相关论文: An algebraic approach to product-form stationary d…
Dynamical systems in biology are complex, and one often does not have comprehensive knowledge about the interactions involved. Chemical reaction network (CRN) inference aims to identify, from observing species concentrations over time, the…
We are interested in quasi-stationarity and quasi-ergodicity when the absorbing boundary is moving. First we show that, in the moving boundary case, the quasi-stationary distribution and the quasi-limiting distribution are not well-defined…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…
Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks.…
Chemical reaction networks (CRNs) are prototypical complex systems because reactions are nonlinear and connected in intricate ways, and they are also essential to understand living systems. Here, I discuss how recent developments in…
We show that if a chemical reaction network (CRN) admits nondegenerate (resp., linearly stable) oscillation, and we add new reversible reactions involving new species to this CRN, then the new CRN so created also admits nondegenerate…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating…
We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
This paper is a survey of various proofs of the so called {\em fundamental theorem of Markov chains}: every ergodic Markov chain has a unique positive stationary distribution and the chain attains this distribution in the limit independent…
Piecewise-Linear in Rates (PWLR) Lyapunov functions are introduced for a class of Chemical Reaction Networks (CRNs). In addition to their simple structure, these functions are robust with respect to arbitrary monotone reaction rates, of…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We address the challenge of identifying all real positive steady states in chemical reaction networks (CRNs) governed by mass-action kinetics. Traditional numerical methods often require specific initial guesses and may fail to find all the…
Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology,…
Much of the theory on chemical-reaction networks (CRNs) has been developed in the ideal-solution limit, where interactions between the solutes are negligible. However, there is a large variety of phenomena in biological cells and…
In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…
In this paper we study the central limit theorem for additive functionals of stationary Markov chains with general state space by using a new idea involving conditioning with respect to both the past and future of the chain. Practically, we…
Molecular computation based on chemical reaction networks (CRNs) has emerged as a promising paradigm for designing programmable biochemical systems. However, the implementation of complex computations still requires excessively large and…
In 2010, Anderson, Craciun, and Kurtz showed that if a deterministically modeled reaction network is complex balanced, then the associated stochastic model admits a stationary distribution that is a product of Poissons \cite{ACK2010}. That…