arXiv subjects

Silin Huang

Publications and source records attributed to Silin Huang.

7 recordsLinked to original sources

arXiv2026

On a distance Laplacian analog of Brouwer's conjecture for several classes of graphs

Zhou et al. (2025) proposed a distance Laplacian analog of Brouwer's conjecture on partial sums of Laplacian eigenvalues, asserting that for any connected graph $G$, $\sum_{i=1}^r \partial_i^L(G)\le W(G)+\binom{r+2}{3},$ where $\partial_i^L(G)$ are the eigenvalues of the distance Laplacian matrix and $W(G)$ is the Wiener index. We prove this inequality for three broad classes of graphs, thereby improving and extending existing results. First, we prove that all connected graphs of diameter at most $D$ satisfy the inequality once the order $n$ satisfies $n\ge\lceil\frac49(D+1)^3\rceil$. Second, we show that the inequality holds for every diameter-$2$ graph with the only exceptions being $K_{1,3}$ at $r=2$ and $K_{1,4}$ at $r=3$. Third, we prove that if the maximum degree is $\Delta(G)=n-k$, then the inequality holds for all $n\ge N(k)$, where $N(2)=10$ and $N(k)=\lceil 5(k-1)^{3/2}\rceil$ for $k\ge 3$. Our proofs rely on decomposing the distance Laplacian matrix into Laplacian matrices of auxiliary graphs whose edges are vertex pairs at distance at least a prescribed value, together with classical eigenvalue inequalities.

math.CO↗

arXiv2026

Sharp $A_\alpha$-Spectral Conditions for Odd $[1,b]$-Factors When $\alpha>1/2$

We solve, for all sufficiently large even orders, the problem proposed by Chen et al. on sharp $A_\alpha$-spectral conditions for the existence of odd $[1,b]$-factors when $\alpha>1/2$. Chen et al. showed that every connected graph of even order $n$ with no odd $[1,b]$-factor has $A_\alpha$-spectral radius at most $\max_{1\le s\le k}\rho_\alpha(G_s)$, where $G_s=K_s\nabla\left(K_{n-(b+1)s-1}\cup(bs+1)K_1\right)$ and $k=\lfloor(n-2)/(b+1)\rfloor$. Thus the problem reduces to finding the graph with the largest $A_\alpha$-spectral radius among these obstruction graphs. We prove that, for every $\alpha\in(1/2,1)$, $\max_{1\le s\le k}\rho_\alpha(G_s)=\max\{\rho_\alpha(G_1),\rho_\alpha(G_k)\}$. Moreover, for each fixed odd $b\ge 3$ and every even $n\ge N_b=(b+1)\max\{2b+3,14\}+2$, there exists a unique $\alpha=\alpha_\ast(n,b)\in(1/2,1)$ at which $\rho_\alpha(G_1)=\rho_\alpha(G_k)$. Consequently, $G_1$ is the unique extremal graph for $1/2<\alpha<\alpha_\ast(n,b)$, both $G_1$ and $G_k$ are extremal at $\alpha=\alpha_\ast(n,b)$, and $G_k$ is the unique extremal graph for $\alpha_\ast(n,b)<\alpha<1$. This gives the exact $A_\alpha$-spectral threshold, together with the sharp exceptional graphs, for odd $[1,b]$-factors when $\alpha>1/2$ and $n\ge N_b$.

math.CO↗

arXiv2026

On the Extremal Energy of Complex Unit Gain Dumbbell Graphs

We study the extremal energy problem for complex unit gain graphs whose underlying graph is the dumbbell graph $D_{r,s,\ell}$. Using switching equivalence, we reduce the spectrum to the real parts of the two cycle gains and obtain an explicit expression of the characteristic polynomial in terms of matching polynomials of natural subgraphs. For the bipartite case, we determine the extremal gain assignments by coefficient comparison. For the non-bipartite cases, we analyze the Coulson integral kernels. Finally, the maximum-energy conditions are determined in all cases, while the minimum-energy conditions are determined except when $r$, $s$, and $\ell$ are all odd. For this remaining case, we alternatively prove sign restrictions for any improvement over $(0,0)$, and prove a Hessian criterion at the origin, which provides a sufficient condition for $(0,0)$ to fail to be an energy minimizer.

math.CO↗

arXiv2026

New Bounds for the Spectral Radius and Low Energy of the $A_α$-Matrix of Digraphs

The $A_α$-matrix of a digraph $D$ is defined as a linear convex combination $α\operatorname{Deg}(D)+(1-α)A(D)$ of the adjacency matrix $A(D)$ and the diagonal out-degree matrix $\operatorname{Deg}(D)$, where $α\in[0,1]$. The low energy of $A_α(D)$ is defined as the sum of the absolute values of the real parts of the eigenvalues of $A_α(D)$. In this paper, we establish new upper bounds for the spectral radius of the $A_α$-matrix and derive two Koolen--Moulton type upper bounds for its low energy, together with characterizations of the equality cases. Numerical comparisons further show that these bounds can be sharper than existing bounds for certain digraph families. Furthermore, when $α=0$, our results recover several classical bounds, and in particular, the low-energy bounds generalizes the classical Koolen--Moulton bound.

math.CO↗

arXiv2025

Substructure Analysis and Cycle Enumeration Methods for Oriented Graphs Based on Parameterizing Hermitian Laplacian Matrices by Galois Conjugates

This paper investigates the principal minors of a parameterized Hermitian Laplacian matrix for oriented graphs. Particularly, we focus on the properties of the matrix for parameters chosen as Galois conjugates of a primitive $p$th root of unity, where $p$ is an odd prime. We demonstrate that under this condition, the product of the corresponding Hermitian Laplacian determinants is an integer power of $p$. This algebraic property forms the basis for a method to enumerate non-vanishing unicyclic graph components within certain substructures. The study is situated within a framework where a variable unit-modulus complex parameter is introduced into the Hermitian Laplacian matrix, which also allows for an examination of relationships among principal minors under different parameters. Our analysis adopts the concept of substructures, defined as vertex-edge pairs $(V',E')$ where edges in $E'$ are not restricted to connecting vertices within $V'$.

math.CO↗

arXiv2024

Generalize Polyp Segmentation via Inpainting across Diverse Backgrounds and Pseudo-Mask Refinement

Inpainting lesions within different normal backgrounds is a potential method of addressing the generalization problem, which is crucial for polyp segmentation models. However, seamlessly introducing polyps into complex endoscopic environments while simultaneously generating accurate pseudo-masks remains a challenge for current inpainting methods. To address these issues, we first leverage the pre-trained Stable Diffusion Inpaint and ControlNet, to introduce a robust generative model capable of inpainting polyps across different backgrounds. Secondly, we utilize the prior that synthetic polyps are confined to the inpainted region, to establish an inpainted region-guided pseudo-mask refinement network. We also propose a sample selection strategy that prioritizes well-aligned and hard synthetic cases for further model fine-tuning. Experiments demonstrate that our inpainting model outperformed baseline methods both qualitatively and quantitatively in inpainting quality. Moreover, our data augmentation strategy significantly enhances the performance of polyp segmentation models on external datasets, achieving or surpassing the level of fully supervised training benchmarks in that domain. Our code is available at https://github.com/497662892/PolypInpainter.

cs.CV↗

arXiv2024

ECC-PolypDet: Enhanced CenterNet with Contrastive Learning for Automatic Polyp Detection

Accurate polyp detection is critical for early colorectal cancer diagnosis. Although remarkable progress has been achieved in recent years, the complex colon environment and concealed polyps with unclear boundaries still pose severe challenges in this area. Existing methods either involve computationally expensive context aggregation or lack prior modeling of polyps, resulting in poor performance in challenging cases. In this paper, we propose the Enhanced CenterNet with Contrastive Learning (ECC-PolypDet), a two-stage training \& end-to-end inference framework that leverages images and bounding box annotations to train a general model and fine-tune it based on the inference score to obtain a final robust model. Specifically, we conduct Box-assisted Contrastive Learning (BCL) during training to minimize the intra-class difference and maximize the inter-class difference between foreground polyps and backgrounds, enabling our model to capture concealed polyps. Moreover, to enhance the recognition of small polyps, we design the Semantic Flow-guided Feature Pyramid Network (SFFPN) to aggregate multi-scale features and the Heatmap Propagation (HP) module to boost the model's attention on polyp targets. In the fine-tuning stage, we introduce the IoU-guided Sample Re-weighting (ISR) mechanism to prioritize hard samples by adaptively adjusting the loss weight for each sample during fine-tuning. Extensive experiments on six large-scale colonoscopy datasets demonstrate the superiority of our model compared with previous state-of-the-art detectors.

cs.CV↗