Related papers: Introductory Lectures on Stochastic Population Sys…

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…

In this paper we analyze the equilibrium properties of a large class of stochastic processes describing the fundamental biological process within bacterial cells, {\em the production process of proteins}. Stochastic models classically used…

We introduce the problem of estimation of the parameters of a dynamically selected population in an infinite sequence of random variables and provide its application in the statistical inference based on record values from a non-stationary…

This paper aims to develop practical applications of the model for the highly technical measure-valued populations developed by the authors in \cite{FanEtal20}. We consider the problem of estimation of parameters in the general age and…

We consider continuous space-time decay-surge population models which are semi- stochastic processes for which deterministically declining populations, bound to fade away, are rein- vigorated at random times by bursts or surges of random…

We present a flexible branching process model for cell population dynamics in synchrony/time-series experiments used to study important cellular processes. Its formulation is constructive, based on an accounting of the unique cohorts in the…

In order to model an epidemic, different approaches can be adopted. Mainly, the deterministic approach and the stochastic one. Recently, a large amount of literature has been published using the two approaches. The aim of this paper is to…

Many complex systems can be described by population models, in which a pool of agents interacts and produces complex collective behaviours. We consider the problem of verifying formal properties of the underlying mathematical representation…

Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…

A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…

The aim of this paper is to tackle part of the program set by Diekmann et al. in their seminal paper Diekmann et al. (2001). We quote "It remains to investigate whether, and in what sense, the nonlinear determin-istic model formulation is…

We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the selection by allowing individuals to sample…

Population stratification is a problem encountered in several areas of biology and public health. We tackle this problem by mapping a population and its elements attributes into a hypergraph, a natural extension of the concept of graph or…

A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…

In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…

We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are…

Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…

Background. It is assumed that the introduction of stochastic in mathematical model makes it more adequate. But there is virtually no methods of coordinated (depended on structure of the system) stochastic introduction into deterministic…

Population genetics lies at the heart of evolutionary theory. This topic forms part of many biological science curricula but is rarely taught to physics students. Since physicists are becoming increasingly interested in biological…