The problem of turbulent diffusion is posed as determining the time evolution of the probability density of the concentration given those for the fluid velocity components, sources, and the initial concentration. At each time, all variables are elements of the Hilbert space L ;(R ), and a finite-dimensional approximation based on expansions in orthonormal basis functions is developed. An expres...

The focus of this paper is a convergence study of the frequency sensitive competitive learning (FSCL) algorithm. We approximate the final phase of FSCL learning by a diffusion process described by the Fokker-Plank equation. Sufficient and necessary conditions are presented for the convergence of the diffusion process to a local equilibrium. The analysis parallels that by Ritter-Schulten (1988) ...

In this paper, we consider the filtering of diffusion processes observed in non-Gaussian noise, when diffusion approximations for the system apply. Standard continuity results show then that the filtering error using the optimal filter for the limit model is close to the error for the limit system. However, this procedure is known to be in general suboptimal. We show that for a certain class of...

Calcium is a vital second messenger used in signal transduction. Calcium controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating and so on. Two theories have been used to simplify the system of reaction-diffusion equations of calcium into a single equation. One is excess buffer approximation (EBA) which assumes that mobile buffer is present in excess and c...

The emerging of social networks opens opportunities for viral marketing. It is a fundamental issue to find a subset of diffusion nodes such that targeting them initially will maximize the range of the information spreading. The problem of finding the most influential spreaders is unfortunately NP-hard. The best known approximation algorithm has been proven to be with an approximation ratio of(1...

The main message of the paper “Is Itô calculus oversold?” by A. Izmailov and B. Shay is, we quote: “However, when applied to the nonlinear interest rate models such as CoxIngersoll-Ross, Itô calculus only gives approximate results (...)” This surprising claim is first supported in the introduction by few words on the “diffusion approximation,” in which the authors seem to suggest that the Strat...

In this paper we develop set of novel Markov chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled...