arXiv subjects

Yongbin Gao

Publications and source records attributed to Yongbin Gao.

9 recordsLinked to original sources

arXiv2026

Spectral radius conditions for edge-disjoint spanning trees in $(k+c)$-edge-connected graphs

Let $τ(G)$ denote the spanning tree packing number of a graph $G$. Recently, Zhang and Fan [J. Graph Theory 112 (2) (2026) 128--144] posed the problem of finding a tight spectral radius condition for an $m$-edge-connected graph $G$ to guarantee $τ(G)\ge k$ for $k+1\le m\le 2k-1$. They solved the cases $m=k$ and $k=2, m=3$. In this paper, we study this problem for all $m=k+c$, where $1\le c\le k-1$. For $1\le c\le k-2$, we obtain a tight spectral radius condition for a $(k+c)$-edge-connected graph to contain $k$ edge-disjoint spanning trees. We also obtain a tight spectral radius condition for $(2k-1)$-edge-connected graphs. In both cases, we give graph families containing all extremal graphs, and the graphs with maximum spectral radius in these families serve as the corresponding extremal graphs. Each graph in these families consists of a large clique and a small remaining part, with certain restrictions on the edges inside the small part and between the two parts. Moreover, for the case $m=k+1$, we further determine the unique extremal graph.

math.CO↗

arXiv2026

Laplacian eigenvalue conditions for edge-disjoint spanning trees and a forest with constraints

Let $k$ be a positive integer and let $G$ be a simple graph of order $n$ with minimum degree $δ$. A graph $G$ is said to have property $P(k, d)$ if it contains $k$ edge-disjoint spanning trees and an additional forest $F$ with edge number $|E(F)| > \frac{d-1}{d}(|V(G)| - 1)$, such that if $F$ is not a spanning tree, then $F$ has a component with at least $d$ edges. Let $D(G)$ be the degree diagonal matrix of $G$. We denote $λ_i$ and $μ_i$ as the $i$th largest eigenvalue of the adjacency matrix $A(G)$ of $G$ and the Laplacian matrix $L(G) = D(G) - A(G)$ of $G$ for $i = 1, 2, \ldots, n$, respectively. In this paper, we investigate the relationship between Laplacian eigenvalues and property $P(k, δ)$. Let $t$ be a positive integer, and define $\mathcal{G}_t$ as the set of simple graphs such that each $G \in \mathcal{G}_t$ contains at least $t+1$ non-empty disjoint proper subsets $V_1, V_2, \ldots, V_{t+1}$ satisfying $V(G) \setminus \bigcup_{i=1}^{t+1} V_i \neq \emptyset$ and edge connectivity $κ'(G) = e(V_i, V(G) \setminus V_i)$ for any $i = 1, 2, \ldots, t+1$. For the class of graphs $\mathcal{G}_1$ with minimum degree $δ$, we provide a sufficient condition involving the third smallest Laplacian eigenvalue $μ_{n-2}(G)$ for a graph $G\in \mathcal{G}_1$ to have property $P(k, δ)$. Similarly, for the class of graphs $\mathcal{G}_2$ with minimum degree $δ$, we establish a corresponding sufficient condition involving the fourth smallest Laplacian eigenvalue $μ_{n-3}(G)$ for a graph $G\in \mathcal{G}_2$ to have property $P(k, δ)$. Furthermore, we extend the spectral conditions for all the results about $μ_{n-2}(G)$, $μ_{n-3}(G)$ and $λ_2(G)$ to the general graph matrices $aD(G) + A(G)$ and $aD(G) + bA(G)$.

math.CO↗

arXiv2026

Distance spectral radius conditions for edge-disjoint spanning trees and a forest with constraints

Let $k\ge 2$ be a positive integer and let $G$ be a simple graph of order $n$ with minimum degree $δ$. A graph $G$ is said to have property $P(k, d)$ if it contains $k$ edge-disjoint spanning trees and an additional forest $F$ with edge number $|E(F)| > \frac{d-1}{d}(n-1)$, such that if $F$ is not a spanning tree, then $F$ has a component with at least $d$ edges. Let $D(G)$ be the distance matrix of $G$. We denote $ρ_D(G)$ as the largest eigenvalue of $D(G)$, which is called the distance spectral radius of $G$. In this paper, we investigate the relationship between the distance spectral radius and the property $P(k, δ)$. We prove that for a connected graph $G$ of order $n \ge 2k+8$ with minimum degree $δ\ge k+2$, if $ρ_D(G) \le ρ_D(K_{k-1} \vee (K_{n-k} \cup K_1))$, then $G$ possesses property $P(k, δ)$. Furthermore, for a connected balanced bipartite graph $G$ of order $n \ge 4k+8$ with minimum degree $δ\ge k+2$, we show that if $ρ_D(G) \le ρ_D(K_{\frac{n}{2}, \frac{n}{2}} \setminus E(K_{1, \frac{n}{2}-k+1}))$, then $G$ also possesses property $P(k, δ)$. Our results generalize the work of Fan et al. [Discrete Appl. Math. 376 (2025), 31--40] from the existence of $k$ edge-disjoint spanning trees to the more refined structural property $P(k, δ)$.

math.CO↗

arXiv2025

Through-the-Earth Magnetic Induction Communication and Networking: A Comprehensive Survey

Magnetic induction (MI) communication (MIC) has emerged as a promising candidate for underground communication networks due to its excellent penetration capabilities. Integration with Space-Air-Ground-Underground (SAGUI) networks in next-generation mobile communication systems requires a well-defined network architecture. A recent discovery in MIC research, MI fast fading, remains in its early stages and presents unique challenges. This paper provides a comprehensive survey on through-the-earth (TTE) MIC, covering MI applications, channel modeling, point-to-point MIC design, relay techniques, network frameworks, and emerging technologies. We compare various MIC applications to highlight TTE-specific challenges and review the principles of channel modeling, addressing both MI slow fading and MI fast fading, along with its potential impact on existing MIC theories. We conduct a fine-grained decomposition of MI channel power gain into four distinct physical parameters, and propose a novel geometric model to analyze MI fast fading. We also summarize MI relay techniques, examine crosstalk effects in relay and high-density networks, and explore key research tasks within the OSI framework for a holistic MI network protocol in SAGUI. To bridge the gaps identified, we propose a MIC framework that supports TCP/IP and Linux, enabling full implementation of existing and emerging MIC solutions. This framework empowers researchers to leverage Linux resources and deep learning platforms for accelerated development of MIC in SAGUI networks. Remaining research challenges, open issues, and promising novel techniques are further identified to advance MIC research.

eess.SY↗

arXiv2024

CrackSegDiff: Diffusion Probability Model-based Multi-modal Crack Segmentation

Integrating grayscale and depth data in road inspection robots could enhance the accuracy, reliability, and comprehensiveness of road condition assessments, leading to improved maintenance strategies and safer infrastructure. However, these data sources are often compromised by significant background noise from the pavement. Recent advancements in Diffusion Probabilistic Models (DPM) have demonstrated remarkable success in image segmentation tasks, showcasing potent denoising capabilities, as evidenced in studies like SegDiff. Despite these advancements, current DPM-based segmentors do not fully capitalize on the potential of original image data. In this paper, we propose a novel DPM-based approach for crack segmentation, named CrackSegDiff, which uniquely fuses grayscale and range/depth images. This method enhances the reverse diffusion process by intensifying the interaction between local feature extraction via DPM and global feature extraction. Unlike traditional methods that utilize Transformers for global features, our approach employs Vm-unet to efficiently capture long-range information of the original data. The integration of features is further refined through two innovative modules: the Channel Fusion Module (CFM) and the Shallow Feature Compensation Module (SFCM). Our experimental evaluation on the three-class crack image segmentation tasks within the FIND dataset demonstrates that CrackSegDiff outperforms state-of-the-art methods, particularly excelling in the detection of shallow cracks. Code is available at https://github.com/sky-visionX/CrackSegDiff.

cs.CV↗

arXiv2024

Fast-Fading Channel and Power Optimization of the Magnetic Inductive Cellular Network

The cellular network of magnetic Induction (MI) communication holds promise in long-distance underground environments. In the traditional MI communication, there is no fast-fading channel since the MI channel is treated as a quasi-static channel. However, for the vehicle (mobile) MI (VMI) communication, the unpredictable antenna vibration brings the remarkable fast-fading. As such fast-fading cannot be modeled by the central limit theorem, it differs radically from other wireless fast-fading channels. Unfortunately, few studies focus on this phenomenon. In this paper, using a novel space modeling based on the electromagnetic field theorem, we propose a 3-dimension model of the VMI antenna vibration. By proposing ``conjugate pseudo-piecewise functions'' and boundary $p(x)$ distribution, we derive the cumulative distribution function (CDF), probability density function (PDF) and the expectation of the VMI fast-fading channel. We also theoretically analyze the effects of the VMI fast-fading on the network throughput, including the VMI outage probability which can be ignored in the traditional MI channel study. We draw several intriguing conclusions different from those in wireless fast-fading studies. For instance, the fast-fading brings more uniformly distributed channel coefficients. Finally, we propose the power control algorithm using the non-cooperative game and multiagent Q-learning methods to optimize the throughput of the cellular VMI network. Simulations validate the derivation and the proposed algorithm.

eess.SP↗

arXiv2024

Towards Few-shot Out-of-Distribution Detection

Out-of-distribution (OOD) detection is critical for ensuring the reliability of open-world intelligent systems. Despite the notable advancements in existing OOD detection methodologies, our study identifies a significant performance drop under the scarcity of training samples. In this context, we introduce a novel few-shot OOD detection benchmark, carefully constructed to address this gap. Our empirical analysis reveals the superiority of ParameterEfficient Fine-Tuning (PEFT) strategies, such as visual prompt tuning and visual adapter tuning, over conventional techniques, including fully fine-tuning and linear probing tuning in the few-shot OOD detection task. Recognizing some crucial information from the pre-trained model, which is pivotal for OOD detection, may be lost during the fine-tuning process, we propose a method termed DomainSpecific and General Knowledge Fusion (DSGF). This approach is designed to be compatible with diverse fine-tuning frameworks. Our experiments show that the integration of DSGF significantly enhances the few-shot OOD detection capabilities across various methods and fine-tuning methodologies, including fully fine-tuning, visual adapter tuning, and visual prompt tuning. The code will be released.

cs.CV↗

arXiv2018

A Wasserstein GAN model with the total variational regularization

It is well known that the generative adversarial nets (GANs) are remarkably difficult to train. The recently proposed Wasserstein GAN (WGAN) creates principled research directions towards addressing these issues. But we found in practice that gradient penalty WGANs (GP-WGANs) still suffer from training instability. In this paper, we combine a Total Variational (TV) regularizing term into the WGAN formulation instead of weight clipping or gradient penalty, which implies that the Lipschitz constraint is enforced on the critic network. Our proposed method is more stable at training than GP-WGANs and works well across varied GAN architectures. We also present a method to control the trade-off between image diversity and visual quality. It does not bring any computation burden.

cs.CV↗

arXiv2018

An Image dehazing approach based on the airlight field estimation

This paper proposes a scheme for single image haze removal based on the airlight field (ALF) estimation. Conventional image dehazing methods which are based on a physical model generally take the global atmospheric light as a constant. However, the constant-airlight assumption may be unsuitable for images with large sky regions, which causes unacceptable brightness imbalance and color distortion in recovery images. This paper models the atmospheric light as a field function, and presents a maximum a-priori (MAP) method for jointly estimating the airlight field, the transmission rate and the haze free image. We also introduce a valid haze-level prior for effective estimate of transmission. Evaluation on real world images shows that the proposed approach outperforms existing methods in single image dehazing, especially when the large sky region is included.

cs.CV↗