73 lines
2.6 KiB
TeX
73 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*{Estimating the adaptation time-constant.}
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Stimulating a neuron with a constant stimulus for an extended period of 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 electroreceptor to a stimulus of
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a certain intensity, i.e. the \textit{contrast} which is also stored
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in the file. The contrast of the stimulus is a measure relative to
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the amplitude of fish's field, it has no unit. The data is sampled
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with 20\,kHz sampling frequency and spike times are given in
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milliseconds relative to the stimulus onset.
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\begin{parts}
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\part Estimate for each stimulus intensity the PSTH and plot
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it. You will see that there are three parts. (i) The first
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200\,ms is the baseline (no stimulus) activity. (ii) During the
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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 Estimate the adaptation time-constant for both the stimulus
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on- and offset. To do this fit an exponential function to the
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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 best fits 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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