In this article we present the modeling of bi-stability view problems described by the activity or firing rates of two interacting population of neurons. Starting from the study of a complex system, the system of stochastic differential equations describing the time evolution of the activity of the two populations of neurons, we point out the strength and weakness of this model and consider its...

In this paper we reconsider in the light of the Nelson stochastic mechanics the idea originally proposed by Bohm and Vigier that arbitrary solutions of the evolution equation for the probabil ity densities always relax in time toward the quantum mechanical density j j derived from the Schr odinger equation The analysis of a few general propositions and of some physical examples show that the ch...

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact ...

We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher order distribution moments. The formalism equally applies to any finite dimensional Schrödinger equation in the presence of a stochasti...

A stochastic simulation algorithm for the computation of multitime correlation functions which is based on the quantum state diffusion model of open systems is developed. The crucial point of the proposed scheme is a suitable extension of the quantum master equation to a doubled Hilbert space which is then unraveled by a stochastic differential equation. PACS numbers: 42.50.Lc,02.70.Lq Heisenbe...

chloride ion ingress in concrete is the main reason of concrete corrosion. in real world both uncertainty and stochasticity are main attributes of almost all measurements including testing and modeling of chloride content profile in concrete. regarding these facts new models should be able to represent at least some of the uncertainties in the predictions. in this paper after inspiration from c...

Stochastic partial differential equations are simply partial differential equations in the presence of uncertainty. Uncertainty, in its simplest form, is modeled by (or taken as) the time derivative (in the sense of distributions) of a Wiener process, known commonly as white noise. The introduction of a random force in a partial differential equation (PDE) arises from the need to explain the fl...

The evolution of a continuous time Markov process with a finite number of states is usually calculated by the Master equation a linear differential equations with a singular generator matrix. We derive a general method for reducing the dimensionality of the Master equation by one by using the probability normalization constraint, thus obtaining a affine differential equation with a (non-singula...