From 77b666634727df424ab19469dd7375e54e852ae1 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 19 Jan 2021 13:28:51 +0100 Subject: [PATCH] [pointprocesses] cleaned up m and pdf files --- pointprocesses/exercises/Makefile | 2 +- pointprocesses/exercises/counthist.pdf | Bin 4653 -> 0 bytes pointprocesses/exercises/hompoissonisih.m | 18 -- pointprocesses/exercises/hompoissonisistats.m | 46 ---- pointprocesses/exercises/hompoissonspikes.m | 19 -- .../exercises/iafisistats-solutions.pdf | Bin 210869 -> 0 bytes pointprocesses/exercises/iafisistats.pdf | Bin 81872 -> 0 bytes pointprocesses/exercises/iafisistats.tex | 142 ------------- .../{code => exercises}/inversegauss.m | 0 .../{code => exercises}/inversegaussplot.m | 0 .../{code => exercises}/lifficurves.m | 0 pointprocesses/{code => exercises}/lifisih.m | 0 .../{code => exercises}/lifisistats.m | 0 pointprocesses/exercises/pointprocesses-2.tex | 200 ++++++++---------- pointprocesses/exercises/pointprocesses-3.tex | 163 -------------- .../exercises/pointprocesses01-de.tex | 198 ----------------- .../exercises/poisson-solutions.pdf | Bin 199254 -> 0 bytes .../poissoncounthistdist100hz100ms.pdf | Bin 3815 -> 0 bytes .../poissoncounthistdist100hz10ms.pdf | Bin 3630 -> 0 bytes pointprocesses/exercises/poissonfano100hz.pdf | Bin 17762 -> 0 bytes pointprocesses/exercises/poissonisihist.pdf | Bin 0 -> 7119 bytes pointprocesses/exercises/poissonisistats.pdf | Bin 26757 -> 0 bytes .../exercises/poissonraster100hz.pdf | Bin 6050 -> 0 bytes .../exercises/poissonserial100hz.pdf | Bin 4366 -> 0 bytes pointprocesses/exercises/psth.tex | 48 ++--- 25 files changed, 106 insertions(+), 730 deletions(-) delete mode 100644 pointprocesses/exercises/counthist.pdf delete mode 100644 pointprocesses/exercises/hompoissonisih.m delete mode 100644 pointprocesses/exercises/hompoissonisistats.m delete mode 100644 pointprocesses/exercises/hompoissonspikes.m delete mode 100644 pointprocesses/exercises/iafisistats-solutions.pdf delete mode 100644 pointprocesses/exercises/iafisistats.pdf delete mode 100644 pointprocesses/exercises/iafisistats.tex rename pointprocesses/{code => exercises}/inversegauss.m (100%) rename pointprocesses/{code => exercises}/inversegaussplot.m (100%) rename pointprocesses/{code => exercises}/lifficurves.m (100%) rename pointprocesses/{code => exercises}/lifisih.m (100%) rename pointprocesses/{code => exercises}/lifisistats.m (100%) delete mode 100644 pointprocesses/exercises/pointprocesses-3.tex delete mode 100644 pointprocesses/exercises/pointprocesses01-de.tex delete mode 100644 pointprocesses/exercises/poisson-solutions.pdf delete mode 100644 pointprocesses/exercises/poissoncounthistdist100hz100ms.pdf delete mode 100644 pointprocesses/exercises/poissoncounthistdist100hz10ms.pdf delete mode 100644 pointprocesses/exercises/poissonfano100hz.pdf create mode 100644 pointprocesses/exercises/poissonisihist.pdf delete mode 100644 pointprocesses/exercises/poissonisistats.pdf delete mode 100644 pointprocesses/exercises/poissonraster100hz.pdf delete mode 100644 pointprocesses/exercises/poissonserial100hz.pdf diff --git a/pointprocesses/exercises/Makefile b/pointprocesses/exercises/Makefile index 0d84b85..2bbd561 100644 --- a/pointprocesses/exercises/Makefile +++ b/pointprocesses/exercises/Makefile @@ -1,3 +1,3 @@ -TEXFILES=$(wildcard pointprocesses-?.tex) +TEXFILES=$(wildcard pointprocesses-?.tex) psth.tex include ../../exercises.mk diff --git a/pointprocesses/exercises/counthist.pdf b/pointprocesses/exercises/counthist.pdf deleted file mode 100644 index 0cbcacf0f1f1812e63431e67b5dc2e875d9b84cd..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 4653 zcmb_Ac~}!?`T|&P)H>G*4 zfGOORY?XYkOKe8w?0R-|)44ST{cDDX`#NjtM}?YA=A)xbitB;>!Lpf;u~(^=@%F6-QAoNZ z<>yByk2JS-i<4vT|1vTVmswS{E5n@C`1K3fS1+w2`m+ZjLt9dWYaTas@6^S;P>!@K z&i15b_7nnafr9s>hk0~eg%}Bpi6r=$8k>Z zi5m?s$Xz{wW>a>Stsl(p=cVZ-89ywaum6{&H!CJhZv+yHb{yecbib-wu5qrgL@x 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Hz, nisi=%d', rate, length( isivec ) ) ) -xlim( [ 0.0 1000.0*xmax ] ) -ylim( [ 0.0 1.1*rate ] ) -legend( 'data', 'poisson' ) -hold off diff --git a/pointprocesses/exercises/hompoissonisistats.m b/pointprocesses/exercises/hompoissonisistats.m deleted file mode 100644 index 7ca3cf3..0000000 --- a/pointprocesses/exercises/hompoissonisistats.m +++ /dev/null @@ -1,46 +0,0 @@ -rates = 1:1:100; -avisi = []; -sdisi = []; -cvisi = []; - -for rate = rates - spikes = hompoissonspikes( 10, rate, 100.0 ); - isivec = isis( spikes ); - av = mean( isivec ); - sd = std( isivec ); - cv = sd/av; - avisi = [ avisi av ]; - sdisi = [ sdisi sd ]; - cvisi = [ cvisi cv ]; -end - -f = figure; -subplot( 1, 3, 1 ); -scatter( rates, 1000.0*avisi, 'b', 'filled' ); -hold on; -plot( rates, 1000.0./rates, 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 1000 ] ); -title( 'Mean ISI [ms]' ); -legend( 'simulation', 'theory 1/\lambda' ); - -subplot( 1, 3, 2 ); -scatter( rates, 1000.0*sdisi, 'b', 'filled' ); -hold on; -plot( rates, 1000.0./rates, 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 1000 ] ) -title( 'Standard deviation ISI [ms]' ); -legend( 'simulation', 'theory 1/\lambda' ); - -subplot( 1, 3, 3 ); -scatter( rates, cvisi, 'b', 'filled' ); -hold on; -plot( rates, ones( size( rates ) ), 'r' ); -hold off; -xlabel( 'Rate \lambda [Hz]' ); -ylim( [ 0 2 ] ) -title( 'CV' ); -legend( 'simulation', 'theory' ); diff --git a/pointprocesses/exercises/hompoissonspikes.m b/pointprocesses/exercises/hompoissonspikes.m deleted file mode 100644 index 43b4e5c..0000000 --- a/pointprocesses/exercises/hompoissonspikes.m +++ /dev/null @@ -1,19 +0,0 @@ -function spikes = hompoissonspikes( trials, rate, tmax ) -% Generate spike times of a homogeneous poisson process -% trials: number of trials that should be generated -% rate: the rate of the Poisson process in Hertz -% tmax: the duration of each trial in seconds -% returns a cell array of vectors of spike times - - dt = 3.33e-5; - p = 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a/pointprocesses/exercises/iafisistats.tex +++ /dev/null @@ -1,142 +0,0 @@ -\documentclass[addpoints,10pt]{exam} -\usepackage{url} -\usepackage{color} -\usepackage{hyperref} -\usepackage{graphicx} - -\pagestyle{headandfoot} -\runningheadrule -\firstpageheadrule - -\firstpageheader{Scientific Computing}{Integrate-and-fire models}{Oct 28, 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{Statistics of integrate-and-fire neurons} - For the following use different variants of the leaky integrate-and-fire models provided in \texttt{lifspikes.m}, - \texttt{lifouspikes.m}, and \texttt{lifadaptspikes.m} do generate some spike train data. - Use the functions you wrote for the Poisson process to analyze the statistics of the spike trains. - \begin{parts} - \part Generate a few trials of the two models for two different inputs - that result in qualitatively different spike trains and display - them in a raster plot. Decide for a noise strength (good values to try are 0.001, 0.01, 0.1, 1). - \begin{solution} - \begin{lstlisting} -spikes = pifspikes( 10, 1.0, 0.5, 0.01 ); -%spikes = pifspikes( 10, 10.0, 0.5, 0.01 ); -%spikes = lifspikes( 10, 11.0, 0.5, 0.001 ); -%spikes = lifspikes( 10, 15.0, 0.5, 0.001 ); -spikeraster( spikes ) - \end{lstlisting} - \mbox{}\\[-3ex] - \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster02}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster10}}\\ - \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster10}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster15}} - \end{solution} - - - \part The inverse Gaussian describes the interspike interval distribution of a PIF driven with white noise: - \[ p(T) = \frac{1}{\sqrt{4\pi D T^3}}\exp\left[-\frac{(T-\langle T \rangle)^2}{4DT\langle T \rangle^2}\right] \] - where $\langle T \rangle$ is the mean interspike interval and - \[ D = \frac{\langle(T - \langle T \rangle)^2\rangle}{2 \langle T \rangle^3} \] - is the diffusion coefficient (variance of the interspike intervals - $T$ divided by two times the mean cubed). Show in two plots how - this distribution depends on $\langle T \rangle$ and $D$. - \begin{solution} - \lstinputlisting{simulations/inversegauss.m} - \lstinputlisting{simulations/inversegaussplot.m} - \colorbox{white}{\includegraphics[width=0.98\textwidth]{inversegauss}} - \end{solution} - - \part Extent your function plotting an interspike interval histogram - to also report the diffusion coefficient $D$. - \begin{solution} - \begin{lstlisting} -... -% annotation: -misi = mean( isis ); -sdisi = std( isis ); -disi = sdisi^2.0/2.0/misi^3; -text( 0.6, 0.7, sprintf( 'mean=%.1f ms', 1000.0*misi ), 'Units', 'normalized' ) -text( 0.6, 0.6, sprintf( 'std=%.1f ms', 1000.0*sdisi ), 'Units', 'normalized' ) -text( 0.6, 0.5, sprintf( 'CV=%.2f', sdisi/misi ), 'Units', 'normalized' ) -text( 0.6, 0.4, sprintf( 'D=%.1f Hz', disi ), 'Units', 'normalized' ) -... - \end{lstlisting} - \end{solution} - - \part Compare intersike interval histograms obtained from the LIF and PIF models with the inverse Gaussian. - \begin{solution} - \lstinputlisting{simulations/lifisih.m} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih01}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih10}}\\ - \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih08}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih16}} - \end{solution} - - \part Plot the firing rate (inverse mean interspike interval), - mean interspike interval, the corresponding standard deviation, - CV, and diffusion coefficient as a function of the input to the LIF - and the PIF with noise strength set to 0.01. - \begin{solution} - \lstinputlisting{simulations/lifisistats.m} - Leaky integrate-and-fire:\\ - \colorbox{white}{\includegraphics[width=0.8\textwidth]{lifisistats}}\\ - Perfect integrate-and-fire:\\ - \colorbox{white}{\includegraphics[width=0.8\textwidth]{pifisistats}} - \end{solution} - - \part Plot the firing rate as a function of input of the LIF and the PIF for various values - of the noise strength. - \begin{solution} - \lstinputlisting{simulations/lifficurves.m} - Leaky integrate-and-fire:\\ - \colorbox{white}{\includegraphics[width=0.7\textwidth]{lifficurves}}\\ - Perfect integrate-and-fire:\\ - \colorbox{white}{\includegraphics[width=0.7\textwidth]{pifficurves}} - \end{solution} - - \part Use the functions for computing serial correlations, count statistics and fano factors - to further explore the statistics of the integrate-and-fire models! - - \end{parts} - -\end{questions} - - -\end{document} diff --git a/pointprocesses/code/inversegauss.m b/pointprocesses/exercises/inversegauss.m similarity index 100% rename from pointprocesses/code/inversegauss.m rename to pointprocesses/exercises/inversegauss.m diff --git a/pointprocesses/code/inversegaussplot.m b/pointprocesses/exercises/inversegaussplot.m similarity index 100% rename from pointprocesses/code/inversegaussplot.m rename to pointprocesses/exercises/inversegaussplot.m diff --git a/pointprocesses/code/lifficurves.m b/pointprocesses/exercises/lifficurves.m similarity index 100% rename from pointprocesses/code/lifficurves.m rename to pointprocesses/exercises/lifficurves.m diff --git a/pointprocesses/code/lifisih.m b/pointprocesses/exercises/lifisih.m similarity index 100% rename from pointprocesses/code/lifisih.m rename to pointprocesses/exercises/lifisih.m diff --git a/pointprocesses/code/lifisistats.m b/pointprocesses/exercises/lifisistats.m similarity index 100% rename from pointprocesses/code/lifisistats.m rename to pointprocesses/exercises/lifisistats.m diff --git a/pointprocesses/exercises/pointprocesses-2.tex b/pointprocesses/exercises/pointprocesses-2.tex index 8af40c9..87ffff3 100644 --- a/pointprocesses/exercises/pointprocesses-2.tex +++ b/pointprocesses/exercises/pointprocesses-2.tex @@ -1,12 +1,12 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\newcommand{\exercisetopic}{Point Processes} -\newcommand{\exercisenum}{X2} +\newcommand{\exercisetopic}{Integrate-and-fire models} +\newcommand{\exercisenum}{13} \newcommand{\exercisedate}{January 19th, 2021} \input{../../exercisesheader} -\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} +\firstpagefooter{Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} @@ -14,113 +14,97 @@ \input{../../exercisestitle} \begin{questions} + \question \textbf{Statistics of integrate-and-fire neurons} + For the following use different variants of the leaky integrate-and-fire models provided in \texttt{lifspikes.m}, + \texttt{lifouspikes.m}, and \texttt{lifadaptspikes.m} do generate some spike train data. + Use the functions you wrote for the Poisson process to analyze the statistics of the spike trains. + \begin{parts} + \part Generate a few trials of the two models for two different inputs + that result in qualitatively different spike trains and display + them in a raster plot. Decide for a noise strength (good values to try are 0.001, 0.01, 0.1, 1). + \begin{solution} + \begin{lstlisting} +spikes = pifspikes( 10, 1.0, 0.5, 0.01 ); +%spikes = pifspikes( 10, 10.0, 0.5, 0.01 ); +%spikes = lifspikes( 10, 11.0, 0.5, 0.001 ); +%spikes = lifspikes( 10, 15.0, 0.5, 0.001 ); +spikeraster( spikes ) + \end{lstlisting} + \mbox{}\\[-3ex] + \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster02}} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifraster10}}\\ + \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster10}} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifraster15}} + \end{solution} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\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 $\lambda$ (gemessen 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 -\[ P = \lambda \cdot \Delta t \] -f\"ur gen\"ugend kleine $\Delta t$. -\begin{parts} - - \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 Benutze diese Funktion um einige Trials von Spikes zu erzeugen - und plotte diese als Spikeraster. - \begin{solution} - \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 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 (fang 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. - \end{solution} - - \part Vergleiche Interspike-Intervall Histogramme von Poisson-Spikes - verschiedener Raten $\lambda$ mit der theoretisch zu erwartenden Verteilung - der Intervalle $T$ des Poisson Prozesses - \[ p(T) = \lambda e^{-\lambda T} \; .\] - \begin{solution} - \lstinputlisting{hompoissonisih.m} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih100hz}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih20hz}} - \end{solution} - - \part \extra Was pasiert mit den Histogrammen, wenn die Binbreite - der Histogramme kleiner als das bei der Erzeugung der Poisson - Spiketrains verwendete $\Delta t$ ist? - \begin{solution} - Die Bins zwischen der durch $\Delta t$ vorgegebenen - Diskretisierung haben den Wert 0. Dadurch werden aber die anderen - durch die Normierung h\"oher als sie sein sollten. - \end{solution} - - \part Plotte den Mittelwert der Interspikeintervalle, die - dazugeh\"orige Standardabweichung und den Variationskoeffizienten - als Funktion der Rate $\lambda$ des Poisson Prozesses. Vergleiche - die Ergebnisse mit den theoretischen Erwartungen (siehe Vorlesungsskript). - \begin{solution} - \lstinputlisting{hompoissonisistats.m} - \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonisistats}} - \end{solution} - - \part Plotte die seriellen Korrelationen von Poisson-Spiketrains und - erkl\"are kurz das Ergebniss. - \begin{solution} - \mbox{}\\[-2ex]\hspace*{2cm} - \colorbox{white}{\includegraphics[width=0.8\textwidth]{poissonserial100hz}}\\ - Alle Korrelationen zwischen Interspikeintervallen sind Null, da - beim Poisson Prozess das Auftreten jedes Spikes unabh\"angig von - den vorherigen Spikes ist. - \end{solution} - - \part Vergleiche Histogramme von Spikecounts gez\"ahlt in Fenstern - der Breite $W$ mit der Poisson Verteilung - \[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \; , \] - wobei die Rate $\lambda$ aus den Daten bestimmt werden - soll. Hinweis: es gibt eine \code{matlab} Funktion, die die - Fakult\"at $n!$ berechnet. - \begin{solution} - %\lstinputlisting{counthist.m} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}} - \end{solution} - - \part Schreibe eine Funktion, die die mittlere Anzahl, die Varianz - und den Fano-Faktor der Anzahl der Spikes in einem Fenster der - Breite $W$ bestimmt. Benutze die Funktion, um diese Parameter f\"ur - verschiedene Fensterbreiten $W$ zu bestimmen. Zwei Plots sollen aus - den Ergebnissen angefertigt werden: (i) Varianz gegen Mittelwert der counts. - (ii) Fano Faktor als Funktion der Fensterbreite. - \begin{solution} - \lstinputlisting{fanoplot.m} - \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonfano100hz}} - \end{solution} - -\end{parts} + \part The inverse Gaussian describes the interspike interval distribution of a PIF driven with white noise: + \[ p(T) = \frac{1}{\sqrt{4\pi D T^3}}\exp\left[-\frac{(T-\langle T \rangle)^2}{4DT\langle T \rangle^2}\right] \] + where $\langle T \rangle$ is the mean interspike interval and + \[ D = \frac{\langle(T - \langle T \rangle)^2\rangle}{2 \langle T \rangle^3} \] + is the diffusion coefficient (variance of the interspike intervals + $T$ divided by two times the mean cubed). Show in two plots how + this distribution depends on $\langle T \rangle$ and $D$. + \begin{solution} + \lstinputlisting{inversegauss.m} + \lstinputlisting{inversegaussplot.m} + \colorbox{white}{\includegraphics[width=0.98\textwidth]{inversegauss}} + \end{solution} + + \part Extent your function plotting an interspike interval histogram + to also report the diffusion coefficient $D$. + \begin{solution} + \begin{lstlisting} +... +% annotation: +misi = mean( isis ); +sdisi = std( isis ); +disi = sdisi^2.0/2.0/misi^3; +text( 0.6, 0.7, sprintf( 'mean=%.1f ms', 1000.0*misi ), 'Units', 'normalized' ) +text( 0.6, 0.6, sprintf( 'std=%.1f ms', 1000.0*sdisi ), 'Units', 'normalized' ) +text( 0.6, 0.5, sprintf( 'CV=%.2f', sdisi/misi ), 'Units', 'normalized' ) +text( 0.6, 0.4, sprintf( 'D=%.1f Hz', disi ), 'Units', 'normalized' ) +... + \end{lstlisting} + \end{solution} + + \part Compare intersike interval histograms obtained from the LIF and PIF models with the inverse Gaussian. + \begin{solution} + \lstinputlisting{lifisih.m} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih01}} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{pifisih10}}\\ + \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih08}} + \colorbox{white}{\includegraphics[width=0.48\textwidth]{lifisih16}} + \end{solution} + + \part Plot the firing rate (inverse mean interspike interval), + mean interspike interval, the corresponding standard deviation, + CV, and diffusion coefficient as a function of the input to the LIF + and the PIF with noise strength set to 0.01. + \begin{solution} + \lstinputlisting{lifisistats.m} + Leaky integrate-and-fire:\\ + \colorbox{white}{\includegraphics[width=0.8\textwidth]{lifisistats}}\\ + Perfect integrate-and-fire:\\ + \colorbox{white}{\includegraphics[width=0.8\textwidth]{pifisistats}} + \end{solution} + + \part Plot the firing rate as a function of input of the LIF and the PIF for various values + of the noise strength. + \begin{solution} + \lstinputlisting{lifficurves.m} + Leaky integrate-and-fire:\\ + \colorbox{white}{\includegraphics[width=0.7\textwidth]{lifficurves}}\\ + Perfect integrate-and-fire:\\ + \colorbox{white}{\includegraphics[width=0.7\textwidth]{pifficurves}} + \end{solution} + + \part Use the functions for computing serial correlations, count statistics and fano factors + to further explore the statistics of the integrate-and-fire models! + + \end{parts} + \end{questions} + \end{document} diff --git a/pointprocesses/exercises/pointprocesses-3.tex b/pointprocesses/exercises/pointprocesses-3.tex deleted file mode 100644 index 1af6dc7..0000000 --- a/pointprocesses/exercises/pointprocesses-3.tex +++ /dev/null @@ -1,163 +0,0 @@ -\documentclass[12pt,a4paper,pdftex]{exam} - -\newcommand{\exercisetopic}{Point Processes} -\newcommand{\exercisenum}{X3} -\newcommand{\exercisedate}{January 19th, 2021} - -\input{../../exercisesheader} - -\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{document} - -\input{../../exercisestitle} - -\begin{questions} - - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \question \qt{Statistik von Spiketrains 2} - In Ilias findet ihr die Dateien \code{poisson.mat}, - \code{pifou.mat}, und \code{lifadapt.mat}. Jede dieser Dateien - enth\"alt mehrere Trials von Spiketrains von einer bestimmten Art - von Neuron. Die Spikezeiten sind in Sekunden gemessen. - - Mit den folgenden Aufgaben wollen wir die Statistik der Spiketrains - der drei Neurone miteinander vergleichen. - - Bereits im letzten \"Ubungszettel erstellte Funktionen d\"urfen (sollen!) - wiederverwendet werden. - \begin{parts} - \part Lade die Spiketrains aus den drei Dateien. Stelle sie in Rasterplots dar. - - \part Plotte die Interspike-Intervall Verteilungen. - - Annotiere die Plots mit dem Mittelwert, der - Standardabweichung, und dem Variationskoeffizienten der - Interspikeintervalle, sowie der mittleren Feuerrate. - - \part Vergleiche die ISI-Histogramme mit der ISI Verteilung eines Poisson Prozesses - der Rate $\lambda$: - \[ p(T) = \lambda e^{-\lambda T} \; .\] - - \part Erstelle Return-Maps f\"ur die drei Spiketrains, also jedes - Interspike-Intervall $T_{i+1}$ gegen das vorherige Intervall $T_i$ - geplottet. - - \part Schreibe eine Funktion, die die seriellen Korrelationen der - Interspikeintervalle f\"ur Lags bis zu \code{maxlag} berechnet und - plottet. Die Seriellen Korrelationen $\rho_k$ f\"ur Lag $k$ der - Interspikeintervalle $T_i$ sind die Korrelationskoeffizienten - zwischen den Interspikeintervallen $T_i$ und den um das Lag $k$ - verschobenen Intervallen $T_{i+k}$: - \[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - - \langle T \rangle) \rangle}{\langle (T_i - \langle T - \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm - var}(T_i)} = {\rm corr}(T_{i+k}, T_i) \] - - Benutze diese Funktion, um die Interspikeintervall-Korrelationen - der drei Neurone zu vergleichen. - \begin{solution} - \lstinputlisting{../code/isiserialcorr.m} - \lstinputlisting{../code/plotserialcorr.m} - \colorbox{white}{\includegraphics[width=1\textwidth]{serialcorr}} - \end{solution} - - \end{parts} - - \continue - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \question \qt{Homogener Poisson Prozess} - Wir wollen den homogenen Poisson Prozess benutzen um Spikes zu - generieren, mit denen wir die Analysfunktionen des vorherigen - Aufgaben \"uberpr\"ufen k\"onnen. - - Ein homogener Poisson Prozess mit der Rate $\lambda$ (gemessen in - Hertz) ist ein Punktprozess, bei dem die Wahrscheinlichkeit eines - Ereignisses unabh\"angig von der Zeit $t$ und unabh\"angig von - vorherigen Ereignissen ist. Wenn wir die Zeitachse in kleine Bins - der Breite $\Delta t$ einteilen, dann ist - \[ P = \lambda \cdot \Delta t \] - die Wahrscheinlichkeit innerhalb eines Bins ein Ereignis (``spike'') - zu erhalten. $\Delta t$ muss daf\"ur klein genug sein, so dass $P<0.1$. - \begin{parts} - - \part Schreibe eine Funktion die $n$ homogene Poisson Spiketrains - einer gegebenen Dauer $T_{max}$ mit Rate $\lambda$ erzeugt. - - Falls das nicht gelingt, benutze f\"ur die folgenden Aufgaben - soweit m\"oglich spikes aus der Datei \code{poisson.mat}. - \begin{solution} - \lstinputlisting{hompoissonspikes.m} - \end{solution} - - \part Benutze diese Funktion um einige Trials von Spikes zu erzeugen - und plotte diese als Spikeraster. - \begin{solution} - \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 Berechne Histogramme aus den Interspikeintervallen von $n$ - Poisson Spiketrains mit der Rate $\lambda=100$\,Hz. Wie viele bins - werden f\"ur ein ``sch\"ones'' ISI-Histogramm ungef\"ahr ben\"otigt? - Ver\"andere \"uber die Dauer $T_{max}$ der Spiketrains und die - Anzahl $n$ der Trials die Anzahl der Intervalle. 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. - \end{solution} - - \part Vergleiche Interspike-Intervall Histogramme von Poisson-Spikes - verschiedener Raten $\lambda$ mit der theoretisch zu erwartenden Verteilung - der Intervalle $T$ des Poisson Prozesses - \[ p(T) = \lambda e^{-\lambda T} \; .\] - Achte darauf, dass die Bins des Histograms nicht kleiner als $\Delta t$ sind! - \begin{solution} - \lstinputlisting{hompoissonisih.m} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih100hz}} - \colorbox{white}{\includegraphics[width=0.48\textwidth]{poissonisih20hz}} - \end{solution} - - \part \extra Was passiert mit den Histogrammen, wenn die Binbreite - der Histogramme kleiner als das bei der Erzeugung der Poisson - Spiketrains verwendete $\Delta t$ ist? - \begin{solution} - Die Bins zwischen der durch $\Delta t$ vorgegebenen - Diskretisierung haben den Wert 0. Dadurch werden aber die anderen - durch die Normierung h\"oher als sie sein sollten. - \end{solution} - - \part Plotte den Mittelwert der Interspikeintervalle, die - dazugeh\"orige Standardabweichung und den Variationskoeffizienten - als Funktion der Rate $\lambda$ des Poisson Prozesses. Vergleiche - die Ergebnisse mit den theoretischen Erwartungen (siehe Vorlesungsskript). - \begin{solution} - \lstinputlisting{hompoissonisistats.m} - \colorbox{white}{\includegraphics[width=0.98\textwidth]{poissonisistats}} - \end{solution} - - \part Plotte die seriellen Korrelationen von Poisson-Spiketrains und - erkl\"are kurz das Ergebniss. - \begin{solution} - \mbox{}\\[-2ex]\hspace*{2cm} - \colorbox{white}{\includegraphics[width=0.8\textwidth]{poissonserial100hz}}\\ - Alle Korrelationen zwischen Interspikeintervallen sind Null, da - beim Poisson Prozess das Auftreten jedes Spikes unabh\"angig von - den vorherigen Spikes ist. - \end{solution} - - \end{parts} - - -\end{questions} - -\end{document} diff --git a/pointprocesses/exercises/pointprocesses01-de.tex b/pointprocesses/exercises/pointprocesses01-de.tex deleted file mode 100644 index ea8674d..0000000 --- a/pointprocesses/exercises/pointprocesses01-de.tex +++ /dev/null @@ -1,198 +0,0 @@ -\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}{\"Ubung} -\fi -\header{{\bfseries\large \stitle}}{{\bfseries\large Punktprozesse}}{{\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{Statistik von Spiketrains} - In Ilias findet ihr die Dateien \code{poisson.mat}, - \code{pifou.mat}, und \code{lifadapt.mat}. Jede dieser Dateien - enth\"alt mehrere Trials von Spiketrains von einer bestimmten Art - von Neuron. Die Spikezeiten sind in Sekunden gemessen. - - Mit den folgenden Aufgaben wollen wir die Statistik der Spiketrains - der drei Neurone miteinander vergleichen. - \begin{parts} - \part Lade die Spiketrains aus den drei Dateien. Achte darauf, - dass sie verschiedene Variablen\-namen bekommen. - \begin{solution} - \begin{lstlisting} - clear all - % not so good: - load poisson.mat - whos - poissonspikes = spikes; - load pifou.mat; - pifouspikes = spikes; - 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} - - \part Schreibe eine Funktion, die die Spikezeiten der ersten - $t_{max}$ Sekunden in einem Rasterplot visualisiert. In jeder - Zeile des Rasterplots wird ein Spiketrain dargestellt. Jeder - einzelne Spike wird als senkrechte Linie zu der Zeit des - Auftretens des Spikes geplottet. Benutze die Funktion, um die - Spikeraster der ersten 1\,s der drei Neurone nebeneinander zu plotten. - \begin{solution} - \lstinputlisting{../code/spikeraster.m} - \lstinputlisting{../code/plotspikeraster.m} - \mbox{}\\[-3ex] - \colorbox{white}{\includegraphics[width=1\textwidth]{spikeraster}} - \end{solution} - - \part Schreibe eine Funktion, die einen einzigen Vektor mit den - Interspikeintervallen aller Trials von Spikezeiten zur\"uckgibt. - \begin{solution} - \lstinputlisting{../code/isis.m} - \end{solution} - - \part Schreibe eine Funktion, die ein normiertes Histogramm aus - einem Vektor von Interspikeintervallen, gegeben in Sekunden, - berechnet und dieses mit richtiger Achsenbeschriftung plottet. - Die Interspikeintervalle sollen dabei in Millisekunden angegeben - werden. Die Funktion soll zus\"atzlich den Mittelwert, die - Standardabweichung, und den Variationskoeffizienten der - Interspikeintervalle berechnen und diese im Plot mit angeben. - - Benutze die vorherige und diese Funktion, um die - Interspikeintervall Verteilung der drei Neurone zu vergleichen. - \begin{solution} - \lstinputlisting{../code/isihist.m} - \lstinputlisting{../code/plotisih.m} - \mbox{}\\[-3ex] - \colorbox{white}{\includegraphics[width=1\textwidth]{isihist}} - \end{solution} - - \part Schreibe eine Funktion, die die seriellen Korrelationen der - Interspikeintervalle f\"ur Lags bis zu \code{maxlag} berechnet und - plottet. Die Seriellen Korrelationen $\rho_k$ f\"ur Lag $k$ der - Interspikeintervalle $T_i$ sind die Korrelationskoeffizienten - zwischen den Interspikeintervallen $T_i$ und den um das Lag $k$ - verschobenen Intervallen $T_{i+k}$: - \[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - - \langle T \rangle) \rangle}{\langle (T_i - \langle T - \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm - var}(T_i)} = {\rm corr}(T_{i+k}, T_i) \] - - Benutze diese Funktion, um die Interspikeintervall-Korrelationen - der drei Neurone zu vergleichen. - \begin{solution} - \lstinputlisting{../code/isiserialcorr.m} - \lstinputlisting{../code/plotserialcorr.m} - \colorbox{white}{\includegraphics[width=1\textwidth]{serialcorr}} - \end{solution} - - \part Schreibe eine Funktion, die aus Spikezeiten - Histogramme aus der Anzahl von Spikes, die in Fenstern gegebener L\"ange $W$ - gez\"ahlt werden, erzeugt und plottet. - - Wende diese Funktion auf die drei - Datens\"atze an. Probiere verschiedene Fenstergr\"o{\ss}en $W$ aus. - \begin{solution} - \lstinputlisting{../code/counthist.m} - \lstinputlisting{../code/plotcounthist.m} - \colorbox{white}{\includegraphics[width=1\textwidth]{counthist}} - \end{solution} - - - \end{parts} - -\end{questions} - -\end{document} \ No newline at end of file diff --git a/pointprocesses/exercises/poisson-solutions.pdf b/pointprocesses/exercises/poisson-solutions.pdf deleted file mode 100644 index 4546a8db101133710506c5cb390747a99382e77f..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 199254 zcmb@s1yChT(=LeH0E4@`yTjn_?(XjH&cWSnaCe6R26r9Yox$Dhp7;Il-Pn!qM(lrM z_r!^g?&|8StjescswW?EMNx5jW(IaR^4W!<6*vweCL#x8Ya%{AI7V4Bdka@fA{I7Q zcA|fOaE#(swytK*M2zCLMy_U}W+o1%W^nxca4xRSW=3{!o@?FOGA{e=$UScw*GV{D z?xB5eyEUtorpdWA-KNTCs)+i8mXWQRX_8`v!~4aLy=6jy#Z;&%?d9V`zCy8|{P*7w z_7AB0#*V9cH}w79r6{4WrOce)GN`hsN)rnxI`k+!nhY?#)OA&URNZbf?M9z*oA^GO zbgU9ozGqEFm7R6Whfeu3a2~3tn;sfn4f{6q(%gOY(4BwdSic-U%>VqW=!|MF_ 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b/pointprocesses/exercises/psth.tex @@ -1,42 +1,20 @@ \documentclass[12pt,a4paper,pdftex]{exam} -\usepackage[german]{babel} -\usepackage{natbib} -\usepackage{graphicx} -\usepackage[small]{caption} -\usepackage{sidecap} -\usepackage{pslatex} -\usepackage{amsmath} -\usepackage{amssymb} -\setlength{\marginparwidth}{2cm} -\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} +\newcommand{\exercisetopic}{Time-dependent firing rates} +\newcommand{\exercisenum}{12} +\newcommand{\exercisedate}{January 19th, 2021} -%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} -\pagestyle{headandfoot} \header{{\bfseries\large Exercise - }}{{\bfseries\large Time-dependent firing rate}}{{\bfseries\large January, 14, 2020}} -\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: - jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{} +\input{../../exercisesheader} -\setlength{\baselineskip}{15pt} -\setlength{\parindent}{0.0cm} -\setlength{\parskip}{0.3cm} -\renewcommand{\baselinestretch}{1.15} +\firstpagefooter{Dr. Jan Grewe}{}{jan.grewe@uni-tuebingen.de} -\newcommand{\code}[1]{\texttt{#1}} -\renewcommand{\solutiontitle}{\noindent\textbf{Solution}\par\noindent} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} -\vspace*{-6.5ex} -\begin{center} - \textbf{\Large Introduction to scientific computing.}\\[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} +\input{../../exercisestitle} \begin{questions} + \question Plot the time-dependent firing rate of a neuron. Calculate the firing rate from the \emph{instantaneous firing rate} (based on the interspike interval). Use the \code{lifoustim.mat}. The dataset @@ -45,14 +23,14 @@ duration of each trial is 30 seconds. \begin{parts} - \part{} Write a function that takes three arguments: the spike + \part Write a function that takes three arguments: the spike times of a single trial, the trial duration and the temporal resolution. The function should return two variables: the time axis and the time-dependent firing rate. - \part{} Write a script that applies the above function to estimate + \part Write a script that applies the above function to estimate the time-dependent firing rate of each trial. Plot the firing rates of the individual responses and the average response as a function of time into the same graph. - \part{} Extend your program that it saves the figure with the width and height of 8.5\,cm using a fontsize of 10\,pt for labels. + \part Extend your program that it saves the figure with the width and height of 8.5\,cm using a fontsize of 10\,pt for labels. See Chapter 3 in the script, or browse the Matlab help for more information. Store the figure in pdf format. \end{parts} @@ -65,10 +43,10 @@ \question{} Some trials are different than the others. \begin{parts} - \part{} Use a rasterplot to identify them. In which sense + \part Use a rasterplot to identify them. In which sense are they different? Save the rasterplot in pdf format. Use the same figure specifications as above and make sure it is properly labeled. - \part{} Identify those trials in which the spike count + \part Identify those trials in which the spike count deviates more than $2\sigma$ (twice the standard deviation) from the average. \end{parts} \end{questions}

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