[projects] add input resistance project

projects/project_input_resistance/input_resistance.tex

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+\documentclass[addpoints,11pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
+%\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*{Estimating cellular properties of different cell types.}
+You will analyse data from intracellular \texit{in vitro} recordings
+of pyramidal neurons from two different maps of the electrosensory
+lateral line lobe (ELL) of the weakly electric fish
+\textit{Apteronotus leptorhynchus}. The resistance and capacitance of
+the membrane are typically estimated by injecting hyperpolarizing
+current pulses into the cell. From the respective responses we can
+calculate the membrane resistance by applying Ohm's law ($U = R \cdot
+I$). To estimate the membrane capacitance we need to fit an
+exponential function $y = a \cdot e^{(b \cdot x)}$to the response to
+get the membrane time-constant $\tau$. With the knowledge of $R$ and
+$\tau$ we can estimate the capacitance $C$ from the simple relation
+$\tau = R \cdot C$.
+
+\begin{questions}
+  \question{} The accompanying dataset (input\_resistance.zip)
+  contains datasets from cells originating from two different parts of
+  the ELL, the medial segment (MS) and the centro-medial segment
+  (CMS). Each mat-file contains four variables. (i) \textit{V} the
+  average membrane potential of 20 repeated current injections, (ii)
+  \textit{V\_std} the across-trial standard deviation of the
+  responses, (iii) \textit{t} a vector representing the recording
+  time (in ms), and (iv) \textit{I} a vector containing the time-course of the
+  injected current.
+  
+  \begin{parts}
+    \part{} Create plots of the raw data. Plot the average response as
+    a function of time. This plot should also show the across-trial
+    variability. Also plot the time-course of the injected
+    current. \\[0.5ex]
+    \part{} Estimate the imput resistances of each cell.\\[0.5ex]
+    \part{} Fit an exponential to the initial few milliseconds of the
+    current-on response. Use a gradient-descent approach to do
+    this.\\[0.5ex]
+    \part{} Estimate the membrane capacitance of each cell. Compare
+    $R$, $I$ and $\tau$ between cells of the two segments.\\[0.5ex]
+    \part{} Optional: use a double exponential and see, if the fit gets better.
+  \end{parts}
+\end{questions}
+
+\end{document}