100 lines
3.4 KiB
TeX
100 lines
3.4 KiB
TeX
\documentclass[addpoints,11pt]{exam}
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\usepackage{url}
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\usepackage{color}
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\usepackage{hyperref}
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\pagestyle{headandfoot}
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\runningheadrule
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\firstpageheadrule
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\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
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-- 11/06/2014}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{}
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\runningfooter{}{}{}
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\pointsinmargin
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\bracketedpoints
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%\printanswers
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%\shadedsolutions
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
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\sffamily
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% \begin{flushright}
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% \gradetable[h][questions]
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% \end{flushright}
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\begin{center}
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\input{../disclaimer.tex}
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\end{center}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{questions}
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\question In the visual cortex V1 orientation sensitive neurons
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respond to bars in dependence on their orientation.
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How is the orientation of a bar encoded by the activity of a
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population of orientation sensisitive neurons?
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In an electrophysiological experiment, 6 neurons have been recorded
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simultaneously. First, the tuning of these neurons was characteried
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by presenting them bars in a range of 12 orientation angles. Each
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orientation was presented 50 times. Each of the \texttt{unit*.mat}
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files contains the responses of one of the neurons. In there,
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\texttt{angles} is a vector with the orientation angles of the bars
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in degrees. \texttt{spikes} is a cell array that contains the
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vectors of spike times for each angle and presentation. The spike
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times are given in seconds. The stimulation with the bar starts a
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time $t_0=0$ and ends at time $t_1=200$\,ms.
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Then the population activity of the 6 neurons was measured in
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response to arbitrarily oriented bars. The responses of the 6
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neurons to 50 presentation of a bar are stored in the
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\texttt{spikes} variables of the \texttt{population*.mat} files.
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The \texttt{angle} variable holds the angle of the presented bar.
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\begin{parts}
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\part Illustrate the spiking activity of the V1 cells in response
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to different orientation angles of the bars by means of spike
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raster plots (of one unit).
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\part Plot the firing rate of each of the 6 neurons as a function
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of the orientation angle of the bar. As the firing rate compute
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the number of spikes in the time interval $0<t<200$\,ms divided by
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200\,ms. The resulting curves are the tuning curves $r(\varphi)$
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of the neurons.
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\part Fit the function \[ r(\varphi) =
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g(1-\cos(\varphi-\varphi_0))/2 \] to the measured tuning curves in
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order to estimated the orientation angle at which the neurons
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respond strongest. In this function $\varphi_0$ is the position of
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the peak (really? How exactly is $\varphi_0$ related to the
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position of the peak? Do you find a better function where
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$\varphi_0$ is identical with the peak position?) and $g$ is a
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gain factor that sets the maximum firing rate.
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\part How can the orientation angle of the presented bar be read
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out from the population activity of the 6 neurons? One is the so
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called ``population vector''. Think of another (simpler) method.
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Load one of the \texttt{population*.mat} files, illustrate the data,
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and estimate the orientation angle of the bar by two different methods.
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\part Compare, illustrate and discuss the performance of your two
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decoding methods.
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\end{parts}
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\end{questions}
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\end{document}
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gains and angles of the 6 neurons:
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14.6 0
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17.1 36
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17.6 72
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14.1 107
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10.7 144
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11.4 181
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