74 lines
2.8 KiB
TeX
74 lines
2.8 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{F-I curves}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
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{email: jan.grewe@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Quantifying the responsiveness of a neuron by its F-I curves}
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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
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function 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 electroreceptor 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 spike times are
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given in milliseconds relative to the stimulus onset.
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\begin{parts}
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\part For each stimulus intensity estimate 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)
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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
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825\,ms.
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\part Extract the neuron's activity for every 50\,ms after
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stimulus onset and for one 50\,ms slice before stimulus onset.
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For each time slice plot the resulting F-I curve by plotting the
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computed firing rates against the corresponding stimulus
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intensity, respectively the contrast.
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\part Fit a Boltzmann function to each of the F-I-curves. The
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Boltzmann function is a sigmoidal function and is defined as
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\begin{equation}
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f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; .
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\end{equation}
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$x$ is the stimulus intensity, $\alpha$ is the starting
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firing rate, $\beta$ the saturation firing rate, $x_0$ defines the
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position of the sigmoid, and $k$ (together with $\alpha-\beta$)
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sets the slope.
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Before you do the fitting, familiarize yourself with the four
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parameter of the Boltzmann function. What is its value for very
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large or very small stimulus intensities? How does the Boltzmann
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function change if you change either of the parameter?
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How could you get good initial estimates for the parameter?
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Do the fits and show the resulting Boltzmann functions together
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with the corresponding data.
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\part Illustrate how the F-I curves change in time also by means
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of the parameter you obtained from the fits with the Boltzmann
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function.
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Which parameter stay the same, which ones change with time?
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Support your conclusion with appropriate statistical tests.
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\part Discuss you results with respect to encoding of different
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stimulus intensities.
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\end{parts}
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\end{questions}
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\end{document}
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