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\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
  -- 11/06/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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  \input{../disclaimer.tex}
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%%%%%%%%%%%%%% 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}