arXiv subjects

Xiumei Wang

Publications and source records attributed to Xiumei Wang.

At least 19 recordsLinked to original sources

arXiv2026

On graphs with $1$-matching and $2$-matching edges

Let $G$ be a graph admitting a perfect matching. An edge is called a {\it $k$-matching edge} if it belongs to exactly $k$ perfect matchings, and a {\it $k^{+}$-matching edge} if it belongs to at least $k$ perfect matchings. Thus, {\it an admissible edge} is a $1^{+}$-matching edge, and a connected graph is {\it matching covered} if every edge is admissible. We call a connected graph {\it $k$-matching covered} if every edge is a $k$-matching edge; in particular, a $2$-matching covered graph is called {\it matching double covered}. Motivated by matching-covered graph theory and the Berge--Fulkerson conjecture (1970s), we introduce the class $\mathfrak{B}$ of connected graphs in which every edge is either a $1$-matching edge or a $2$-matching edge, and no perfect matching contains edges of both types. In particular, every matching double covered graph belongs to $\mathfrak{B}$. Using ear decompositions and tight-cut decompositions, we establish a complete structural characterization of graphs in $\mathfrak{B}$. These characterizations reveal how restrictions on the number of perfect matchings containing each edge determine the global structure of the corresponding matching-covered graphs.

math.CO↗

arXiv2026

Identifying Topological Invariants of Non-Hermitian Systems via Domain-Adaptive Multimodal Model for Mathematics

Identifying topological invariants are endowed with profound physical connotations in the fields of condensed matter physics. However, they are often limited by the failure of standard theorems and high computational costs. Traditional machine learning methods typically treat this problem as a black-box regression, which fails to learn the underlying mathematical structures of lattices. To this end, we propose a straightforward yet powerful multimodal model that fundamentally improves topological invariants discovery through two key methodological innovations. First, instead of feeding raw data into a standard network, our model introduces a dual-track alignment mechanism. This mechanism treats eigenvalues as context sequences and eigenvectors as matrix structures, enabling the model to naturally capture the interrelated algebraic and geometric properties of topological states. Second, to resolve the common problem where deep learning models make numerical mistakes in exact mathematical calculations, we use a tool-integrated reasoning paradigm. Within this paradigm, the neural network acts as a logical controller to calculate discrete topological indices. This design eliminates the uncertainty of deep learning, ensuring zero-error calculations from continuous physical data. We demonstrate that our model can accurately reconstruct complex three-dimensional generalized Brillouin zones and achieve 97% accuracy in calculating non-Bloch Chern numbers in long-range transition systems. By combining the flexible logic of multimodal artificial intelligence with the rigorous precision of symbolic computation, this work provides a reliable and highly versatile tool for exploring exotic topological phases.

cond-mat.other↗

arXiv2026

Inference-Time Scaling for Visual AutoRegressive modeling by Searching Representative Samples

While inference-time scaling has significantly enhanced generative quality in large language and diffusion models, its application to vector-quantized (VQ) visual autoregressive modeling (VAR) remains unexplored. We introduce VAR-Scaling, the first general framework for inference-time scaling in VAR, addressing the critical challenge of discrete latent spaces that prohibit continuous path search. We find that VAR scales exhibit two distinct pattern types: general patterns and specific patterns, where later-stage specific patterns conditionally optimize early-stage general patterns. To overcome the discrete latent space barrier in VQ models, we map sampling spaces to quasi-continuous feature spaces via kernel density estimation (KDE), where high-density samples approximate stable, high-quality solutions. This transformation enables effective navigation of sampling distributions. We propose a density-adaptive hybrid sampling strategy: Top-k sampling focuses on high-density regions to preserve quality near distribution modes, while Random-k sampling explores low-density areas to maintain diversity and prevent premature convergence. Consequently, VAR-Scaling optimizes sample fidelity at critical scales to enhance output quality. Experiments in class-conditional and text-to-image evaluations demonstrate significant improvements in inference process. The code is available at https://github.com/WD7ang/VAR-Scaling.

cs.CV↗

arXiv2025

The spectral radii and extremal graphs of two types of minimal graphs

A connected nontrivial graph $G$ is {\it matching covered} if every edge of $G$ is contained in some perfect matching of $G$. A matching covered graph $G$ is {\it minimal} if $G-e$ is not matching covered for each edge $e$ of $G$. A graph is said to be {\it factor-critical} if $G-v$ has a perfect matching for every $v\in V(G)$. A factor-critical graph $G$ is said to be {\it minimal factor-critical} if $G-e$ is not factor-critical graph for each edge $e\in E(G)$. In this paper, by employing ear decomposition and edge-exchange techniques, the greatest spectral radii of minimal matching covered bipartite graphs and minimal factor-critical graphs are determined, and the corresponding extremal graphs are characterized.

math.CO↗

arXiv2025

Claw-free bricks that every $b$-invariant edge is solitary

A graph $G$ is a brick if it is 3-connected and $G-\{u,v\}$ has a perfect matching for any two distinct vertices $u$ and $v$ of $G$. Lucchesi and Murty proposed a problem concerning the characterization of bricks, distinct from $K_4$, $\overline{C_6}$ and the Petersen graph, in which every $b$-invariant edge is solitary. In this paper, we present a characterization of this problem when the bricks are claw-free.

math.CO↗

arXiv2025

Waveguiding in two-dimensional Floquet non-Abelian topological insulators

Topological phases characterized by non-Abelian charges have garnered increasing attention recently. Although Floquet (periodic-driving) higher-order topological phases have been explored at the single-particle level, the role of interactions in non-Abelian topological insulators with multiple entangled energy gaps remains incompletely understood. In this work, we extend previous research by investigating higher-order topological phases featuring non-Abelian charges through Floquet engineering. Here we construct a model for two-dimensional non-Abelian higher-order topological phases on a square lattice subjected to two-step periodic driving. We find that the corner and edge states emerge and appear in all energy gaps despite the quaternion charge being trivial. Moreover, spatially exchanging the driving generates exotic interface modes-a hallmark of non-Abelian dynamics, namely non-commutativity. Notably, the non-zero composite Chern number demonstrates the non-triviality of the Floquet non-Abelian system with. We further reveal that the configuration of these quaternion-charge edge states is entirely determined by the quadruple degenerate phase-band singularities in the time evolution. Our work provides a platform for studying higher-order topological states and non-equilibrium quantum dynamics.

cond-mat.mes-hall↗

arXiv2025

Three-period evolution in a photonic Floquet extended Su-Schrieffer-Heeger waveguide array

Periodic driving can induce the emergence of topological pi modes, and their superposition with zero modes leads to two-period dynamics. Introducing long-range couplings enables the realization of larger topological winding numbers, which correspond to multiple pairs of degenerate edge states under open boundary conditions. In this work, we construct a Floquet extended Su-Schrieffer-Heeger (SSH) model by introducing a two-step periodic driving and next-nearest-neighbor coupling into the static SSH chain simultaneously. Remarkably, we identify anomalous edge states with quasienergies -+pi/3T and -+2pi/3T. In order to reveal the dynamical features of these anomalous edge states, we elaborately adjust the optical parameters and ultimately achieve a successful mapping of the model onto a photonic waveguide array. Subsequently, through numerical simulation of the wave equation, we observe the unique behavior of three-period evolution. Our work may serve as a reference for realizing period-multiplied dynamics, and the anomalous edge states discussed here might also find applications in quantum computation.

physics.optics↗

arXiv2025

Low-Energy Boundary-State Emergence and Delocalization in Finite-sized Mosaic Wannier-Stark Lattices

The mosaic Wannier Stark lattice has gained increasing prominence as a disorder free system exhibiting unconventional localization behavior induced by spatially periodic Stark potentials. In the infinite size limit, exact spectral analysis reveals an almost pure point spectrum. There is no true mobility edge, except for (M 1) isolated extended states, which are accompanied by weakly localized modes with diverging localization lengths. Motivated by this spectral structure, we investigate the mosaic Wannier Stark model under finite-size. In such systems, additional low energy boundary localized states emerge due to boundary residuals when the system length is not commensurate with the modulation period. These states are effectively distinguished and identified using the inverse participation ratio (IPR) and spatial expectation values. To explore their response to non-Hermitian perturbations, complex on site potentials are introduced to simulate gain and loss. As the non-Hermitian strength increases, only the weakly localized states undergo progressive delocalization, exhibiting a smooth crossover from localization to spatial extension.

cond-mat.other↗

arXiv2025

Amortized Clustering Assistant Classification of Anomalous Hybrid Floquet Modes in a Periodically Driven non-Hermitian Lattice

The interplay between Floquet periodically driving and non-Hermiticity could bring about intriguing novel phenomena with anomalous Floquet topological phases of a finite-size, tight-binding lattice model. How to efficiently investigate on quasi-energy and eigenfield of a non-Hermitian Floquet system with complicated driving protocol remains a challenging task. In this work, we define a somewhat complex driving protocol for a bipartite lattice system and discover two nontrivial topological phases that support Floquet {\pi} mode. Thereafter, we introduce unsupervised learning method in order to explore distribution features of system eigenfunctions under different magnitude of system energy gain/loss. We utilize the idea of amortized clustering and construct an algorithm selector that could dynamically upgrade with increasing gain/loss as input parameter. Proper employment of the selector enables us to reveal the regulation of dynamic localization from abundant possible wave function distribution in two-dimension lattice in another efficient way. In addition, our work provides a feasible methodology via machine learning method to assist in classification of Floquet modes.

cond-mat.other↗

arXiv2025

Solid bricks that every $b$-invariant edge is solitary

A graph $G$ is a brick if it is 3-connected and $G-\{u,v\}$ has a perfect matching for any two distinct vertices $u$ and $v$ of $G$. A brick $G$ is solid if for any two vertex disjoint odd cycles $C_1$ and $C_2$ of $G$, $G-(V(C_1)\cup V(C_2))$ has no perfect matching. Lucchesi and Murty proposed a problem concerning the characterization of bricks, distinct from $K_4$, $\overline{C_6}$ and the Petersen graph, in which every $b$-invariant edge is solitary. In this paper, we show that for a solid brick $G$ of order $n$ that is distinct from $K_4$, every $b$-invariant edge of $G$ is solitary if and only if $G$ is a wheel $W_n$.

math.CO↗

arXiv2025

A Composable Multimodal Framework for cine CMR-Text-Driven Prediction of Heart Failure Outcomes

Objective. Heart failure is one of the leading causes of death worldwide, with millions of deaths each year, according to data from the World Health Organization (WHO) and other public health agencies. While significant progress has been made in the field of heart failure, leading to improved survival rates and improvement of ejection fraction, there remains substantial unmet needs, due to the complexity and multifactorial characteristics. This study aims to propose and evaluate a composable strategy framework for assessment and treatment optimization in heart failure, designed to provide more holistic patient evaluation and management. Approach. The framework leverages multi-modal algorithms to analyze a comprehensive range of patient data, explicitly integrating cine cardiac magnetic resonance (cine CMR) sequences, structured clinical metrics (e.g., lab results, demographics), and unstructured textual records (e.g., medical history, prescriptions). By integrating these various data sources, our framework offers a more holistic evaluation and optimized treatment plan for patients. Main results. The multi-modal framework demonstrates superior accuracy in HF prognosis prediction compared to single-modal AI algorithms. Additionally, it enables a detailed evaluation of the impact of various pathological indicators on HF outcomes. Significance. By integrating heterogeneous clinical data in a systematic manner, this approach supports more comprehensive prognosis assessment and facilitates optimized, personalized treatment planning for heart failure patients.

cs.LG↗

arXiv2025

Exact solution of the relationship between the eigenvalue discreteness and the behavior of eigenstates in Su-Schrieffer-Heeger lattices

Eigenstate localization and bulk-boundary correspondence are fundamental phenomena in one-dimensional (1D) Su-Schrieffer-Heeger (SSH) lattices. The eigenvalues discreteness and the eigenstates localization exhibit a high degree of consistency as system information evolve. We explore the relationship between the eigenvalue discreteness and the eigenstates behavior in 1D SSH lattices. The discreteness fraction and the inverse participation ratio (IPR) combined with a Taylor expansion are utilized to describe the relationship. In the Hermitian case, we employ the bulk-edge correspondence and the perturbation theory to derive an exact solution considering both zero and non-zero modes. We also extend our analysis to the non-Hermitian cases, assuming that eigenvalues remain purely real. Our findings reveal a logarithmic relationship between the degree of eigenvalue discreteness and eigenstates localization, which holds under both the Hermitian and non-Hermitian conditions. This result is fully consistent with the theoretical predictions.

cond-mat.other↗

arXiv2024

Self-Attention Assistant Classification of Non-Hermitian Phases in Two-Dimensional Lattice

Classification of the non-Hermitian phases in high-dimensional lattice becomes challenging due to interplay of the band topology and non-Hermiticity. The significant increase in data dimensions and the number of categories has rendered traditional supervised learning and unsupervised manifold learning failed. Here, we propose the self-attention assistant machine learning for clustering non-Hermitian phases in two-dimensional lattice. By incorporating the self-attention mechanism, the model can effectively capture long-range dependencies and important patterns, resulting in a more compact and information-rich latent space. It can achieve Altland-Zirnbauer classification with Bloch vector dataset and distinguish the phases of eigenstates' localized behavior with the competition between non-Hermitian skin effect and topological localization. Our results provide a general method for characterizing non-Hermitian phases in two-dimensional lattice via machine learning.

cond-mat.other↗

arXiv2024

Self-Reasoning Assistant Learning for non-Abelian Gauge Fields Design

Non-Abelian braiding has attracted substantial attention because of its pivotal role in describing the exchange behaviour of anyons, in which the input and outcome of non-Abelian braiding are connected by a unitary matrix. Implementing braiding in a classical system can assist the experimental investigation of non-Abelian physics. However, the design of non-Abelian gauge fields faces numerous challenges stemmed from the intricate interplay of group structures, Lie algebra properties, representation theory, topology, and symmetry breaking. The extreme diversity makes it a powerful tool for the study of condensed matter physics. Whereas the widely used artificial intelligence with data-driven approaches has greatly promoted the development of physics, most works are limited on the data-to-data design. Here we propose a self-reasoning assistant learning framework capable of directly generating non-Abelian gauge fields. This framework utilizes the forward diffusion process to capture and reproduce the complex patterns and details inherent in the target distribution through continuous transformation. Then the reverse diffusion process is used to make the generated data closer to the distribution of the original situation. Thus, it owns strong self-reasoning capabilities, allowing to automatically discover the feature representation and capture more subtle relationships from the dataset. Moreover, the self-reasoning eliminates the need for manual feature engineering and simplifies the process of model building. Our framework offers a disruptive paradigm shift to parse complex physical processes, automatically uncovering patterns from massive datasets.

cs.LG↗

arXiv2024

Composable Generation Strategy Framework Enabled Bidirectional Design on Topological Circuits

Topological insulators show important properties, such as topological phase transitions and topological edge states. Although these properties and phenomena can be simulated by well-designed circuits, it is undoubtedly difficult to design such topological circuits due to the complex physical principles and calculations involved. Therefore, achieving a framework that can automatically to complete bidirectional design of topology circuits is very significant. Here, we propose an effective bidirectional collaborative design framework with strong task adaptability, which can automatically generate specific results according to our requirements. In the framework, a composable generation strategy is employed, which involves building a shared multimodal space by bridging alignment in the diffusion process. For simplicity, a series of two-dimensional (2D) Su-Schrieffer-Heeger (SSH) circuits are constructed with different structural parameters. The framework at first is applied to find the relationship between the structural information and topological features. Then, the correctness of the results through experimental measurements can be verified by the automatically generated circuit diagram following the manufacture of Printed Circuit Board (PCB). The framework is demonstrated by achieving good results in the reverse design of circuit structures and forward prediction of topological edge states, reaching an accuracy of 94%. Overall, our research demonstrates the enormous potential of the proposed bidirectional deep learning framework in complex tasks and provides insights for collaborative design tasks.

physics.app-ph↗

arXiv2024

Observation of Klein bottle quadrupole topological insulators in electric circuits

The Klein bottle Benalcazar-Bernevig-Hughes (BBH) insulator phase plays a pivotal role in understanding higher-order topological phases. The insulator phase is characterized by a unique feature: a nonsymmorphic glide symmetry that exists within momentum space, rather than real space. This characteristic transforms the Brillouin zone's fundamental domain into a structure of Klein bottle. Here, we report an observation of a Klein bottle topoelectrical model under gauge fields. To provide a comprehensive understanding of the different corner distributions of odd and even unit cells, we present theoretical calculations and demonstrate that the symmetry properties significantly affect the topological nature. These theoretical predictions are confirmed by experimental results, which demonstrate the practical feasibility of such topological configurations in electronic circuits. Our work establishes a vital connection between the realms of condensed matter physics and circuit systems, thereby paving a pathway for investigating exotic condensed matter physics.

cond-mat.mes-hall↗

arXiv2024

Removable edges in near-bipartite bricks

An edge $e$ of a matching covered graph $G$ is removable if $G-e$ is also matching covered. The notion of removable edge arises in connection with ear decompositions of matching covered graphs introduced by Lovász and Plummer. A nonbipartite matching covered graph $G$ is a brick if it is free of nontrivial tight cuts. Carvalho, Lucchesi, and Murty proved that every brick other than $K_4$ and $\overline{C_6}$ has at least $Δ-2$ removable edges. A brick $G$ is near-bipartite if it has a pair of edges $\{e_1,e_2\}$ such that $G-\{e_1,e_2\}$ is a bipartite matching covered graph. In this paper, we show that in a near-bipartite brick $G$ with at least six vertices, every vertex of $G$, except at most six vertices of degree three contained in two disjoint triangles, is incident with at most two nonremovable edges; consequently, $G$ has at least $\frac{|V(G)|-6}{2}$ removable edges. Moreover, all graphs attaining this lower bound are characterized.

math.CO↗

arXiv2024

Claw-free minimal matching covered graphs

A matching covered graph $G$ is minimal if for each edge $e$ of $G$, $G-e$ is not matching covered. An edge $e$ of a matching covered graph $G$ is removable if $G-e$ is also matching covered. Thus a matching covered graph is minimal if and only if it is free of removable edges. For bipartite graphs, Lovász and Plummer gave a characterization of bipartite minimal matching covered graphs. For bricks, Lovász showed that the only bricks that are minimal matching covered are $K_4$ and $\overline{C_6}$. In this paper, we present a complete characterization of minimal matching covered graphs that are claw-free. Moreover, for cubic claw-free matching covered graphs that are not minimal matching covered, we obtain the number of their removable edges (with respect to their bricks), and then prove that they have at least 12 removable edges (the bound is sharp).

math.CO↗