Worked on pointprocess exercises

pointprocesses/exercises/pointprocesses01.tex

@@ -103,6 +103,7 @@ jan.benda@uni-tuebingen.de}
     \begin{solution}
       \begin{lstlisting}
         clear all
+        % not so good:
         load poisson.mat
         whos
         poissonspikes = spikes;
@@ -111,6 +112,14 @@ jan.benda@uni-tuebingen.de}
         load lifadapt.mat;
         lifadaptspikes = spikes;
         clear spikes;
+        % better:
+        clear all
+        x = load( 'poisson.mat' );
+        poissonspikes = x.spikes;
+        x = load( pifou.mat' );
+        pifouspikes = x.spikes;
+        x = load( 'lifadapt.mat' );
+        lifadaptspikes = x.spikes;
       \end{lstlisting}
     \end{solution}
     

pointprocesses/exercises/pointprocesses02.tex

@@ -11,11 +11,11 @@
 \usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
 \pagestyle{headandfoot}
 \ifprintanswers
-\newcommand{\stitle}{: L\"osungen}
+\newcommand{\stitle}{L\"osungen}
 \else
-\newcommand{\stitle}{}
+\newcommand{\stitle}{\"Ubung}
 \fi
-\header{{\bfseries\large \"Ubung 6\stitle}}{{\bfseries\large Statistik}}{{\bfseries\large 27. Oktober, 2015}}
+\header{{\bfseries\large \stitle}}{{\bfseries\large Punktprozesse 2}}{{\bfseries\large 27. Oktober, 2015}}
 \firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email:
 jan.benda@uni-tuebingen.de}
 \runningfooter{}{\thepage}{}
@@ -89,26 +89,27 @@ jan.benda@uni-tuebingen.de}
 \begin{questions}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\question \qt{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 
+\question \qt{Homogener Poisson Prozess}
+Wir wollen den homogenen Poisson Prozess benutzen um Spikes zu generieren,
+mit denen wir die Analysfunktionen des vorherigen \"Ubungszettel \"uberpr\"ufen k\"onnen.
+
+Ein homogener Poisson Prozess mit der Rate $\lambda$ (measured in Hertz) ist ein Punktprozess,
+bei dem die Wahrschienlichkeit eines Ereignisses unabh\"angig von der Zeit $t$ und
+unabh\"angig von vorherigen Ereignissen ist.
+Die Wahrscheinlichkeit $P$ eines Ereignisses innerhalb eines Bins der Breite $\Delta t$ ist
 \[ P = \lambda \cdot \Delta t \]
-for sufficiently small $\Delta t$.
+f\"ur gen\"ugend kleine $\Delta t$.
 \begin{parts}
   
-  \part Write a function that generates $n$ homogeneous Poisson spike trains of a given duration $T_{max}$
-  with rate $\lambda$.
+  \part Schreibe eine Funktion die $n$ homogene Poisson Spiketrains
+  einer gegebenen Dauer $T_{max}$ mit rate $\lambda$ erzeugt.
   \begin{solution}
     \lstinputlisting{hompoissonspikes.m}
   \end{solution}
   
-  \part Using this function, generate a few trials and display them in a raster plot.
+  \part Benutze diese Funktion um einige Trials von Spikes zu erzeugen
+  und plotte diese als Spikeraster.
   \begin{solution}
-    \lstinputlisting{../code/spikeraster.m}
     \begin{lstlisting}
       spikes = hompoissonspikes( 10, 100.0, 0.5 );
       spikeraster( spikes )
@@ -117,41 +118,31 @@ for sufficiently small $\Delta t$.
     \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{../code/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{../code/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?
+  \part Berechne Histogramme aus den Interspikeintervallen von $n$
+  Poisson Spiketrains mit der Rate $\lambda=100$\,Hz. Ver\"andere
+  \"uber die Dauer $T_{max}$ der Spiketrains und die Anzahl $n$ der
+  Trials die Anzahl der Intervalle und ver\"andere auch die Binbreite
+  des Histograms (fange mit 1\,ms an). Wieviele Interspikeintervalle
+  werden ben\"otigt um ein ``sch\"ones'' Histogramm zu erhalten? Wie
+  lange m\"usste man also von dem Neuron ableiten?
   \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.
+    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
+  \part Vergleiche das Histogramm mit der zu erwartenden Verteilung
+  der Intervalle $T$ des Poisson Prozesses
   \[ p(T) = \lambda e^{-\lambda T} \]
-  for various rates $\lambda$.
+  mit rate $\lambda$.
   \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 $\Delta t$ 
+  \part \extra Was pasiert mit den Histogrammen, wenn die Binbreite der Histogramme kleiner
+  als das bei der Erzeugung der $\Delta t$ der 
   used for generating the Poisson spikes?
   \begin{solution}
     The bins between the discretization have zero entries. Therefore