improved projects

projects/project_adaptation_fit/adaptation_fit.tex

@@ -11,10 +11,10 @@
 
 
 %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
-\section*{Estimating the adaptation time-constant.}
+\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 and is ubiquitous. Your task here is to
+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}.
@@ -26,27 +26,41 @@ electroreceptors of the weakly electric fish \textit{Apteronotus
   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 relative to the stimulus onset.
+  milliseconds (not seconds!) relative to the stimulus onset.
   \begin{parts}
-    \part Estimate for each stimulus intensity the 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 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 to the
-    data. For the decay use:
+    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) = y_0 + A \cdot e^{-\frac{t}{\tau}},
+       f_{A,\tau,y_0}(t) = A \cdot e^{-\frac{t}{\tau}} + y_0,
     \end{equation}
-    where $y_0$ the offset, $A$ the amplitude, $t$ the time, $\tau$
-    the time-constant.
-    For the increasing phases use an exponential of the form:
-    \begin{equation}
-       f_{A,\tau, y_0}(t) = y_0 + A \cdot \left(1 - e^{-\frac{t}{\tau}}\right ),
-    \end{equation}
-    \part Plot the best fits into the data.
-    \part Plot the estimated time-constants as a function of stimulus intensity.
+    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}