Nathanial Burch

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This paper is concerned with the modeling and simulation of large stochastic networks in which the propagation of information through the network is governed by probabilistic rules. We are interested in understanding the effects of routing strategies that vary the tendency of transmission depending on the state of the network and of the effects of(More)
The evaluation and assessment of the design of large wireless networks is an important problem in numerous applications. Direct simulation is a traditional approach for studying such networks but is severely limited in its utility as the size of the network increases. This necessitates other means for studying large networks, one of which is the modeling of(More)
A useful perspective to take when studying anomalous diffusion processes is that of a continuous-time random walk and its associated generalized master equation. We derive the generalized master equations for continuous-time random walks that are restricted to a bounded domain and compare numerical solutions with kernel-density estimates of the(More)
Abstract. This paper investigates the exit-time for a broad class of symmetric finite-range jump processes via the corresponding master equation, a nonlocal diffusion equation suitably constrained. In direct analogy to the classical diffusion equation with a homogeneous Dirichlet boundary condition, the nonlocal diffusion equation is augmented with a(More)
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