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QTuf3@2Efg&Zm0qHU$t&+i2wiq literal 0 HcmV?d00001 From 1556c960375d91a171761755ef433c7b8c87443e Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 27 Oct 2015 22:15:39 +0100 Subject: [PATCH 2/6] split plotting_spike trains. add spike trains as new chapter --- .../lecture}/images/binned_rate.png | Bin .../lecture}/images/convolved_rate.png | Bin .../lecture}/images/instantaneous_rate.png | Bin .../lecture}/images/rasterplot.png | Bin .../lecture}/images/sta.pdf | 0 .../lecture/plotting.tex | 289 +------------ spike_trains/lecture/psth_sta.tex | 389 ++++++++++++++++++ 7 files changed, 391 insertions(+), 287 deletions(-) rename {programming/lectures => spike_trains/lecture}/images/binned_rate.png (100%) rename {programming/lectures => spike_trains/lecture}/images/convolved_rate.png (100%) rename {programming/lectures => spike_trains/lecture}/images/instantaneous_rate.png (100%) rename {programming/lectures => spike_trains/lecture}/images/rasterplot.png (100%) rename {programming/lectures => spike_trains/lecture}/images/sta.pdf (100%) rename programming/lectures/plotting_spike_trains.tex => spike_trains/lecture/plotting.tex (54%) create mode 100644 spike_trains/lecture/psth_sta.tex diff --git a/programming/lectures/images/binned_rate.png b/spike_trains/lecture/images/binned_rate.png similarity index 100% rename from programming/lectures/images/binned_rate.png rename to spike_trains/lecture/images/binned_rate.png diff --git a/programming/lectures/images/convolved_rate.png b/spike_trains/lecture/images/convolved_rate.png similarity index 100% rename from programming/lectures/images/convolved_rate.png rename to spike_trains/lecture/images/convolved_rate.png diff --git a/programming/lectures/images/instantaneous_rate.png b/spike_trains/lecture/images/instantaneous_rate.png similarity index 100% rename from programming/lectures/images/instantaneous_rate.png rename to spike_trains/lecture/images/instantaneous_rate.png diff --git a/programming/lectures/images/rasterplot.png b/spike_trains/lecture/images/rasterplot.png similarity index 100% rename from programming/lectures/images/rasterplot.png rename to spike_trains/lecture/images/rasterplot.png diff --git a/programming/lectures/images/sta.pdf b/spike_trains/lecture/images/sta.pdf similarity index 100% rename from programming/lectures/images/sta.pdf rename to spike_trains/lecture/images/sta.pdf diff --git a/programming/lectures/plotting_spike_trains.tex b/spike_trains/lecture/plotting.tex similarity index 54% rename from programming/lectures/plotting_spike_trains.tex rename to spike_trains/lecture/plotting.tex index 0926fbd..b2426bd 100644 --- a/programming/lectures/plotting_spike_trains.tex +++ b/spike_trains/lecture/plotting.tex @@ -101,10 +101,9 @@ \begin{frame} \frametitle{Grundlagen der Programmierung} - \frametitle{Tagesmen\"u} + \frametitle{Inhalt} \begin{enumerate} \item Graphische Darstellung von Daten - \item Spiketrain Analyse \end{enumerate} \end{frame} @@ -356,288 +355,4 @@ saveas(fig, 'spike_detection.pdf', 'pdf') \end{enumerate} \end{frame} - -\begin{frame}[plain] -\huge{2. Spiketrain Analyse} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Rasterplot} - \begin{figure} - \centering - \includegraphics[width=0.375\columnwidth]{images/rasterplot} - \end{figure} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Rasterplot} - \"Ubung: - \begin{enumerate} - \item Ladet die Datei: \code{lifoustim.mat} aus dem - Ilias Ordner. - \item Der Datensatz enth\"alt die Zeiten von Aktionspotentialen. - \item Erzeugt einen sch\"onen Rasterplot der Zellantworten, speichert ihn. - \item Welche Information liefert er, welche Information ist schwer - abzulesen? - \end{enumerate} -\end{frame} - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH} - - Darstellung der Feurreate eines Neuron als Funktion der Zeit. Es - gibt verschiedene Methoden dieses \textbf{P}eri \textbf{S}timulus - \textbf{T}ime \textbf{H}istogram zu erstellen. - \begin{enumerate} - \item Auf Basis der \textit{instantanen} Feuerrate. - \item Auf Basis des Zeithistogramms. - \item Durch Faltung der Zellantwort mit einem Gauss Kern. - \end{enumerate} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} - \Large{Berechnung des PSTHs durch die Instantane Feurerrate:} - \normalsize - \begin{enumerate} - \item Die Feuerrate kann aus dem Abstand zwischen zwei - aufeinanderfolgenden Aktionspotentialen - (\textbf{Interspikeinterval}) berechnet werden. \pause - \item Die \textbf{Instantane Feuerrate} wird aus dem Kehrwert des - Interspikeintervals berechnet. - \end{enumerate} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} - \begin{figure} - \centering - \includegraphics[width=0.9\columnwidth]{images/instantaneous_rate} - \end{figure} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} - Berechnung des PSTHs durch die Instantane Feurerrate: - \textbf{Vorteile:} - - \begin{enumerate} - \item Sehr einfach zu Berechnen. - \item Macht keine Annahmen \"uber ein Zeitraster, oder die Zeitskala - der neuronalen Verarbeitung. - \end{enumerate} - - \textbf{Nachteile:} - \begin{enumerate} - \item Die Feuerrate ist nie null, auch wenn f\"ur lange Zeit kein - Aktionspotential auftritt. - \item Verh\"alt sich im Fourrier Raum nicht sehr sch\"on. - \end{enumerate} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} - \Large{Binning Methode:} - \normalsize - \begin{enumerate} - \item Die Zeitachse wird in gleich gro{\ss}e Abschnitte ``bins'' - unterteilt. - \item F\"ur jedes ``bin'' wird die Anzahl vorkommender - Aktionspotentiale gez\"ahlt. - \item Der Spike-count pro bin muss nun noch in die Rate umgerechnet - werden. - \end{enumerate} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} - \begin{figure} - \includegraphics[width=0.9\columnwidth]{images/binned_rate} - \end{figure} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} - - Berechnung des PSTHs durch die Binning Methode: - - \textbf{Vorteile:} - \begin{enumerate} - \item Sehr einfach zu Berechnen. - \item Zeigt nur da Aktivit\"at an, wo auch Aktionspotentiale - generiert wurden. - \end{enumerate} - - \textbf{Nachteile:} - \begin{enumerate} - \item Mach Annahmen \"uber die relevante Zeitskala neuronaler - Verarbeitung. - \item Die Zeitachse wird diskretisiert. - \item Verh\"alt sich im Fourrier Raum nicht sehr sch\"on. - \end{enumerate} -\end{frame} - - -\begin{frame}[fragile] - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Faltungsmethode ---} - \Large{Faltung mit einem Gauss Kern:} - \normalsize - \[r_{est}(t) = \int_{-\infty}^{\infty}d\tau \omega(\tau)\rho(t-\tau) \] - - wobei $\omega(\tau)$ der Gauss Kern und $\rho(t)$ die Antwortfunktion ist. - - Gl\"ucklicherweise m\"ussen wir das nicht selbst implementieren... -\end{frame} - - -\begin{frame}[fragile] - \frametitle{Spiketrain Analyse} - \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Faltungsmethode ---} - \large Algortihmus: - \normalsize - \begin{enumerate} - \item Die neuronalen Antworten werden ``bin\"ar'' ausgedr\"uckt. - \item Ein Filterkern wird berechnet, der das Integral 1 hat. - \item Mithilfe der Faltung (\code{conv} Funktion) wird jede 1 durch - den ``Kern'' ersetzt.\\ - \code{conv(x, kern, 'mode', 'same')} - \end{enumerate} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Feurerrate als Funktion der Zeit --- Faltungsmethode ---} - \begin{figure} - \includegraphics[width=0.9\columnwidth]{images/convolved_rate} - \end{figure} -\end{frame} - - -\begin{frame} - \frametitle{Spiketrain Analyse} - \framesubtitle{Feurerrate als Funktion der Zeit --- Faltungsmethode ---} - \textbf{Vorteile:} - \begin{enumerate} - \item Sehr ``nat\"urliche'' erscheinende Darstellung. - \item Sehr gutes Verhalten im Fourrier Raum. - \end{enumerate} - - \textbf{Nachteile:} - \begin{enumerate} - \item Relativ rechenintensiv. - \item Macht Annahmen \"uber die Zeitskalen neuronaler Verarbeitung. - \end{enumerate} -\end{frame} - -\begin{frame}[plain] - \huge{3. Analyse der Beziehung zwischen Stimulus und Antwort} -\end{frame} - - -\begin{frame}[fragile] - \frametitle{Spiketrain Analyse} - \framesubtitle{Spike-Triggered-Average} - \begin{itemize} - \item[] Die Antworten darzustellen ist gut und sch\"on, aber was sagt es uns?\pause - \item[] Idealerweise wollen wir die Antworten in Beziehung zum - hervorrufenden Stimulus setzen. - \item[] Eine Methode ist der sogenannte \textbf{Spike-Triggered-Average} (STA). - \end{itemize} -\end{frame} - - -\begin{frame}[fragile] - \frametitle{Spiketrain Analyse} - \framesubtitle{Spike-Triggered-Average} - - Der STA stellt den (mittleren) Stimulus dar, der zu einem - Aktionspotential gef\"uhrt hat: - - \begin{equation} - STA(\tau) = \frac{1}{\langle n \rangle} \left\langle \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \right\rangle - \end{equation} - Wobei: $\tau$ ist eine bestimmte Zeit relativ zur Zeit eines - Aktionspotentials, $t_i$ ist der Zeitpunkt eines APs, $s(t)$ ist der - Stimulus.\\ - - Leider m\"ussen wir das selbst implementieren... -\end{frame} - - -\begin{frame}[fragile] - \frametitle{Spiketrain Analyse} - \framesubtitle{Spike-Triggered-Average} - \large{Algorithmus:} - \normalsize - \begin{enumerate} - \item Der \textbf{STA} ist der mittlere Stimulus, der zu einem Aktionspotential f\"uhrt. - \item F\"ur jeden Spike wird ein entsprechender Abschnitt um die Zeit des Spikes herausgeschnitten. - \item Die einzelen Stimulussegmente werden gemittelt. - \end{enumerate}\pause - \begin{figure} - \centering - \includegraphics[width=0.5\columnwidth]{images/sta} - \end{figure} -\end{frame} - -\begin{frame}[fragile] - \frametitle{Spiketrain Analyse} - \framesubtitle{Spike-Triggered-Average} - \vspace{-1em} - \begin{figure} - \centering - \includegraphics[width=0.6\columnwidth]{images/sta} - \end{figure} - \pause - \vspace{-0.5em} - Welche Information liefert der \textbf{STA}? - \small - \begin{enumerate} - \item Gibt es eine Beziehung zwischen Stimulus und Antwort?\pause - \item Gibt es eine Verz\"ogerung zwischen Stimulus und Antwort? Wie - gro{\ss} ist diese?\pause - \item Wie weit h\"angt das Auftreten eines Aktionspotentials von der - Vergangenheit ab? \pause - \item Kann die Zelle in die Zukunft sehen? - \end{enumerate} -\end{frame} - -\end{document} - - - -\begin{frame} [fragile] - \frametitle{Spiketrain Analyse} - \framesubtitle{\"Ubung} - \begin{enumerate} - \item Berechnet die Feuerrate eines Neurons mit einer der drei Methoden. - \item Die Abbildung soll f\"ur eine einspaltige Abbildung im - \textit{Journal of Neuroscience} geeignet sein - (\url{http://www.jneurosci.org/site/misc/ifa_illustrations.xhtml}). - \item Erzeugt/ver\"andert/erweitert das Programm zum plotten so, dass - die Abbildung automatisch erstellt und gespeichert wird. - \item Speichert die Abbildung als pdf. - \item Ladet den Stimulus aus dem Ilias Ordner und benutzt die - \verb+subplot+ Funktion um den Stimulus zu der neuronalen - Aktivit\"at zu plotten. - \end{enumerate} -\end{frame} \ No newline at end of file +\end{document} \ No newline at end of file diff --git a/spike_trains/lecture/psth_sta.tex b/spike_trains/lecture/psth_sta.tex new file mode 100644 index 0000000..a89676a --- /dev/null +++ b/spike_trains/lecture/psth_sta.tex @@ -0,0 +1,389 @@ +\documentclass{beamer} +\usepackage{xcolor} +\usepackage{listings} +\usepackage{pgf} +%\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade} +%\usepackage{multimedia} + +\usepackage[english]{babel} +\usepackage{movie15} +\usepackage[latin1]{inputenc} +\usepackage{times} +\usepackage{amsmath} +\usepackage{bm} +\usepackage[T1]{fontenc} +\usepackage[scaled=.90]{helvet} +\usepackage{scalefnt} +\usepackage{tikz} +\usepackage{ textcomp } +\usepackage{soul} +\usepackage{hyperref} +\definecolor{lightblue}{rgb}{.7,.7,1.} +\definecolor{mygreen}{rgb}{0,1.,0} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode +{ + \usetheme{Singapore} + \setbeamercovered{opaque} + \usecolortheme{tuebingen} + \setbeamertemplate{navigation symbols}{} + \usefonttheme{default} + \useoutertheme{infolines} + % \useoutertheme{miniframes} +} + +\AtBeginSection[] +{ + \begin{frame} + \begin{center} + \Huge \insertsectionhead + \end{center} + % \frametitle{\insertsectionhead} + % \tableofcontents[currentsection,hideothersubsections] + \end{frame} +} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + +\setbeamertemplate{blocks}[rounded][shadow=true] + +\title[]{Scientific Computing -- Grundlagen der Programmierung } +\author[]{Jan Grewe\\Abteilung f\"ur Neuroethologie\\ + Universit\"at T\"ubingen} + +\institute[Wissenschaftliche Datenverarbeitung]{} + \date{12.10.2015 - 06.11.2015} + %\logo{\pgfuseimage{../../resources/UT_BM_Rot_RGB.pdf}} + +\subject{Einf\"uhrung in die wissenschaftliche Datenverarbeitung} +\vspace{1em} +\titlegraphic{ + \includegraphics[width=0.5\linewidth]{../../resources/UT_WBMW_Rot_RGB} +} +%%%%%%%%%% configuration for code +\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 + } +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newcommand{\mycite}[1]{ +\begin{flushright} +\tiny \color{black!80} #1 +\end{flushright} +} + +\newcommand{\code}[1]{\texttt{#1}} + +\input{../../latex/environments.tex} +\makeatother + +\begin{document} + +\begin{frame}[plain] + \frametitle{} + \vspace{-1cm} + \titlepage % erzeugt Titelseite +\end{frame} + +\begin{frame} + \frametitle{Spiketrain Analyse} + \frametitle{Inhalt} + \begin{enumerate} + \item Peri Stimulus Time Histogram + \item Spike-triggered average + \end{enumerate} +\end{frame} + + +\begin{frame}[plain] +\huge{1. Peri Stimulus Time Histogram, PSTH} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Rasterplot} + \begin{figure} + \centering + \includegraphics[width=0.375\columnwidth]{images/rasterplot} + \end{figure} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Rasterplot} + \"Ubung: + \begin{enumerate} + \item Ladet die Datei: \code{lifoustim.mat} aus dem + Ilias Ordner. + \item Der Datensatz enth\"alt die Zeiten von Aktionspotentialen. + \item Erzeugt einen sch\"onen Rasterplot der Zellantworten, speichert ihn. + \item Welche Information liefert er, welche Information ist schwer + abzulesen? + \end{enumerate} +\end{frame} + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH} + + Darstellung der Feurreate eines Neuron als Funktion der Zeit. Es + gibt verschiedene Methoden dieses \textbf{P}eri \textbf{S}timulus + \textbf{T}ime \textbf{H}istogram zu erstellen. + \begin{enumerate} + \item Auf Basis der \textit{instantanen} Feuerrate. + \item Auf Basis des Zeithistogramms. + \item Durch Faltung der Zellantwort mit einem Gauss Kern. + \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} + \Large{Berechnung des PSTHs durch die Instantane Feurerrate:} + \normalsize + \begin{enumerate} + \item Die Feuerrate kann aus dem Abstand zwischen zwei + aufeinanderfolgenden Aktionspotentialen + (\textbf{Interspikeinterval}) berechnet werden. \pause + \item Die \textbf{Instantane Feuerrate} wird aus dem Kehrwert des + Interspikeintervals berechnet. + \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} + \begin{figure} + \centering + \includegraphics[width=0.9\columnwidth]{images/instantaneous_rate} + \end{figure} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} + Berechnung des PSTHs durch die Instantane Feurerrate: + \textbf{Vorteile:} + + \begin{enumerate} + \item Sehr einfach zu Berechnen. + \item Macht keine Annahmen \"uber ein Zeitraster, oder die Zeitskala + der neuronalen Verarbeitung. + \end{enumerate} + + \textbf{Nachteile:} + \begin{enumerate} + \item Die Feuerrate ist nie null, auch wenn f\"ur lange Zeit kein + Aktionspotential auftritt. + \item Verh\"alt sich im Fourrier Raum nicht sehr sch\"on. + \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} + \Large{Binning Methode:} + \normalsize + \begin{enumerate} + \item Die Zeitachse wird in gleich gro{\ss}e Abschnitte ``bins'' + unterteilt. + \item F\"ur jedes ``bin'' wird die Anzahl vorkommender + Aktionspotentiale gez\"ahlt. + \item Der Spike-count pro bin muss nun noch in die Rate umgerechnet + werden. + \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} + \begin{figure} + \includegraphics[width=0.9\columnwidth]{images/binned_rate} + \end{figure} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} + + Berechnung des PSTHs durch die Binning Methode: + + \textbf{Vorteile:} + \begin{enumerate} + \item Sehr einfach zu Berechnen. + \item Zeigt nur da Aktivit\"at an, wo auch Aktionspotentiale + generiert wurden. + \end{enumerate} + + \textbf{Nachteile:} + \begin{enumerate} + \item Mach Annahmen \"uber die relevante Zeitskala neuronaler + Verarbeitung. + \item Die Zeitachse wird diskretisiert. + \item Verh\"alt sich im Fourrier Raum nicht sehr sch\"on. + \end{enumerate} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Faltungsmethode ---} + \Large{Faltung mit einem Gauss Kern:} + \normalsize + \[r_{est}(t) = \int_{-\infty}^{\infty}d\tau \omega(\tau)\rho(t-\tau) \] + + wobei $\omega(\tau)$ der Gauss Kern und $\rho(t)$ die Antwortfunktion ist. + + Gl\"ucklicherweise m\"ussen wir das nicht selbst implementieren... +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Faltungsmethode ---} + \large Algortihmus: + \normalsize + \begin{enumerate} + \item Die neuronalen Antworten werden ``bin\"ar'' ausgedr\"uckt. + \item Ein Filterkern wird berechnet, der das Integral 1 hat. + \item Mithilfe der Faltung (\code{conv} Funktion) wird jede 1 durch + den ``Kern'' ersetzt.\\ + \code{conv(x, kern, 'mode', 'same')} + \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Feurerrate als Funktion der Zeit --- Faltungsmethode ---} + \begin{figure} + \includegraphics[width=0.9\columnwidth]{images/convolved_rate} + \end{figure} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Feurerrate als Funktion der Zeit --- Faltungsmethode ---} + \textbf{Vorteile:} + \begin{enumerate} + \item Sehr ``nat\"urliche'' erscheinende Darstellung. + \item Sehr gutes Verhalten im Fourrier Raum. + \end{enumerate} + + \textbf{Nachteile:} + \begin{enumerate} + \item Relativ rechenintensiv. + \item Macht Annahmen \"uber die Zeitskalen neuronaler Verarbeitung. + \end{enumerate} +\end{frame} + +\begin{frame}[plain] + \huge{2. Analyse der Beziehung zwischen Stimulus und Antwort} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Spike-Triggered-Average} + \begin{itemize} + \item[] Die Antworten darzustellen ist gut und sch\"on, aber was sagt es uns?\pause + \item[] Idealerweise wollen wir die Antworten in Beziehung zum + hervorrufenden Stimulus setzen. + \item[] Eine Methode ist der sogenannte \textbf{Spike-Triggered-Average} (STA). + \end{itemize} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Spike-Triggered-Average} + + Der STA stellt den (mittleren) Stimulus dar, der zu einem + Aktionspotential gef\"uhrt hat: + + \begin{equation} + STA(\tau) = \frac{1}{\langle n \rangle} \left\langle \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \right\rangle + \end{equation} + Wobei: $\tau$ ist eine bestimmte Zeit relativ zur Zeit eines + Aktionspotentials, $t_i$ ist der Zeitpunkt eines APs, $s(t)$ ist der + Stimulus.\\ + + Leider m\"ussen wir das selbst implementieren... +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Spike-Triggered-Average} + \large{Algorithmus:} + \normalsize + \begin{enumerate} + \item Der \textbf{STA} ist der mittlere Stimulus, der zu einem Aktionspotential f\"uhrt. + \item F\"ur jeden Spike wird ein entsprechender Abschnitt um die Zeit des Spikes herausgeschnitten. + \item Die einzelen Stimulussegmente werden gemittelt. + \end{enumerate}\pause + \begin{figure} + \centering + \includegraphics[width=0.5\columnwidth]{images/sta} + \end{figure} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Spike-Triggered-Average} + \vspace{-1em} + \begin{figure} + \centering + \includegraphics[width=0.6\columnwidth]{images/sta} + \end{figure} + \pause + \vspace{-0.5em} + Welche Information liefert der \textbf{STA}? + \small + \begin{enumerate} + \item Gibt es eine Beziehung zwischen Stimulus und Antwort?\pause + \item Gibt es eine Verz\"ogerung zwischen Stimulus und Antwort? Wie + gro{\ss} ist diese?\pause + \item Wie weit h\"angt das Auftreten eines Aktionspotentials von der + Vergangenheit ab? \pause + \item Kann die Zelle in die Zukunft sehen? + \end{enumerate} +\end{frame} + +\end{document} + + +\begin {frame} + \framesubtitle{Spiketrain Analyse} + \framesubtitle{Weitere Themen} + \begin{enumerate} + \item Tuningkurven. + \item Stimulusrekonstruktion mittels STA. + \item Kreuzkorrelation. + \item Fourier Analyse, Transferfunktion, Kohärenz. + \item Reverse Rekonstruktion. + \end{enumerate} +\end{frame} \ No newline at end of file From 96997a8299e9f1b95d9506c791c57c7a4cdea82c Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 27 Oct 2015 23:24:04 +0100 Subject: [PATCH 3/6] moving and some work --- programming/lectures/Makefile | 2 +- .../lectures}/plotting.tex | 0 .../code/firing_rates.py | 61 +++++++++++++++++-- .../exercises/psth.tex | 0 .../{psth_sta.tex => psth_sta-slides.tex} | 2 +- 5 files changed, 59 insertions(+), 6 deletions(-) rename {spike_trains/lecture => programming/lectures}/plotting.tex (100%) rename {programming => spike_trains}/code/firing_rates.py (78%) rename programming/exercises/plotting_psth.tex => spike_trains/exercises/psth.tex (100%) rename spike_trains/lecture/{psth_sta.tex => psth_sta-slides.tex} (99%) diff --git a/programming/lectures/Makefile b/programming/lectures/Makefile index dec2459..355432d 100644 --- a/programming/lectures/Makefile +++ b/programming/lectures/Makefile @@ -1,5 +1,5 @@ TEXFILES=$(wildcard *.tex) -TEXFILES=boolean_logical_indexing.tex control_structures.tex data_structures.tex plotting_spike_trains.tex programming_basics.tex scripts_functions.tex sta_stc.tex variables_datatypes.tex vectors_matrices.tex +TEXFILES=boolean_logical_indexing.tex control_structures.tex data_structures.tex plotting.tex programming_basics.tex scripts_functions.tex sta_stc.tex variables_datatypes.tex vectors_matrices.tex PDFFILES=$(TEXFILES:.tex=.pdf) diff --git a/spike_trains/lecture/plotting.tex b/programming/lectures/plotting.tex similarity index 100% rename from spike_trains/lecture/plotting.tex rename to programming/lectures/plotting.tex diff --git a/programming/code/firing_rates.py b/spike_trains/code/firing_rates.py similarity index 78% rename from programming/code/firing_rates.py rename to spike_trains/code/firing_rates.py index b38dac8..4871e5b 100644 --- a/programming/code/firing_rates.py +++ b/spike_trains/code/firing_rates.py @@ -62,7 +62,7 @@ def plot_isi_rate(spike_times, max_t=30, dt=1e-4): ax1.vlines(times[times < (50000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) ax1.set_ylabel("skpikes", fontsize=12) set_axis_fontsize(ax1, 12) - + ax1.set_xlim([0, 5]) ax2.plot(time, rate, label="instantaneous rate, trial 1") ax2.set_ylabel("firing rate [Hz]", fontsize=12) ax2.legend(fontsize=12) @@ -191,8 +191,61 @@ def plot_conv_rate(spike_times, sigma=0.05, max_t=30, dt=1e-4): plt.close() +def plot_comparison(spike_times, bin_width, sigma, max_t=30., dt=1e-4): + times = np.squeeze(spike_times[0][0]) + time, conv_rate = get_convolved_rate(times, sigma) + time, inst_rate = get_instantaneous_rate(times) + time, binn_rate = get_binned_rate(times, bin_width) + + fig = plt.figure() + ax1 = fig.add_subplot(411) + ax2 = fig.add_subplot(412) + ax3 = fig.add_subplot(413) + ax4 = fig.add_subplot(414) + + ax1.vlines(times[times < (100000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) + ax1.set_ylabel("spikes", fontsize=10) + ax1.set_xlim([1.5, 3.5]) + ax1.set_ylim([0, 1]) + ax1.set_yticks([0, 1]) + set_axis_fontsize(ax1, 10) + ax1.set_xticklabels([]) + + ax2.plot(time, inst_rate, label="instantaneous rate") + ax2.set_ylabel("firing rate [Hz]", fontsize=10) + ax2.legend(fontsize=10) + ax2.set_xlim([1.5, 3.5]) + ax2.set_ylim([0, 300]) + set_axis_fontsize(ax2, 10) + ax2.set_xticklabels([]) + + ax3.plot(time, binn_rate, label="binned rate") + ax3.set_ylabel("firing rate [Hz]", fontsize=10) + ax3.legend(fontsize=10) + ax3.set_xlim([1.5, 3.5]) + ax3.set_ylim([0, 300]) + set_axis_fontsize(ax3, 10) + ax3.set_xticklabels([]) + + ax4.plot(time, conv_rate, label="convolved rate") + ax4.set_xlabel("times [s]", fontsize=10) + ax4.set_ylabel("firing rate [Hz]", fontsize=10) + ax4.legend(fontsize=10) + ax4.set_xlim([1.5, 3.5]) + ax4.set_ylim([0, 300]) + set_axis_fontsize(ax4, 10) + + fig.set_size_inches(7.5, 5) + fig.subplots_adjust(left=0.1, bottom=0.125, top=0.95, right=0.95, ) + fig.set_facecolor("white") + fig.savefig("../lecture/images/psth_comparison.pdf") + plt.close() + + if __name__ == "__main__": spike_times = spio.loadmat('lifoustim.mat')["spikes"] - plot_isi_rate(spike_times) - plot_bin_rate(spike_times, 0.05) - plot_conv_rate(spike_times, 0.025) + # plot_isi_rate(spike_times) + # plot_bin_rate(spike_times, 0.05) + # plot_conv_rate(spike_times, 0.025) + plot_comparison(spike_times, 0.05, 0.025) + diff --git a/programming/exercises/plotting_psth.tex b/spike_trains/exercises/psth.tex similarity index 100% rename from programming/exercises/plotting_psth.tex rename to spike_trains/exercises/psth.tex diff --git a/spike_trains/lecture/psth_sta.tex b/spike_trains/lecture/psth_sta-slides.tex similarity index 99% rename from spike_trains/lecture/psth_sta.tex rename to spike_trains/lecture/psth_sta-slides.tex index a89676a..668716d 100644 --- a/spike_trains/lecture/psth_sta.tex +++ b/spike_trains/lecture/psth_sta-slides.tex @@ -383,7 +383,7 @@ \item Tuningkurven. \item Stimulusrekonstruktion mittels STA. \item Kreuzkorrelation. - \item Fourier Analyse, Transferfunktion, Kohärenz. + \item Fourier Analyse, Transferfunktion, Kohärenz. \item Reverse Rekonstruktion. \end{enumerate} \end{frame} \ No newline at end of file From b17fafdc736df5dc4e16a8c929c59ca51f1c6465 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 27 Oct 2015 23:25:39 +0100 Subject: [PATCH 4/6] new files --- spike_trains/lecture/Makefile | 20 ++ .../lecture/beamercolorthemetuebingen.sty | 61 +++++ .../lecture/images/psth_comparison.pdf | Bin 0 -> 184616 bytes spike_trains/lecture/psth_sta.tex | 36 +++ spike_trains/lecture/spike_trains-chapter.tex | 226 ++++++++++++++++++ 5 files changed, 343 insertions(+) create mode 100644 spike_trains/lecture/Makefile create mode 100644 spike_trains/lecture/beamercolorthemetuebingen.sty create mode 100644 spike_trains/lecture/images/psth_comparison.pdf create mode 100644 spike_trains/lecture/psth_sta.tex create mode 100644 spike_trains/lecture/spike_trains-chapter.tex diff --git a/spike_trains/lecture/Makefile b/spike_trains/lecture/Makefile new file mode 100644 index 0000000..96b7d0e --- /dev/null +++ b/spike_trains/lecture/Makefile @@ -0,0 +1,20 @@ +TEXFILES=$(wildcard *.tex) +TEXFILES=psth_sta.tex + +PDFFILES=$(TEXFILES:.tex=.pdf) + +pdf : $(PDFFILES) + +$(PDFFILES) : %.pdf : %.tex + pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true + +clean : + rm -f *~ $(TEXFILES:.tex=.aux) $(TEXFILES:.tex=.log) $(TEXFILES:.tex=.out) $(TEXFILES:.tex=.nav) $(TEXFILES:.tex=.snm) $(TEXFILES:.tex=.toc) $(TEXFILES:.tex=.vrb) + +cleanall : clean + rm -f $(PDFFILES) + +watch : + while true; do ! make -q pdf && make pdf; sleep 0.5; done + + diff --git a/spike_trains/lecture/beamercolorthemetuebingen.sty b/spike_trains/lecture/beamercolorthemetuebingen.sty new file mode 100644 index 0000000..c4a5da6 --- /dev/null +++ b/spike_trains/lecture/beamercolorthemetuebingen.sty @@ -0,0 +1,61 @@ +% Copyright 2007 by Till Tantau +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% See the file doc/licenses/LICENSE for more details. + +\usepackage{color} +\definecolor{karminrot}{RGB}{165,30,55} +\definecolor{gold}{RGB}{180,160,105} +\definecolor{anthrazit}{RGB}{50 ,65 ,75 } + +\mode + +\setbeamercolor*{normal text}{fg=anthrazit,bg=white} +\setbeamercolor*{alerted text}{fg=anthrazit} +\setbeamercolor*{example text}{fg=anthrazit} +\setbeamercolor*{structure}{fg=gold,bg=karminrot} + +\providecommand*{\beamer@bftext@only}{% + \relax + \ifmmode + \expandafter\beamer@bftext@warning + \else + \expandafter\bfseries + \fi +} +\providecommand*{\beamer@bftext@warning}{% + \ClassWarning{beamer} + {Cannot use bold for alerted text in math mode}% +} + +\setbeamerfont{alerted text}{series=\beamer@bftext@only} + +\setbeamercolor{palette primary}{fg=karminrot,bg=white} +\setbeamercolor{palette secondary}{fg=gold,bg=white} +\setbeamercolor{palette tertiary}{fg=anthrazit,bg=white} +\setbeamercolor{palette quaternary}{fg=black,bg=white} + +\setbeamercolor{sidebar}{bg=karminrot!100} + +\setbeamercolor{palette sidebar primary}{fg=karminrot} +\setbeamercolor{palette sidebar secondary}{fg=karminrot} +\setbeamercolor{palette sidebar tertiary}{fg=karminrot} +\setbeamercolor{palette sidebar quaternary}{fg=karminrot} + +\setbeamercolor{item projected}{fg=black,bg=black!20} + 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+\graphicspath{{figures/}} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} + +\include{psth_sta} + +\end{document} + From eef177f7eeac2e92511daff75f1007603ef0706a Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 27 Oct 2015 23:34:15 +0100 Subject: [PATCH 5/6] figure for psth method comparsion, some introductory words for spiketrain chapter --- spike_trains/code/firing_rates.py | 2 +- spike_trains/lecture/psth_sta.tex | 17 ++++++++++++++--- 2 files changed, 15 insertions(+), 4 deletions(-) diff --git a/spike_trains/code/firing_rates.py b/spike_trains/code/firing_rates.py index 4871e5b..0f02e87 100644 --- a/spike_trains/code/firing_rates.py +++ b/spike_trains/code/firing_rates.py @@ -193,7 +193,7 @@ def plot_conv_rate(spike_times, sigma=0.05, max_t=30, dt=1e-4): def plot_comparison(spike_times, bin_width, sigma, max_t=30., dt=1e-4): times = np.squeeze(spike_times[0][0]) - time, conv_rate = get_convolved_rate(times, sigma) + time, conv_rate = get_convolved_rate(times, bin_width/np.sqrt(12.)) time, inst_rate = get_instantaneous_rate(times) time, binn_rate = get_binned_rate(times, bin_width) diff --git a/spike_trains/lecture/psth_sta.tex b/spike_trains/lecture/psth_sta.tex index 33bf2fb..57ea7a3 100644 --- a/spike_trains/lecture/psth_sta.tex +++ b/spike_trains/lecture/psth_sta.tex @@ -27,10 +27,21 @@ ist das sog. Peri Stimulus Zeithistogramm (peri stimulus time histogram, PSTH). Es wird der zeitliche Verlauf der Feuerrate $r(t)$ dargestellt. Die Einheit der Feuerrate ist Hertz, das heisst, die Anzahl Aktionspotentiale pro Sekunde. Dabei gibt es verschiedene -Methoden diese zu bestimmen. Jede dieser Methoden hat ihre Vor- und -Nachteile. Abbildung \ref{psthfig} zeigt drei dieser Methoden. +Methoden diese zu bestimmen. Drei solcher Methoden sind in Abbildung +\ref{psthfig} dargestellt. \begin{figure} - \includegraphics[width=0.75\columnwidth]{images/psth_comparison} + \includegraphics[width=\columnwidth]{images/psth_comparison} \caption{}\label{psthfig} \end{figure} + + + +\section{Spike triggered Average} + +Der Spike triggered average (STA) ist der mittlere Stimulus, der zu +einem Aktionspotential in der neuronalen Antwort f\"uhrt. + +\begin{equation} + STA(\tau) = \frac{1}{\langle n \rangle} \left\langle \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \right\rangle +\end{equation} From 6b1de050c42b211451a8fba19b54c88a6f49da52 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Wed, 28 Oct 2015 09:10:00 +0100 Subject: [PATCH 6/6] bufixes --- spike_trains/exercises/psth.tex | 22 +++++++++++++--------- 1 file changed, 13 insertions(+), 9 deletions(-) diff --git a/spike_trains/exercises/psth.tex b/spike_trains/exercises/psth.tex index 8dcee53..8145a16 100644 --- a/spike_trains/exercises/psth.tex +++ b/spike_trains/exercises/psth.tex @@ -37,17 +37,21 @@ \end{center} \begin{questions} - \question Graphische Darstellung der zeitabh\"angigen Antwort eines - Neurons. PSTH auf Basis der instantanen Feuerrate. Verwendet den Datensatz \code{} + \question Stellt die zeitabh\"angigen Feuerrate eines Neurons als + PSTH dar. Das PSTH soll auf Basis der instantanen Feuerrate (des + Interspikeintervals) berechnet werden. Verwendet den Datensatz + \code{lifoustim.mat}. Dieser enth\"at drei Variablen: 1. die + Spikezeiten, 2. den Stimulus und 3. die zeitliche Aufl\"osung. Die + Dauer eines Trials betr\"agt 30 Sekunden. \begin{parts} \part Schreibt eine Funktion, die einen Vektor mit Spikezeiten, die Dauer des Trials, und die zeitliche Aufl\"osung entgegennimmt - und die Zeitachse sowie die Feuerrate zur\"uckgiebt. + und die Zeitachse sowie die Feuerrate zur\"uckgibt. \part Benutzt diese Funktion in einem Skript und stellt das PSTH eines einzelnen Trials sowie den Mittelwert \"uber alle Trials dar. - \part Erweitert das Programm so, dass die Abbildung den Standards - z.B. vom \textit{Journal of Neuroscience} entspricht + \part Erweitert das Programm so, dass die Abbildung den Richtlinien + des \textit{Journal of Neuroscience} entspricht (Schriftgr\"o{\ss}e, Abbildungsgr\"o{\ss}e). \part Die Abbildung sollte als pdf gespeichert werden. \end{parts} @@ -62,13 +66,13 @@ Abbildungen sollten nat\"urlich ``publikationsreif'' sein und gespeichert werden. - \question Einige trials sind anders als die \"Ubrigen. Benutzt den - Rasterplot um sie zu finden. Speichert alle Abbildungen in - ``publikationsreifer'' Form. + \question Einige Trials sind anders als die \"Ubrigen. Benutzt den + Rasterplot um sie zu finden. Alle erstellten Abbildungen sollen in + ``publikationsreifer'' Form gespeichert werden. \begin{parts} \part Benutzt den Rasterplot um sie zu finden. \part Plottet die Verteilung der Spike counts. - \part Filtert all die trials heraus, deren spike count mehr als + \part Filtert all die Trials heraus, deren Spikecount mehr als $2\sigma$ vom Mittelwert abweicht. \part Plottet das PSTH vor und nach dem Filtern. \end{parts}