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[project_ficurve] improved task

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Jan Benda 2020-01-20 17:39:46 +01:00
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projects/project_ficurves/ficurves.tex
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@ -27,17 +27,17 @@ to the stimulus onset.
\question Estimate the $f$-$I$-curve for the onset and the steady \question Estimate the $f$-$I$-curve for the onset and the steady
state response. state response.
\begin{parts} \begin{parts}
\part Estimate for each stimulus intensity the average response \part Estimate for each stimulus intensity the time course of the
(PSTH) and plot it. You will see that there are three parts: (i) trial-averaged response (PSTH) and plot it. You will see that
The first 200\,ms is the baseline (no stimulus) activity. (ii) there are three parts: (i) The first 200\,ms is the baseline (no
During the next 1000\,ms the stimulus was switched on. (iii) After stimulus) activity. (ii) During the next 1000\,ms the stimulus was
stimulus offset the neuronal activity was recorded for further switched on. (iii) After stimulus offset the neuronal activity was
825\,ms. recorded for further 825\,ms.
\part Extract the neuron's activity in 50\,ms time windows before \part Extract the neuron's activity (mean over trials and standard
stimulus onset (baseline activity), immediately after stimulus deviation) in 50\,ms time windows before stimulus onset (baseline
onset (onset response), and 50\,ms before stimulus offset (steady activity), immediately after stimulus onset (onset response), and
state response). 50\,ms before stimulus offset (steady state response).
Plot the resulting $f$-$I$ curves by plotting the three computed Plot the resulting $f$-$I$ curves by plotting the three computed
firing rates against the corresponding stimulus intensities firing rates against the corresponding stimulus intensities
@ -45,8 +45,9 @@ to the stimulus onset.
\end{parts} \end{parts}
\question Fit a Boltzmann function to each of the $$-$I$-curves. The \question Fit a Boltzmann function to the onset and steady-state
Boltzmann function is a sigmoidal function and is defined as $f$-$I$-curves. The 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}
@ -64,13 +65,10 @@ to the stimulus onset.
\part Do the fits and show the resulting Boltzmann functions \part Do the fits and show the resulting Boltzmann functions
together with the corresponding data. together with the corresponding data.
\part Illustrate how the fit to the $f$-$I$ curves changes during \part Use a statistical test to evaluate which of the onset and
the fitting process. You can plot the parameters as a function of steady-state responses differ significantly from the baseline
fit iterations. Which parameter stay the same, which ones change activity.
with time?
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.