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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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\begin{document}
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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 $I$). The neuron has an adaptatation
  current that adapts the firing rate with a slow time constant down.

  Explore the dependence of interspike interval correlations on the firing rate,
  adaptation time constant and noise level.

  \begin{parts}
    \part The neuron is a neuron with an adaptation current. 
    It is implemented in the file \texttt{lifadaptspikes.m}.  Call it
    with the following parameters:
    \begin{lstlisting}
      trials = 10;
      tmax = 50.0;
      input = 10.0;  % the input I
      Dnoise = 1e-2;  % noise strength
      adapttau = 0.1;  % adaptation time constant in seconds
      adaptincr = 0.5;  % adaptation strength

      spikes = lifadaptspikes( trials, input, tmax, Dnoise, adapttau, adaptincr );
    \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},
    and the adaptation time constant via \texttt{adapttau}.

    \part Measure the intensity-response curve of the neuron, that is the mean firing rate 
    as a function of the input for a range of inputs from 0 to 120.

    \part Compute the correlations between each interspike interval $T_i$ and the next one $T_{i+1}$
    (serial interspike interval correlation at lag  1). Plot this correlation as a function of the 
    firing rate by varying the input as in (a).

    \part How does this dependence change for different values of the adaptation 
    time constant \texttt{adapttau}?  Use values between 10\,ms and
    1\,s for \texttt{adapttau}.

    \part Determine the firing rate at which the minimum interspike interval correlation
    occurs. How does the minimum correlation and this firing rate
    depend on the adaptation time constant \texttt{adapttau}?

    \part How do the results change if the level of the intrinsic noise \texttt{Dnoise} is modified?
    Use values of 1e-4, 1e-3, 1e-2, 1e-1, and 1 for \texttt{Dnoise}.


    \uplevel{If you still have time you can continue with the following question:}

    \part How do the interspike interval distributions look like for the different noise levels
    at some example values for the input and the adaptation time constant?

 \end{parts}

\end{questions}

\end{document}