added fano factor exercise

pointprocesses/code/fanoplot.m

@@ -0,0 +1,37 @@
+function fanoplot( 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;
+    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 );
+    end
+    
+    subplot( 1, 2, 1 );
+    scatter( mc, vc, 'filled' );
+    xlabel( 'Mean count' );
+    ylabel( 'Count variance' );
+
+    subplot( 1, 2, 2 );
+    scatter( 1000.0*windows, ff, 'filled' );
+    xlabel( 'Window W [ms]' );
+    ylabel( 'Fano factor' );
+end
+

pointprocesses/code/spikecounts.m

@@ -0,0 +1,29 @@
+function counts = spikecounts(spikes, w)
+% Compute vector of spike counts.
+%
+% counts = spikecounts(spikes, w)
+%
+% Arguments:
+%   spikes: a cell array of vectors of spike times in seconds
+%   w: observation window duration in seconds for computing the counts
+%
+% Returns:
+%   counts: vector of spike counts
+
+    % collect spike counts:
+    tmax = spikes{1}(end);
+    counts = [];
+    for k = 1:length(spikes)
+        times = spikes{k};
+%       alternative 1: count the number of spikes in each window:
+%         for tk = 0:w:tmax-w
+%             nn = sum((times >= tk) & (times < tk+w));
+%             %nn = length(find((times >= tk) & (times < tk+w)));
+%             counts = [counts nn];
+%         end
+%     alternative 2: use the hist() function to do that!
+        tbins = 0.5*w:w:tmax-0.5*w;
+        nn = hist(times, tbins);
+        counts = [counts nn];
+    end
+end

pointprocesses/exercises/pointprocesses01.tex

@@ -173,7 +173,8 @@ jan.benda@uni-tuebingen.de}
       \colorbox{white}{\includegraphics[width=1\textwidth]{isihist}}
     \end{solution}
   
-    \part XXX Add return map!!! XXX Write a function that computes and plots the serial
+    % XXX Add return map!!! XXX
+    \part Write a function that computes and plots the serial
     correlations of interspike intervals for lags upto
     \code{maxlag}. The serial correlations $\rho_k$ for lag $k$ of the
     interspike intervals $T_i$ are the correlation coefficients
@@ -192,6 +193,28 @@ jan.benda@uni-tuebingen.de}
       \colorbox{white}{\includegraphics[width=1\textwidth]{serialcorr}}
     \end{solution}
 
+    \part Write a function that counts and returns the number of
+    spikes in windows of a given width $W$.
+
+    Use this function to generate a histogram of spike counts for the
+    data of the three types of neurons. Use 100\,ms for the window
+    width.
+    \begin{solution}
+      \lstinputlisting{../code/spikecounts.m}
+      % XXX
+    \end{solution}
+
+    \part Write a function that computes for a range from window
+    widths the mean, the variance and the Fano factor of the
+    corresponding spike counts.  The function should the 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
+    \end{solution}
+
   \end{parts}
   
 \end{questions}