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Computer viruses are an extremely important aspect of computer security, and understanding their spread and extent is an important component of any defensive strategy. Epidemiological models have been proposed to deal with this issue, and we present one such here. We consider a modiÿcation of the Susceptible–Infected–Susceptible (SIS) epidemiological model… (More)
For a certain class of two-dimensional lattices, lattice-dual pairs are shown to have the same bond-percolation critical exponents. A computational proof is given for the martini lattice and its dual to illustrate the method. The result is generalized to a class of lattices that allows the equality of bond-percolation critical exponents for lattice-dual… (More)
Recent mathematical results regarding percolation thresholds are relevant to efforts to find universal formulas for the percolation threshold. This Brief Report uses exact solutions and recent rigorous bounds for site and bond percolation thresholds to demonstrate that any universal formula based on only the dimension and the coordination number must… (More)
Rigorous bounds for the bond percolation critical probability are determined for three Archimedean lattices: Consequently, the bond percolation critical probability of the (3, 12 2) lattice is strictly larger than those of the other ten Archimedean lattices. Thus, the (3, 12 2) bond percolation critical probability is possibly the largest of any… (More)
The subgraph relation defines a partial order on graphs. In this paper, we determine this partial order completely for the Archimedean and Laves lattices.