75 lines
2.6 KiB
TeX
75 lines
2.6 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}{11/02/2015
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-- 11/05/2015}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
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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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\section*{Reverse reconstruction of the stimulus evoking neuronal responses.}
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To analyse encoding properties of a neuron one often calculates the
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Spike-Triggered-Average (STA).
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\[ STA(\tau) = \frac{1}{\langle n \rangle} \left\langle
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\displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \right\rangle \]
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The STA is the average stimulus that led to a spike in the neuron and
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can calculated by cutting out snippets form the stimulus centered on
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the respective spike time. The Spike-Triggered-Average can be used to
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reconstruct the stimulus a neuron has been stimulated with.
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\begin{questions}
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\question In the accompanying files you find the spike responses of
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P-units and pyramidal neurons of the weakly electric fish
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\textit{Apteronotus leptorhynchus}. The respective stimuli are
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stored in separate files. The data is sampled with 20\,kHz temporal
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resolution and spike times are given in seconds. Start with the
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P-unit and, in the end, apply the same functions to the pyramidal
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data.
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\begin{parts}
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\part Estimate the STA and plot it.
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\part Implement a function that does the reconstruction of the
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stimulus using the STA.
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\part Implement a function that estimates the reconstruction
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error using the mean-square-error and express it relative to the
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variance of the original stimulus.
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\begin{equation}
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err = \frac{1}{N} \cdot \displaystyle\sum^{N}_{i=1}(x_i - \bar{x})^2,
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\end{equation}
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with $N$ the number of data points, $x_i$ the current value and
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$\bar{x}$, the average of all $x$.
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\part Analyze the robustness of the reconstruction: Estimate
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the STA with less and less data and estimate the reconstruction
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error.
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\part Plot the reconstruction error as a function of the data
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amount used to estimate the STA.
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\part Repeat the above steps for the pyramidal neuron, what do you
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observe?
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\end{parts}
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\end{questions}
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\end{document}
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