Related papers: A path integral formulation of the Wright-Fisher p…
We develop an iterative global solution scheme for the backward Kolmogorov equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several alleles at the…
We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…
We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent…
We investigate the properties of a Wright-Fisher diffusion process started from frequency x at time 0 and conditioned to be at frequency y at time T. Such a process is called a bridge. Bridges arise naturally in the analysis of selection…
In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the…
The path integral for Darcy's law with a stochastic conductivity, which characterizes flow through random porous media, is used as a basis for Wilson renormalization-group (RG) calculations in momentum space. A coarse graining procedure is…
The Fleming-Viot process describes a system of $N$ particles diffusing on a graph with an absorbing site. Whenever one of the particles is absorbed, it is replaced by a new particle at the position of one of the $N-1$ remaining particles.…
We consider particle filters with weakly informative observations (or `potentials') relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of continuous-time…
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the…
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…
We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kac formula. First, a new interpretation of the…
The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…
The two-parameter Poisson--Dirichlet diffusion, introduced in 2009 by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman's one-parameter Poisson--Dirichlet distribution and to certain Fleming--Viot…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
Coupled Wright-Fisher diffusions have been recently introduced to model the temporal evolution of finitely-many allele frequencies at several loci. These are vectors of multidimensional diffusions whose dynamics are weakly coupled among…
In this paper, we propose a drift-diffusion process on the probability simplex to study stochastic fluctuations in probability spaces. We construct a counting process for linear detailed balanced chemical reactions with finite species such…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
We present DeepTract, a deep-learning framework for estimating white matter fibers orientation and streamline tractography. We adopt a data-driven approach for fiber reconstruction from diffusion weighted images (DWI), which does not assume…
We provide a detailed description of the structure of the transition probabilities and of the hitting distributions of boundary components of a manifold with corners for a degenerate strong Markov process arising in population genetics. The…