Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized threshold-based epidemics in random graphs: the power of
  extreme values   Bootstrap percolation is a well-known activation process in a graph, in which
a node becomes active when it has at least $r$ active neighbors. Such process,
originally studied on regular structures, has been recently investigated also
in the context of random graphs, where it can serve as a simple model for a
wide variety of cascades, such as the spreading of ideas, trends, viral
contents, etc. over large social networks. In particular, it has been shown
that in $G(n,p)$ the final active set can exhibit a phase transition for a
sub-linear number of seeds. In this paper, we propose a unique framework to
study similar sub-linear phase transitions for a much broader class of graph
models and epidemic processes. Specifically, we consider i) a generalized
version of bootstrap percolation in $G(n,p)$ with random activation thresholds
and random node-to-node influences; ii) different random graph models,
including graphs with given degree sequence and graphs with community structure
(block model). The common thread of our work is to show the surprising
sensitivity of the critical seed set size to extreme values of distributions,
which makes some systems dramatically vulnerable to large-scale outbreaks. We
validate our results running simulation on both synthetic and real graphs.

9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
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The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph