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Dong Ye

Dong Ye contributes to research discovery and scholarly infrastructure.

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Published work

6 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.

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 $γ(G)\le \lfloor 5n/16\rfloor$.

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.

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&#39;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.