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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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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.
\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.
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.
\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?
\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.
\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}