71 lines
2.4 KiB
TeX
71 lines
2.4 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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\section*{Estimating the time-constant of adaptation.}
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Stimulating a neuron with a constant stimulus for an extended time
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often leads to a strong initial response that relaxes over time. This
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process is called adaptation and is ubiquitous. Your task here is to
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estimate the time-constant of the firing-rate adaptation in P-unit
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electroreceptors of the weakly electric fish \textit{Apteronotus
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leptorhynchus}.
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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 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
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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)
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During the next 1000 ms the stimulus was switched on. (iii) After
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stimulus offset the neuronal activity was recorded for further 825
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ms.
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\part Estimate the adaptation time-constant of the adaptation for
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both the stimulus on- and offset. To do this fit an exponential
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function to the data. For the decay use:
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\begin{equation}
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f_{A,\tau,y_0}(t) = y_0 + A \cdot e^{-\frac{t}{\tau}},
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\end{equation}
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where $y_0$ the offset, $A$ the amplitude, $t$ the time, $\tau$
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the time-constant.
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For the increasing phases use an exponential of the form:
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\begin{equation}
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f_{A,\tau, y_0}(t) = y_0 + A \cdot \left(1 - e^{-\frac{t}{\tau}}\right ),
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\end{equation}
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\part Plot the decays into the data.
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\part Plot the estimated time-constants as a function of stimulus intensity.
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\end{parts}
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\end{questions}
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\end{document}
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