Search Results (348)

In the intelligent transportation system of smart cities, object detection from UAV aerial imagery serves as the core technical support for traffic flow monitoring, violation detection, and emergency response. However, traffic objects captured from UAV perspectives typically exhibit extremely low pixel occupancy and are embedded in complex backgrounds, leading to three fundamental limitations in existing detection methods: insufficient utilization of global context information, inaccurate weak feature enhancement, and severe feature scale confusion. To address these challenges, this paper proposes ContextTiny-Net, an ultra-tiny object detection network built upon multi-dimensional symmetry design principles for urban UAV scenarios. Specifically, we first construct a global–local perception symmetric MetaFormer backbone and a hierarchical scale symmetric four-layer detection head, which achieves full-coverage detection from ultra-tiny to regular traffic objects with minimal computational overhead. Second, we design an information-theoretic and spatial-distribution-complementary symmetric-weak feature enhancement module, which accurately locates and strengthens weakly activated regions of small objects from two mutually complementary and symmetric dimensions. Finally, we propose a cross-scale decoupling symmetric feature fusion module and a symmetric Gaussian distribution-based normalized Wasserstein distance loss, which effectively eliminate scale confusion and significantly improve the robustness of small object bounding box regression. Extensive experiments on three mainstream benchmarks (AI-TOD, VisDrone, and COCO) demonstrate that ContextTiny-Net outperforms state-of-the-art methods in both overall detection accuracy and ultra-tiny object detection performance, verifying the effectiveness of the proposed symmetry-enhanced design paradigm. Full article

Occlusion introduces severe structural asymmetry into pedestrian representations by corrupting body topology, breaking cross-scale semantic continuity, and destabilizing identity geometry. Rather than treating occluded person re-identification (ReID) as a local visibility completion problem, this work reformulates it as a topology-preserved symmetry restoration problem: recovering symmetric identity structure from asymmetrically corrupted observations. Under this view, we present the Topology-Stable Person Re-identification Network (TSP-Net), a unified visual framework with three coordinated components: structural restoration, cross-scale symmetry alignment, and prototype-stabilized identity geometry. Specifically, Topology-Guided Occlusion and Visibility Modeling (TOVM) serves as the structural restoration component, and is realized by a closed loop of the Topology-Aware Occlusion Simulator (TOS) and the Topology-Aware Visibility Estimation (TVE) branch; Semantic-Anchored Cross-Scale Fusion (SACF) performs symmetry-consistent semantic recovery across hierarchical features; and the Prototype-Stabilized Supervision Loss (PSS Loss) regularizes identity embeddings toward topology-consistent manifold centers through momentum-updated prototypes. Experimental results on both occluded and holistic benchmarks show that TSP-Net is effective for learning occlusion-robust person representations. These findings suggest that restoring topology-preserved symmetry is a promising route for robust person re-identification under structural corruption. Full article

Consecutive k-out-of-n:G systems are widely used reliability models in engineering and communications, and their survival functions possess an inherent structural symmetry under the condition $2k\ge n$. This paper investigates the extropy characteristics of such systems under the condition $2k\ge n$, which admits a tractable closed-form representation of the survival function. A closed-form expression for the extropy of the system lifetime is derived using a probability integral transform and a density-quantile representation, which separates the symmetric structural contribution from the baseline distributional component. Bounds, stochastic ordering results based on a density-quantile order, and a characterization theorem are established. A nonparametric spacing-based estimator is proposed, its consistency is proved under explicit regularity conditions, and bootstrap confidence intervals are provided. Monte Carlo simulations under three component lifetime distributions (Weibull, Gamma, and Pareto II) demonstrate that the estimator is consistent, with bias and root mean squared error decreasing monotonically as sample size increases. A sensitivity analysis confirms the adequacy of the default window size rule. The proposed framework extends extropy to structured reliability systems and provides a practical nonparametric estimation tool with implementation guidelines, illustrated via a real data example on glass fiber breaking strengths. Full article

Industrial defect image generation is an effective way to alleviate data scarcity and class imbalance in visual inspection. In industrial images, defects usually appear as local asymmetric perturbations on globally regular background structures, which makes defect synthesis dependent on both background consistency and local anomaly fidelity. Existing generative methods still face difficulties when only limited anomalous samples are available, especially in representing fine-grained discrepancies among defect categories, coordinating global and local branches across diffusion stages, and constraining small defect regions and their boundary transitions. To address these issues, this paper develops a symmetry-aware multi-constraint diffusion framework based on the dual-branch architecture of DualAnoDiff. The framework treats multi-class industrial defect generation as a joint optimization problem involving class-conditioned discrepancy representation, diffusion-stage-aware branch coordination, and saliency-guided regional supervision. First, Class-Conditioned Shared-Basis LoRA (CSB-LoRA) models category-specific defect characteristics by combining cross-class shared low-rank bases with class-dependent coefficients, allowing common structural priors and class-specific asymmetric patterns to be represented simultaneously. Second, Temporal Dual-branch Attention Modulation (TDAM) adjusts branch interaction, background information injection, and residual feature fusion according to the denoising stage, so that the generation process can gradually shift from global structure restoration to local defect refinement. Third, Saliency-Guided Reconstruction Loss (SGRL) applies stronger spatial constraints to defect regions and boundary neighborhoods, improving local detail preservation and defect-background continuity. Experiments on the MVTec AD dataset show that the proposed method improves both generation quality and perceptual diversity compared with DualAnoDiff. The average IS increases from 1.93 to 2.07, and IC-LPIPS increases from 0.38 to 0.41. When the generated samples are used for downstream defect segmentation, AP-P improves from 84.5% to 85.7%, and F1-P improves from 78.8% to 79.3%. These results indicate that the generated samples can serve as useful synthetic training data for few-shot and class-imbalanced industrial inspection. Full article

Reconstructing building models from urban SAR tomography (TomoSAR) point clouds is often constrained by limited resolution, low positioning accuracy in elevation, as well as data incompleteness and artifacts caused by microwave imaging mechanisms. These challenges seriously restrict the extraction of high-accuracy building models with structural details from TomoSAR point clouds. This paper proposes a refined urban building modeling method that effectively utilizes structural priors, including directionality, orthogonality, and potential symmetry. First, a piecewise fitting strategy integrated with density-based segmentation is employed to iteratively estimate the main directions of the buildings and capture finer geometric variations of complex façade footprints than simple-plane approximations. Second, a roof extraction algorithm combining an adaptive Doug-las–Peucker approach with symmetry evaluation and constraints is developed to regularize roof outlines and repair data defects. Crucially, to handle extreme cases where roof data are entirely missing, a novel building width estimation method based on building shadow analysis is proposed. Experiments conducted on the SARMV3D-1.0 and SARMV3D-3.0 point cloud datasets demonstrate that the proposed method significantly enhances reconstruction accuracy and geometric fidelity in urban regions compared to state-of-the-art approaches. Full article

The Q-Learning Relational Game (QLRG) framework provides a theoretically rigorous method for identifying minimal winning coalitions in online social networks (OSNs) under the restrictive assumption of global agent symmetry or uniform matroid structure. Real-world OSNs, however, exhibit significant asymmetry. This paper introduces the Cluster-Based Q-Learning Relational Game (C-QLRG), a practical extension that relaxes the global symmetry requirement by leveraging community structure. We partition the agent set into communities with bounded internal variation and represent the state solely by community membership counts of the seed set. Because the closure operator already captures all eventual influence spread, the problem reduces to a sequential seed selection task where the agent decides, at each step, from which community to add the next seed. We prove that the optimal Q-function of a suitably regularized reach-efficiency objective is Lipschitz continuous and derive a performance bound for the learned policy. The full algorithm is presented, and its complexity is analyzed. Empirical evaluations on a synthetic asymmetric network and Zachary’s Karate Club demonstrate that C-QLRG is highly sensitive to reward parameters, where default settings lead to premature stopping, but parameter tuning combined with a corrected minimality verification recovers high-efficiency coalitions by removing non-contributing agents. With tuned parameters, C-QLRG produces a near-winning coalition of size 11 and 99% reach on the synthetic network, surpassing the greedy baseline’s efficiency (size 12) despite a one-node coverage gap, while identifying the optimal winning coalition of size 1 on the Karate Club dataset, matching all baselines. The framework thus offers a principled trade-off between model fidelity and scalability, with the reward design choice being critical for practical deployment. Full article

Symmetry operations are usually studied within the frameworks of group theory, geometry, and operator algebra. In the present work, a Ramsey-theoretic approach to symmetry is developed. Symmetry operations are treated as operators serving as vertices of complete bi-colored graphs, called symmetry graphs (SGs). Two symmetry operators are connected by a maroon edge when they commute and by a teal edge when they do not commute. Thus, the commutation structure of a symmetry group is transformed into a combinatorial object suitable for Ramsey-theoretic analysis. The introduced coloring is generally non-transitive, leading naturally to nontrivial complete bi-colored graphs constrained simultaneously by group-theoretical and combinatorial principles. It is shown that every symmetry graph containing six vertices necessarily contains either a monochromatic commuting triangle or a monochromatic non-commuting triangle as a direct consequence of the classical Ramsey theorem $R\left(\mathrm{3,3}\right)=6$. The framework is illustrated for the symmetry groups of the equilateral triangle, regular tetrahedron, crystallographic point groups, infinite Cairo pentagonal tilings, and the triangular Ising ferromagnet. Higher-order structures, including teal quadrangles, second-order graph symmetries, infinite monochromatic cliques, and Lie-algebraic constraints arising from the Jacobi identity, are discussed. The proposed framework establishes a new connection between symmetry theory, Ramsey theory, graph theory, crystallography, and operator algebra. Full article

The complexity of a graph, defined as its number of spanning trees, serves as a key measure of network reliability. Stacked graphs constitute a significant and versatile class of graphs, formed by superimposing multiple copies of a base graph upon a shared central vertex set. Their inherent layered symmetry and structural regularity make them compelling models for a wide range of real-world networks, including multi-tier communication systems, hierarchical data networks, and resilient distributed architectures. Moreover, their systematic construction from well-known graph families renders the study of their complexity both mathematically rich and algorithmically meaningful. In this paper, we derive closed-form formulas for the complexity of several stacked graph families based on path- and cycle-based structures with a central vertex, including stacked fan and wheel graphs, stacked double fan and double wheel graphs, and stacked path flower, cycle flower, and gear graphs. The derivations are based on techniques from linear algebra, matrix theory, and Chebyshev polynomials. Full article

Accurate prediction of slope displacement from high-frequency GNSS monitoring data is critical for early warning of landslides and tailings dam failures. However, existing deep learning approaches often neglect the spatial coordination imposed by geological structures and fail to decouple abrupt deformation signals from background noise, leading to non-physical oscillations and inconsistent long-term predictions. To address these limitations, this paper proposes a Symmetry-Aware Physics-Guided Spatio-Temporal Graph Network (PG-STGN). First, a geological hierarchy-aware graph is constructed by integrating geometric proximity with prior knowledge of exploration levels, where the resulting adjacency matrix is symmetric by design and reflects the physical symmetry of deformation interactions among monitoring points at the same elevation. A hierarchical masking mechanism restricts feature aggregation to physically connected neighborhoods while preserving this symmetry. Second, an improved dual-path temporal convolutional network (iTCN) decouples high-frequency abrupt variations from low-frequency evolutionary trends, enabling both sensitive detection of sudden deformation and stable tracking of long-term creep. Third, a physics-consistent loss function combining first-order temporal differencing and graph Laplacian regularization enforces kinematic smoothness and spatial coordination; the Laplacian itself is derived from the symmetric adjacency matrix, ensuring symmetric regularization across the monitoring network. Evaluated on a real-world slope GNSS dataset from a large-scale mining project, PG-STGN reduces mean squared error (MSE) by approximately 23.7% and achieves a global R² of 0.924, outperforming state-of-the-art spatio-temporal models. Ablation studies confirm that the symmetric physics-guided graph, dual-path decoupling, and consistency loss are each essential for suppressing spurious correlations and maintaining physically plausible predictions. The proposed framework provides a robust, interpretable, and symmetry-constrained solution for automated slope monitoring under complex geological conditions. Full article

Symmetry plays a fundamental role in the structural analysis of lattice-based systems, particularly in graphene-like molecular structures. In chemical graph theory, counting independent sets is equivalent to computing the Merrifield–Simmons (M–S) index, a key descriptor of molecular stability in conjugated systems. Most existing exact counting methods rely on regular lattice symmetry, where structural uniformity simplifies computation; however, these approaches are difficult to extend to irregular graphs, where symmetry breaking introduces non-local dependencies and increases computational complexity. This paper proposes an asymmetry-aware algorithmic framework based on Hamiltonian traversals and a traversal-induced pathwidth parameter $w\left(G\right)$, defined through backward dependencies. Our method organizes non-local adjacencies into a bounded set of structured constraints, enabling a dynamic programming scheme over a reduced state space. The resulting algorithm runs in time $\mathcal{O}\left(2^{w\left(G\right)}·\mathrm{poly}\left(n\right)\right)$ and is fixed-parameter tractable with respect to $w\left(G\right)$. The results demonstrate that asymmetry-aware traversal strategies enable efficient exact enumeration in irregular mesh graph families, providing a robust computational framework for analyzing molecular descriptors in graphene-based structures with topological defects such as Stone–Wales transformations. Full article

We derive the charged-lepton mass chain from the Recognition Composition Law (RCL) together with normalization, curvature normalization, and standard regularity. Through the theorem chain Tr1–Tr8, these postulates fix the golden ratio $\phi = \left(1+\sqrt{5}\right)/2$, the minimal period T_min = 8, the selected dimension D = 3, and the cube integers entering the master mass law. The charged-lepton formula is then assembled from the coherence scale, the lepton-sector baseline, the charge correction, and the derived generation steps. All parameters are discrete structural inputs, integers from cube geometry, named symmetry factors, and one external mathematical constant, rather than continuously adjustable dials. The construction is a structural constraint on the effective charged-lepton flavor pattern, not a replacement for the electroweak Higgs mechanism or for the full Standard Model quantum field theory. At the conversion stage to the International System of Units (SI), the electron fixes the single calibration anchor ${\tau }_0$, while the fine-structure constant $\alpha$ enters only as a fixed external dimensionless constant in the refinement layer. The phrase “zero continuously adjustable parameters” refers to the dimensionless content of the framework: the anchor ${\tau }_0$ is a unit-scale calibration fixed by the measured electron mass and cancels identically from every charged-lepton mass ratio. With that one anchor set, the remaining charged leptons become forward predictions: $m_{\mu }\in \left(\mathrm{105.5,105.9}\right) \mathrm{M}\mathrm{e}\mathrm{V}$ and $m_{\tau }\in \left(\mathrm{1774,1779}\right) \mathrm{M}\mathrm{e}\mathrm{V}$, with relative errors below $0.3\%$ and $0.2\%$, respectively. Floating-point evaluation gives $m_{\mu }\approx 105.658 \mathrm{M}\mathrm{e}\mathrm{V}$ and $m_{\tau }\approx 1776.71 \mathrm{M}\mathrm{e}\mathrm{V}$. Full article

Knowledge graph completion (KGC) is commonly studied under static settings, whereas real-world knowledge graphs evolve continuously with newly emerging entities, relations, and facts. In continual knowledge graph completion (CKGC), the model is required to absorb newly arrived knowledge while retaining historical prediction ability. A central difficulty is that incremental knowledge is heterogeneous: some information reflects reusable cross-session schema regularities, whereas other information corresponds to volatile session-specific factual updates. Existing CKGC methods usually model these signals within a single adaptation stream, which can increase interference during sequential learning. To address this issue, we propose a schema–session decoupled adaptation framework for session-aware CKGC. Specifically, the framework introduces a shared Schema-LoRA to accumulate reusable schema knowledge across sessions and a session-specific Session-LoRA to capture local instance-level updates in each session. To further improve adaptation stability, Orthogonal Gradient Projection and Session-EWC are applied to the instance-adaptation branch to reduce harmful gradient interference and excessive parameter drift during current-session training. In addition, we adopt a two-stage retrieve–rerank inference pipeline that combines lightweight candidate retrieval with language model reranking to balance effectiveness and efficiency. Experimental results on both static and continual KGC benchmarks show that the proposed framework achieves competitive static performance and improves top-rank prediction and final averaged performance over observed sessions under the session-aware CKGC protocol. From a functional-symmetry perspective, Schema-LoRA and Session-LoRA act as two additive adaptation branches around the frozen backbone, separately modeling reusable schema regularity and evolving factual variation. These findings suggest that schema–session decoupling is an effective design choice for session-aware continual knowledge graph completion. Full article

We study two-tone factors in edge-connected regular graphs and claw-free cubic graphs under red-blue vertex colorings. A two-tone factor is a spanning subgraph in which vertices of different colors are assigned different allowed degree sets. For edge-connected regular graphs, we prove an existence theorem for two-tone $\left(\right\{k\},\{k,k+2\left\}\right)$-factors under arbitrary red-blue colorings and describe a constructive factor-theoretic route to matching-type formulations. For the claw-free cubic setting, we show that the natural arbitrary-coloring extension for $\left(\right\{0,1\},\{2,3\left\}\right)$-factors is false in general. Nevertheless, we prove a restricted positive result when the graph has a triangle decomposition and the coloring is constant on each triangle, and we give a mask-consistency characterization for triangle-inflated cubic graphs. The computational section is therefore framed as an implementation and proof-audit study: it certifies recovered factors in the regular case, cross-checks claw-free cubic stress tests by independent MILP and mask-CSP formulations, and explains why only provable restrictions are retained as theorems. From the perspective of symmetry, the contrast identifies a boundary between symmetry-stable and symmetry-fragile colored degree constraints. Full article

The averaging effect is a distinctive property possessed by fractional operators. In recent years, it has emerged as a powerful tool in the study of qualitative properties of solutions to fractional elliptic and parabolic equations. In this article, we systematically summarize and prove various forms of the averaging effects for both fractional elliptic and parabolic equations, from the simplest one to the one under very relaxed conditions, including versions for antisymmetric functions. We then present examples to illustrate how to apply these effects to obtain radial symmetry and monotonicity for solutions in a unit ball and in a half space. In addition, we derive averaging effects for fractional Monge–Ampère operators and for fractional p-Laplacians, which will be potentially applied to obtain qualitative properties for solutions to equations involving these operators. Compared with the traditional approaches, methods based on the averaging effect require substantially weaker regularity assumptions and can even accommodate unbounded solutions. Full article

This paper investigates the closed-form solvability and dynamical behavior of a class of nonlinear triangular difference systems with overlapping indices, emphasizing the role of coefficient symmetry and asymmetry in determining the qualitative behavior of the system. A unified analytical framework is developed by transforming the original nonlinear system into equivalent linear or multiplicative difference equations, thereby enabling the derivation of explicit general solutions for various parameter configurations. The results show that the structure of the coefficients plays a fundamental role in determining stability, periodicity, and long-term dynamics. In particular, symmetric configurations tend to produce regular and more structured periodic behavior, whereas asymmetric configurations lead to more irregular oscillatory patterns and increased sensitivity to initial conditions. These theoretical findings are supported by numerical simulations and graphical illustrations, which demonstrate how variations in coefficient values and signs influence the evolution of the system. Finally, an application to discrete survival dynamics is presented, illustrating the capability of the proposed model to describe interacting survival processes under both symmetric and asymmetric parameter regimes, thereby highlighting its potential relevance in the study of applied discrete dynamical systems. Full article