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

programming/exercises/STA/sta.m

@@ -0,0 +1,18 @@
+function [st_avg, std_sta, valid_spikes]= sta(stimulus, spike_times, count, sampling_rate)
+
+snippets = zeros(numel(spike_times), 2*count);
+valid_spikes = 1;
+for i = 1:numel(spike_times)
+    t = spike_times(i);
+    index = round(t*sampling_rate);
+    if index <= count || (index + count) > length(stimulus)
+        continue
+    end
+    snippets(valid_spikes,:) = stimulus(index-count:index+count-1);
+    valid_spikes = valid_spikes + 1;
+end
+
+snippets(end-(end-valid_spikes):end,:) = [];
+
+st_avg = mean(snippets, 1);
+std_sta = std(snippets,[],1);

programming/exercises/STA/sta_script.m

@@ -0,0 +1,67 @@
+clear 
+clc
+
+%% load data
+load p-unit_spike_times.mat
+load p-unit_stimulus.mat
+sample_rate = 20000;
+
+%% calculate STA
+all_times = [];
+for i = 1:length(spike_times)
+    all_times = cat(1, all_times, spike_times{i});
+end
+
+[st_average, sta_sd, num] = sta(stimulus(:,2), all_times, 1000, sample_rate);
+fig = figure();
+set(fig, 'PaperUnits', 'centimeters');
+set(fig, 'PaperSize', [11.7 9.0]);
+set(fig, 'PaperPosition',[0.0 0.0 11.7 9.0]);
+set(fig,'Color', 'white')
+plot(((1:length(st_average))-1000)/sample_rate, st_average)
+xlabel('time [s]')
+ylabel('stimulus')
+
+%% reverse reconstruction
+
+% make binary representation of the spike times
+binary_spikes = zeros(size(stimulus, 1), length(spike_times));
+estimated_stims = zeros(size(binary_spikes));
+for i = 1:length(spike_times)
+    binary_spikes(round(spike_times{i}*sample_rate), i) = 1;
+    estimated_stims(:,i) = conv(binary_spikes(:,i), st_average, 'same');
+end
+
+fig = figure();
+set(fig, 'PaperUnits', 'centimeters');
+set(fig, 'PaperSize', [11.7 9.0]);
+set(fig, 'PaperPosition',[0.0 0.0 11.7 9.0]);
+set(fig,'Color', 'white')
+plot(stimulus(:,1), stimulus(:,2), 'displayname','original')
+hold on
+plot(stimulus(:,1), mean(estimated_stims,2), 'r', 'displayname', 'reconstruction')
+xlabel('time [s]')
+ylabel('stimulus')
+legend show
+
+%% calculate STC
+
+% we need to downsample the data otherwise the covariance matrixs gets too
+% large 20Khz to 1kHz
+
+% downsampled_binary = zeros(size(stimulus, 1)/20, length(spike_times));
+downsampled_stim = zeros(size(stimulus,1)/20,1);
+
+% for i = 1:length(spike_times)
+%     indices = round(spike_times{i}.*1000);
+%     indices(indices < 1) = [];
+%     downsampled_binary(indices, i) = 1;
+% end
+for i = 1:length(downsampled_stim)
+    start_index = (i-1) * 20 + 1;
+    downsampled_stim(i) = mean(stimulus(start_index:start_index+19,2));
+end
+
+[st_average, ~, ~] = sta(downsampled_stim, all_times, 50, 1000);
+
+

programming/lectures/sta_stc.tex

@@ -0,0 +1,380 @@
+\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<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}
+    % \frametitle{\insertsectionhead}
+    % \tableofcontents[currentsection,hideothersubsections]
+  \end{frame}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
+
+\setbeamertemplate{blocks}[rounded][shadow=true]
+
+\title[]{Introduction to Scientific Computing --  \\
+Cross-Correlation, Spike--Triggered--Average and Reverse Reconstruction}
+\author[]{Jan Grewe\\Abteilung f\"ur Neuroethologie\\
+  Universit\"at T\"ubingen}
+
+\institute[Introduction to Scientific Computing]{}
+ \date{2014/10/13 - 2014/11/07}
+ %\logo{\pgfuseimage{../../resources/UT_BM_Rot_RGB.pdf}}
+
+\subject{Einf\"uhrung in 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}
+}
+
+\input{../../latex/environments.tex}
+\makeatother
+ 
+\begin{document} 
+
+\begin{frame}[plain]
+  \frametitle{}
+  \vspace{-1cm}
+  \titlepage % erzeugt Titelseite
+\end{frame}
+
+
+\begin{frame}[plain]
+  \frametitle{Rekapitulation}
+  \begin{enumerate}
+  \item PSTH\pause
+  \end{enumerate}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Introduction to scientific computing}
+  \frametitle{Menue}
+  \begin{enumerate}
+  \item Cross-correlation
+  \item Estimation of the Spike--Triggered--Average -- STA
+  \item Reverse reconstruction
+  \end{enumerate}
+\end{frame}
+
+
+\begin{frame}[plain]
+  \huge{1. Recapitulation: PSTH}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Recapitulation}
+  \only<1>{
+    \framesubtitle{Displaying the neuronal response over time - Rasterplot}
+    \begin{figure}
+      \centering
+      \includegraphics[width=0.375\columnwidth]{images/rasterplot}
+    \end{figure}    
+  }
+  \only<2>{
+    \framesubtitle{Displaying the neuronal response over time - PSTH}
+    \begin{figure}
+      \centering
+      \includegraphics[width=0.5\columnwidth]{images/conv}
+    \end{figure}
+  }
+\end{frame}
+
+
+\begin{frame}[plain]
+  \huge{2. Relating stimulus and response}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{How can we relate the response to the stimulus?}
+    \begin{figure}
+      \centering
+      \includegraphics[height=0.9\textheight]{images/conv_stim}
+    \end{figure}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Cross--correlation}
+  The cross - correlation for (time) discrete data is defined as:
+  \begin{equation}
+    Q_{rs}(\tau) = \frac{1}{2\cdot N-|\tau|} \displaystyle\sum^{T}_{\tau=-T}{r(t) \cdot s(t-\tau)} \cdot \Delta \tau
+  \end{equation}
+  \pause
+  Don't worry, this is already implemented in MATLAB!
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Cross--correlation}
+    \footnotesize
+  \begin{lstlisting}
+[c,lags] = xcorr(stimulus, response, 10000, 'unbiased');
+fig = figure();
+set(fig, 'PaperUnits', 'centimeters');
+set(fig, 'PaperSize', [11.7 9.0]);
+set(fig, 'PaperPosition',[0.0 0.0 11.7 9.0]);
+set(fig,'Color', 'white')
+plot(lags/sample_rate, c)
+xlabel('lag [s]')
+ylabel('correlation')
+  \end{lstlisting}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Cross--correlation}
+  \begin{figure}
+    \includegraphics[width=0.5\linewidth]{images/correlation}
+  \end{figure}
+\end{frame}
+
+
+
+\begin{frame}[fragile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Cross--correlation - Exercises} 
+  \begin{enumerate}
+  \item calculate the cross-correlation between two vectors of random
+    numbers.
+  \item Calculate the cross-correlation between one of these vectors
+    and itself (auto-correlation).
+  \item Calculate the cross-correlation between one vector and a
+    time-shifted version of itself (use \verb+circshift+ to do this).
+  \end{enumerate}
+  \textbf{Note:} Select max\_lag to be less than 10\% of the length of
+  your vectors!
+  \begin{enumerate}
+  \item Create the cross correlation of the p-unit data and stimulus.
+  \item \textbf{Note:} you have to convert the spike\_times to a PSTH!
+  \item Find out the position of the correlation peak. 
+  \item What does this tell you?
+  \end{enumerate}
+\end{frame}
+
+
+\begin{frame}[plain]
+  \huge{2. Spike--Triggered--Average --- STA}
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Spike--Triggered--Average --- STA} 
+
+  The \textbf{STA} is the average stimulus that led to a spike in the
+  neuron.
+
+  \begin{equation}
+    STA(\tau) = \left\langle \frac{1}{n} \displaystyle\sum^{i=1}_{n}{s(t_i - \tau)} \right\rangle
+  \end{equation}
+  
+  Sadly, we need to implement this ourselves.\newline\newline\pause
+  \vspace{1em}
+  \noindent
+  \textbf{Algorithm:}
+  \begin{enumerate}
+  \item For each spike a snippet is taken from the respective stimulus.
+  \item The snippets are averaged.
+  \end{enumerate}
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Spike--Triggered--Average -- STA}
+  \vspace{-1em}
+  \begin{figure}
+    \centering
+    \includegraphics[width=0.65\columnwidth]{images/sta}
+  \end{figure}
+  \pause
+  \vspace{-0.5em}
+  What does the \textbf{STA} tell us?
+  \begin{enumerate}
+  \item Is there a relation between stimulus and response? \pause
+  \item Is there a lag between them and how large is it? \pause
+  \item How far in the past does a neuron encode? \pause
+  \item Can it see into the future?
+  \end{enumerate}
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{STA -- Exercises}
+  \textbf{Exercise:}
+  \begin{enumerate}
+    \item Write a function \verb+sta(x, y, count, sample_rate)+ that
+      takes the stimulus (x), the response (y, as spike times), the
+      number (count) of sampling points it should cut out from the
+      stimulus and the sampling\_rate to convert from times to
+      indices.
+    \item \textbf{Beware:} sometimes the spike\_time may be too close
+      to the beginning or the end of the stimulus to cut out enough
+      data.
+    \item Calculate the STA for P-unt data.
+  \end{enumerate}
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Spike--Triggered--Average -- STA}
+  What does the \textbf{STA} tell us?
+  \begin{figure}
+    \centering
+    \includegraphics[width=0.25\columnwidth]{images/sta}
+  \end{figure}
+  \begin{enumerate}
+  \item Is there a relation between stimulus and response?\pause
+  \item Is there a lag between them and how large is it?\pause
+  \item How far in the past does a neuron encode?\pause
+  \item Can it see into the future?
+  \end{enumerate}
+\end{frame}
+
+
+\begin{frame}[plain]
+  \huge{3. Reverse reconstruction using the \textbf{STA}}
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Reverse reconstruction using the \textbf{STA}}
+  \textbf{Basic idea:}\newline
+  \begin{itemize}
+  \item The \textbf{STA} is the average stimlus that led to a spike. \pause
+  \item The other way round: Whenever we observe a spike, the stimulus
+    was likely to have looked like the \textbf{STA}.\pause
+  \item Thus, we should be able to reconstruct how the stimulus looked
+    like to evoke the observed response.
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Reverse reconstruction using the \textbf{STA}}
+  \textbf{Algorithm:}\newline
+  \begin{enumerate}
+  \item Estimate the \textbf{STA}. \pause
+  \item Create a binary representation of the spike train (vector of
+    \verb+zeros+ in which each \textbf{1} signals the occurence of a
+    spike).\pause
+  \item Use the STA as a Kernel (compare to the spike convolution
+    method to create the PSTH) and convolve (\verb+conv+) it with the
+    \textbf{STA}.
+  \end{enumerate}
+  \textbf{Exercise:}
+  \begin{enumerate}
+  \item Reconstruct the stimulus from the P-unit data.
+  \item Plot original and reconstructed stimulus into the same plot.
+  \item Are they similar? In which instances are they different?
+  \end{enumerate}
+\end{frame}
+
+\end{document}
+
+\begin{frame}[plain]
+  \huge{4. Spike--Triggered--Covariance \textbf{STC}}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Spike--Triggered--Covariance \textbf{STC}}
+  \textbf{Problem:}
+  \begin{itemize}
+  \item The \textbf{STA} is a linear filter.
+  \item It can only reveal linear relationships between stimulus and response.\pause
+  \end{itemize}
+  \vspace{1em}
+  Further relations can be recovered using the Spike-triggered-covariance.\pause
+  \begin{equation}
+    STC = \frac{1}{N-1} \cdot \displaystyle\sum_{n=1}^{N}[\overrightarrow{s}(t_n) - STA]
+                     [\overrightarrow{s}(t_n) - STA]^T
+  \end{equation}
+  where:\\ $N$ is the total number of spikes,
+  $\overrightarrow{s}(t_n)$ the stimulus snippet for the $n^{th}$
+  spike, and $STA$ the Spike-Triggered-Average.
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Relating stimulus and response}
+  \framesubtitle{Spike--Triggered--Covariance}
+  \begin{itemize}
+  \item 
+  \end{itemize}
+\end{frame}
+
+
+\end{document}