Source author record

Dong Ye

Dong Ye appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record

Catalog footprint

What is connected

14works
4topics
4close collaborators

Actions

Connect this record

Log in to claim

Research graph

See the researcher in context

Open full explorer

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

14 published item(s)

preprint2026arXiv

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.

preprint2020arXiv

Existence and non-existence results for the higher order Hardy-Hénon equation revisited

This paper is devoted to studies of non-negative, non-trivial (classical, punctured, or distributional) solutions to the higher order Hardy-Hénon equations \[ (-Δ)^m u = |x|^σu^p \] in $\mathbf R^n$ with $p > 1$. We show that the condition \[ n - 2m - \frac{2m+σ}{p-1} >0 \] is necessary for the existence of distributional solutions. For $n \geq 2m$ and $σ> -2m$, we prove that any distributional solution satisfies an integral equation and a weak super polyharmonic property. We establish some sufficient conditions for punctured or classical solution to be a distributional solution. As application, we show that if $n \geq 2m$ and $σ> -2m$, there is no non-negative, non-trivial, classical solution to the equation if \[ 1 < p < \frac{n+2m+2σ}{n-2m}. \] At last, we prove that for for $n > 2m$, $σ> -2m$ and $$p \geq \frac{n+2m+2σ}{n-2m},$$ there exist positive, radially symmetric, classical solutions to the equation.

preprint2015arXiv

Conformal metrics in ${\mathbb R}^{2m}$ with constant $Q$-curvature and arbitrary volume

We study the polyharmonic problem $Δ^m u = \pm e^u$ in ${\mathbb R}^{2m}$, with $m \geq 2$. In particular, we prove that {\sl for any} $V > 0$, there exist radial solutions of $Δ^m u = -e^u$ such that $$\int_{{\mathbb R}^{2m}} e^u dx = V.$$ It implies that for $m$ odd, given arbitrary volume $V > 0$, there exist conformal metrics $g$ on ${\mathbb R}^{2m}$ with positive constant $Q$-curvature and vol$(g) =V$. This answers some open questions in Martinazzi's work.

preprint2015arXiv

Graph Invertibility and Median Eigenvalues

Let $(G,w)$ be a weighted graph with a weight-function $w: E(G)\to \mathbb R\backslash\{0\}$. A weighted graph $(G,w)$ is invertible to a new weighted graph if its adjacency matrix is invertible. A graph inverse has combinatorial interest and can be applied to bound median eigenvalues of a graph such as have physical meanings in Quatumn Chemistry. In this paper, we characterize the inverse of a weighted graph based on its Sachs subgraphs that are spanning subgraphs with only $K_2$ or cycles (or loops) as components. The characterization can be used to find the inverse of a weighted graph based on its structures instead of its adjacency matrix. If a graph has its spectra split about the origin, i.e., half of eigenvalues are positive and half of them are negative, then its median eigenvalues can be bounded by estimating the largest and smallest eigenvalues of its inverse. We characterize graphs with a unique Sachs subgraph and prove that these graphs has their spectra split about the origin if they have a perfect matching. As applications, we show that the median eigenvalues of stellated graphs of trees and corona graphs belong to different halves of the interval $[-1,1]$.

preprint2014arXiv

Dominating Plane Triangulations

In 1996, Tarjan and Matheson proved that if $G$ is a plane triangulated disc with $n$ vertices, $γ(G)\le n/3$, where $γ(G)$ denotes the domination number of $G$. Furthermore, they conjectured that the constant $1/3$ could be improved to $1/4$ for sufficiently large $n$. Their conjecture remains unsettled. In the present paper, it is proved that if $G$ is a hamiltonian plane triangulation with $|V(G)|=n$ vertices and minimum degree at least 4, then $γ(G)\le\max\{\lceil 2n/7\rceil, \lfloor 5n/16\rfloor\}$. It follows immediately that if $G$ is a 4-connected plane triangulation with $n$ vertices, then $γ(G)\le\max\{\lceil 2n/7\rceil, \lfloor 5n/16\rfloor\} $. It then follows that if $n\ge 26$, then $γ(G)\le \lfloor 5n/16\rfloor$.

preprint2014arXiv

Remarks on two fourth order elliptic problems in whole space

We are interested in entire solutions for the semilinear biharmonic equation $Δ^{2}u=f(u)$ in $\R^N$, where $f(u)=e^{u}$ or $-u^{-p}\ (p>0)$. For the exponential case, we prove that any classical entire solution verifies $-Δu>0$ without any restriction, which completes the results in \cite{Dupaigne, xu-wei} and yields a nonexistence result in $\R^2$ ; we obtain also a refined asymptotic expansion of radial separatrix solution for $N=3$, which answers a question in \cite{Berchio}. For the negative power case, we show the nonexistence of the classical entire solution for any $0<p\leq1$.

preprint2013arXiv

Face-width of Pfaffian Braces and Polyhex Graphs on Surfaces

A graph $G$ is Pfaffian if it has an orientation such that each central cycle $C$ (i.e. $C$ is even and $G-V(C)$ has a perfect matching) has an odd number of edges directed in either direction of the cycle. The number of perfect matchings of Pfaffian graphs can be computed in polynomial time. In this paper, by applying the characterization of Pfaffian braces due to Robertson, Seymour and Thomas [Ann. Math. 150 (1999) 929-975], and independently McCuaig [Electorn. J. Combin. 11 (2004) #R79], we show that every embedding of a Pfaffian brace on a surface with positive genus has face-width at most 3. For a Pfaffian cubic brace, we obtain further structure properties which are useful in characterizing Pfaffian polyhex graphs. Combining with polyhex graphs with face-width 2, we show that a bipartite polyhex graph is Pfaffian if and only if it is isomorphic to the cube, the Heawood graph or $C_k\times K_2$ for even integers $k\ge 6$, and all non-bipartite polyhex graphs are Pfaffian.

preprint2012arXiv

On stable solutions of biharmonic problem with polynomial growth

We prove the nonexistence of smooth stable solution to the biharmonic problem $Δ^2 u= u^p$, $u>0$ in $\R^N$ for $1 < p < \infty$ and $N < 2(1 + x_0)$, where $x_0$ is the largest root of the following equation: $$x^4 - \frac{32p(p+1)}{(p-1)^2}x^2 + \frac{32p(p+1)(p+3)}{(p-1)^3}x -\frac{64p(p+1)^2}{(p-1)^4} = 0.$$ In particular, as $x_0 > 5$ when $p > 1$, we obtain the nonexistence of smooth stable solution for any $N \leq 12$ and $p > 1$. Moreover, we consider also the corresponding problem in the half space $\R^N_+$, or the elliptic problem $Δ^2 u= ł(u+1)^p$ on a bounded smooth domain $Ø$ with the Navier boundary conditions. We will prove the regularity of the extremal solution in lower dimensions. Our results improve the previous works.

preprint2011arXiv

Classification and nondegeneracy of $SU(n+1)$ Toda system with singular sources

We consider the following Toda system Δu_i + \D \sum_{j = 1}^n a_{ij}e^{u_j} = 4πγ_{i}δ_{0} \text{in}\mathbb R^2, \int_{\mathbb R^2}e^{u_i} dx < \infty, \forall 1\leq i \leq n, where $γ_{i} > -1$, $δ_0$ is Dirac measure at 0, and the coefficients $a_{ij}$ form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result: $$\sum_{j=1}^n a_{ij}\int_{\R^2}e^{u_j} dx = 4π(2+γ_i+γ_{n+1-i}), \;\;\forall\; 1\leq i \leq n.$$ This generalizes the classification result by Jost and Wang for $γ_i=0$, $\forall \;1\leq i\leq n$. (ii) We prove that if $γ_i+γ_{i+1}+...+γ_j \notin \mathbb Z$ for all $1\leq i\leq j\leq n$, then any solution $u_i$ is \textit{radially symmetric} w.r.t. 0. (iii) We prove that the linearized equation at any solution is \textit{non-degenerate}. These are fundamental results in order to understand the bubbling behavior of the Toda system.

preprint2011arXiv

Regularity of the extremal solution for some elliptic problems with advection

In this note, we investigate the regularity of extremal solution $u^*$ for semilinear elliptic equation $-\triangle u+c(x)\cdot\nabla u=λf(u)$ on a bounded smooth domain of $\mathbb{R}^n$ with Dirichlet boundary condition. Here $f$ is a positive nondecreasing convex function, exploding at a finite value $a\in (0, \infty)$. We show that the extremal solution is regular in low dimensional case. In particular, we prove that for the radial case, all extremal solution is regular in dimension two.

preprint2010arXiv

A Hardy-Moser-Trudinger inequality

In this paper we obtain an inequality on the unit disc $B$ in the plane, which improves the classical Moser-Trudinger inequality and the classical Hardy inequality at the same time. Namely, there exists a constant $C_0>0$ such that \[ \int_B e^{\frac {4πu^2}{H(u)}} dx \le C_0 < \infty, \quad \forall\; u\in C^\infty_0(B),\] where $$H(u) := \int_B |\n u|^2 dx - \int_B \frac {u^2}{(1-|x|^2)^2} dx.$$ This inequality is a two dimensional analog of the Hardy-Sobolev-Maz'ya inequality in higher dimensions, which was recently intensively studied. We also prove that the supremum is achieved in a suitable function space, which is an analog of the celebrated result of Carleson-Chang for the Moser-Trudinger inequality.