Related papers: EWF : simulating exact paths of the Wright--Fisher…
Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright-Fisher diffusion and the Kingman coalescent, where the former describes the stochastic…
Diffusion probability models have shown significant promise in offline reinforcement learning by directly modeling trajectory sequences. However, existing approaches primarily focus on time-domain features while overlooking frequency-domain…
We study the fixation and stationary behavior of the Lambda-Wright-Fisher process with parent-independent mutation and finitely many types, a jump-diffusion model for allele frequency dynamics in large populations with potentially large…
We first revisit the multi-allelic mutation-fitness balance problem, especially when mutations obey a house of cards condition, where the discrete-time deterministic evolutionary dynamics of the allelic frequencies derives from a…
Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. And the multi-types Galton-Watson forest is a random model of population growth without space or…
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…
Graph generation addresses the problem of generating new graphs that have a data distribution similar to real-world graphs. While previous diffusion-based graph generation methods have shown promising results, they often struggle to scale…
A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of…
In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium…
The distribution of genetic polymorphisms in a population contains information about the mutation rate and the strength of natural selection at a locus. Here, we show that the Poisson Random Field (PRF) method of population-genetic…
This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to…
We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional…
Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to…
For multivariant Wright-Fisher models in population genetics, we introduce equilibrium states, expressed by fluctuations of probability ratio, in contrast to the traditionally used fluctuations, expressed by the difference between the…
Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…
Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…
Diffusion bridge models have shown great promise in image restoration by explicitly connecting clean and degraded image distributions. However, they often rely on complex and high-cost trajectories, which limit both sampling efficiency and…
Transport and the approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative…
Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem…
We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency…