arXiv subjects

Shujie Chen

Publications and source records attributed to Shujie Chen.

7 recordsLinked to original sources

arXiv2026

Sufficient conditions for $(K_2 \cup kK_1)$-free graphs to be Hamilton-connected

The toughness of a non-complete graph $G$, denoted $\tau(G)$, is defined as \[ \tau(G) = \min\left\{ \frac{|S|}{\omega(G-S)} : S \subseteq V(G),\ \omega(G-S) \geq 2 \right\}, \] where $\omega(G-S)$ is the number of components of $G - S$. For a complete graph $G$, we define $\tau(G) = \infty$. A graph $G$ is $t$-tough if $\tau(G) \geq t$. For a positive integer $k$, a graph $G$ is $(K_2 \cup kK_1)$-free if it contains no induced subgraph isomorphic to $K_2 \cup kK_1$. Recently, Liu \cite{liu} showed that every $2k$-connected $(K_2 \cup kK_1)$-free graph $G$ with $\tau(G) > 1$ is Hamilton-connected. In this paper, we strengthen this result by proving that every $(k+1)$-connected $(K_2 \cup kK_1)$-free graph $G$ with $\tau(G) > 1$ and minimum degree $\delta(G) \geq 2k$ is Hamilton-connected. Moreover, by imposing restrictions to the independence number $\alpha(G)$, we prove that every $k$-connected $(K_2 \cup kK_1)$-free graph $G$ of order $n$ with $2k+1 \leq \alpha(G) < \frac{n}{2}$ and $\delta(G) \geq 2k$ is Hamilton-connected, and that the bounds on $\alpha(G)$ are sharp.

math.CO↗

arXiv2026

Extremal problems on disjoint path covers of graphs

In 1962, Erd\H{o}s characterized the maximum size of nonhamiltonian graphs of order $n$ with minimum degree at least $k$. Later, Ning and Peng [Combin. Probab. Comput. 29 (2020) 128-136] extended Erd\H{o}s's results to the clique condition and provided the maximum clique number for nonhamiltonian graphs of order $n$ with minimum degree at least $k$. Recently, Zhang [European J. Combin. 112 (2023) 103728] determined the maximum number of $s$-cliques in nonhamiltonian graphs with prescribed order and minimum degree. A natural extension is to characterize the maximum number of $s$-cliques under other graph properties. Notably, disjoint path cover problems are closely related to Hamiltonicity. In this paper, we generalize results on Hamiltonicity and establish sufficient conditions for a graph to possess one-to-one, one-to-many and many-to-many $t$-disjoint path covers in terms of the number of cliques and the $\alpha$-spectral radius, respectively. Furthermore, we characterize the extremal graphs that attain these bounds respectively.

math.CO↗

arXiv2025

EDFFDNet: Towards Accurate and Efficient Unsupervised Multi-Grid Image Registration

Previous deep image registration methods that employ single homography, multi-grid homography, or thin-plate spline often struggle with real scenes containing depth disparities due to their inherent limitations. To address this, we propose an Exponential-Decay Free-Form Deformation Network (EDFFDNet), which employs free-form deformation with an exponential-decay basis function. This design achieves higher efficiency and performs well in scenes with depth disparities, benefiting from its inherent locality. We also introduce an Adaptive Sparse Motion Aggregator (ASMA), which replaces the MLP motion aggregator used in previous methods. By transforming dense interactions into sparse ones, ASMA reduces parameters and improves accuracy. Additionally, we propose a progressive correlation refinement strategy that leverages global-local correlation patterns for coarse-to-fine motion estimation, further enhancing efficiency and accuracy. Experiments demonstrate that EDFFDNet reduces parameters, memory, and total runtime by 70.5%, 32.6%, and 33.7%, respectively, while achieving a 0.5 dB PSNR gain over the state-of-the-art method. With an additional local refinement stage,EDFFDNet-2 further improves PSNR by 1.06 dB while maintaining lower computational costs. Our method also demonstrates strong generalization ability across datasets, outperforming previous deep learning methods.

cs.CV↗

arXiv2024

SSHNet: Unsupervised Cross-modal Homography Estimation via Problem Reformulation and Split Optimization

We propose a novel unsupervised cross-modal homography estimation learning framework, named Split Supervised Homography estimation Network (SSHNet). SSHNet reformulates the unsupervised cross-modal homography estimation into two supervised sub-problems, each addressed by its specialized network: a homography estimation network and a modality transfer network. To realize stable training, we introduce an effective split optimization strategy to train each network separately within its respective sub-problem. We also formulate an extra homography feature space supervision to enhance feature consistency, further boosting the estimation accuracy. Moreover, we employ a simple yet effective distillation training technique to reduce model parameters and improve cross-domain generalization ability while maintaining comparable performance. The training stability of SSHNet enables its cooperation with various homography estimation architectures. Experiments reveal that the SSHNet using IHN as homography estimation network, namely SSHNet-IHN, outperforms previous unsupervised approaches by a significant margin. Even compared to supervised approaches MHN and LocalTrans, SSHNet-IHN achieves 47.4% and 85.8% mean average corner errors (MACEs) reduction on the challenging OPT-SAR dataset.

cs.CV↗

arXiv2024

Representation Alignment Contrastive Regularization for Multi-Object Tracking

Achieving high-performance in multi-object tracking algorithms heavily relies on modeling spatio-temporal relationships during the data association stage. Mainstream approaches encompass rule-based and deep learning-based methods for spatio-temporal relationship modeling. While the former relies on physical motion laws, offering wider applicability but yielding suboptimal results for complex object movements, the latter, though achieving high-performance, lacks interpretability and involves complex module designs. This work aims to simplify deep learning-based spatio-temporal relationship models and introduce interpretability into features for data association. Specifically, a lightweight single-layer transformer encoder is utilized to model spatio-temporal relationships. To make features more interpretative, two contrastive regularization losses based on representation alignment are proposed, derived from spatio-temporal consistency rules. By applying weighted summation to affinity matrices, the aligned features can seamlessly integrate into the data association stage of the original tracking workflow. Experimental results showcase that our model enhances the majority of existing tracking networks' performance without excessive complexity, with minimal increase in training overhead and nearly negligible computational and storage costs.

cs.CV↗

arXiv2022

Hierarchical Contrast for Unsupervised Skeleton-based Action Representation Learning

This paper targets unsupervised skeleton-based action representation learning and proposes a new Hierarchical Contrast (HiCo) framework. Different from the existing contrastive-based solutions that typically represent an input skeleton sequence into instance-level features and perform contrast holistically, our proposed HiCo represents the input into multiple-level features and performs contrast in a hierarchical manner. Specifically, given a human skeleton sequence, we represent it into multiple feature vectors of different granularities from both temporal and spatial domains via sequence-to-sequence (S2S) encoders and unified downsampling modules. Besides, the hierarchical contrast is conducted in terms of four levels: instance level, domain level, clip level, and part level. Moreover, HiCo is orthogonal to the S2S encoder, which allows us to flexibly embrace state-of-the-art S2S encoders. Extensive experiments on four datasets, i.e., NTU-60, NTU-120, PKU-MMD I and II, show that HiCo achieves a new state-of-the-art for unsupervised skeleton-based action representation learning in two downstream tasks including action recognition and retrieval, and its learned action representation is of good transferability. Besides, we also show that our framework is effective for semi-supervised skeleton-based action recognition. Our code is available at https://github.com/HuiGuanLab/HiCo.

cs.CV↗

arXiv2016

Dynamical properties of the Rabi model

We study the dynamical properties of the quantum Rabi model within a systematic expansion method. Based on the observation that the parity symmetry of the Rabi model is kept during the evolution of the states, we decompose the initial state and the time-dependent one into a part of a positive and a negative parity expanded by the superposition of the coherent states. The evolutions for the corresponding positive and the negative parity are obtained, where the expansion coefficients in the dynamical equations are known from the recurrence relation derived.

quant-ph↗