相关论文: Spinal constructions for continuous type-space bra…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…
We give constructions of age-structured branching processes without or with immigration as pathwise unique solutions to stochastic integral equations. A necessary and sufficient condition for the ergodicity of the model with immigration is…
In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…
The theoretical understanding of pattern formation in active systems remains a central problem of interest. Heterogeneous flocks made up of multiple species can exhibit a remarkable diversity of collective states that cannot be obtained…
In this paper, we introduce a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent…
The prospect of informed and optimal decision-making regarding the operation and maintenance (O&M) of structures provides impetus to the development of structural health monitoring (SHM) systems. A probabilistic risk-based framework for…
Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…
Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense…
Understanding the large-scale physics is crucial for the spin foam approach to quantum gravity. We tackle this challenge from a statistical physics perspective using simplified, yet feature-rich models. In particular, this allows us to…
We consider a stochastic, continuous state and time opinion model where each agent's opinion locally interacts with other agents' opinions in the system, and there is also exogenous randomness. The interaction tends to create clusters of…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
We describe a general approach to the construction of a state evolution corresponding to the Markov generator of a spatial birth-and-death dynamics in $\mathbb{R}^d$. We present conditions on the birth-and-death intensities which are…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban…
We consider a branching process with Poissonian immigration where individuals have inheritable types. At rate theta, new individuals singly enter the total population and start a new population which evolves like a supercritical,…