85 lines
3.6 KiB
TeX
85 lines
3.6 KiB
TeX
\documentclass[12pt,a4paper,pdftex]{exam}
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\usepackage[german]{babel}
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\usepackage{natbib}
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\usepackage{graphicx}
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\usepackage[small]{caption}
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\usepackage{sidecap}
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\usepackage{pslatex}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\setlength{\marginparwidth}{2cm}
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\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
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%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
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\pagestyle{headandfoot} \header{{\bfseries\large Exercise
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}}{{\bfseries\large Correlation of stimulus and response}}{{\bfseries\large December 19, 2017}}
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\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
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jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{}
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\setlength{\baselineskip}{15pt}
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\setlength{\parindent}{0.0cm}
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\setlength{\parskip}{0.3cm}
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\renewcommand{\baselinestretch}{1.15}
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\newcommand{\code}[1]{\texttt{#1}}
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\renewcommand{\solutiontitle}{\noindent\textbf{Solution:}\par\noindent}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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\vspace*{-6.5ex}
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\begin{center}
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\textbf{\Large Introduction to scientific computing}\\[1ex]
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{\large Jan Grewe, Jan Benda}\\[-3ex]
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Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\
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\end{center}
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\begin{questions}
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\question Estimate the time-dependent firing rate of a neuron. Use
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the ``convoluion'' method to do it. The dataset \code{lifoustim.mat}
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contains three variables. 1st the spike times in different trials,
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2nd the stimulus, and 3rd the temporal resolution. The total
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duration of each trial amounts to 30 seconds.
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\begin{parts}
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\part{} Write a function that estimates the firing rate with the
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``convolution'' method. This function should take four input
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arguments: (i) a vector of spike times, (ii) the temporal
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resolution of the recording, (iii) the duration of the
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trial, and (iv) the standard deviation of the applied Gaussian
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kernel. The function should return two variables: (i) the firing
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rate, and (ii) a vector representing time.
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\part{} Write a script that uses this function to estimate the
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firing rate of all trial. Plot the mean (across trials) firing
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rate as a function of time. Use two different kernel standard
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deviations (e.g. 20\,ms and 100\,ms).
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\part{} Save the figure according the style defined by the
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\emph{J. Neuroscience} (figure width 1, 1.5, or two columns, 8.5,
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11.6, or 17.6\,cm, respectively; fontsize 10 pt). Save the figure
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as pdf.
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\end{parts}
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\question In a previous exercise you were asked to estimate the
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correlation between a set of independent variables and the
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respective measurements (Chapter 6.4 in the script). We can use
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this function to learn a few things about the relation between
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stimulus and response.
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\begin{parts}
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\part{} Estimate the firing rate of the neuronal response using one
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of the three methods. Use the same dataset as before.
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\part{} Calculate the correlation of stimulus and response.
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\part{} Calculate the correlation of stimulus and response
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while shifting the response relative to the stimulus in a range
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$\pm$ 50\,ms (1\,ms steps).
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\part{} Plot these correlations as a function of the temporal shift
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(often called lag).
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\part{} What is the maximum correlation and at which lag does it occur?
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\part{} What could this tell us about the neuronal response properties?
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\end{parts}
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\end{questions}
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\end{document}
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