Related papers: Diffusion-mediated adsorption versus absorption at…
The work described is concerned with the way micron-size particles attached to a surface are resuspended when exposed to a turbulent flow. An improved version of the Rock'n'Roll model (Reeks and Hall, 2001) is developed where this model…
We study a class of stochastic resetting (SR) processes in which a diffusing particle alternates between free motion and confinement by an externally controlled potential. When the particle is recaptured, it undergoes a return trajectory…
The relation between the jump length probability distribution function and the spectral line profile in resonance atomic radiation trapping is considered for Partial Frequency Redistribution (PFR) between absorbed and reemitted radiation.…
We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient:…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…
A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…
In dynamic decision-making scenarios across business and healthcare, leveraging sample trajectories from diverse populations can significantly enhance reinforcement learning (RL) performance for specific target populations, especially when…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
The canonical Evans--Majumdar model for diffusion with stochastic resetting to the origin assumes that resetting takes zero time: upon resetting the diffusing particle is teleported back to the origin to start its motion anew. However, in…
We propose residual denoising diffusion models (RDDM), a novel dual diffusion process that decouples the traditional single denoising diffusion process into residual diffusion and noise diffusion. This dual diffusion framework expands the…
Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…
In this paper, conditional denoising diffusion probabilistic models (DDPMs) are proposed to enhance the data transmission and reconstruction over wireless channels. The underlying mechanism of DDPM is to decompose the data generation…
We consider the paradigm of an overdamped Brownian particle in a potential well, which is modulated through an external protocol, in the presence of stochastic resetting. Thus, in addition to the short range diffusive motion, the particle…