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In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…
Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities. In recent years, the use of randomized methods to sample from the vast space…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…
For a continuous state branching process with two types of individuals which are subject to selection and density dependent competition, we characterize the joint evolution of population size, type configurations and genealogies as the…
This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…
In this note, we investigate the relationship between probabilistic updating mechanisms and discrete-time replicator-mutator dynamics. We consider the recently shown connection between Bayesian updating and replicator dynamics and extend it…
In this paper, we study the distributionally robust joint chance constrained Markov decision process. {Utilizing the logarithmic transformation technique,} we derive its deterministic reformulation with bi-convex terms under the…
The replicator-mutator dynamic was originally derived to model the evolution of language, and since the model was derived in such a general manner, it has been applied to the dynamics of social behavior and decision making in multi-agent…
Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…
In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
A Markovian model of group-structured (two-level) population dynamics features births, deaths, and migrations of individuals, and fission and extinction of groups. These models are useful for studying group selection and other evolutionary…
A steady influx of a single deleterious multilocus genotype will impose genetic load on the resident population and leave multiple descendants carrying various numbers of the foreign alleles. Provided that the foreign types are rare at…
In this brief note, we find formulas for the distribution and the transition probability matrices of a stochastic process described as a time-reversion in a finite time window of a Markov chain, with cluster observation of the Markov state…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…