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Jan Benda
2015-11-02 09:36:45 +01:00
parent 0bdc7eab98
commit ce2345acdb
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projects/project_fano_slope/fano_slope.tex
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@@ -6,8 +6,8 @@
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
-- 11/06/2014}
\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
-- 11/05/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
@@ -53,18 +53,19 @@
\begin{questions}
\question You are recording the activity of a neuron in response to
two different stimuli $I_1$ and $I_2$ (think of them, for example,
of two sound waves with different intensities $I_1$ and
$I_2$). Within an observation time of duration $W$ the neuron
responds stochastically with $n_i$ spikes.
of two sound waves with different intensities $I_1$ and $I_2$ and
you measure the activity af an auditory neuron). Within an
observation time of duration $W$ the neuron responds stochastically
with $n$ spikes.
How well can an upstream neuron discriminate the two stimuli based
on the spike counts $n_i$? How does this depend on the slope of the
on the spike counts $n$? How does this depend on the slope of the
tuning curve of the neural responses? How is this related to the
fano factor (the ratio between the variance and the mean of the
spike counts)?
The neuron is implemented in the file \texttt{lifboltzmanspikes.m}.
Call it with the following parameters:
The neuron is implemented in the file \texttt{lifboltzmanspikes.m}.
Call it with the following parameters:
\begin{lstlisting}
trials = 10;
tmax = 50.0;
@@ -85,21 +86,24 @@ spikes = lifboltzmanspikes( trials, input, tmax, Dnoise, imax, ithresh, slope );
\begin{parts}
\part
First, show two raster plots for the responses to the two differrent stimuli.
First, show two raster plots for the responses to the two
differrent stimuli.
\part Measure the tuning curve of the neuron with respect to the input. That is,
compute the mean firing rate as a function of the input
strength. Find an appropriate range of input values. Do this for
different values of the \texttt{slope} parameter (values between
0.1 and 2.0).
\part Measure the tuning curve of the neuron with respect to the
input. That is, compute the mean firing rate as a function of the
input strength. Find an appropriate range of input values. Do
this for different values of the \texttt{slope} parameter (values
between 0.1 and 2.0).
\part Generate histograms of the spike counts within $W=200$\,ms of the
responses to the two differrent stimuli $I_1$ and $I_2$. How do they depend on the slope
of the tuning curve of the neuron?
\part Generate histograms of the spike counts within $W=200$\,ms
of the responses to the two differrent stimuli $I_1$ and
$I_2$. How do they depend on the slope of the tuning curve of the
neuron?
\part Think about a measure based on the spike count histograms that quantifies how well
the two stimuli can be distinguished based on the spike
counts. Plot the dependence of this measure as a function of the observation time $W$.
\part Think about a measure based on the spike count histograms
that quantifies how well the two stimuli can be distinguished
based on the spike counts. Plot the dependence of this measure as
a function of the observation time $W$.
For which slopes can the two stimuli be well discriminated?
@@ -110,22 +114,26 @@ spikes = lifboltzmanspikes( trials, input, tmax, Dnoise, imax, ithresh, slope );
$I_2$. Find the threshold $n_{thresh}$ that results in the best
discrimination performance.
\part Also plot the Fano factor as a function of the slope. How is it related to the discriminability?
\part Also plot the Fano factor as a function of the slope. How is
it related to the discriminability?
\uplevel{If you still have time you can continue with the following questions:}
\uplevel{If you still have time you can continue with the
following questions:}
\part You may change the difference between the two stimuli $I_1$ and $I_2$
as well as the intrinsic noise of the neuron via \texttt{Dnoise}
(change it in factors of ten, higher values will make the
responses more variable) and repeat your analysis.
\part You may change the difference between the two stimuli $I_1$
and $I_2$ as well as the intrinsic noise of the neuron via
\texttt{Dnoise} (change it in factors of ten, higher values will
make the responses more variable) and repeat your analysis.
\part For $I_1=10$ the mean firing is about $80$\,Hz. When changing the slope of the tuning curve
this firing rate may also change. Improve your analysis by finding for each slope the input
that results exactly in a firing rate of $80$\,Hz. Set $I_2$ on unit above $I_1$.
\part For $I_1=10$ the mean firing is about $80$\,Hz. When
changing the slope of the tuning curve this firing rate may also
change. Improve your analysis by finding for each slope the input
that results exactly in a firing rate of $80$\,Hz. Set $I_2$ on
unit above $I_1$.
\part How does the dependence of the stimulus discrimination performance on the slope change
when you set both $I_1$ and $I_2$ such that they evoke $80$ and
$100$\,Hz firing rate, respectively?
\part How does the dependence of the stimulus discrimination
performance on the slope change when you set both $I_1$ and $I_2$
such that they evoke $80$ and $100$\,Hz firing rate, respectively?
\end{parts}