From 19a3694444476b22acef7ea0d316be8a9f59c4c7 Mon Sep 17 00:00:00 2001
From: jeanpouget-abadie <jean.pougetabadie@gmail.com>
Date: Sun, 1 Feb 2015 20:45:29 -0500
Subject: small changes

---
 paper/sections/linear_threshold.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'paper/sections/linear_threshold.tex')

diff --git a/paper/sections/linear_threshold.tex b/paper/sections/linear_threshold.tex
index 2c0fb62..5eb7cf9 100644
--- a/paper/sections/linear_threshold.tex
+++ b/paper/sections/linear_threshold.tex
@@ -1,9 +1,9 @@
-In the Linear Threshold Model, each node $j\in V$ has a threshold $t_j$ from the interval $[0,1]$. Furthermore, there is a weight $\Theta_{i,j}\in[0,1]$ for each edge $(i,j)$, such that the sum of incoming weights is less than $1$: $\forall j\in V$, $\sum_{i=1}^m \Theta_{i,j} \leq 1$. Nodes remain active until the end of the cascade, which is reached when no new susceptible nodes become active.
+In the Linear Threshold Model, each node $j\in V$ has a threshold $t_j$ from the interval $[0,1]$. Furthermore, there is a weight $\Theta_{i,j}\in[0,1]$ for each edge $(i,j)$, such that the sum of incoming weights is less than $1$: $\forall j\in V$, $\sum_{i=1}^m \Theta_{i,j} \leq 1$. 
 
 Nodes can be either susceptible or active. At each time step, each susceptible
-node $j$ becomes active if the sum of the incoming weights from active parents is greater than $j$'s threshold $t_j$. 
+node $j$ becomes active if the sum of the incoming weights from active parents is greater than $j$'s threshold $t_j$. Nodes remain active until the end of the cascade, which is reached when no new susceptible nodes become active.
 
-We formalize the model in the following way: let $X^t$ be the indicator variable of the set of active nodes at time step $t-1$, then:
+As such, the source nodes are chosen, the process is entirely deterministic. Let $X^t$ be the indicator variable of the set of active nodes at time step $t-1$, then:
 \begin{equation}
     X^{t+1}_j = \left[\sum_{i=1}^m \Theta_{i,j}X^t_i > t_j\right]
     = \left[\inprod{\theta_j}{X^t} > t_j \right]
-- 
cgit v1.2.3-70-g09d2

