Jan Bs projects

projects/project_noiseficurves/Makefile

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+latex:
+	pdflatex *.tex > /dev/null
+	pdflatex *.tex > /dev/null
+
+clean:
+	rm -rf *.log *.aux *.zip *.out auto
+	rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+	zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m

projects/project_noiseficurves/lifspikes.m

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+function spikes = lifspikes( trials, input, tmaxdt, D )
+% Generate spike times of a leaky integrate-and-fire neuron
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+%         in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+    
+    tau = 0.01;
+    if nargin < 4
+        D = 1e0;
+    end
+    vreset = 0.0;
+    vthresh = 10.0;
+    dt = 1e-4;
+    
+    if length( input ) == 1
+        input = input * ones( ceil( tmaxdt/dt ), 1 );
+    else
+        dt = tmaxdt;
+    end
+    spikes = cell( trials, 1 );
+    for k=1:trials
+        times = [];
+        j = 1;
+        v = vreset;
+        noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
+        for i=1:length( noise )
+            v = v + ( - v + noise(i) + input(i))*dt/tau;
+            if v >= vthresh
+                v = vreset;
+                times(j) = i*dt;
+                j = j + 1;
+            end
+        end
+        spikes{k} = times;
+    end
+end

projects/project_noiseficurves/noiseficurves.tex

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+\documentclass[addpoints,10pt]{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{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+% captionpos=t,
+ xleftmargin=2em,
+ xrightmargin=1em,
+% aboveskip=10pt,
+ %title=\lstname,
+% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
+ }
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{questions}
+  \question You are recording the activity of a neuron in response to
+  constant stimuli of intensity $I$ (think of that, for example,
+  of sound waves with intensities $I$).
+
+  Measure the tuning curve (also called the intensity-response curve) of the
+  neuron.  That is, what is the firing rate of the neuron's response
+  as a function of the input $I$. How does this depend on the level of
+  the intrinsic noise of the neuron?
+
+  \begin{parts}
+    \part The neuron is implemented in the file \texttt{lifspikes.m}.
+    Call it with the following parameters:
+    \begin{lstlisting}
+      trials = 10;
+      tmax = 50.0;
+      input = 10.0;  % the input I
+      Dnoise = 1.0;  % noise strength
+
+      spikes = lifspikes( trials, input, tmax, Dnoise );
+    \end{lstlisting}
+    The returned \texttt{spikes} is a cell array with \texttt{trials} elements, each being a vector
+    of spike times (in seconds) computed for a duration of \texttt{tmax} seconds.
+    The input is set via the \texttt{input} variable, the noise strength via \texttt{Dnoise}.
+
+    \part First set the noise \texttt{Dnoise=0} (no noise). Compute and plot the firing rate
+    as a function of the input for inputs ranging from 0 to 20.
+
+    \part Do the same for various noise strength \texttt{Dnoise}. Use $D_{noise} = 1e-3$,
+    1e-2, and 1e-1. How does the intrinsic noise influence the response curve?
+
+    \part Show some interspike interval histograms for some interesting values of the input 
+    and the noise strength.
+
+ \end{parts}
+
+\end{questions}
+
+\end{document}