\right] \]
+  where $\langle T \rangle$ is the mean interspike interval and $D$
+  is the diffusion coefficient.
+  \vfill
+  \includegraphics[width=0.45\textwidth]{lifisihdistr08}\hfill
+  \includegraphics[width=0.45\textwidth]{lifisihdistr16}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Interval statistics of PIF}
+  For the perfect integrate-and-fire (PIF)
+  \[ \tau \frac{dV}{dt} =  RI + D\xi \]
+  (the canonical model or supra-threshold firing on a limit cycle)\\
+  the Inverse Gaussian describes exactly the interspike interval distribution.
+  \vfill
+  \includegraphics[width=0.45\textwidth]{pifisihdistr01}\hfill
+  \includegraphics[width=0.45\textwidth]{pifisihdistr10}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Interval return map of LIF}
+  LIF $I=15.7$:
+  \includegraphics[width=1\textwidth]{lifreturnmap16}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Serial correlations of LIF}
+  LIF $I=15.7$:
+  \includegraphics[width=1\textwidth]{lifserial16}\\
+  Integrate-and-fire driven with white noise are still renewal processes!
+\end{frame}
+
+\begin{frame}
+  \frametitle{Count statistics of LIF}
+  LIF $I=15.7$:
+  \includegraphics[width=1\textwidth]{liffano16}\\
+  Fano factor is not one!
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+  \frametitle{Interval statistics of LIF with OU noise}
+  \begin{eqnarray*}
+    \tau \frac{dV}{dt} & = & -V + RI + U \\
+    \tau_{OU} \frac{dU}{dt} & = & - U + D\xi
+  \end{eqnarray*}
+  Ohrnstein-Uhlenbeck noise is lowpass filtered white noise.
+  \includegraphics[width=0.45\textwidth]{lifouisihdistr08-100ms}\hfill
+  \includegraphics[width=0.45\textwidth]{lifouisihdistr16-100ms}\\
+  More peaky than the inverse Gaussian!
+\end{frame}
+
+\begin{frame}
+  \frametitle{Interval return map of LIF with OU noise}
+  LIF $I=15.7$, $\tau_{OU}=100$\,ms:
+  \includegraphics[width=1\textwidth]{lifoureturnmap16-100ms}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Serial correlations of LIF with OU noise}
+  LIF $I=15.7$, $\tau_{OU}=100$\,ms:
+  \includegraphics[width=1\textwidth]{lifouserial16-100ms}\\
+  OU-noise introduces positive interval correlations!
+\end{frame}
+
+\begin{frame}
+  \frametitle{Count statistics of LIF with OU noise}
+  LIF $I=15.7$, $\tau_{OU}=100$\,ms:
+  \includegraphics[width=1\textwidth]{lifoufano16-100ms}\\
+  Fano factor increases with count window duration.
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+  \frametitle{Interval statistics of LIF with adaptation}
+  \begin{eqnarray*}
+    \tau \frac{dV}{dt} & = & -V - A + RI + D\xi \\
+    \tau_{adapt} \frac{dA}{dt} & = & - A
+  \end{eqnarray*}
+  Adaptation $A$ with time constant $\tau_{adapt}$ and increment $\Delta A$ at spike.
+  \includegraphics[width=0.45\textwidth]{lifadaptisihdistr08-100ms}\hfill
+  \includegraphics[width=0.45\textwidth]{lifadaptisihdistr65-100ms}\\
+  Similar to LIF with white noise.
+\end{frame}
+
+\begin{frame}
+  \frametitle{Interval return map of LIF with adaptation}
+  LIF $I=10$, $\tau_{adapt}=100$\,ms:
+  \includegraphics[width=1\textwidth]{lifadaptreturnmap10-100ms}\\
+  Negative correlation at lag one.
+\end{frame}
+
+\begin{frame}
+  \frametitle{Serial correlations of LIF with adaptation}
+  LIF $I=10$, $\tau_{adapt}=100$\,ms:
+  \includegraphics[width=1\textwidth]{lifadaptserial10-100ms}\\
+  Adaptation with white noise introduces negative interval correlations!
+\end{frame}
+
+\begin{frame}
+  \frametitle{Count statistics of LIF with adaptation}
+  LIF $I=10$, $\tau_{adapt}=100$\,ms:
+  \includegraphics[width=1\textwidth]{lifadaptfano10-100ms}\\
+  Fano factor decreases with count window duration.
+\end{frame}
+
+
+\end{document}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Non stationary}
+\subsection{Inhomogeneous Poisson process}
+\subsection{Firing rate}
+\subsection{Instantaneous rate}
+\subsection{Autocorrelation}
+\subsection{Crosscorrelation}
+\subsection{Joint PSTH}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Renewal process}
+\subsection{Superthreshold firing}
+\subsection{Subthreshold firing}
+\section{Non-renewal processes}
+\subsection{Bursting}
+\subsection{Resonator}
+
+
+\subsection{Standard distributions}
+\subsubsection{Gamma}
+\subsubsection{How to read ISI histograms}
+refractoriness, poisson tail, sub-, supra-threshold, missed spikes
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Correlation with stimulus}
+\subsection{Tuning curve}
+\subsection{Linear filter}
+\subsection{Spatiotemporal receptive field}
+\subsection{Generalized linear model}
+
+\begin{frame}
+\end{frame}
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--- a/pointprocesses/lecture/pointprocessscetchA.pdf
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+  /Title (pointprocessscetchB.tex)
+  /Subject (gnuplot plot)
+  /Creator (gnuplot 4.6 patchlevel 4)
+  /Author (jan)
+%  /Producer (gnuplot)
+%  /Keywords ()
+  /CreationDate (Sun Oct 26 17:34:18 2014)
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--- a/pointprocesses/lecture/pointprocessscetchB.gpt
+++ b/pointprocesses/lecture/pointprocessscetchB.gpt
@@ -0,0 +1,204 @@
+set out 'pointprocessscetchB.tex'
+
+set border 0
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+set label 1 '\normalsize Event times $\{t_i\}$'
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+set label 10 "$t_{8}$" at 7.81657, -0.6 center
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+set origin 0, 0.4
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+set label 3 "$T_{1}$" at 1.20025, -0.5 center
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+unset label 8
+unset label 9
+unset label 10
+unset arrow 3
+unset arrow 4
+unset arrow 5
+unset arrow 6
+unset arrow 7
+unset arrow 8
+unset arrow 9
+unset arrow 10
+
+set origin 0, 0
+set size 1, 0.4
+set border 2
+set yrange [-0.5:10.5]
+set ytics 2 nomirror out
+set arrow 1 from 0, 0.0 to 11, 0.0 head filled
+set label 2 'Time' at 11, -2.2 center
+set label 1 '\normalsize Event counts $\{ n_i \}$' at graph -0.07, graph 1.2
+plot '-' w l lt 1 lc rgb 'black' lw 3, \
+     '-' w p lt 1 lc rgb 'black' pt 7 ps 1.5 lw 2, \
+     '-' w p lt 1 lc rgb 'white' pt 7 ps 1.0 lw 2, \
+     '-' w p lt 1 lc rgb 'black' pt 7 ps 1.5 lw 2
+0 0
+0.724649 0
+
+0.724649 1
+1.67586 1
+
+1.67586 2
+3.02389 2
+
+3.02389 3
+3.57466 3
+
+3.57466 4
+4.15121 4
+
+4.15121 5
+5.00412 5
+
+5.00412 6
+6.64549 6
+
+6.64549 7
+7.81657 7
+
+7.81657 8
+9.77964 8
+
+9.77964 9
+10.7899 9
+e
+0.724649 0
+1.67586 1
+3.02389 2
+3.57466 3
+4.15121 4
+5.00412 5
+6.64549 6
+7.81657 7
+9.77964 8
+e
+0.724649 0
+1.67586 1
+3.02389 2
+3.57466 3
+4.15121 4
+5.00412 5
+6.64549 6
+7.81657 7
+9.77964 8
+e
+0.724649 1
+1.67586 2
+3.02389 3
+3.57466 4
+4.15121 5
+5.00412 6
+6.64549 7
+7.81657 8
+9.77964 9
+e
+
+unset multiplot
--- a/pointprocesses/lecture/pointprocessscetchB.pdf
+++ b/pointprocesses/lecture/pointprocessscetchB.pdf
--- a/pointprocesses/lecture/pointprocessscetchB.tex
+++ b/pointprocesses/lecture/pointprocessscetchB.tex
@@ -0,0 +1,130 @@
+% GNUPLOT: LaTeX picture with Postscript
+\begingroup
+  \makeatletter
+  \providecommand\color[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package color not loaded in conjunction with
+      terminal option `colourtext'%
+    }{See the gnuplot documentation for explanation.%
+    }{Either use 'blacktext' in gnuplot or load the package
+      color.sty in LaTeX.}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\includegraphics[2][]{%
+    \GenericError{(gnuplot) \space\space\space\@spaces}{%
+      Package graphicx or graphics not loaded%
+    }{See the gnuplot documentation for explanation.%
+    }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
+    \renewcommand\includegraphics[2][]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \@ifundefined{ifGPcolor}{%
+    \newif\ifGPcolor
+    \GPcolortrue
+  }{}%
+  \@ifundefined{ifGPblacktext}{%
+    \newif\ifGPblacktext
+    \GPblacktexttrue
+  }{}%
+  % define a \g@addto@macro without @ in the name:
+  \let\gplgaddtomacro\g@addto@macro
+  % define empty templates for all commands taking text:
+  \gdef\gplbacktext{}%
+  \gdef\gplfronttext{}%
+  \makeatother
+  \ifGPblacktext
+    % no textcolor at all
+    \def\colorrgb#1{}%
+    \def\colorgray#1{}%
+  \else
+    % gray or color?
+    \ifGPcolor
+      \def\colorrgb#1{\color[rgb]{#1}}%
+      \def\colorgray#1{\color[gray]{#1}}%
+      \expandafter\def\csname LTw\endcsname{\color{white}}%
+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
+      \expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
+      \expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
+      \expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
+      \expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
+      \expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
+      \expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
+      \expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
+      \expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
+    \else
+      % gray
+      \def\colorrgb#1{\color{black}}%
+      \def\colorgray#1{\color[gray]{#1}}%
+      \expandafter\def\csname LTw\endcsname{\color{white}}%
+      \expandafter\def\csname LTb\endcsname{\color{black}}%
+      \expandafter\def\csname LTa\endcsname{\color{black}}%
+      \expandafter\def\csname LT0\endcsname{\color{black}}%
+      \expandafter\def\csname LT1\endcsname{\color{black}}%
+      \expandafter\def\csname LT2\endcsname{\color{black}}%
+      \expandafter\def\csname LT3\endcsname{\color{black}}%
+      \expandafter\def\csname LT4\endcsname{\color{black}}%
+      \expandafter\def\csname LT5\endcsname{\color{black}}%
+      \expandafter\def\csname LT6\endcsname{\color{black}}%
+      \expandafter\def\csname LT7\endcsname{\color{black}}%
+      \expandafter\def\csname LT8\endcsname{\color{black}}%
+    \fi
+  \fi
+  \setlength{\unitlength}{0.0500bp}%
+  \begin{picture}(6462.00,3740.00)%
+    \gplgaddtomacro\gplbacktext{%
+      \csname LTb\endcsname%
+      \put(122,3587){\makebox(0,0)[l]{\strut{}\normalsize Event times $\{t_i\}$}}%
+      \put(6329,2947){\makebox(0,0){\strut{}Time}}%
+      \put(910,2865){\makebox(0,0){\strut{}$t_{1}$}}%
+      \put(1412,2865){\makebox(0,0){\strut{}$t_{2}$}}%
+      \put(2123,2865){\makebox(0,0){\strut{}$t_{3}$}}%
+      \put(2413,2865){\makebox(0,0){\strut{}$t_{4}$}}%
+      \put(2717,2865){\makebox(0,0){\strut{}$t_{5}$}}%
+      \put(3167,2865){\makebox(0,0){\strut{}$t_{6}$}}%
+      \put(4033,2865){\makebox(0,0){\strut{}$t_{7}$}}%
+      \put(4650,2865){\makebox(0,0){\strut{}$t_{8}$}}%
+      \put(5685,2865){\makebox(0,0){\strut{}$t_{9}$}}%
+    }%
+    \gplgaddtomacro\gplfronttext{%
+    }%
+    \gplgaddtomacro\gplbacktext{%
+      \csname LTb\endcsname%
+      \put(122,2465){\makebox(0,0)[l]{\strut{}\normalsize Intervals $\{T_i\}, \; T_i = t_{i+1} - t_i$}}%
+      \put(6329,1825){\makebox(0,0){\strut{}Time}}%
+      \put(1161,1770){\makebox(0,0){\strut{}$T_{1}$}}%
+      \put(1767,1770){\makebox(0,0){\strut{}$T_{2}$}}%
+      \put(2268,1770){\makebox(0,0){\strut{}$T_{3}$}}%
+      \put(2565,1770){\makebox(0,0){\strut{}$T_{4}$}}%
+      \put(2942,1770){\makebox(0,0){\strut{}$T_{5}$}}%
+      \put(3600,1770){\makebox(0,0){\strut{}$T_{6}$}}%
+      \put(4341,1770){\makebox(0,0){\strut{}$T_{7}$}}%
+      \put(5168,1770){\makebox(0,0){\strut{}$T_{8}$}}%
+    }%
+    \gplgaddtomacro\gplfronttext{%
+    }%
+    \gplgaddtomacro\gplbacktext{%
+      \colorrgb{0.00,0.00,0.00}%
+      \put(333,268){\makebox(0,0)[r]{\strut{}$0$}}%
+      \colorrgb{0.00,0.00,0.00}%
+      \put(333,460){\makebox(0,0)[r]{\strut{}$2$}}%
+      \colorrgb{0.00,0.00,0.00}%
+      \put(333,652){\makebox(0,0)[r]{\strut{}$4$}}%
+      \colorrgb{0.00,0.00,0.00}%
+      \put(333,844){\makebox(0,0)[r]{\strut{}$6$}}%
+      \colorrgb{0.00,0.00,0.00}%
+      \put(333,1036){\makebox(0,0)[r]{\strut{}$8$}}%
+      \colorrgb{0.00,0.00,0.00}%
+      \put(333,1228){\makebox(0,0)[r]{\strut{}$10$}}%
+      \csname LTb\endcsname%
+      \put(122,1487){\makebox(0,0)[l]{\strut{}\normalsize Event counts $\{ n_i \}$}}%
+      \put(6329,57){\makebox(0,0){\strut{}Time}}%
+    }%
+    \gplgaddtomacro\gplfronttext{%
+    }%
+    \gplbacktext
+    \put(0,0){\includegraphics{pointprocessscetchB}}%
+    \gplfronttext
+  \end{picture}%
+\endgroup
--- a/pointprocesses/lecture/poissoncounthist100hz100ms.pdf
+++ b/pointprocesses/lecture/poissoncounthist100hz100ms.pdf
--- a/pointprocesses/lecture/poissoncounthist100hz10ms.pdf
+++ b/pointprocesses/lecture/poissoncounthist100hz10ms.pdf
--- a/pointprocesses/lecture/poissoncounthistdist100hz100ms.pdf
+++ b/pointprocesses/lecture/poissoncounthistdist100hz100ms.pdf
--- a/pointprocesses/lecture/poissoncounthistdist100hz10ms.pdf
+++ b/pointprocesses/lecture/poissoncounthistdist100hz10ms.pdf
--- a/pointprocesses/lecture/poissonfano100hz.pdf
+++ b/pointprocesses/lecture/poissonfano100hz.pdf
--- a/pointprocesses/lecture/poissonisih100hz.pdf
+++ b/pointprocesses/lecture/poissonisih100hz.pdf
--- a/pointprocesses/lecture/poissonisihexp100hz.pdf
+++ b/pointprocesses/lecture/poissonisihexp100hz.pdf
--- a/pointprocesses/lecture/poissonisihexp20hz.pdf
+++ b/pointprocesses/lecture/poissonisihexp20hz.pdf
--- a/Show More
+++ b/Show More