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We investigate the regularity of the strongly continuous semigroup associated with a system of two coupled second order evolution equations with indirect damping, whose stability was recently studied by Hao et al. By deriving the asymptotic…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…
A general stochastic traffic cellular automaton (CA) model, which includes slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well known traffic CA models such as…
Chemical reactions in cell are subject to intense stochastic fluctuations. An important question is how the fundamental physiological behavior of cell is kept stable against those noisy perturbations. In this paper a stochastic model of…
While analyzing mobile systems we often approximate the actual coverage surface and assume an ideal cell shape. In a multi-cellular network, because of its tessellating nature, a hexagon is more preferred than a circular geometry. Despite…
We study a continuous time stochastic process on strings made of two types of particles, whose dynamics mimics the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as…
Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
We study the dynamics of a seeding experiment where a fibrous scaffold material is colonized by two types of cell populations. The specific application that we have in mind is related to the idea of meniscus tissue regeneration. In order to…
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…
Various and ubiquitous information systems are being used in monitoring, exchanging, and collecting information. These systems are generating massive amount of event sequence logs that may help us understand underlying phenomenon. By…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
Cell growth and gene expression, essential elements of all living systems, have long been the focus of biophysical interrogation. Advances in single-cell methods have invigorated theoretical studies into these processes. However, until…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…
We study the large-time behavior of a class of periodically driven macroscopic systems. We find, for a certain range of the parameters of either the system or the driving fields, the time-averaged asymptotic behavior effectively is that of…