相关论文: Mean-field interacting multi-type birth-death proc…

The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…

Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework…

A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is…

This paper concerns the modeling and numerical simulation of the process of speciation. In particular, given conditions for which one or more speciation events within an ecosystem occur, our aim is to develop the necessary modeling and…

We investigate the macroscopic time evolution and stationary states of a mean field generalized contact process in $\mathbb{R}^d$. The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a…

Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…

Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species' abundances, albeit at vastly different scales. The…

The origin of life poses a problem of combinatorial feasibility: How can temporally supported functional organization arise in exponentially branching assembly spaces when unguided exploration behaves as a memoryless random walk? We show…

Extreme mutation rates in microbes and cancer cells can result in error-induced extinction (EEX), where every descendant cell eventually acquires a lethal mutation. In this work, we investigate critical birth-death processes with $n$…

We propose the following simple stochastic model for phylogenetic trees. New types are born and die according to a birth and death chain. At each birth we associate a fitness to the new type sampled from a fixed distribution. At each death…

In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…

Mean-field models are often used to approximate Markov processes with large state-spaces. One-step processes, also known as birth-death processes, are an important class of such processes and are processes with state space…

Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth,…

We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…

In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of…

We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…

Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This…

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…