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[projects] updated mutual information and noisy ficurves

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janscience
2020-01-22 18:50:47 +01:00
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projects/project_noiseficurves/noiseficurves.tex
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@@ -9,49 +9,50 @@
\input{../instructions.tex}
You are recording the activity of neurons that differ in the strength
of their intrinsic noise in response to constant stimuli of intensity
$I$ (think of that, for example, as a current $I$ injected via a
patch-electrode into the neuron).
We first characterize the neurons by their tuning curves (also called
intensity-response curve). That is, what is the mean firing rate of
the neuron's response as a function of the constant input current $I$?
In the second part we demonstrate how intrinsic noise can be useful
for encoding stimuli on the example of the so called ``subthreshold
stochastic resonance''.
The neuron is implemented in the file \texttt{lifspikes.m}. Call it
with the following parameters:\\[-7ex]
\begin{lstlisting}
trials = 10;
tmax = 50.0;
current = 10.0; % the constant input current I
Dnoise = 1.0; % noise strength
spikes = lifspikes(trials, current, 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 current is set via the
\texttt{current} variable, the strength of the intrinsic noise via
\texttt{Dnoise}. If \texttt{current} is a single number, then an input
current of that intensity is simulated for \texttt{tmax}
seconds. Alternatively, \texttt{current} can be a vector containing an
input current that changes in time. In this case, \texttt{tmax} is
ignored, and you have to provide a value for the input current for
every 0.0001\,seconds.
Think of calling the \texttt{lifspikes()} function as a simple way of
doing an electrophysiological experiment. You are presenting a
stimulus with a constant intensity $I$ that you set. The neuron
responds to this stimulus, and you record this response. After
detecting the timepoints of the spikes in your recordings you get what
the \texttt{lifspikes()} function returns. In addition you can record
from different neurons with different noise properties by setting the
\texttt{Dnoise} parameter to different values.
\begin{questions}
\question You are recording the activity of a neuron in response to
constant stimuli of intensity $I$ (think of that, for example,
as a current $I$ injected via a patch-electrode into the neuron).
Measure the tuning curve (also called the intensity-response curve) of the
neuron. That is, what is the mean firing rate of the neuron's response
as a function of the constant input current $I$?
How does the intensity-response curve of a neuron depend on the
level of the intrinsic noise of the neuron?
How can intrinsic noise be usefull for encoding stimuli?
The neuron is implemented in the file \texttt{lifspikes.m}. Call it
with the following parameters:\\[-7ex]
\begin{lstlisting}
trials = 10;
tmax = 50.0;
current = 10.0; % the constant input current I
Dnoise = 1.0; % noise strength
spikes = lifspikes(trials, current, 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 current is set
via the \texttt{current} variable, the strength of the intrinsic
noise via \texttt{Dnoise}. If \texttt{current} is a single number,
then an input current of that intensity is simulated for
\texttt{tmax} seconds. Alternatively, \texttt{current} can be a
vector containing an input current that changes in time. In this
case, \texttt{tmax} is ignored, and you have to provide a value
for the input current for every 0.0001\,seconds.
Think of calling the \texttt{lifspikes()} function as a simple way
of doing an electrophysiological experiment. You are presenting a
stimulus with a constant intensity $I$ that you set. The neuron
responds to this stimulus, and you record this response. After
detecting the timepoints of the spikes in your recordings you get
what the \texttt{lifspikes()} function returns. In addition you
can record from different neurons with different noise properties
by setting the \texttt{Dnoise} parameter to different values.
\question Tuning curves
\begin{parts}
\part First set the noise \texttt{Dnoise=0} (no noise). Compute
and plot the neuron's $f$-$I$ curve, i.e. the mean firing rate
@@ -64,37 +65,43 @@ spikes = lifspikes(trials, current, tmax, Dnoise);
\part Compute the $f$-$I$ curves of neurons with various noise
strengths \texttt{Dnoise}. Use for example $D_{noise} = 10^{-3}$,
$10^{-2}$, and $10^{-1}$.
$10^{-2}$, and $10^{-1}$. Depending on the resulting curves you
might want to try additional noise levels.
How does the intrinsic noise influence the response curve?
How does the intrinsic noise level influence the tuning curves?
What are possible sources of this intrinsic noise?
\part Show spike raster plots and interspike interval histograms
of the responses for some interesting values of the input and the
noise strength. For example, you might want to compare the
responses of the four different neurons to the same input, or by
the same resulting mean firing rate.
responses of the different neurons to the same input, or by the
same resulting mean firing rate.
How do the responses differ?
\end{parts}
\question Subthreshold stochastic resonance
Let's now use as an input to the neuron a 1\,s long sine wave $I(t)
= I_0 + A \sin(2\pi f t)$ with offset current $I_0$, amplitude $A$,
and frequency $f$. Set $I_0=5$, $A=4$, and $f=5$\,Hz.
\part Let's now use as an input to the neuron a 1\,s long sine
wave $I(t) = I_0 + A \sin(2\pi f t)$ with offset current $I_0$,
amplitude $A$, and frequency $f$. Set $I_0=5$, $A=4$, and
$f=5$\,Hz.
\begin{parts}
\part Do you get a response of the noiseless ($D_{noise}=0$) neuron?
Do you get a response of the noiseless ($D_{noise}=0$) neuron?
\part What happens if you increase the noise strength?
What happens if you increase the noise strength?
\part What happens at really large noise strengths?
What happens at really large noise strengths?
\part Generate some example plots that illustrate your findings.
Generate some example plots that illustrate your findings.
Explain the encoding of the sine wave based on your findings
\part Explain the encoding of the sine wave based on your findings
regarding the $f$-$I$ curves.
\end{parts}
\part Why is this phenomenon called ``subthreshold stochastic resonance''?
\end{parts}
\end{questions}