Merge branch 'master' of raven.am28.uni-tuebingen.de:scientificComputing

Well, I just fiddeled around in fano.tex and forgot to make a git pull
before....

programming/lectures/sta_stc.tex

@@ -99,14 +99,6 @@ Cross-Correlation, Spike--Triggered--Average and Reverse Reconstruction}
 \end{frame}
 
 
-\begin{frame}[plain]
-  \frametitle{Rekapitulation}
-  \begin{enumerate}
-  \item PSTH\pause
-  \end{enumerate}
-\end{frame}
-
-
 \begin{frame}
   \frametitle{Introduction to scientific computing}
   \frametitle{Menue}
@@ -119,7 +111,7 @@ Cross-Correlation, Spike--Triggered--Average and Reverse Reconstruction}
 
 
 \begin{frame}[plain]
-  \huge{1. Recapitulation: PSTH}
+  \huge{1. Recapitulation: Plotting neuronal activity as a function of time.}
 \end{frame}
 
 
@@ -142,6 +134,17 @@ Cross-Correlation, Spike--Triggered--Average and Reverse Reconstruction}
 \end{frame}
 
 
+\begin{frame}
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Displaying the neuronal response over time - PSTH}
+  \begin{itemize}
+  \item What does this tell us? \pause
+  \item Wouldn't it be more interesting to relate the response to the stimulus?!
+  \end{itemize}
+\end{frame}
+
+
+
 \begin{frame}[plain]
   \huge{2. Relating stimulus and response}
 \end{frame}
@@ -152,7 +155,7 @@ Cross-Correlation, Spike--Triggered--Average and Reverse Reconstruction}
   \framesubtitle{How can we relate the response to the stimulus?}
     \begin{figure}
       \centering
-      \includegraphics[height=0.9\textheight]{images/conv_stim}
+      \includegraphics[height=0.75\textheight]{images/conv_stim}
     \end{figure}
 \end{frame}
 
@@ -201,20 +204,34 @@ ylabel('correlation')
   \frametitle{Relating stimulus and response}
   \framesubtitle{Cross--correlation - Exercises} 
   \begin{enumerate}
-  \item calculate the cross-correlation between two vectors of random
+  \item Calculate the cross-correlation between two vectors of random
     numbers.
   \item Calculate the cross-correlation between one of these vectors
     and itself (auto-correlation).
   \item Calculate the cross-correlation between one vector and a
     time-shifted version of itself (use \verb+circshift+ to do this).
+  \item Generate two vectors of random numbers, one having a (slight)
+    correlation with the other.
+  \item Calculate the correlation coefficient (\verb+corrcoef+).
+  \item Calculate the cross-correlation.
+  \item Calculate the the correlation coefficient between the one
+    vector and a \verb+circshif+ted version of the other.
+  \item Calculate the cross-correlation of these.
+  \item Find out the maximum correlation and its position.
   \end{enumerate}
   \textbf{Note:} Select max\_lag to be less than 10\% of the length of
   your vectors!
+\end{frame}
+
+
+\begin{frame}[fagile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Cross--correlation - Exercises} 
   \begin{enumerate}
   \item Create the cross correlation of the p-unit data and stimulus.
   \item \textbf{Note:} you have to convert the spike\_times to a PSTH!
   \item Find out the position of the correlation peak. 
-  \item What does this tell you?
+  \item What does it tell you?
   \end{enumerate}
 \end{frame}
 
@@ -273,8 +290,8 @@ ylabel('correlation')
   \begin{enumerate}
     \item Write a function \verb+sta(x, y, count, sample_rate)+ that
       takes the stimulus (x), the response (y, as spike times), the
-      number (count) of sampling points it should cut out from the
+      number (count) of sample points it should cut out from the
-      stimulus and the sampling\_rate to convert from times to
+      stimulus and the sample\_rate to convert from times to
       indices.
     \item \textbf{Beware:} sometimes the spike\_time may be too close
       to the beginning or the end of the stimulus to cut out enough
@@ -284,23 +301,6 @@ ylabel('correlation')
 \end{frame}
 
 
-\begin{frame}[fragile]
-  \frametitle{Relating stimulus and response}
-  \framesubtitle{Spike--Triggered--Average -- STA}
-  What does the \textbf{STA} tell us?
-  \begin{figure}
-    \centering
-    \includegraphics[width=0.25\columnwidth]{images/sta}
-  \end{figure}
-  \begin{enumerate}
-  \item Is there a relation between stimulus and response?\pause
-  \item Is there a lag between them and how large is it?\pause
-  \item How far in the past does a neuron encode?\pause
-  \item Can it see into the future?
-  \end{enumerate}
-\end{frame}
-
-
 \begin{frame}[plain]
   \huge{3. Reverse reconstruction using the \textbf{STA}}
 \end{frame}

projects/project_numbers/Makefile

@@ -0,0 +1,10 @@
+latex:
+	pdflatex *.tex > /dev/null
+	pdflatex *.tex > /dev/null
+
+clean:
+	rm -rf *.log *.aux *.zip *.out auto
+	rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+	zip `basename *.tex .tex`.zip *.pdf *.dat *.mat

projects/project_numbers/numbers.tex

@@ -0,0 +1,60 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
+  -- 11/06/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{questions}
+  \question The accompanying data {\tt Neuron22.mat} stores a single
+  data matrix {\tt data\_unsorted} containing spike from a neuron in
+  macaque prefrontal cortex. The task of the monkey was to
+  discriminate point sets with 1 to 4 points. The first column
+  contains the number of points shown plus one. The remaining columns
+  contain the spike response across 1300ms. During the first 500ms the
+  monkey was fixating a target. The next 800ms the stimulus was
+  shown. This was followed by 1000ms delay time before the monkey was
+  allowed to respond. 
+  
+  \begin{parts}
+    \part Plot the data in an appropriate way. 
+    \part Sort the trials according to the stimulus presented and
+    compute the firing rate (in Hz) in the time interval
+    500-1300ms. Plot the firing rate in an appropriate way. 
+    \part Use an appropriate test to determine whether the firing rate
+    in that interval is significantly different for 1 vs. 4 points
+    shown.
+  \end{parts}
+\end{questions}
+
+
+
+
+
+\end{document}

projects/project_spectra/Makefile

@@ -0,0 +1,10 @@
+latex:
+	pdflatex *.tex > /dev/null
+	pdflatex *.tex > /dev/null
+
+clean:
+	rm -rf *.log *.aux *.zip *.out auto
+	rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+	zip `basename *.tex .tex`.zip *.pdf *.dat *.mat

projects/project_spectra/spectra.tex

@@ -0,0 +1,61 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
+  -- 11/06/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{questions}
+  \question The accompanying file contains ten stimulus and response
+  sequences of a P-Unit of a weakly electric fish {\em Apteronotus
+    leptorhynchus}. Another matrix contains the corresponding {\em
+    electric organ discharge (EOD)} of the fish. The sampling rate is
+  100kHz.
+  \begin{parts}
+    \part Split the data in non-overlapping 200ms windows and plot
+    them in an appropriate way. 
+    \part Compute the autocorrelation of the spike response as well as
+    the cross-correlation between stimulus and spike response. 
+    \part Determine the fundamental stimulus frequency and the EOD
+    frequency using a Fourier transform. 
+    \part Convolve the spike responses (windows) with a Gaussian of
+    appropriate size and compute the average Fourier amplitude
+    spectrum of the spike response. Plot the result in an appropriate
+    way. 
+    \part Determine whether you can find peas in the amplitude
+    spectrum at the fundamental frequency of the EOD and/or the
+    stimulus and/or their difference. 
+  \end{parts}
+\end{questions}
+
+
+
+
+
+\end{document}

statistics/lecture_statistics02.tex

@@ -369,12 +369,12 @@ incubation. The following plot depicts the mean thymus gland weights in (mg):
       the the first $80$ datapoints, and repeat the following steps
       $m=500$ times:
       \begin{enumerate}
-      \item draw $50$ data points from $x$ with replacement
+      \item draw $80$ data points from $x$ with replacement
       \item compute their mean and store it
       \end{enumerate}
       Look at the standard deviation of the computed means.
     \item Compare the result to the standard deviation of the original
-      $50$ data points and the standard error.
+      $80$ data points and the standard error.
     \end{itemize}
   \end{task}
 \end{frame}

statistics/matlab/invg_loglikelihood.m

@@ -1,4 +1,5 @@
 function ll = invg_loglikelihood(x, p)
     mu = p(1);
     lambda = p(2);
-    ll = mean(.5*(log(lambda) - log(2*pi) - 3*log(x)) - lambda*(x-mu).^2./(2*mu^2*x));
+    ll = .5*(log(lambda) - log(2*pi) - 3*log(x)) - ...
+        lambda*(x-mu).^2./(2*mu^2*x);

statistics/matlab/lserr.m

@@ -1,4 +1,4 @@
-function [err, grad] = lserr(param, x, y)
+function [err, grad] = lserr(x, y, param)
     err = mean( (param(1)*x + param(2) - y).^2 );
     
     if nargout == 2