From eef177f7eeac2e92511daff75f1007603ef0706a Mon Sep 17 00:00:00 2001
From: Jan Grewe <jan.grewe@g-node.org>
Date: Tue, 27 Oct 2015 23:34:15 +0100
Subject: [PATCH] figure for psth method comparsion, some introductory words
 for spiketrain chapter

---
 spike_trains/code/firing_rates.py |  2 +-
 spike_trains/lecture/psth_sta.tex | 17 ++++++++++++++---
 2 files changed, 15 insertions(+), 4 deletions(-)

diff --git a/spike_trains/code/firing_rates.py b/spike_trains/code/firing_rates.py
index 4871e5b..0f02e87 100644
--- a/spike_trains/code/firing_rates.py
+++ b/spike_trains/code/firing_rates.py
@@ -193,7 +193,7 @@ def plot_conv_rate(spike_times, sigma=0.05, max_t=30, dt=1e-4):
 
 def plot_comparison(spike_times, bin_width, sigma, max_t=30., dt=1e-4):
     times = np.squeeze(spike_times[0][0])
-    time, conv_rate = get_convolved_rate(times, sigma)
+    time, conv_rate = get_convolved_rate(times, bin_width/np.sqrt(12.))
     time, inst_rate = get_instantaneous_rate(times)
     time, binn_rate = get_binned_rate(times, bin_width)
    
diff --git a/spike_trains/lecture/psth_sta.tex b/spike_trains/lecture/psth_sta.tex
index 33bf2fb..57ea7a3 100644
--- a/spike_trains/lecture/psth_sta.tex
+++ b/spike_trains/lecture/psth_sta.tex
@@ -27,10 +27,21 @@ ist das sog. Peri Stimulus Zeithistogramm (peri stimulus time
 histogram, PSTH). Es wird der zeitliche Verlauf der Feuerrate $r(t)$
 dargestellt. Die Einheit der Feuerrate ist Hertz, das heisst, die
 Anzahl Aktionspotentiale pro Sekunde. Dabei gibt es verschiedene
-Methoden diese zu bestimmen. Jede dieser Methoden hat ihre Vor- und
-Nachteile. Abbildung \ref{psthfig} zeigt drei dieser Methoden. 
+Methoden diese zu bestimmen. Drei solcher Methoden sind in Abbildung
+\ref{psthfig} dargestellt.
 
 \begin{figure}
-  \includegraphics[width=0.75\columnwidth]{images/psth_comparison}
+  \includegraphics[width=\columnwidth]{images/psth_comparison}
   \caption{}\label{psthfig}
 \end{figure}
+
+
+
+\section{Spike triggered Average}
+
+Der Spike triggered average (STA) ist der mittlere Stimulus, der zu
+einem Aktionspotential in der neuronalen Antwort f\"uhrt.
+
+\begin{equation}
+  STA(\tau) = \frac{1}{\langle n \rangle} \left\langle  \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \right\rangle
+\end{equation}