In current paper, we put forward a reaction-diffusion system for West Nile virus in spatial heterogeneous and time almost periodic environment with free boundaries to investigate the influences of the habitat differences and seasonal variations on th...
This paper aims to explore the temporal-spatial spreading and asymptotic behaviors of West Nile virus by a reaction-advection-diffusion system with free boundaries, especially considering the impact of advection term on the extinction and persistence...
In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on $-\infty\leq a<b\leq \infty$ in terms of their ability to access the boundary (Feller's test for explosions) and to enter the interior from the boundary....
The inherent ambiguity in defining visual concepts poses significant challenges for modern generative models, such as the diffusion-based Text-to-Image (T2I) models, in accurately learning concepts from a single image. Existing methods lack a systema...
Parameter generation has long struggled to match the scale of today large vision and language models, curbing its broader utility. In this paper, we introduce Recurrent Diffusion for Large Scale Parameter Generation (RPG), a novel framework that gene...
In this paper, we prove some qualitative properties of pushed fronts for the periodic reaction-diffusion-equation with general monostable nonlinearities. Especially, we prove the exponential behavior of pushed fronts when they are approaching their u...
We investigate the inside structure of one-dimensional reaction-diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the fronts are made of several components with identical diffusion and gro...
The linear super-Burnett coefficient gives corrections to the diffusion equation in the form of higher derivatives of the density. Like the diffusion coefficient, it can be expressed in terms of integrals of correlation functions, but involving fou...
Text-to-image (T2I) diffusion models have achieved widespread success due to their ability to generate high-resolution, photorealistic images. These models are trained on large-scale datasets, like LAION-5B, often scraped from the internet. However,...
This paper introduces Ali-AUG, a novel single-step diffusion model for efficient labeled data augmentation in industrial applications. Our method addresses the challenge of limited labeled data by generating synthetic, labeled images with precise fea...
Existing theories of gun violence predict stable spatial concentrations and contagious diffusion of gun violence into surrounding areas. Recent empirical studies have reported confirmatory evidence of such spatiotemporal diffusion of gun violence. Ho...
Measurements of lateral diffusion of proteins in a membrane typically assume that the movement of the protein occurs in a flat plane. Real membranes, however, are subject to thermal fluctuations, leading to movement of an inclusion into the third d...
We introduce a simple yet effective technique for estimating lighting from a single low-dynamic-range (LDR) image by reframing the task as a chrome ball inpainting problem. This approach leverages a pre-trained diffusion model, Stable Diffusion XL, t...
Video diffusion models, trained on large-scale datasets, naturally capture correspondences of shared features across frames. Recent works have exploited this property for tasks such as optical flow prediction and tracking in a zero-shot setting. Moti...
Representation Autoencoders (RAEs) have shown distinct advantages in diffusion modeling on ImageNet by training in high-dimensional semantic latent spaces. In this work, we investigate whether this framework can scale to large-scale, freeform text-to...
We assume that the state of a number of nodes in a network could be investigated if necessary, and study what configuration of those nodes could facilitate a better solution for the diffusion-source-localization (DSL) problem. In particular, we formu...
In this study, the impact of turbulent diffusion on mixing of biochemical reaction models is explored by implementing and validating different models. An original codebase called CHAD (Coupled Hydrodynamics and Anaerobic Digestion) is extended to inc...
We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity,...
The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for nonlinear c...
Diffusion state distance (DSD) is a metric on the vertices of a graph, motivated by bioinformatic modeling. Previous results on the convergence of DSD to a limiting metric relied on the definition being based on symmetric or reversible random walk on...