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Partial differential equations (p.d.e) equipped of spatial derivatives of fractional order capture anomalous transport behaviors observed in diverse fields of Science. A number of numerical methods approximate their solutions in dimension…
In this paper we consider mathematical modeling of the dynamics of self-organized patterning of spatially confined human embryonic stem cells (hESCs) treated with BMP4 (gastruloids) described in recent experimental works. In the first part…
By formulating data samples' formation as a Markov denoising process, diffusion models achieve state-of-the-art performances in a collection of tasks. Recently, many variants of diffusion models have been proposed to enable controlled…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Reaction-diffusion equations are commonly used to model a diverse array of complex systems, including biological, chemical, and physical processes. Typically, these models are phenomenological, requiring the fitting of parameters to…
Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good…
We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
Temperature gradients represent energy sources that can be harvested to generate steady reaction or transport fluxes. Technological developments could lead to the transfer of free energy from heat sources and sinks to chemical systems for…
We propose a probabilistic derivation of the so-called chemical diffusion master equation (CDME) and describe an infinite dimensional moment generating function method for finding its analytical solution. CDMEs model by means of an infinite…
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
We consider a model of lattice gas dynamics in the d-dimensional cubic lattice in the presence of disorder. If the particle interaction is only mutual exclusion and if the disorder field is given by i.i.d. bounded random variables, we prove…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a…
We propose a solution formula for chemical diffusion master equations of birth and death type. These equations, proposed and formalized in the recent paper [5], aim at incorporating the spatial diffusion of molecules into the description…