Started working on pointprocesses

bootstrap/lecture/Makefile

@@ -1,22 +1,29 @@
 BASENAME=bootstrap
+
 PYFILES=$(wildcard *.py)
 PYPDFFILES=$(PYFILES:.py=.pdf)
 
-pdf : $(BASENAME)-chapter.pdf $(PYPDFFILES)
+all : pdf 
+
+# script:
+pdf : $(BASENAME)-chapter.pdf
 
-$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex
+$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex $(PYPDFFILES)
 	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
 
 $(PYPDFFILES) : %.pdf : %.py
 	python $<
 
 clean :
-	rm -f *~ $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out $(BASENAME).aux $(BASENAME).log
+	rm -f *~ 
+	rm -f $(BASENAME).aux $(BASENAME).log
+	rm -f $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out
+	rm -f $(PYPDFFILES) $(GPTTEXFILES)
 
 cleanall : clean
 	rm -f $(BASENAME)-chapter.pdf
 
-watch :
+watchpdf :
 	while true; do ! make -q pdf && make pdf; sleep 0.5; done
 
 

likelihood/lecture/Makefile

@@ -1,22 +1,29 @@
 BASENAME=likelihood
+
 PYFILES=$(wildcard *.py)
 PYPDFFILES=$(PYFILES:.py=.pdf)
 
-pdf : $(BASENAME)-chapter.pdf $(PYPDFFILES)
+all : pdf 
+
+# script:
+pdf : $(BASENAME)-chapter.pdf
 
-$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex
+$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex $(PYPDFFILES)
 	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
 
 $(PYPDFFILES) : %.pdf : %.py
 	python $<
 
 clean :
-	rm -f *~ $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out $(BASENAME).aux $(BASENAME).log
+	rm -f *~ 
+	rm -f $(BASENAME).aux $(BASENAME).log
+	rm -f $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out
+	rm -f $(PYPDFFILES) $(GPTTEXFILES)
 
 cleanall : clean
 	rm -f $(BASENAME)-chapter.pdf
 
-watch :
+watchpdf :
 	while true; do ! make -q pdf && make pdf; sleep 0.5; done
 
 

pointprocesses/exercises/Makefile

@@ -0,0 +1,35 @@
+BASENAME=pointprocesses
+TEXFILES=$(wildcard $(BASENAME)??.tex)
+EXERCISES=$(TEXFILES:.tex=.pdf)
+SOLUTIONS=$(EXERCISES:pointprocesses%=pointprocesses-solutions%)
+
+.PHONY: pdf exercises solutions watch watchexercises watchsolutions clean
+
+pdf : $(SOLUTIONS) $(EXERCISES)
+
+exercises : $(EXERCISES)
+
+solutions : $(SOLUTIONS)
+
+$(SOLUTIONS) : pointprocesses-solutions%.pdf : pointprocesses%.tex instructions.tex
+	{ echo "\\documentclass[answers,12pt,a4paper,pdftex]{exam}"; sed -e '1d' $<; } > $(patsubst %.pdf,%.tex,$@)
+	pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) || true
+	rm $(patsubst %.pdf,%,$@).[!p]*
+
+$(EXERCISES) : %.pdf : %.tex instructions.tex
+	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
+
+watch :
+	while true; do ! make -q pdf && make pdf; sleep 0.5; done
+
+watchexercises :
+	while true; do ! make -q exercises && make exercises; sleep 0.5; done
+
+watchsolutions :
+	while true; do ! make -q solutions && make solutions; sleep 0.5; done
+
+clean :
+	rm -f *~ *.aux *.log *.out
+
+cleanup : clean
+	rm -f $(SOLUTIONS) $(EXERCISES)

pointprocesses/exercises/instructions.tex

@@ -0,0 +1,11 @@
+\vspace*{-6.5ex}
+\begin{center}
+\textbf{\Large Einf\"uhrung in die wissenschaftliche Datenverarbeitung}\\[1ex]
+{\large Jan Grewe, Jan Benda}\\[-3ex]
+Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\
+\end{center}
+
+\ifprintanswers%
+\else
+
+\fi

pointprocesses/exercises/pointprocesses01.tex

@@ -0,0 +1,202 @@
+\documentclass[12pt,a4paper,pdftex]{exam}
+
+\usepackage[german]{babel}
+\usepackage{pslatex}
+\usepackage[mediumspace,mediumqspace,Gray]{SIunits}      % \ohm, \micro
+\usepackage{xcolor}
+\usepackage{graphicx}
+\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
+
+%%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
+\pagestyle{headandfoot}
+\ifprintanswers
+\newcommand{\stitle}{: L\"osungen}
+\else
+\newcommand{\stitle}{}
+\fi
+\header{{\bfseries\large \"Ubung 6\stitle}}{{\bfseries\large Statistik}}{{\bfseries\large 27. Oktober, 2015}}
+\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email:
+jan.benda@uni-tuebingen.de}
+\runningfooter{}{\thepage}{}
+
+\setlength{\baselineskip}{15pt}
+\setlength{\parindent}{0.0cm}
+\setlength{\parskip}{0.3cm}
+\renewcommand{\baselinestretch}{1.15}
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+  language=Matlab,
+  basicstyle=\ttfamily\footnotesize,
+  numbers=left,
+  numberstyle=\tiny,
+  title=\lstname,
+  showstringspaces=false,
+  commentstyle=\itshape\color{darkgray},
+  breaklines=true,
+  breakautoindent=true,
+  columns=flexible,
+  frame=single,
+  xleftmargin=1em,
+  xrightmargin=1em,
+  aboveskip=10pt
+}
+
+%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{bm} 
+\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}}
+
+%%%%% page breaks %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcommand{\continue}{\ifprintanswers%
+\else
+\vfill\hspace*{\fill}$\rightarrow$\newpage%
+\fi}
+\newcommand{\continuepage}{\ifprintanswers%
+\newpage
+\else
+\vfill\hspace*{\fill}$\rightarrow$\newpage%
+\fi}
+\newcommand{\newsolutionpage}{\ifprintanswers%
+\newpage%
+\else
+\fi}
+
+%%%%% new commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcommand{\qt}[1]{\textbf{#1}\\}
+\newcommand{\pref}[1]{(\ref{#1})}
+\newcommand{\extra}{--- Zusatzaufgabe ---\ \mbox{}}
+\newcommand{\code}[1]{\texttt{#1}}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document}
+
+\input{instructions}
+
+
+\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 
+\[ P = \lambda \cdot \Delta t \]
+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{../code/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{../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?
+  \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 ../code 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{../code/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{../code/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{../code/fano.m}
+    \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonfano100hz}}
+  \end{solution}
+  
+\end{parts}
+
+\end{questions}
+
+\end{document}

pointprocesses/exercises/poisson.tex

@@ -1,160 +0,0 @@
-\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}

pointprocesses/lecture/Makefile

@@ -1,142 +1,70 @@
 BASENAME=pointprocesses
 
-TEXFILE=$(BASENAME).tex
+PYFILES=$(wildcard *.py)
-DVIFILE=$(BASENAME).dvi
+PYPDFFILES=$(PYFILES:.py=.pdf)
-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
+all: pdf slides thumbs
-.PHONY: epsfigs
+
+# script:
+pdf : $(BASENAME)-chapter.pdf
+$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex $(GPTTEXFILES) $(PYPDFFILES)
+	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
 
 
+# slides:
+slides: $(BASENAME)-slides.pdf
+$(BASENAME)-slides.pdf : $(BASENAME)-slides.tex $(GPTTEXFILES) $(PYPDFFILES)
+	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
+
 # thumbnails:
-thumbs: $(THUMBNAILSFILE)
+thumbs: $(BASENAME)-handout.pdf
-$(THUMBNAILSFILE): $(TEXFILE) $(GPTTEXFILES)
+$(BASENAME)-handout.pdf: $(BASENAME)-slides.tex $(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'
+	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
+watchslides :
-html : $(HTMLTEXFILE) $(GPTTEXFILES)
+	while true; do ! make -q slides && make slides; sleep 0.5; done
-	rm -f $(HTMLDIR)/*
+
-	htlatex $<
+# python plots:
-	mkdir -p $(HTMLDIR)
+$(PYPDFFILES) : %.pdf: %.py
-	mv $(HTMLBASENAME).html $(HTMLDIR)
+	python $<
-	mv $(HTMLBASENAME)*.* $(HTMLDIR)
+
-	mv z*.gif $(HTMLDIR)
+# gnuplot plots:
-	cd $(HTMLDIR); for i in *.gif; do convert -page +0+0 $$i tmp.gif; mv tmp.gif $$i; done; rmtex $(HTMLBASENAME)
+$(GPTTEXFILES) : %.tex: %.gpt whitestyles.gp
-
-#$(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 $(BASENAME).aux $(BASENAME).log
-	rm -f $(GPTTEXFILES)
+	rm -f $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out
+	rm -f $(BASENAME)-slides.aux $(BASENAME)-slides.log $(BASENAME)-slides.out $(BASENAME)-slides.toc $(BASENAME)-slides.nav $(BASENAME)-slides.snm $(BASENAME)-slides.vrb
+	rm -f $(PYPDFFILES) $(GPTTEXFILES)
 
-cleanup :
+cleanall : clean
-	rm -f *~
+	rm -f $(BASENAME)-chapter.pdf $(BASENAME)-slides.pdf $(BASENAME)-handout.pdf
-	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 pdf:        make the pdf file of the script.\n"\
-	"make foils:  make black&white postscript foils of the talk.\n"\
+	"make slides:     make the pdf file of the slides.\n"\
 	"make thumbs:     make color thumbnails of the talk.\n"\
-	"make again: run latex and make the pdf file of the talk,\n"\
+	"make watchpdf:   make the pdf file of the script\n"\
-        "            no matter whether you changed the .tex file or not.\n\n"\
+        "                 whenever the tex file is modified.\n"\
-	"make watchpdf:   make the pdf file of the talk\n"\
+	"make watchpdf:   make the pdf file of the slides\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"\
+        "                 just leave the source files and the final .pdf files.\n"\
 	"make cleanup:    remove all intermediate files as well as\n"\
-        "                 the final .ps and .pdf files.\n"\
+        "                 the final .pdf files.\n"\
-	"make cleanplots: move all unused .gpt and .dat files\n"\
-        "                 into unusedplots/ and unuseddata/, respectively."

pointprocesses/lecture/pointprocesses-slides.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},
+ backgroundcolor=\color{blue!10},
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+ captionpos=b,
+ xleftmargin=1em,
+ xrightmargin=1em,
+ aboveskip=10pt
+ }
+
+ 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\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}

pointprocesses/lecture/pointprocesses.tex

@@ -1,412 +1,168 @@
-\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},
- backgroundcolor=\color{blue!10},
- breaklines=true,
- breakautoindent=true,
- columns=flexible,
- frame=single,
- captionpos=b,
- xleftmargin=1em,
- xrightmargin=1em,
- aboveskip=10pt
- }
-
- 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{document} 
+\chapter{\tr{Point processes}{Punktprozesse}}
-
-\begin{frame}[plain]
-  \frametitle{}
-  \vspace{-1cm}
-  \titlepage % erzeugt Titelseite
-\end{frame}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{figure}[t]
-\begin{frame}
+  \texpicture{pointprocessscetchB}
-  \frametitle{Content}
+  \caption{\label{pointprocessscetchfig}Ein Punktprozess ist eine
-  \tableofcontents
+    Abfolge von Zeitpunkten $t_i$ die auch durch die Intervalle
-\end{frame}
+    $T_i=t_{i+1}-t_i$ oder die Anzahl der Ereignisse $n_i$ beschrieben
-
+    werden kann. }
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\end{figure}
-\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
+Ein zeitlicher Punktprozess ist ein stochastischer Prozess der eine Abfolge von Ereignissen zu den Zeiten $\{t_i\}$, $t_i \in \reZ$ generiert.
-  at times $\{t_i\}$, $t_i \in \reZ$.
 
-  For each point process there is an underlying continuous-valued
+Jeder Punktprozess wird durch einen sich in der Zeit kontinuierlichen
-  process evolving in time. The associated point process occurs when
+entwickelnden Prozess generiert. Wann immer dieser Prozess eine Schwelle \"uberschreitet
-  the underlying continuous process crosses a threshold.
+wird ein Ereigniss des Punktprozesses erzeugt. Zum Beispiel:
-  Examples:
 \begin{itemize}
-  \item Spikes/heartbeat: generated by the dynamics of the membrane potential of neurons/heart cells.
+\item Aktionspotentiale/Herzschlag: wird durch die Dynamik des
-  \item Earth quakes: generated by the pressure dynamics between the tectonic plates on either side of a geological fault line.
+  Membranpotentials eines Neurons/Herzzelle erzeugt.
-  \item Onset of cricket/frogs/birds/... songs: generated by the dynamics of the state of a nervous system.
+\item Erdbeben: wird durch die Dynamik des Druckes zwischen
+  tektonischen Platten auf beiden Seiten einer geologischen Verwerfung
+  erzeugt.
+\item Zeitpunkt eines Grillen/Frosch/Vogelgesangs: wird durch die
+  Dynamic des Nervensystems und des Muskelapparates erzeugt.
 \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}
+\section{Rate eines Punktprozesses}
-
-\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}
+\section{Intervall Statistiken}
+
+\begin{figure}[t]
+  \includegraphics[width=0.45\textwidth]{poissonisih100hz}\hfill
+  \includegraphics[width=0.45\textwidth]{lifisih16}
+  \caption{\label{isihfig}Interspike-Intervall Histogramme von einem Poisson Prozess (links)
+    und einem Integrate-and-Fire Neuron (rechts).}
+\end{figure}
+
+\subsection{First order (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}
+\subsection{Interval return maps}
-  \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}
+\begin{figure}[t]
-  \frametitle{Serial interval correlations}
+  \begin{minipage}[t]{0.49\textwidth}
+    LIF $I=10$, $\tau_{adapt}=100$\,ms:\\
+    \includegraphics[width=1\textwidth]{lifadaptreturnmap10-100ms}
+  \end{minipage}
+  \hfill
+  \begin{minipage}[t]{0.49\textwidth}
+    LIF $I=15.7$, $\tau_{OU}=100$\,ms:\\
+    \includegraphics[width=1\textwidth]{lifoureturnmap16-100ms}
+  \end{minipage}
+  \caption{\label{returnmapfig}Interspike-Intervall return maps.}
+\end{figure}
+
+\subsection{Serial correlations of the intervals}
 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}
+$\rho_0=1$ (correlation of each interval with itself).
-  \item $\rho_0=1$ (correlation of each interval with itself).
+
-  \item Poisson process: $\rho_k =0$ for $k>0$ (renewal process!) 
+\begin{figure}[t]
-  \end{itemize}
+  \begin{minipage}[t]{0.49\textwidth}
-  \vfill
+    LIF $I=10$, $\tau_{adapt}=100$\,ms:\\
-  \includegraphics[width=0.7\textwidth]{poissonserial100hz}
+    \includegraphics[width=1\textwidth]{lifadaptserial10-100ms}
-\end{frame}
+  \end{minipage}
+  \hfill
+  \begin{minipage}[t]{0.49\textwidth}
+    LIF $I=15.7$, $\tau_{OU}=100$\,ms:\\
+    \includegraphics[width=1\textwidth]{lifouserial16-100ms}
+  \end{minipage}
+  \caption{\label{serialcorrfig}Serial correlations.}
+\end{figure}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Count statistics}
 
-\begin{frame}
+\begin{figure}[t]
-  \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}
+  \caption{\label{countstatsfig}Count Statistik.}
+\end{figure}
 
-\begin{frame}
+Histogram of number of events $N$ (counts) within observation window of duration $W$.
-  \frametitle{Count statistics of Poisson process}
-  Poisson distribution:
-  \[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \]
 
-  \vfill
+\subsection{Fano factor}
-  \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}\hfill
+
-  \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}
+\begin{figure}[t]
-\end{frame}
+  \begin{minipage}[t]{0.49\textwidth}
+    Poisson process $\lambda=100$\,Hz:\\
+    \includegraphics[width=1\textwidth]{poissonfano100hz}
+  \end{minipage}
+  \hfill
+  \begin{minipage}[t]{0.49\textwidth}
+    LIF $I=10$, $\tau_{adapt}=100$\,ms:\\
+    \includegraphics[width=1\textwidth]{lifadaptfano10-100ms}
+  \end{minipage}
+  \caption{\label{fanofig}Fano factor.}
+\end{figure}
 
-\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}
+\section{\tr{Homogeneous Poisson process}{Homogener Poisson Prozess}}
-  \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}
+\begin{figure}[t]
-  \frametitle{Interval return map of LIF with adaptation}
+  \includegraphics[width=1\textwidth]{poissonraster100hz}
-  LIF $I=10$, $\tau_{adapt}=100$\,ms:
+  \caption{\label{hompoissonfig}Rasterplot von Poisson-Spikes.}
-  \includegraphics[width=1\textwidth]{lifadaptreturnmap10-100ms}\\
+\end{figure}
-  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}
 
+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 $\Delta t$
-\section{Non stationary}
+is
-\subsection{Inhomogeneous Poisson process}
+\[ P=\lambda \cdot \Delta t \]
-\subsection{Firing rate}
+for a Poisson process with rate $\lambda$.
-\subsection{Instantaneous rate}
-\subsection{Autocorrelation}
-\subsection{Crosscorrelation}
-\subsection{Joint PSTH}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Statistics of homogeneous Poisson process}
-\section{Renewal process}
-\subsection{Superthreshold firing}
-\subsection{Subthreshold firing}
-\section{Non-renewal processes}
-\subsection{Bursting}
-\subsection{Resonator}
 
+\begin{figure}[t]
+  \includegraphics[width=0.45\textwidth]{poissonisihexp20hz}\hfill
+  \includegraphics[width=0.45\textwidth]{poissonisihexp100hz}
+  \caption{\label{hompoissonisihfig}Interspike interval histograms of poisson spike train.}
+\end{figure}
 
-\subsection{Standard distributions}
+\begin{itemize}
-\subsubsection{Gamma}
+\item Exponential distribution of intervals $T$: $p(T) = \lambda e^{-\lambda T}$
-\subsubsection{How to read ISI histograms}
+\item Mean interval $\mu_{ISI} = \frac{1}{\lambda}$
-refractoriness, poisson tail, sub-, supra-threshold, missed spikes
+\item Variance of intervals $\sigma_{ISI}^2 = \frac{1}{\lambda^2}$
+\item Coefficient of variation $CV_{ISI} = 1$
+\item Serial correlation $\rho_k =0$ for $k>0$ (renewal process!)   
+\item Fano factor $F=1$
+\end{itemize}
 
+\subsection{Count statistics of Poisson process}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{figure}[t]
-\section{Correlation with stimulus}
+  \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}\hfill
-\subsection{Tuning curve}
+  \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}
-\subsection{Linear filter}
+  \caption{\label{hompoissoncountfig}Count statistics of poisson spike train.}
-\subsection{Spatiotemporal receptive field}
+\end{figure}
-\subsection{Generalized linear model}
 
-\begin{frame}
+Poisson distribution:
-\end{frame}
+\[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \]

pointprocesses/lecture/pointprocessscetchA.eps

@@ -1,7 +1,7 @@
 %!PS-Adobe-2.0 EPSF-2.0
 %%Title: pointprocessscetchA.tex
 %%Creator: gnuplot 4.6 patchlevel 4
-%%CreationDate: Sun Oct 26 14:09:12 2014
+%%CreationDate: Sun Oct 25 21:47:09 2015
 %%DocumentFonts: 
 %%BoundingBox: 50 50 373 135
 %%EndComments
@@ -433,7 +433,7 @@ SDict begin [
   /Author (jan)
 %  /Producer (gnuplot)
 %  /Keywords ()
-  /CreationDate (Sun Oct 26 14:09:12 2014)
+  /CreationDate (Sun Oct 25 21:47:09 2015)
   /DOCINFO pdfmark
 end
 } ifelse

pointprocesses/lecture/pointprocessscetchB.eps

@@ -1,7 +1,7 @@
 %!PS-Adobe-2.0 EPSF-2.0
 %%Title: pointprocessscetchB.tex
 %%Creator: gnuplot 4.6 patchlevel 4
-%%CreationDate: Sun Oct 26 17:34:18 2014
+%%CreationDate: Sun Oct 25 21:47:09 2015
 %%DocumentFonts: 
 %%BoundingBox: 50 50 373 237
 %%EndComments
@@ -433,7 +433,7 @@ SDict begin [
   /Author (jan)
 %  /Producer (gnuplot)
 %  /Keywords ()
-  /CreationDate (Sun Oct 26 17:34:18 2014)
+  /CreationDate (Sun Oct 25 21:47:09 2015)
   /DOCINFO pdfmark
 end
 } ifelse

scientificcomputing-script.tex

@@ -59,7 +59,8 @@
 
 % figures:
 \setlength{\fboxsep}{0pt}
-\newcommand{\texpicture}[1]{{\sffamily\footnotesize\input{#1.tex}}}
+\newcommand{\texinputpath}{}
+\newcommand{\texpicture}[1]{{\sffamily\footnotesize\input{\texinputpath#1.tex}}}
 %\newcommand{\texpicture}[1]{\fbox{\sffamily\footnotesize\input{#1.tex}}}
 %\newcommand{\texpicture}[1]{\setlength{\fboxsep}{2mm}\fbox{#1}}
 %\newcommand{\texpicture}[1]{}
@@ -213,7 +214,7 @@
   \arabic{theexercise}:}\newline \newcommand{\exercisesource}{#1}}%
   {\ifthenelse{\equal{\exercisesource}{}}{}{\ifthenelse{\value{theexercise}>\value{maxexercise}}{}{\medskip\lstinputlisting{\codepath\exercisesource}}}\medskip\stepcounter{theexercise}}
 
-\graphicspath{{statistics/lecture/}{statistics/lecture/figures/}{bootstrap/lecture/}{bootstrap/lecture/figures/}{likelihood/lecture/}{likelihood/lecture/figures/}}
+\graphicspath{{statistics/lecture/}{statistics/lecture/figures/}{bootstrap/lecture/}{bootstrap/lecture/figures/}{likelihood/lecture/}{likelihood/lecture/figures/}{pointprocesses/lecture/}{pointprocesses/lecture/figures/}}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -233,4 +234,8 @@
 \renewcommand{\codepath}{likelihood/code/}
 \include{likelihood/lecture/likelihood}
 
+\renewcommand{\codepath}{pointprocesses/code/}
+\renewcommand{\texinputpath}{pointprocesses/lecture/}
+\include{pointprocesses/lecture/pointprocesses}
+
 \end{document}

statistics/lecture/Makefile

@@ -1,22 +1,29 @@
 BASENAME=statistics
+
 PYFILES=$(wildcard *.py)
 PYPDFFILES=$(PYFILES:.py=.pdf)
 
-pdf : $(BASENAME)-chapter.pdf $(PYPDFFILES)
+all : pdf 
+
+# script:
+pdf : $(BASENAME)-chapter.pdf
 
-$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex
+$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex $(PYPDFFILES)
 	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
 
 $(PYPDFFILES) : %.pdf : %.py
 	python $<
 
 clean :
-	rm -f *~ $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out $(BASENAME).aux $(BASENAME).log
+	rm -f *~ 
+	rm -f $(BASENAME).aux $(BASENAME).log
+	rm -f $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out
+	rm -f $(PYPDFFILES) $(GPTTEXFILES)
 
 cleanall : clean
 	rm -f $(BASENAME)-chapter.pdf
 
-watch :
+watchpdf :
 	while true; do ! make -q pdf && make pdf; sleep 0.5; done
 
 

statistics/lecture/boxwhisker.py

@@ -43,5 +43,5 @@ ax.annotate('maximum',
 ax.boxplot( x, whis=100.0 )
 plt.tight_layout()
 plt.savefig('boxwhisker.pdf')
-plt.show()
+#plt.show()
 

statistics/lecture/correlation.py

@@ -5,7 +5,6 @@ plt.xkcd()
 fig = plt.figure( figsize=(6,5) )
 n = 200
 for k, r  in enumerate( [ 1.0, 0.6, 0.0, -0.9 ] ) :
-    print r
     x = np.random.randn( n )
     y = r*x + np.sqrt(1.0-r*r)*np.random.randn( n )
     ax = fig.add_subplot( 2, 2, k+1 )
@@ -30,5 +29,4 @@ for k, r  in enumerate( [ 1.0, 0.6, 0.0, -0.9 ] ) :
 
 plt.tight_layout()
 plt.savefig('correlation.pdf')
-plt.show()
+#plt.show()
-

statistics/lecture/diehistograms.py

@@ -28,5 +28,4 @@ ax.set_ylabel( 'Probability' )
 ax.hist([x2, x1], bins, normed=True, color=['#FFCC00', '#FFFF66' ])
 plt.tight_layout()
 fig.savefig( 'diehistograms.pdf' )
-plt.show()
+#plt.show()
-

statistics/lecture/median.py

@@ -29,5 +29,4 @@ ax.plot(x,g, 'b', lw=4)
 ax.plot([0.0, 0.0], [0.0, 0.45], 'k', lw=2 )
 plt.tight_layout()
 fig.savefig( 'median.pdf' )
-plt.show()
+#plt.show()
-

statistics/lecture/nonlincorrelation.py

@@ -39,4 +39,4 @@ ax.scatter( x, z )
 
 plt.tight_layout()
 plt.savefig('nonlincorrelation.pdf')
-plt.show()
+#plt.show()

statistics/lecture/pdfhistogram.py

@@ -35,5 +35,5 @@ ax.hist(r, 20, normed=True, color='#FFCC00')
 
 plt.tight_layout()
 fig.savefig( 'pdfhistogram.pdf' )
-plt.show()
+#plt.show()
 

statistics/lecture/pdfprobabilities.py

@@ -32,5 +32,4 @@ ax.fill_between( x[(x>x1)&(x<x2)], 0.0, g[(x>x1)&(x<x2)], color='#cc0000' )
 ax.plot(x,g, 'b', lw=4)
 plt.tight_layout()
 fig.savefig( 'pdfprobabilities.pdf' )
-plt.show()
+#plt.show()
-

statistics/lecture/quartile.py

@@ -46,5 +46,4 @@ ax.plot([q[0], q[0]], [0.0, 0.4], 'k', lw=2 )
 ax.plot([q[2], q[2]], [0.0, 0.4], 'k', lw=2 )
 plt.tight_layout()
 fig.savefig( 'quartile.pdf' )
-plt.show()
+#plt.show()
-