70 lines
2.2 KiB
TeX
70 lines
2.2 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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\section*{Quantifying the responsiveness of a neuron using the F-I curve.}
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The responsiveness of a neuron is often quantified using an F-I
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curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a function
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of the stimulus \textbf{I}ntensity.
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\begin{questions}
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\question In the accompanying datasets you find the
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\textit{spike\_times} of an P-unit electrorecptor of the weakly
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electric fish \textit{Apteronotus leptorhynchus} to a stimulus of a
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certain intensity, i.e. the \textit{contrast}. The contrast is also
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part of the file name itself.
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\begin{parts}
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\part Estimate for each stimulus intensity the average response
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(PSTH) and plot it. You will see that there are three parts. (i)
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The first 200 ms is the baseline (no stimulus) activity. (ii) During
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the next 1000 ms the stimulus was switched on. (iii) After stimulus
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offset the neuronal activity was recorded for further 825 ms.
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\part Extract the neuron's activity in the first 50 ms after stimulus onset
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and plot it against the stimulus intensity, respectively the
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contrast, in an appropriate way.
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\part Fit a Boltzmann function to the FI-curve. The Boltzmann function
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is defined as:
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\begin{equation}
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y=\frac{\alpha-\beta}{1+e^{(x-x_0)/dx}}+\beta,
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\end{equation}
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where $\alpha$ is the starting firing rate, $\beta$ the saturation
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firing rate, $x$ the current stimulus intensity, $x_0$ starting
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stimulus intensity, and $dx$ a measure of the slope.
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\part Plot the fit into the data.
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\end{parts}
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\end{questions}
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\end{document}
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