Related papers: Fractional Gray-Scott Model: Well-posedness, Discr…
Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…
In this study, the numerical solutions of reaction-diffusion systems are investigated via the trigonometric quintic B-spline nite element collocation method. These equations appear in various disciplines in order to describe certain…
Feature selection is fundamental to robust data-centric AI, but most existing methods optimize predictive performance under a single data distribution. This often selects spurious features that fail under distribution shifts. Motivated by…
In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical ($\alpha=1$) differential equation in the fractional case (here using fractional…
We propose a simple and easy-to-implement scheme for a renormalon-free gluon condensate (GC) matrix element, which is analogous to implementations of short-distance heavy-quark mass renormalization schemes existing in the literature already…
The Grey System Theory (GST) is a powerful mathematical framework employed for modeling systems with uncertain or incomplete information. This paper proposes an integration of the GST with time scales, a generalized approach that…
Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of…
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite…
In this article, we consider discrete schemes for a fractional diffusion equation involving a tempered fractional derivative in time. We present a semi-discrete scheme by using the local discontinuous Galerkin (LDG) discretization in the…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
Recent advances in diffusion models attempt to handle conditional generative tasks by utilizing a differentiable loss function for guidance without the need for additional training. While these methods achieved certain success, they often…
This work is devoted to the design of interior penalty discontinuous Galerkin (dG) schemes that preserve maximum principles at the discrete level for the steady transport and convection-diffusion problems and the respective transient…
Color constancy methods often struggle to generalize across different camera sensors due to varying spectral sensitivities. We present GCC, which leverages diffusion models to inpaint color checkers into images for illumination estimation.…
A direct discontinuous Galerkin (DDG) finite element method is developed for solving fractional convection-diffusion and Schr\"{o}dinger type equations with a fractional Laplacian operator of order $\alpha$ $(1<\alpha<2)$. The fractional…
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…
Offline Goal-Conditioned Reinforcement Learning (Offline GCRL) is an important problem in RL that focuses on acquiring diverse goal-oriented skills solely from pre-collected behavior datasets. In this setting, the reward feedback is…
Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
This article introduces cyclic fractional Gaussian noise (cfGn), a stochastic model that integrates second-order cyclostationarity with long-range dependence property. While classical cyclostationary processes are widely discussed in the…
Gaussian Conditional Random Fields (GCRF), as a structured regression model, is designed to achieve higher regression accuracy than unstructured predictors at the expense of execution time, taking into account the objects similarities and…