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Connectivity Threshold of Random Geometric Graphs with Cantor Distributed Vertices
Cantor distribution connectivity threshold random geometric graph singular distributions
2012/4/18
For connectivity of \emph{random geometric graphs}, where there is no density for underlying distribution of the vertices, we consider $n$ i.i.d. \emph{Cantor} distributed points on $[0,1]$. We show t...
A Structure Theorem for Poorly Anticoncentrated Gaussian Chaoses and Applications to the Study of Polynomial Threshold Functions
Structure Theorem Anticoncentrated Gaussian Chaoses Study of Polynomial Threshold Functions
2012/4/18
We prove a structural result for degree-$d$ polynomials. In particular, we show that any degree-$d$ polynomial, $p$ can be approximated by another polynomial, $p_0$, which can be decomposed as some fu...
SIR epidemics on a scale-free spatial nested modular network with a non-trivial threshold
Epidemics SIR Reed-Frost percolation long-range directed scale-free modular nested communities hierarchical
2011/8/30
Abstract: We propose a class of random scale-free spatial networks with nested community structures and analyze Reed-Frost epidemics with community related independent transmissions. We show that the ...
Opinion dynamics with confidence threshold: an alternative to the Axelrod model
stochastic processes Opinion dynamics homophily
2010/4/6
The voter model and the Axelrod model are two of the main stochastic processes that describe the spread of opinions on networks. The former includes social influence, the tendency of individuals to be...