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Diffstat (limited to 'supplements')
| -rw-r--r-- | supplements/.texpadtmp/main.aux | 21 | ||||
| -rw-r--r-- | supplements/.texpadtmp/main.log | 461 | ||||
| -rw-r--r-- | supplements/.texpadtmp/main.synctex.gz | bin | 0 -> 35420 bytes | |||
| -rw-r--r-- | supplements/cascade-distribution.pdf | bin | 0 -> 8587 bytes | |||
| -rw-r--r-- | supplements/main.pdf | bin | 0 -> 349399 bytes | |||
| -rw-r--r-- | supplements/main.tex | 16 |
6 files changed, 495 insertions, 3 deletions
diff --git a/supplements/.texpadtmp/main.aux b/supplements/.texpadtmp/main.aux new file mode 100644 index 0000000..41e3d8b --- /dev/null +++ b/supplements/.texpadtmp/main.aux @@ -0,0 +1,21 @@ +\relax +\@writefile{toc}{\contentsline {section}{\numberline {1}Hawkes contagion model}{1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Background}{1}} +\newlabel{eq:rate}{{2}{1}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Our model}{2}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.2.1}Infection rate}{2}} +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Diagram of a Hawkes process. STILL NEED TO MAKE A FIGURE.}}{3}} +\newlabel{fig:hawkes-diagram}{{1}{3}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.2.2}Likelihood}{3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Finding the background rate}{3}} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces 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.}}{4}} +\newlabel{fig:background}{{2}{4}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Learning the parameters [THIBAUT FILL IN THIS SECTION]}{5}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.5}Inferring infections}{5}} +\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces The distribution of cascade sizes follows a power-law distribution.}}{6}} +\newlabel{fig:cascade-sizes}{{3}{6}} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.6}Experiments with synthetic data}{6}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.1}Generating networks}{6}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.2}Simulating contagions}{7}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.6.3}Results}{7}} +\@writefile{toc}{\contentsline {section}{\numberline {2}Regarding causality [THIBAUT WRITE THIS 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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} |