Related papers: A path integral formulation of the Wright-Fisher p…
The d-dimensional Lambda-Fleming-Viot generator acting on functions g(x), with x being a vector of d allele frequencies, can be written as a Wright-Fisher generator acting on functions g with a modified random linear argument of x induced…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and…
{\bf Abstract} The trajectory of the frequency of an allele which begins at $x$ at time $0$ and is known to have frequency $z$ at time $T$ can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when $x=z=0$ are…
Understanding propagation structures in graph diffusion processes, such as epidemic spread or misinformation diffusion, is a fundamental yet challenging problem. While existing methods primarily focus on source localization, they cannot…
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 $N$,…
Fisher's fundamental theorem of natural selection states that the rate of change in a population's mean fitness equals its additive genetic variance in fitness. This implies that mean fitness should not decline in a constant environment,…
Using graphical methods based on a `lookdown' and pruned version of the {\em ancestral selection graph}, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection,…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
Scattering of matter waves through slits has been explored using the Feynman Path Integral formalism. We explicitly plot the near-zero probability densities to analyse the behaviour near the slit. Upon doing so, intriguing patterns emerge,…
We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of…
In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman--Kac…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
We apply a Lindeberg principle under the Markov process setting to approximate the Wright-Fisher model with neutral $r$-alleles using a diffusion process, deriving an error rate based on a function class distance involving fourth-order…
Using a probabilistic neural network and Lagrangian observations from the Global Drifter Program, we model the single particle transition probability density function (pdf) of ocean surface drifters. The transition pdf is represented by a…
Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time…
We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path integral method to compute the effective diffusion coefficient perturbatively to lowest order in the…