Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Use of Enumerative Combinatorics for proving the applicability of an
  asymptotic stability result on discrete-time SIS epidemics in complex
  networks   In this paper, we justify by the use of Enumerative Combinatorics, that the
results obtained in \cite{Alarcon1}, where is analysed the complex dynamics of
an epidemic model to identify the nodes that contribute the most to the
propagation process and because of that are good candidates to be controlled in
the network in order to stabilize the network to reach the extinction state, is
applicable in almost all the cases. The model analysed was proposed in
\cite{Gomez1} %et al. [Phys.Rev.E 84, 036105(2011)] and results obtained in
\cite{Alarcon1} implies that it is not necessary to control all nodes, but only
a minimal set of nodes if the topology of the network is not regular. This
result could be important in the spirit of considering policies of isolation or
quarantine of those nodes to be controlled. Simulation results were presented
in \cite{Alarcon1} for large free-scale and regular networks, that corroborate
the theoretical findings. In this article we justify the applicability of the
controllability result obtained in \cite{Alarcon1} in almost all the cases by
means of the use of Combinatorics. {\em Mathematics Subjects Classification}:
05A16,34H20,58E25 {\em Keywords}: Asymptotic Graph Enumeration Problems;
Network control; virus spreading.

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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th