Related papers: An explicit transition density expansion for a mul…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
In this article, three models are considered, they are the infinitely-many-neutral-alleles model \cite{MR615945}, infinite dimensional diffusion associated with two-parameter Poisson-Dirichlet distribution \cite{MR2596654} and the…
Fisher waves have been studied recently in the specific case of diffusion-limited reversible coalescence, A+A<-->A, on the line. An exact analysis of the particles concentration showed that waves propagate from a stable region to an…
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…
Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…
Pre-trained stable diffusion models (SD) have shown great advances in visual correspondence. In this paper, we investigate the capabilities of Diffusion Transformers (DiTs) for accurate dense correspondence. Distinct from SD, DiTs exhibit a…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to…
In this paper, we develop a novel high-dimensional time-varying coefficient estimation method, based on high-dimensional It\^o diffusion processes. To account for high-dimensional time-varying coefficients, we first estimate local (or…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
This paper proposes a new pipeline for long-tail (LT) recognition. Instead of re-weighting or re-sampling, we utilize the long-tailed dataset itself to generate a balanced proxy that can be optimized through cross-entropy (CE).…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…
We establish a simple criterion for locating points where the transition density of a degenerate diffusion is strictly positive. Throughout, we assume that the diffusion satisfies a stochastic differential equation (SDE) on $\mathbf{R}^d$…
The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fittest dispersal rate for a population in a bounded domain, and,…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
We develop a general transfer-matrix formalism for determining the growth rate of the Rayleigh-Taylor instability in a fluid system with spatially varying density and viscosity. We use this formalism to analytically and numerically treat…
Current video deblurring methods have limitations in recovering high-frequency information since the regression losses are conservative with high-frequency details. Since Diffusion Models (DMs) have strong capabilities in generating…
Diffusion models, capable of high-quality image generation, receive unparalleled popularity for their ease of extension. Active users have created a massive collection of domain-specific diffusion models by fine-tuning base models on…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl…