Cleanup of model section

1 files changed, 10 insertions, 7 deletions

diff --git a/finale/sections/model.tex b/finale/sections/model.tex
index 3fe316a..4917bfb 100644
--- a/finale/sections/model.tex
+++ b/finale/sections/model.tex
@@ -1,7 +1,7 @@
-The GLC model is described over a directed graph $G = (V, \Theta)$. Denoting by
-$k=|V|$ the number of nodes in the graph, $\Theta\in\R_{+}^{k\times k}$ is the
-matrix of edge weights. Note that $\Theta$ implicitly defines the edge set $E$ of
-the graph through the following equivalence:
+The GLC model is described over a directed weighted graph $G = (V, \Theta)$.
+Denoting by $k=|V|$ the number of nodes in the graph, $\Theta\in\R_{+}^{k\times
+k}$ is the matrix of edge weights. Note that $\Theta$ implicitly defines the
+edge set $E$ of the graph through the following equivalence:
 \begin{displaymath}
     (u,v)\in E\Leftrightarrow \Theta_{u,v} > 0,\quad
     (u,v)\in V^2
@@ -30,9 +30,12 @@ we have:
 where $\bt_i$ is the $i$th column of $\Theta$. The function $f:\R\to[0,1]$ can
 be interpreted as the inverse link function of the model. Finally, the
 transitions in \cref{eq:markov} occur independently for each $i$. A cascade
-continues until no infected nodes remains. As noted in \cite{pouget} many
-commonly studied contagion models can be cast as specific instances of the GLC
-model.
+continues until no infected nodes remains.
+
+As noted in \cite{pouget} many commonly studied contagion models can be cast as
+specific instances of the GLC model. In particular the Independent Cascade
+model of \cite{Kempe:03} which we will use as a running example corresponds to
+the specific case where $f(z) = 1 - e^{-z}$.
 
 \Cref{eq:markov} and a source distribution $p_s$ together completely specify
 the probability distribution of a cascade $\mathbf{x} = (x_t)_{t\geq 0}$ given