\documentclass[addpoints,11pt]{exam} \usepackage{url} \usepackage{color} \usepackage{hyperref} \pagestyle{headandfoot} \runningheadrule \firstpageheadrule \firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014 -- 11/06/2014} %\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014} \firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe} \runningfooter{}{}{} \pointsinmargin \bracketedpoints %\printanswers %\shadedsolutions \begin{document} %%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%% \sffamily % \begin{flushright} % \gradetable[h][questions] % \end{flushright} \begin{center} \input{../disclaimer.tex} \end{center} %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% \section*{Quantifying the responsiveness of a neuron using the F-I curve.} The responsiveness of a neuron is often quantified using an F-I curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a function of the stimulus \textbf{I}ntensity. \begin{questions} \question In the accompanying datasets you find the \textit{spike\_times} of an P-unit electrorecptor of the weakly electric fish \textit{Apteronotus leptorhynchus} to a stimulus of a certain intensity, i.e. the \textit{contrast}. The contrast is also part of the file name itself. \begin{parts} \part Estimate for each stimulus intensity the average response (PSTH) and plot it. You will see that there are three parts. (i) The first 200 ms is the baseline (no stimulus) activity. (ii) During the next 1000 ms the stimulus was switched on. (iii) After stimulus offset the neuronal activity was recorded for further 825 ms. \part Extract the neuron's activity in the last 200 ms before stimulus offset and plot it against the stimulus intensity or the contrast, respectively. \part Fit a Boltzmann function to the FI-curve. The Boltzmann function is defined as: \begin{equation} y=\frac{\alpha-\beta}{1+e^{(x-x_0)/\Delta x}}+\beta, \end{equation} where $\alpha$ is the starting firing rate, $\beta$ the saturation firing rate, $x$ the current stimulus intensity, $x_0$ starting stimulus intensity, and $\Delta x$ a measure of the slope. \end{parts} \end{questions} \end{document}