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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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1
projects/README
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@ -42,6 +42,7 @@ no statistics
9) project_mutualinfo 9) project_mutualinfo
OK, medium OK, medium
Example code is missing
10) project_noiseficurves 10) project_noiseficurves
OK, simple-medium OK, simple-medium

77
projects/project_ficurves/ficurves.tex
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@ -1,9 +1,9 @@
\documentclass[a4paper,12pt,pdftex]{exam} \documentclass[a4paper,12pt,pdftex]{exam}
\newcommand{\ptitle}{F-I curves} \newcommand{\ptitle}{f-I curves}
\input{../header.tex} \input{../header.tex}
\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}% \firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.grewe@uni-tuebingen.de} {email: jan.benda@uni-tuebingen.de}
\begin{document} \begin{document}
@ -11,63 +11,68 @@
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section{Quantifying the responsiveness of a neuron using the F-I curve} \section{Quantifying the responsiveness of a neuron using the f-I
The responsiveness of a neuron is often quantified using an F-I curve}
curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a The responsiveness of a neuron is often quantified using an $f$-$I$
function of the stimulus \textbf{I}ntensity. 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 In the accompanying datasets you find the \textit{spike\_times} of an
\textit{Apteronotus leptorhynchus} to a stimulus of a certain P-unit electroreceptor of the weakly electric fish \textit{Apteronotus
intensity, i.e. the \textit{contrast}. The spike times are given in leptorhynchus} to a stimulus of a certain intensity, i.e. the
milliseconds relative to the stimulus onset. \textit{contrast}. The spike times are given in milliseconds relative
to the stimulus onset.
\begin{questions} \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} \begin{parts}
\part Estimate for each stimulus intensity the average response \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) The first 200\,ms is the baseline (no stimulus) activity. (ii)
During the next 1000\,ms the stimulus was switched on. (iii) After During the next 1000\,ms the stimulus was switched on. (iii) After
stimulus offset the neuronal activity was recorded for further stimulus offset the neuronal activity was recorded for further
825\,ms. 825\,ms.
\part Extract the neuron's activity in a 50\,ms time window immediately \part Extract the neuron's activity in 50\,ms time windows before
after stimulus onset (onset response) and 50\,ms before stimulus offset (steady state response). 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 Plot the resulting $f$-$I$ curves by plotting the three computed
computed firing rates against the corresponding stimulus firing rates against the corresponding stimulus intensities
intensity, respectively the contrast. (contrasts).
\end{parts} \end{parts}
\question{} Fit a Boltzmann function to each of the F-I-curves. The \question Fit a Boltzmann function to each of the $$-$I$-curves. The
Boltzmann function is a sigmoidal function and is defined as Boltzmann function is a sigmoidal function and is defined as
\begin{equation} \begin{equation}
f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; . f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; .
\end{equation} \end{equation}
$x$ is the stimulus intensity, $\alpha$ is the starting $x$ is the stimulus intensity, $\alpha$ is the starting firing rate,
firing rate, $\beta$ the saturation firing rate, $x_0$ defines the $\beta$ the saturation firing rate, $x_0$ defines the position of
position of the sigmoid, and $k$ (together with $\alpha-\beta$) the sigmoid, and $k$ (together with $\alpha-\beta$) sets the slope.
sets the slope.
\begin{parts} \begin{parts}
\part{} Before you do the fitting, familiarize yourself with the four \part Before you do the fitting, familiarize yourself with the
parameters of the Boltzmann function. What is its value for very four parameters of the Boltzmann function. What is its value for
large or very small stimulus intensities? How does the Boltzmann very large or very small stimulus intensities? How does the
function change if you change the parameters? Boltzmann function change if you change the parameters?
\part Can you get good initial estimates for the parameters?
\part{} Can you get good initial estimates for the parameters? \part Do the fits and show the resulting Boltzmann functions
\part{} Do the fits and show the resulting Boltzmann functions together together with the corresponding data.
with the corresponding data.
\part{} Illustrate how fit to the F-I curves changes during the fitting \part Illustrate how the fit to the $f$-$I$ curves changes during
process. You can plot the parameters as a function fit iterations. the fitting process. You can plot the parameters as a function of
Which parameter stay the same, which ones change with time? fit iterations. Which parameter stay the same, which ones change
with time?
Support your conclusion with appropriate statistical tests. Support your conclusion with appropriate statistical tests.
\part{} Discuss you results with respect to encoding of different \part Discuss you results with respect to encoding of different
stimulus intensities. stimulus intensities.
\end{parts} \end{parts}
\end{questions} \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 Vary the time step $\Delta t$ by factors of 10 and discuss
accuracy of numerical solutions. What is a good time step? accuracy of numerical solutions. What is a good time step?
Why is $V=0$ the resting potential of this neuron? Why is $V=0$ the resting potential of this neuron?
\part Response of the passive membrane to a step input. \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? 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 Measure the amplitude of the voltage responses evoked by the
sinusoidal inputs as the maximum of the last 900\,ms of the sinusoidal inputs as the maximum of the last 900\,ms of the
responses. Plot the amplitude of the response as a function of 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 How does the filter function depend on the membrane time constant?
constant?
\part Leaky integrate-and-fire neuron. \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} \begin{parts}
\part First set the noise \texttt{Dnoise=0} (no noise). Compute \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 and plot the neuron's $f$-$I$ curve, i.e. the mean firing rate
of spikes within the recording time \texttt{tmax} divided by (number of spikes within the recording time \texttt{tmax} divided
\texttt{tmax} and averaged over trials) as a function of the input by \texttt{tmax} and averaged over trials) as a function of the
current for inputs ranging from 0 to 20. input current for inputs ranging from 0 to 20.
How are different stimulus intensities encoded by the firing rate How are different stimulus intensities encoded by the firing rate
of this neuron? of this neuron?

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