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Dong Ye

Publications and source records attributed to Dong Ye.

At least 19 recordsLinked to original sources
arXiv2026

Concavity Properties of Robin Solutions on $C^{3,1}$ Uniformly Convex Domains

We prove that, on a bounded uniformly convex domain of class $C^{3,1}$, the first Robin eigenfunction is strictly log-concave and the Robin torsion function is strictly $1/2$-concave for all sufficiently large Robin parameters. This means that Conjecture 1.1 of Andrews, Clutterbuck and Hauer holds for uniformly convex $C^{3,1}$ domains in any dimension, and settles an open problem posed by Crasta and Fragal\`a when the domain has $C^{3,1}$ regularity. Our proof derives suitable uniform $C^2$-decay estimates by maximum principle arguments, thereby removing the imposed higher-order boundary regularity assumption required previously.

math.AP↗
arXiv2026

Comparison principles and symmetry for subquadratic fractional $p$-Laplacian equations

This paper establishes a new comparison principle framework for the subquadratic fractional $p$-Laplacian, i.e.~$1 < p < 2$ under minimal regularity assumptions, that has remained a significant challenging issue due to the singularity of the operator. Our results provide the essential analytical tools required for the moving plane method in this setting. We prove first a weak comparison principle for $(-\Delta)_p^s u = f(u)$ in bounded domains with sufficiently small measure, where only the boundedness of the weak solution is required. More importantly, we establish a strong comparison principle for continuous weak solutions in the parameter range $s \in (0, \frac{1}{2})$ and $\frac{1}{1-s} < p < 2$. Our proof introduces a localized barrier function and does not require any H\"{o}lder regularity of the weak solution, nor any smoothness of the domain. This presents a substantial contrast over previous study, which relied heavily on H\"older or even $C^{1,1}$ regularity. As a direct application, we employ these comparison principles to prove the symmetry of weak solutions to $(-\Delta)_p^s u = f(u)$ under mild assumptions, which significantly extend existing symmetry theories for nonlocal quasilinear equations.

math.AP↗
arXiv2026

Asymptotically sharp Hardy-Rellich inequalities on lattices

We determine the sharp asymptotic behavior of the optimal constants in the discrete Hardy-Rellich inequalities on the lattice $\mathbb{Z}^d$. For every fixed integer $m\ge 1$, let ${\mathcal C}_{m,d}$ be the best constant in the $m$-th order Hardy-Rellich inequality. We prove that $$\lim_{d\to\infty}\frac{\mathcal C_{m,d}}{d^m}=2^m.$$ Our approach combines a Fourier reduction to weighted inequalities with the flat torus and general weighted Hardy-Rellich identities of first and second order. A key novelty is the use of probabilistic concentration estimates, specifically Hoeffding's inequality and entropy methods, to handle estimates involving the anisotropic weight $\omega^\gamma$ $(\gamma\geq 1)$ where $$\omega(x)=\sum_{j=1}^{d} \Big(\sin\frac{x_j}{2}\Big)^2$$ in a dimension-uniform manner. These tools yield asymptotically sharp weighted estimates on the torus, from which the lattice inequalities follow by iteration.

math.AP↗
arXiv2026

Network Knowledge Prior Guided Learning for Data-Efficient Surface Defect Detection

Deep learning-based methods have become the de facto standard for industrial defect detection. However, their data-hungry nature and inherent "black-box" characteristics often lead to performance bottlenecks and limited trustworthiness in real-world applications. To address these challenges, this paper proposes a novel knowledge-guided loss function that seamlessly integrates model interpretability into the training process without incurring any additional inference cost. Our method operates in two phases: first, a primary classification network is trained, and its explanations, in the form of saliency maps, are generated as prior knowledge. Second, a multi-task learning framework is established, where the main task performs classification, and an auxiliary task imposes consistency between the saliency maps of the final model and the primary model. This consistency is enforced by a dedicated knowledge-guided loss term, effectively acting as a powerful regularizer to steer the model towards robust feature representations. Extensive experiments on multiple public defect datasets demonstrate that our approach consistently enhances the performance of baseline models in terms of accuracy and AP. Moreover, visual analysis reveals that the proposed method yields more concentrated and human-intelligible saliency maps. This work presents a simple yet effective paradigm for bridging the gap between model performance and interpretability, paving the way for more reliable and high-performing vision systems in industrial quality inspection.

cs.CV↗
arXiv2026

When Can We Trust Deep Neural Networks? Towards Reliable Industrial Deployment with an Interpretability Guide

The deployment of AI systems in safety-critical domains, such as industrial defect inspection, autonomous driving, and medical diagnosis, is severely hampered by their lack of reliability. A single undetected erroneous prediction can lead to catastrophic outcomes. Unfortunately, there is often no alternative but to place trust in the outputs of a trained AI system, which operates without an internal safeguard to flag unreliable predictions, even in cases of high accuracy. We propose a post-hoc explanation-based indicator to detect false negatives in binary defect detection networks. To our knowledge, this is the first method to proactively identify potentially erroneous network outputs. Our core idea leverages the difference between class-specific discriminative heatmaps and class-agnostic ones. We compute the difference in their intersection over union (IoU) as a reliability score. An adversarial enhancement method is further introduced to amplify this disparity. Evaluations on two industrial defect detection benchmarks show our method effectively identifies false negatives. With adversarial enhancement, it achieves 100\% recall, albeit with a trade-off for true negatives. Our work thus advocates for a new and trustworthy deployment paradigm: data-model-explanation-output, moving beyond conventional end-to-end systems to provide critical support for reliable AI in real-world applications.

cs.CV↗
arXiv2026

Radially symmetric transition-layer solutions in mass-conserving reaction-diffusion systems with bistable nonlinearity

Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis suggest that such models can support stationary patterns with sharp internal interfaces. In this work, we establish for a general class of bistable MCRD systems the existence of nonconstant radially symmetric stationary solutions with a single internal transition layer on an $N$-dimensional ball, for general spatial dimension $N$. Our approach incorporates the global mass constraint directly into a refined matched-asymptotic framework complemented by a uniform spectral/linear analysis. Beyond mere existence, our framework yields arbitrarily high-order asymptotic approximations of the constructed solutions together with quantitative uniform error estimates, which provides a quantitative higher-dimensional theory of transition-layer patterns in MCRD systems and a rigorous justification for their use in modeling phase separation and pattern formation in biological and ecological settings.

math.AP↗
arXiv2026

Calibration Method of Spacecraft-Inertial Sensor Center-of-Mass Offset for the Taiji Gravitational Wave Detection Mission under Science Mode

Accurately calibrating the center-of-mass (CoM) offset between the spacecraft (SC) and the inertial sensor test mass (TM) is crucial for space-based gravitational-wave (GW) antennas, such as LISA and Taiji. Current calibration methods require additional spacecraft maneuvers that disrupt science data continuity and inter-satellite links, compromising the coherence of gravitational wave signals. Here, we present a maneuver-free calibration scheme that directly estimates the CoM offset vector using only standard science-mode measurements from inertial sensors, interferometers, and differential wavefront sensors. By embedding the CoM offset induced coupling acceleration as an extended state in a model-based adaptive Kalman filter, we achieve estimation accuracy of 0.01-1.5 mm across all axes with a maximum error below 1%. This approach enables continuous, high-precision calibration during nominal observation runs, ensuring continuous and coherent gravitational wave data collection while maintaining the required precision, and also facilitating advanced DFACS functions such as performance evaluations and fault diagnosis. For LISA-like missions, where data continuity is paramount for detecting faint gravitational wave signals, this method will enhance scientific output and reliability.

gr-qc↗
arXiv2025

Packing Independent Cliques in $K_4$-minor-free Graphs

Let $G$ be a graph and $S$ be a set of cliques of $G$. The set $S$ is an indeque set if every component of $G[S]$, the subgraph induced by vertices of $S$, is a clique. In this paper, we prove that the indeque ratio of $K_4$-minor-free graphs is $\frac 1 2$, which settle two conjectures of Biro, Collado and Zamora. We also show that the indeque ratio of subcubic graphs is $\frac 1 2$.

math.CO↗
arXiv2025

Sample-Centric Multi-Task Learning for Detection and Segmentation of Industrial Surface Defects

Industrial surface defect inspection for sample-wise quality control (QC) must simultaneously decide whether a given sample contains defects and localize those defects spatially. In real production lines, extreme foreground-background imbalance, defect sparsity with a long-tailed scale distribution, and low contrast are common. As a result, pixel-centric training and evaluation are easily dominated by large homogeneous regions, making it difficult to drive models to attend to small or low-contrast defects-one of the main bottlenecks for deployment. Empirically, existing models achieve strong pixel-overlap metrics (e.g., mIoU) but exhibit insufficient stability at the sample level, especially for sparse or slender defects. The root cause is a mismatch between the optimization objective and the granularity of QC decisions. To address this, we propose a sample-centric multi-task learning framework and evaluation suite. Built on a shared-encoder architecture, the method jointly learns sample-level defect classification and pixel-level mask localization. Sample-level supervision modulates the feature distribution and, at the gradient level, continually boosts recall for small and low-contrast defects, while the segmentation branch preserves boundary and shape details to enhance per-sample decision stability and reduce misses. For evaluation, we propose decision-linked metrics, Seg_mIoU and Seg_Recall, which remove the bias of classical mIoU caused by empty or true-negative samples and tightly couple localization quality with sample-level decisions. Experiments on two benchmark datasets demonstrate that our approach substantially improves the reliability of sample-level decisions and the completeness of defect localization.

cs.CV↗
arXiv2025

On Sharp Heisenberg Uncertainty Principle and the stability

In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical harmonic decomposition and the Hardy inequalities, we revise two families of inequalities. We give firstly an affirmative answer in dimension four to Cazacu-Flynn-Lam's conjecture [JFA, 2022] for the sharp Hydrogen Uncertainty Principle, and improve the recent estimates of Chen-Tang [arXiv:2508.15221v1] in $\mathbb{R}^2$ and $\mathbb{R}^3$. On the other hand, we identify the best constants and extremal functions for two stability estimates associated to $\|Δu\|_2 \|r\nabla u\|_2 - \frac{N+2}{2}\|\nabla u\|^2_2$ in $\mathbb{R}^N$ ($N \geq 2$), studied recently by Duong-Nguyen [CVPDE, 2025] and Do-Lam-Lu-Zhang [arXiv:2505.02758v1].

math.AP↗
arXiv2025

Quantization of blow-up masses for the Finsler $N$-Liouville equation

The quantization results for blow-up phenomena play crucial roles in the analysis of partial differential equations. Here we quantify the blow-up masses to the following Finsler $N$-Liouville equation $$-Q_{N}u_{n}=V_{n}e^{u_{n}}\quad\mbox{in}~ Ω\subset \mathbb{R}^{N}, N \ge 2.$$ Our study generalizes the classical result of Li-Shafrir [Indiana Univ. Math.J.,1994] for Liouville equation, Wang-Xia's work for anisotropic Liouville equation in $\mathbb{R}^2$ [JDE, 2012], and Esposito-Lucia's for the $N$-Laplacian case in $\mathbb{R}^N$ ($N \geq 3$) in their recent paper [CVPDE, 2024].

math.AP↗
arXiv2025

A Goal-Oriented Reinforcement Learning-Based Path Planning Algorithm for Modular Self-Reconfigurable Satellites

Modular self-reconfigurable satellites refer to satellite clusters composed of individual modular units capable of altering their configurations. The configuration changes enable the execution of diverse tasks and mission objectives. Existing path planning algorithms for reconfiguration often suffer from high computational complexity, poor generalization capability, and limited support for diverse target configurations. To address these challenges, this paper proposes a goal-oriented reinforcement learning-based path planning algorithm. This algorithm is the first to address the challenge that previous reinforcement learning methods failed to overcome, namely handling multiple target configurations. Moreover, techniques such as Hindsight Experience Replay and Invalid Action Masking are incorporated to overcome the significant obstacles posed by sparse rewards and invalid actions. Based on these designs, our model achieves a 95% and 73% success rate in reaching arbitrary target configurations in a modular satellite cluster composed of four and six units, respectively.

cs.RO↗
arXiv2025

Region-Aware CAM: High-Resolution Weakly-Supervised Defect Segmentation via Salient Region Perception

Surface defect detection plays a critical role in industrial quality inspection. Recent advances in artificial intelligence have significantly enhanced the automation level of detection processes. However, conventional semantic segmentation and object detection models heavily rely on large-scale annotated datasets, which conflicts with the practical requirements of defect detection tasks. This paper proposes a novel weakly supervised semantic segmentation framework comprising two key components: a region-aware class activation map (CAM) and pseudo-label training. To address the limitations of existing CAM methods, especially low-resolution thermal maps, and insufficient detail preservation, we introduce filtering-guided backpropagation (FGBP), which refines target regions by filtering gradient magnitudes to identify areas with higher relevance to defects. Building upon this, we further develop a region-aware weighted module to enhance spatial precision. Finally, pseudo-label segmentation is implemented to refine the model's performance iteratively. Comprehensive experiments on industrial defect datasets demonstrate the superiority of our method. The proposed framework effectively bridges the gap between weakly supervised learning and high-precision defect segmentation, offering a practical solution for resource-constrained industrial scenarios.

cs.CV↗
arXiv2025

On sharp anisotropic Hardy inequalities

Recently, Yanyan Li and Xukai Yan showed the following interesting Hardy inequalities with anisotropic weights: Let $n\geq 2$, $p \geq 1$, $pα> 1-n$, $p(α+ β)> -n$, then there exists $C > 0$ such that $$\||x|^β|x'|^{α+1} \nabla u\|_{L^p(\mathbb{R}^n)} \geq C\||x|^β|x'|^αu\|_{L^p(\mathbb{R}^n)}, \quad \forall\; u\in C_c^1(\mathbb{R}^n).$$ Here $x' = (x_1,\ldots, x_{n-1}, 0)$ for $x = (x_i) \in \mathbb{R}^n$. In this note, we will determine the best constant for the above estimate when $p=2$ or $β\geq 0$. Moreover, as refinement for very special case of Li-Yan's result in Adv. Math. 2023, we provide explicit estimate for the anisotropic $L^p$-Caffarelli-Kohn-Nirenberg inequality.

math.AP↗
arXiv2025

Normal conformal metrics with prescribed $Q$-Curvature in $\mathbb{R}^{2n}$

We consider the $Q$-curvature equation \begin{equation}\label{0.1} (-Δ)^n u = K(x)e^{2nu}\quad\text{in} ~\mathbb{R}^{2n} \ (n \geq 2) \end{equation} where $K$ is a given non constant continuous function. Under mild growth control on $K$, we get a necessary condition on the total curvature $Λ_u$ for any normal conformal metric $g_u = e^{2u}|dx|^2$ satisfying $Q_{g_u} = K$ in $\mathbb{R}^{2n}$, or equivalently, solutions to equation with logarithmic growth at infinity. Inversely, when $K$ is nonpositive satisfying polynomial growth control, we show the existence of normal conformal metrics with quasi optimal range of total curvature and precise asymptotic behavior at infinity. If furthermore $K$ is radial symmetric, we establish the same existence result without any growth assumption on $K$.

math.AP↗
arXiv2024

Higher order Hardy-Rellich identities

In this paper, we show Hardy-Rellich identities for polyharmonic operators $Δ^m$ and radial Laplacian $Δ_r^m$ in $\mathbb{R}^n$ with Hardy-Hénon weight $|x|^α$ for all $m, n\in \mathbb{N}, α\in \mathbb{R}$. Moreover, the iterative method is applied to give Hardy-Rellich equalities with general weights on Riemannian manifolds. These identities provide naturally an alternative approach to obtain and improve Hardy-Rellich type inequalities. As example of application, we extend several Rellich inequalities of Tertikas-Zographopoulos (Adv. Math. 2007) to the weighted case; using equality with weights involving logarithmic, we show another new weighted Rellich estimate between integrals of $Δu$ and $|\nabla u|$; we establish also a Rellich identity involving the Laplace-Beltrami operator $Δ_\mathbb{H}$ and the radial Laplacian $Δ_{ρ, \mathbb{H}}$ of the hyperbolic space $\mathbb{H}^n$, which yields in particular brand-new Rellich inequalities for $\|Δ_\mathbb{H} u\|$ in $\mathbb{H}^3$ and $\mathbb{H}^4$.

math.AP↗
arXiv2024

Remark on a special class of Finsler $p$-Laplacian equation

We investigate the anisotropic elliptic equation $-Δ_p^H u = g(u)$. Recently, Esposito, Riey, Sciunzi, and Vuono introduced an anisotropic Kelvin transform in their work \cite{ERSV2022} under the $(H_M)$ condition, where $H(ξ)=\sqrt{\langle Mξ,ξ\rangle}$ with a positive definite symmetric matrix $M$. Here, we emphasize that under the $(H_M)$ assumption, the Finsler $p$-Laplacian and the classical $p$-Laplacian operator are equivalent following a linear transformation. This equivalence offers us a more direct route to derive the pivotal findings presented in \cite{ERSV2022}. While this equivalence is crucial and noteworthy, to our knowledge, it has not been explicitly stated in the current literature.

math.AP↗
arXiv2023

One dimensional sharp discrete Hardy-Rellich inequalities

In this paper, we establish discrete Hardy-Rellich inequalities on $\mathbb{N}$ with $Δ^\frac{\ell}{2}$ and optimal constants, for any $\ell \geq 1$. As far as we are aware, these sharp inequalities are new for $\ell \geq 3$. Our approach is to use weighted equalities to get some sharp Hardy inequalities using shifting weights, then to settle the higher order cases by iteration. We provide also a new Hardy-Leray type inequality on $\mathbb{N}$ with the same constant as the continuous setting. Furthermore, the main ideas work also for general graphs or the $\ell^p$ setting.

math.AP↗