Related papers: Analysis and rejection sampling of Wright-Fisher d…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…
Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(\pm T)=0 conditioned to stay above the semicircle c_T(t)=\sqrtT^2-t^2. In the limit of large T, the fluctuation scale of b(t)-c_T(t) is T^{1/3} and its…
A simple two-species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking. The model is a generalization of the bridge model for which…
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…
The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-B\'{e}nard convection. The spatiotemporal structure of convection rolls propagating downstream in an externally…
Fish migration is a mass movement that affects the hydrosphere and ecosystems. While it occurs on multiple temporal scales, including daily and intraday fluctuations, the latter remains less studied. In this study, for a stochastic…
Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright-Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known…
The recently introduced two-parameter Poisson-Dirichlet diffusion extends the infinitely-many-neutral-alleles model, related to Kingman's distribution and to Fleming-Viot processes. The role of the additional parameter has been shown to…
We study the evolution of a pathogen with two allelic types infecting a population of hosts, where within-host type frequencies evolve in discrete time. Our framework is built on a two-parameter family of transition kernels on [0,1], which…
The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling…
Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination…
We construct a reliable estimation of evolutionary parameters within the Wright-Fisher model, which describes changes in allele frequencies due to selection and genetic drift, from time-series data. Such data exists for biological…
Consider a two-type Moran population of size $N$ with selection and mutation, where the selective advantage of the fit individuals is amplified at extreme environmental conditions. Assume selection and mutation are weak with respect to $N$,…
In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright-Fisher diffusions. Our approach provides an unbiased estimator of the likelihood function and is based on exact simulation…
The Moran discrete process and the Wright-Fisher modelare the most popular models in population genetics. It is common tounderstand the dynamics of these models to use an approximating diffusionprocess, called Wright-Fisher diffusion. Here,…
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…
In this paper we explore the numerical study. of the Nonlinear Behavior of Suspension Bridge Models. The study of suspension bridges is one of the classic problems of mechanical vibrations, one of the most famous collapses of which was that…
In this article we consider a family of real-valued diffusion processes on the time interval $[0,1]$ indexed by their prescribed initial value $x \in \mathbb{R}$ and another point in space, $y \in \mathbb{R}$. We first present an…
A quantitative model of the mobility of functionalized particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles anchored through…
The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…