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[projects] fixed my projects

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Jan Benda 2020-01-20 17:06:42 +01:00
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commit 13f826addc
5 changed files with 65 additions and 60 deletions
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1
projects/README
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@ -42,6 +42,7 @@ no statistics
9) project_mutualinfo
OK, medium
Example code is missing
10) project_noiseficurves
OK, simple-medium

101
projects/project_ficurves/ficurves.tex
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@ -1,9 +1,9 @@
\documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{F-I curves}
\newcommand{\ptitle}{f-I curves}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
{email: jan.grewe@uni-tuebingen.de}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}
\begin{document}
@ -11,64 +11,69 @@
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section{Quantifying the responsiveness of a neuron using the F-I curve}
The responsiveness of a neuron is often quantified using an F-I
curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a
function of the stimulus \textbf{I}ntensity.
In the accompanying datasets you find the \textit{spike\_times} of an
P-unit electroreceptor of the weakly electric fish
\textit{Apteronotus leptorhynchus} to a stimulus of a certain
intensity, i.e. the \textit{contrast}. The spike times are given in
milliseconds relative to the stimulus onset.
\section{Quantifying the responsiveness of a neuron using the f-I
curve}
The responsiveness of a neuron is often quantified using an $f$-$I$
curve. The $f$-$I$ curve plots the \textbf{f}iring rate of the neuron
as a function of the stimulus \textbf{I}ntensity.
In the accompanying datasets you find the \textit{spike\_times} of an
P-unit electroreceptor of the weakly electric fish \textit{Apteronotus
leptorhynchus} to a stimulus of a certain intensity, i.e. the
\textit{contrast}. The spike times are given in milliseconds relative
to the stimulus onset.
\begin{questions}
\question{Estimate the FI-curce for the onset and the steady state response.}
\question Estimate the $f$-$I$-curve for the onset and the steady
state response.
\begin{parts}
\part Estimate for each stimulus intensity the average response
(PSTH) and plot it. You will see that there are three parts. (i)
(PSTH) and plot it. You will see that there are three parts: (i)
The first 200\,ms is the baseline (no stimulus) activity. (ii)
During the next 1000\,ms the stimulus was switched on. (iii) After
stimulus offset the neuronal activity was recorded for further
825\,ms.
\part Extract the neuron's activity in a 50\,ms time window immediately
after stimulus onset (onset response) and 50\,ms before stimulus offset (steady state response).
\part Extract the neuron's activity in 50\,ms time windows before
stimulus onset (baseline activity), immediately after stimulus
onset (onset response), and 50\,ms before stimulus offset (steady
state response).
For each plot the resulting F-I curve by plotting the
computed firing rates against the corresponding stimulus
intensity, respectively the contrast.
Plot the resulting $f$-$I$ curves by plotting the three computed
firing rates against the corresponding stimulus intensities
(contrasts).
\end{parts}
\question{} Fit a Boltzmann function to each of the F-I-curves. The
Boltzmann function is a sigmoidal function and is defined as
\begin{equation}
f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; .
\end{equation}
$x$ is the stimulus intensity, $\alpha$ is the starting
firing rate, $\beta$ the saturation firing rate, $x_0$ defines the
position of the sigmoid, and $k$ (together with $\alpha-\beta$)
sets the slope.
\begin{parts}
\part{} Before you do the fitting, familiarize yourself with the four
parameters of the Boltzmann function. What is its value for very
large or very small stimulus intensities? How does the Boltzmann
function change if you change the parameters?
\part{} Can you get good initial estimates for the parameters?
\part{} Do the fits and show the resulting Boltzmann functions together
with the corresponding data.
\part{} Illustrate how fit to the F-I curves changes during the fitting
process. You can plot the parameters as a function fit iterations.
Which parameter stay the same, which ones change with time?
Support your conclusion with appropriate statistical tests.
\part{} Discuss you results with respect to encoding of different
stimulus intensities.
\question Fit a Boltzmann function to each of the $$-$I$-curves. The
Boltzmann function is a sigmoidal function and is defined as
\begin{equation}
f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; .
\end{equation}
$x$ is the stimulus intensity, $\alpha$ is the starting firing rate,
$\beta$ the saturation firing rate, $x_0$ defines the position of
the sigmoid, and $k$ (together with $\alpha-\beta$) sets the slope.
\begin{parts}
\part Before you do the fitting, familiarize yourself with the
four parameters of the Boltzmann function. What is its value for
very large or very small stimulus intensities? How does the
Boltzmann function change if you change the parameters?
\part Can you get good initial estimates for the parameters?
\part Do the fits and show the resulting Boltzmann functions
together with the corresponding data.
\part Illustrate how the fit to the $f$-$I$ curves changes during
the fitting process. You can plot the parameters as a function of
fit iterations. Which parameter stay the same, which ones change
with time?
Support your conclusion with appropriate statistical tests.
\part Discuss you results with respect to encoding of different
stimulus intensities.
\end{parts}
\end{questions}

9
projects/project_lif/lif.tex
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@ -52,7 +52,6 @@ time = [0.0:dt:tmax]; % t_i
Vary the time step $\Delta t$ by factors of 10 and discuss
accuracy of numerical solutions. What is a good time step?
Why is $V=0$ the resting potential of this neuron?
\part Response of the passive membrane to a step input.
@ -72,15 +71,15 @@ time = [0.0:dt:tmax]; % t_i
What do you observe?
\part Transfer function of the passive neuron.
\part Filter function of the passive neuron.
Measure the amplitude of the voltage responses evoked by the
sinusoidal inputs as the maximum of the last 900\,ms of the
responses. Plot the amplitude of the response as a function of
input frequency. This is the transfer function of the passive neuron.
input frequency. This is the filter function of the passive
neuron.
How does the transfer function depend on the membrane time
constant?
How does the filter function depend on the membrane time constant?
\part Leaky integrate-and-fire neuron.

8
projects/project_noiseficurves/noiseficurves.tex
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@ -54,10 +54,10 @@ spikes = lifspikes(trials, current, tmax, Dnoise);
\begin{parts}
\part First set the noise \texttt{Dnoise=0} (no noise). Compute
and plot neuron's $f$-$I$ curve, i.e. the mean firing rate (number
of spikes within the recording time \texttt{tmax} divided by
\texttt{tmax} and averaged over trials) as a function of the input
current for inputs ranging from 0 to 20.
and plot the neuron's $f$-$I$ curve, i.e. the mean firing rate
(number of spikes within the recording time \texttt{tmax} divided
by \texttt{tmax} and averaged over trials) as a function of the
input current for inputs ranging from 0 to 20.
How are different stimulus intensities encoded by the firing rate
of this neuron?

6
projects/project_populationvector/populationvector.tex
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@ -39,7 +39,7 @@
\begin{parts}
\part Illustrate the spiking activity of the V1 cells in response
to different orientation angles of the bars by means of spike
raster plots (of one unit).
raster plots (of a single unit).
\part Plot the firing rate of each of the 6 neurons as a function
of the orientation angle of the bar. As the firing rate compute
@ -48,7 +48,7 @@
of the neurons.
\part Fit the function \[ r(\varphi) =
g(1+\cos(\varphi-\varphi_0))/2 \] to the measured tuning curves in
g(1+\cos(2(\varphi-\varphi_0)))/2 \] to the measured tuning curves in
order to estimated the orientation angle at which the neurons
respond strongest. In this function $\varphi_0$ is the position of
the peak and $g$ is a gain factor that sets the maximum firing
@ -69,7 +69,7 @@
data, and estimate the orientation angle of the bar from single
trial data by the two different methods.
\part Compare, illustrate and discuss the performance of your two
\part Compare, illustrate and discuss the performance of the two
decoding methods by using all of the recorded responses (all
\texttt{population*.mat} files). How exactly is the orientation of
the bar encoded? How robust is the estimate of the orientation