[projects] fixes and improvements

projects/project_stimulus_reconstruction/stimulus_reconstruction.tex

@@ -20,11 +20,11 @@ $i_{th}$ spike. $\tau$ is a temporal shift relative to the spike
 time. For the beginning let $\tau$ assume values in the range
 $\pm50$\,ms. The STA can be estimated by cutting out snippets from the
 stimulus that are centered on the respective spike time and by
-subsequently averaging them. The STA can be used to reconstruct the
-stimulus from the neuronal response. The reconstructed stimulus can
-then be compared to the original stimulus and provides a good
-impression about the features that are encoded in the neuronal
-response.
+subsequently averaging these stimulus snippets. The STA can be used to
+reconstruct the stimulus from the neuronal response (reverse
+reconstruction). The reconstructed stimulus can then be compared to
+the original stimulus and provides a good impression about the
+features that are encoded in the neuronal response.
 
 \begin{questions}
   \question In the accompanying data files you find the spike
@@ -34,22 +34,15 @@ response.
   stored in separate files. The neron is stimulated with an amplitude
   modulation of the fish's own electric field. The stored stimulus
   trace is the modulator that is applied to the field and is
-  dimensionless, i.e. it has not unit. The data is sampled with
+  dimensionless, i.e. it has no unit. The data is sampled with
   20\,kHz temporal resolution and spike times are given in
   seconds. Start with the P-unit and, in the end, apply the same
-  analyzes/functions to the responses from the pyramidal neuron.
+  analyzes/functions to the pyramidal cell.
   \begin{parts}
     \part Estimate the STA and plot it. What does it tell?
     \part Implement a function that does the reverse reconstruction and uses the STA to reconstruct the stimulus.
-    \part Implement a function that estimates the reconstruction 
-    error using the mean-square-error and express it relative to the
-    variance of the original stimulus.
-    \begin{equation}
-      err = \frac{1}{N} \cdot \displaystyle\sum^{N}_{i=1}(x_i - \bar{x})^2,
-    \end{equation}
-    with $N$ the number of data points, $x_i$ the current value and
-    $\bar{x}$, the average of all $x$.
-    \part Analyze the robustness of the reconstruction: Estimate 
+    \part Implement a function that estimates the reconstruction quality.
+    \part Test the robustness of the reconstruction: Estimate 
     the STA with less and less data and estimate the reconstruction
     error.
     \part Plot the reconstruction error as a function of the amount of data