finished solutions for spike counts

pointprocesses/code/fanoplot.m

@@ -1,37 +1,33 @@
-function fanoplot( spikes )
+function fanoplot(spikes, titles)
-% computes fano factor as a function of window size
+% computes and plots fano factor as a function of window size
 % spikes: a cell array of vectors of spike times
-
+% titles: string that is used as a title for the plots
-    tmax = spikes{1}(end);
+    windows = logspace(-3.0, -0.5, 100);
-    windows = 0.01:0.05:0.01*tmax;
     mc = windows;
     vc = windows;
     ff = windows;
     for j = 1:length(windows)
-        w = windows( j );
+        w = windows(j);
-        % collect counts:
+        counts = spikecounts(spikes, w);
-        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 );
+        mc(j) = mean(counts);
-        vc(j) = var( n );
+        vc(j) = var(counts);
-        ff(j) = vc( j )/mc( j );
+        ff(j) = vc(j)/mc(j);
     end
     
-    subplot( 1, 2, 1 );
+    subplot(1, 2, 1);
-    scatter( mc, vc, 'filled' );
+    scatter(mc, vc, 'filled');
-    xlabel( 'Mean count' );
+    title(titles);
-    ylabel( 'Count variance' );
+    xlabel('Mean count');
+    ylabel('Count variance');
 
-    subplot( 1, 2, 2 );
+    subplot(1, 2, 2);
-    scatter( 1000.0*windows, ff, 'filled' );
+    scatter(1000.0*windows, ff, 'filled');
-    xlabel( 'Window W [ms]' );
+    title(titles);
-    ylabel( 'Fano factor' );
+    xlabel('Window [ms]');
+    ylabel('Fano factor');
+    xlim(1000.0*[windows(1) windows(end)])
+    ylim([0.0 1.1]);
+    set(gca, 'XScale', 'log');
 end
 

pointprocesses/code/fanoplots.m

@@ -0,0 +1,9 @@
+spikes{1} = poissonspikes;
+spikes{2} = pifouspikes;
+spikes{3} = lifadaptspikes;
+idents = {'poisson', 'pifou', 'lifadapt'};
+for k = 1:3
+    figure(k)
+    fanoplot(spikes{k}, titles{k});
+    savefigpdf(gcf, sprintf('fanoplots%s.pdf', idents{k}), 20, 7);
+end

pointprocesses/code/spikecounts.m

@@ -15,13 +15,14 @@ function counts = spikecounts(spikes, w)
     counts = [];
     for k = 1:length(spikes)
         times = spikes{k};
-%       alternative 1: count the number of spikes in each window:
+%       method 1: count the number of spikes in each window:
 %         for tk = 0:w:tmax-w
 %             nn = sum((times >= tk) & (times < tk+w));
+%             %nn = length(times((times >= tk) & (times < tk+w)));
 %             %nn = length(find((times >= tk) & (times < tk+w)));
 %             counts = [counts nn];
 %         end
-%     alternative 2: use the hist() function to do that!
+%     method 2: use the hist() function to do that!
         tbins = 0.5*w:w:tmax-0.5*w;
         nn = hist(times, tbins);
         counts = [counts nn];

pointprocesses/code/spikecountshists.m

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

pointprocesses/exercises/pointprocesses01.tex

@@ -195,7 +195,7 @@ jan.benda@uni-tuebingen.de}
     
   \end{parts}
 
-  \continue
+  \continuepage
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
   \question \qt{Statistics of spike counts}
   Now let's have a look at the statistics of the spike counts.
@@ -208,18 +208,25 @@ jan.benda@uni-tuebingen.de}
     width.
     \begin{solution}
       \lstinputlisting{../code/spikecounts.m}
-      % XXX
+      \newsolutionpage
+      \lstinputlisting{../code/spikecountshists.m}
+      \colorbox{white}{\includegraphics[width=1\textwidth]{spikecountshists}}
     \end{solution}
 
-    \part Write a function that computes for a range from window
+    \newsolutionpage
+    \part Write a function that computes for a range of window
     widths the mean, the variance and the Fano factor of the
-    corresponding spike counts.  The function should the generate two
+    corresponding spike counts.  The function should generate two
     plots. One showing the spike count variance in dependence on the
     mean spike count. The other plot showing the Fano factor as a
     function of window width.
     \begin{solution}
       \lstinputlisting{../code/fanoplot.m}
-      % XXX
+      \newsolutionpage
+      \lstinputlisting{../code/fanoplots.m}
+      \colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotspoisson}}
+      \colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotspifou}}
+      \colorbox{white}{\includegraphics[width=1\textwidth]{fanoplotslifadapt}}
     \end{solution}
 
   \end{parts}