init project_face_selectivity

projects/project_face_selectivity/Makefile

@@ -0,0 +1,3 @@
+ZIPFILES=
+
+include ../project.mk

projects/project_face_selectivity/gaze_following.tex

@@ -0,0 +1,67 @@
+\documentclass[a4paper,12pt,pdftex]{exam}
+
+\newcommand{\ptitle}{Adaptation time-constant}
+\input{../header.tex}
+\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
+{email: jan.grewe@uni-tuebingen.de}
+
+\begin{document}
+
+\input{../instructions.tex}
+
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Estimating the adaptation time-constant}
+Stimulating a neuron with a constant stimulus for an extended period of time
+often leads to a strong initial response that relaxes over time. This
+process is called adaptation. Your task here is to
+estimate the time-constant of the firing-rate adaptation in P-unit
+electroreceptors of the weakly electric fish \textit{Apteronotus
+  leptorhynchus}.
+
+\begin{questions}
+  \question In the accompanying datasets you find the
+  \textit{spike\_times} of an P-unit electroreceptor to a stimulus of
+  a certain intensity, i.e. the \textit{contrast} which is also stored
+  in the file. The contrast of the stimulus is a measure relative to
+  the amplitude of fish's field, it has no unit. The data is sampled
+  with 20\,kHz sampling frequency and spike times are given in
+  milliseconds (not seconds!) relative to the stimulus onset.
+  \begin{parts}
+    \part Estimate for each stimulus intensity the PSTH. 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. Find an appropriate bin-width
+    for the PSTH.
+
+    \part Estimate the adaptation time-constant for both the stimulus
+    on- and offset. To do this fit an exponential function
+    $f_{A,\tau,y_0}(t)$ to appropriate regions of the data:
+    \begin{equation}
+       f_{A,\tau,y_0}(t) = A \cdot e^{-\frac{t}{\tau}} + y_0,
+    \end{equation}
+    where $t$ is time, $A$ the (positive or negative) amplitude of the
+    exponential decay, $\tau$ the adaptation time-constant, and $y_0$
+    an offset.
+
+    Before you do the fitting, familiarize yourself with the three
+    parameter of the exponential function. What is the value of
+    $f_{A,\tau,y_0}(t)$ at $t=0$? What is the value for large times? How does
+    $f_{A,\tau,y_0}(t)$ change if you change either of the parameter?
+
+    Which of the parameter could you directly estimate from the data
+    (without fitting)?
+
+    How could you get good estimates for the other parameter?
+
+    Do the fit and show the resulting exponential function together
+    with the data.
+
+    \part Do the estimated time-constants depend on stimulus intensity?
+
+    Use an appropriate statistical test to support your observation.
+  \end{parts}
+\end{questions}
+
+\end{document}