Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: SIR-Hawkes: Linking Epidemic Models and Hawkes Processes to Model
  Diffusions in Finite Populations   Among the statistical tools for online information diffusion modeling, both
epidemic models and Hawkes point processes are popular choices. The former
originate from epidemiology, and consider information as a viral contagion
which spreads into a population of online users. The latter have roots in
geophysics and finance, view individual actions as discrete events in
continuous time, and modulate the rate of events according to the self-exciting
nature of event sequences. Here, we establish a novel connection between these
two frameworks. Namely, the rate of events in an extended Hawkes model is
identical to the rate of new infections in the Susceptible-Infected-Recovered
(SIR) model after marginalizing out recovery events -- which are unobserved in
a Hawkes process. This result paves the way to apply tools developed for SIR to
Hawkes, and vice versa. It also leads to HawkesN, a generalization of the
Hawkes model which accounts for a finite population size. Finally, we derive
the distribution of cascade sizes for HawkesN, inspired by methods in
stochastic SIR. Such distributions provide nuanced explanations to the general
unpredictability of popularity: the distribution for diffusion cascade sizes
tends to have two modes, one corresponding to large cascade sizes and another
one around zero.

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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin