68,702 research outputs found
The real-time growth rate of stochastic epidemics on random intersection graphs
This paper is concerned with the growth rate of SIR
(Susceptible-Infectious-Recovered) epidemics with general infectious period
distribution on random intersection graphs. This type of graph is characterized
by the presence of cliques (fully connected subgraphs). We study epidemics on
random intersection graphs with a mixed Poisson degree distribution and show
that in the limit of large population sizes the number of infected individuals
grows exponentially during the early phase of the epidemic, as is generally the
case for epidemics on asymptotically unclustered networks. The Malthusian
parameter is shown to satisfy a variant of the classical Euler-Lotka equation.
To obtain these results we construct a coupling of the epidemic process and a
continuous-time multitype branching process, where the type of an individual is
(essentially) given by the length of its infectious period. Asymptotic results
are then obtained via an embedded single-type Crump-Mode-Jagers branching
process
On Topological Properties of Wireless Sensor Networks under the q-Composite Key Predistribution Scheme with On/Off Channels
The q-composite key predistribution scheme [1] is used prevalently for secure
communications in large-scale wireless sensor networks (WSNs). Prior work
[2]-[4] explores topological properties of WSNs employing the q-composite
scheme for q = 1 with unreliable communication links modeled as independent
on/off channels. In this paper, we investigate topological properties related
to the node degree in WSNs operating under the q-composite scheme and the
on/off channel model. Our results apply to general q and are stronger than
those reported for the node degree in prior work even for the case of q being
1. Specifically, we show that the number of nodes with certain degree
asymptotically converges in distribution to a Poisson random variable, present
the asymptotic probability distribution for the minimum degree of the network,
and establish the asymptotically exact probability for the property that the
minimum degree is at least an arbitrary value. Numerical experiments confirm
the validity of our analytical findings.Comment: Best Student Paper Finalist in IEEE International Symposium on
Information Theory (ISIT) 201
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