From e3edc14ce0d5bea1e7120552fed71f407e130b53 Mon Sep 17 00:00:00 2001
From: Ben Green <bgreen@g.harvard.edu>
Date: Tue, 15 Sep 2015 22:49:14 -0400
Subject: updated figures in draft

---
 supplements/main.tex | 16 +++++++++++++---
 1 file changed, 13 insertions(+), 3 deletions(-)

(limited to 'supplements/main.tex')

diff --git a/supplements/main.tex b/supplements/main.tex
index 10e1a52..72a0950 100644
--- a/supplements/main.tex
+++ b/supplements/main.tex
@@ -88,7 +88,7 @@ With our infection rate fully-defined, we can now formulate the likelihood funct
 \begin{figure}
 \centering
 \includegraphics{hawkes-diagram}
-\caption{Caption}
+\caption{Diagram of a Hawkes process. STILL NEED TO MAKE A FIGURE.}
 \label{fig:hawkes-diagram}
 \end{figure}
 
@@ -108,7 +108,7 @@ M(t) = 3.78 + 1.63 \sin(\frac{2\pi}{365.24} t + 4.36)
 \begin{figure}
 \centering
 \includegraphics{background}
-\caption{Caption}
+\caption{The background rate $M(t)$ learned to describe the data. Each dot represents the number of infections (fatal and nonfatal) that occurred on a given day.}
 \label{fig:background}
 \end{figure}
 
@@ -150,9 +150,19 @@ $\mu_0 = 1.1845e-05$, $\alpha = 0.00317$, and $\beta = 0.0039$.
 \lambda_v(t) = 1.1845\e{-5} \left[1 + 0.43 \sin\left(\frac{2\pi}{365.24} t + 4.36\right) \right] + \sum_{u \in V} \frac{0.00317}{\text{dist}(u,v)} 0.0039 e^{-0.0039(t-t_u)}
 \end{equation}
 
-\subsection{Cascade recovery}
+\subsection{Inferring infections}
+[how we determine background vs peer infection]
 We can estimate if a person was primarily infected via peer contagion by comparing the contributions from the background rate and from his or her peers.
 
+We take this approach one step further to determine the person most responsible for infecting each of these 7,016 individuals infected by social contagion.
+
+\begin{figure}
+\centering
+\includegraphics[width=.6\textwidth]{cascade-distribution}
+\caption{The distribution of cascade sizes follows a power-law distribution.}
+\label{fig:cascade-sizes}
+\end{figure}
+
 \subsection{Experiments with synthetic data}
 
 \subsubsection{Generating networks}
-- 
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