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

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Fabian Sinz 2014-10-30 18:46:14 +01:00
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programming/exercises/STA/p-unit_spike_times.mat Normal file
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programming/exercises/STA/p-unit_stimulus.mat Normal file
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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);

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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);

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\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}