Poisson-Boltzmann electrostatics is a well established model in biophysics; however, its application to large-scale biomolecular processes such as protein-protein encounter is still limited by the efficiency and memory constraints of existing numerical techniques. In this article, we present an efficient and accurate scheme that incorporates recently developed numerical techniques to enhance ou...

We review some recent results on multiwavelet methods for solving integral and partial differential equations and present an efficient representation of operators using discontinuous multiwavelet bases, including the case for singular integral operators. Numerical calculus using these representations produces fast O(N) methods for multiscale solution of integral equations when combined with low...

The linear Vlasov-Poisson system for homogeneous, stable equilibria is solved by means of a novel integral transform that is a generalization of the Hilbert transform. The integral transform provides a means for describing the dynamics of the continuous spectrum that is well-known to occur in this system. The results are interpreted in the context of Hamiltonian systems theory, where it is show...

All known ways to analytically continue automorphic L-functions involve integral representations using the corresponding automorphic forms. The simplest cases, extending Hecke’s treatment of GL2, need no further analytic devices and very little manipulation beyond Fourier-Whittaker expansions. [1] Poisson summation is a sufficient device for several accessible classes of examples, as in Riemann...

This paper describes a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process. The method is an extension of Berman & Turner’s (1992) device for maximizing the likelihoods of inhomogeneous spatial Poisson processes. For a very wide class of spatial point process models the likelihood is intractable, while the pseudolikelihood is known...

In this paper, we study forward-backward doubly stochastic differential equations driven by Brownian motions and Poisson process (FBDSDEP in short). Both the probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations (SPDIEs in short) and stochastic Hamiltonian systems arising in stochastic optimal control problems with random jum...

The Poisson boundary of a group G with a probability measure μ on it is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an integral representation of bounded μ-harmonic functions on G. In this paper we develop a new method of identifying the Poisson boundary based on entropy estimat...

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial differential equation without integral term. This differential form is valid for statedependent Poisson rates and we use it to characterize, via...

In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Poisson equation is presented. First of all, through the multipole expansion and local expansion for the basic solution of the kernel function of the ...