arXiv subjects

Chang-Hong Wu

Publications and source records attributed to Chang-Hong Wu.

11 recordsLinked to original sources

arXiv2026

Harnack-type inequalities and traveling waves for non-cooperative nonlocal diffusion systems

In this paper, we establish a system-wide $\ell^1$-norm Harnack-type inequality for positive solutions of weakly coupled nonlocal diffusion systems on $\mathbb{R}$, without assuming cooperativity or irreducibility of the coupling matrices. As a primary application, we integrate this analytical tool with a rescaling argument to establish the existence of the minimal wave speed for traveling waves for a class of non-cooperative nonlocal diffusion systems with network structures. Furthermore, we derive the precise asymptotic behavior of wave profiles at negative infinity. This is achieved by combining Harnack-type inequalities and Ikehara's theorem with Riesz projections to analyze singularities of vector-valued Laplace transforms.

math.AP↗

arXiv2026

On the logarithmic correction of transition fronts in shifting environments

In this paper, we investigate the location of the spreading front and convergence to traveling wave profile of solutions to the Fisher-KPP equation in the following two cases: (i) in unbounded domains with an expanding boundary; (ii) on the real line where the environment function has a shifting jump discontinuity. Our approach is based on extending ideas in Bramson's seminal work in 1983, and applying gluing technique to construct super/subsolutions.

math.AP↗

arXiv2026

Invasion Fronts in Shifting Habitats and Competition Systems: A Hamilton-Jacobi Approach and Nonlocal Effects

We review recent developments in the study of spreading phenomena in reaction--diffusion equations arising from ecological invasion models. Motivated by the conjecture of Shigesada and Kawasaki on staged invasions, we discuss how competition systems can lead to effective scalar models with shifting habitats. We present the Hamilton--Jacobi approach for determining spreading speeds and revisit the result of {Li--Bewick--Shang--Fagan} (2014) from this perspective. We then describe the emergence of nonlocally pulled fronts when the shifting habitat connects regions of distinct positive growth rates. Recent results including the works of Lam--Yu (2022) and Lam--Nadin--Yu (2025) are surveyed. We also discuss spreading phenomena in competition systems, predator-prey systems, and the existence of various classes of entire solutions. Finally, we discuss the logarithmic correction for invasion waves in moving environments and prove a new result.

math.AP↗

arXiv2026

AttnRegDeepLab: A Two-Stage Decoupled Framework for Interpretable Embryo Fragmentation Grading

Assessing embryo fragmentation is crucial for predicting IVF success, yet manual grading is prone to subjectivity, and existing AI models struggle with clinical interpretability and segmentation errors. We propose AttnRegDeepLab, a Multi-Task Learning (MTL) framework designed to solve these challenges. The model enhances a DeepLabV3+ decoder with Attention Gates to filter out cytoplasmic noise and retain sharp contour details. It also introduces a Multi-Scale Regression Head with Feature Injection, guiding the segmentation process with global grading priors to eliminate systematic area estimation errors. Based on a two-stage decoupled training strategy and a range-based loss for weakly labeled data, our method resolves MTL gradient conflicts. AttnRegDeepLab yields high grading precision and excellent segmentation quality (Dice coefficient = 0.729), avoiding the trade-off between contour integrity and grading accuracy seen under standard joint optimization. This provides a reliable, clinically interpretable tool balancing visual and quantitative accuracy.

cs.CV↗

arXiv2025

Beyond Data Scarcity Optimizing R3GAN for Medical Image Generation from Small Datasets

Medical image datasets frequently exhibit significant class imbalance, a challenge that is further amplified by the inherently limited sample sizes that characterize clinical imaging data. Using human embryo time-lapse imaging (TLI) as a case study, this work investigates how generative adversarial networks (GANs) can be optimized for small datasets to generate realistic and diagnostically meaningful images. Based on systematic experiments with R3GAN, we established effective training strategies and designed an optimized configuration for 256x256-resolution datasets, featuring a full burn-in phase and a low, gradually increasing gamma range (5 to 40). The generated samples were used to balance an imbalanced embryo dataset, leading to substantial improvement in classification performance. The recall and F1-score of the three-cell (t3) class increased from 0.06 to 0.69 and from 0.11 to 0.60, respectively, without compromising the performance of other classes. These results demonstrate that tailored R3GAN training strategies can effectively alleviate data scarcity and improve model robustness in small-scale medical imaging tasks.

eess.IV↗

arXiv2025

Linear vs. nonlinear speed selection of the front propagation into unstable states

In this paper, we mainly consider the speed selection problem for the classical Lotka-Volterra competition system. For the first time, we propose a sufficient and necessary condition for this long-standing problem from a new point of view. Moreover, our results can also reveal the essence of the linearly selected problem for the monostable dynamical system from the observation of the decay rate of the minimal traveling wave solution.

math.AP↗

arXiv2024

On the propagation speed of the single monostable equation

In this paper, we first focus on the speed selection problem for the reaction-diffusion equation of the monostable type. By investigating the decay rates of the minimal traveling wave front, we propose a sufficient and necessary condition that reveals the essence of propagation phenomena. Moreover, since our argument relies solely on the comparison principle, it can be extended to more general monostable dynamical systems, such as nonlocal diffusion equations.

math.AP↗

arXiv2022

Sharp estimates for the spreading speeds of the Lotka-Volterra competition-diffusion system: the strong-weak type

We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is not linear determined, we establish the precise asymptotic behavior of the solution of the Cauchy problem in two different situations: (i) one species is an invasive one and the other is a native species; (ii) both two species are invasive species.

math.AP↗

arXiv2021

Global existence and uniqueness of solutions for one-dimensional reaction-interface systems

In this paper, we provide a mathematical framework in studying the wave propagation with the annihilation phenomenon in excitable media. We deal with the existence and uniqueness of solutions to a one-dimensional free boundary problem (called a reaction--interface system) arising from the singular limit of a FitzHugh--Nagumo type reaction--diffusion system. Because of the presence of the annihilation, interfaces may intersect each other. We introduce the notion of weak solutions to study the continuation of solutions beyond the annihilation time. Under suitable conditions, we show that the free boundary problem is well-posed.

math.AP↗

arXiv2020

Sharp estimates for the spreading speed of the Lotka-Volterra diffusion system with strong competition

This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one and the other is a native one or both are invasive species. Our results seem to be the first that provide a precise spreading speed and profile for such a strong competition system. Among other things, our analysis relies on the construction of new types of supersolution and subsolution, which are optimal in certain sense.

math.AP↗

arXiv2017

Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries

We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under suitable assumptions, both species in the system can successfully spread into the available environment, but their spreading speeds are different, and their population masses tend to segregate, with the slower spreading competitor having its population concentrating on an expanding ball, say Bt, and the faster spreading competitor concentrating on a spherical shell outside Bt that disappears to infinity as time goes to infinity.

math.AP↗