The present models and simulation algorithms of intracellular stochastic kinetics are usually based on the premise that diffusion is so fast that the concentrations of all the involved species are homogeneous in space. However, recents experimental measurements of intracellular diffusion constants indicate that the assumption of a homogeneous well-stirred cytosol is not necessarily valid even f...

We study a parabolic population model in the full space and prove the global in time existence of a weak solution. This model consists of two strongly coupled diffusion equations describing the population densities of two competing species. The system features intrinsic growth, interand intra-specific competition of the species, as well as diffusion, cross-diffusion and self-diffusion, and drif...

We study a parabolic population model in the full space and prove the global in time existence of a weak solution. This model consists of two strongly coupled diffusion equations describing the population densities of two competing species. The system features intrinsic growth, interand intra-specific competition of the species, as well as diffusion, cross-diffusion and self-diffusion, and drif...

This paper presents a shortest path search algorithm using a model of excitable reaction-diffusion dynamics. In our previous work, we have proposed a framework of Digital Reaction-Diffusion System (DRDS)—a model of a discrete-time discrete-space reaction-diffusion system useful for nonlinear signal processing tasks. In this paper, we design a special DRDS, called an “excitable DRDS,” which emul...

This article presents stability analytical results of a two component reaction-diffusion system with linear cross-diffusion posed on continuously evolving domains. First the model system is mapped from a continuously evolving domain to a reference stationary frame resulting in a system of partial differential equations with time-dependent coefficients. Second, by employing appropriately asympto...

The problem of optimal fixed lag smoothing of a diffusion process, xt is to estimate xt−τ for t > τ , given the output of a nonlinear noisy sensor up to time t. The nonlinear filtering-smoothing problem is to estimate both xt and xt−τ . The optimal estimators are the conditional expectations of the processes, given the measurements. We derive evolution equations for both the normalized and unno...