Search Results (138)

Forecasting real-world time series in domains with strong event sensitivity and regional variability poses unique challenges, as predictive models must account for sudden disruptions, heterogeneous contextual factors, and structural differences across locations. In tackling these challenges, we draw on the concept of symmetry that refers to the balance and invariance patterns across temporal, multimodal, and structural dimensions, which help reveal consistent relationships and recurring patterns within complex systems. This study is based on two multimodal datasets covering 12 tourist regions and more than 3 years of records, ensuring robustness and practical relevance of the results. In many applications, such as monitoring economic indicators, assessing operational performance, or predicting demand patterns, short-term fluctuations are often triggered by discrete events, policy changes, or external incidents, which conventional statistical and deep learning approaches struggle to model effectively. To address these limitations, we propose an event-aware multimodal time-series forecasting framework with graph-based regional transfer built upon an enhanced PatchTST backbone. The framework unifies multimodal feature extraction, event-sensitive temporal reasoning, and graph-based structural adaptation. Unlike Informer, Autoformer, FEDformer, or PatchTST, our model explicitly addresses naive multimodal fusion, event-agnostic modeling, and weak cross-regional transfer by introducing an event-aware Multimodal Encoder, a Temporal Event Reasoner, and a Multiscale Graph Module. Experiments on diverse multi-region multimodal datasets demonstrate that our method achieves substantial improvements over eight state-of-the-art baselines in forecasting accuracy, event response modeling, and transfer efficiency. Specifically, our model achieves a 15.06% improvement in the event recovery index, a 15.1% reduction in MAE, and a 19.7% decrease in event response error compared to PatchTST, highlighting its empirical impact on tourism event economics forecasting. Full article

Location-based services (LBSs), which are used for navigation, tracking, and mapping across digital devices and social platforms, establish a user’s position and deliver tailored experiences. Collecting and sharing such trajectory datasets with analysts for business purposes raises critical privacy concerns, as both symmetry in recurring behavior mobility patterns and asymmetry in irregular movement mobility patterns in sensitive locations collectively expose highly identifiable information, resulting in re-identification risks, trajectory disclosure, and location inference. In response, several privacy preservation models have been proposed, including k-anonymity, l-diversity, t-closeness, LKC-privacy, differential privacy, and location-based approaches. However, these models still exhibit privacy issues, including sensitive location inference (e.g., hospitals, pawnshops, prisons, safe houses), disclosure from duplicate trajectories revealing sensitive places, and the re-identification of unique locations such as homes, condominiums, and offices. Efforts to address these issues often lead to utility loss and computational complexity. To overcome these limitations, we propose a new ($\xi$, $ϵ$)-privacy model that combines data generalization and suppression with sliding windows and R-Tree structures, where sliding windows partition large trajectory graphs into simplified subgraphs, R-Trees provide hierarchical indexing for spatial generalization, and suppression removes highly identifiable locations. The model addresses both symmetry and asymmetry in mobility patterns by balancing generalization and suppression to protect privacy while maintaining data utility. Symmetry-driven mechanisms that enhance resistance to inference attacks and support data confidentiality, integrity, and availability are core requirements of cryptography and information security. An experimental evaluation on the City80k and Metro100k datasets confirms that the ($\xi$, $ϵ$)-privacy model addresses privacy issues with reduced utility loss and efficient scalability, while validating robustness through relative error across query types in diverse analytical scenarios. The findings provide evidence of the model’s practicality for large-scale location data, confirming its relevance to secure computation, data protection, and information security applications. Full article

In intuitionistic fuzzy 2-normed spaces, there are numerous symmetries in the topological structures and mapping theorems. In this work, we present the concept of an intuitionistic fuzzy 2-normed space(IF2NS) and demonstrate its structural properties using illustrative examples. This approach unifies and broadens the scope of both classical 2-normed spaces and intuitionistic fuzzy normed spaces when specific conditions are met. We introduce the idea of fuzzy open balls and explore the convergence of sequences with respect to the topology derived from the intuitionistic fuzzy 2-norm. In addition, we define left and right N-Cauchy sequences relative to the topologies ${\tau }_N$ and ${\tau }_{N^{-1}}$ and analyze their convergence characteristics. Special attention is given to the inherent symmetry of the 2-norm, where the magnitude of a pair of vectors remains invariant under exchange of arguments, and to the balanced interaction between membership and non-membership functions in the intuitionistic fuzzy setting. This intrinsic symmetry is further reflected in the proofs of the open mapping and closed graph theorems, which naturally preserve the symmetric structure of the underlying space The paper culminates with the formulation and proof of the open mapping theorem that can be considered for its symmetric properties and the closed graph theorem in the context of IF2NS, thereby generalizing essential theorems of functional analysis to this fuzzy setting. Full article

In this study, the extended (3 + 1)-dimensional Jimbo–Miwa equation, which has not been previously studied using Lie symmetry techniques, is the focus. We derive new symmetry reductions and exact invariant solutions, including lump and rogue wave structures. Additionally, precise solitary wave solutions of the extended (3 + 1)-dimensional Jimbo–Miwa equation using the multivariate generalized exponential rational integral function technique (MGERIF) are studied. The extended (3 + 1)-dimensional Jimbo–Miwa equation is crucial for studying nonlinear processes in optical communication, fluid dynamics, materials science, geophysics, and quantum mechanics. The multivariate generalized exponential rational integral function approach offers advantages in addressing challenges involving exponential, hyperbolic, and trigonometric functions formulated based on the generalized exponential rational function method. The solutions provided by MGERIF have numerous applications in various fields, including mathematical physics, condensed matter physics, nonlinear optics, plasma physics, and other nonlinear physical equations. The graphical features of the generated solutions are examined using 3D surface graphs and contour plots, with theoretical derivations. This visual technique enhances our understanding of the identified answers and facilitates a more profound discussion of their practical applications in real-world scenarios. We employ the MGERIF approach to develop a technique for addressing integrable systems, providing a valuable framework for examining nonlinear phenomena across various physical contexts. This study’s outcomes enhance both nonlinear dynamical processes and solitary wave theory. Full article

This paper presents a new coupled fixed-point theorem for a pair of set-valued mappings acting on the Cartesian product of $(m_1, m_2)$- and $(n_1, n_2)$-quasi-metric spaces. Within the general, non-symmetric quasi-metric setting, we establish the existence of an approximate coupled fixed point. Moreover, under the additional assumption of $q_0$-symmetry, we guarantee the existence of a coupled fixed point. Together, these results extend and unify several known theorems in fixed-point theory for quasi-metric and asymmetric spaces. We illustrate the obtained results regarding fixed points when the underlying space is equipped with a graph structure and, thus, sufficient conditions are found to guarantee the existence of a subgraph with a loop with a length greater than or equal to 2. Full article

The purpose of few-shot relation extraction (RE) is to recognize the relationship between specific entity pairs in text when there are a limited number of labeled samples. A few-shot RE method based on a prototype network, which constructs relation prototypes by relying on the support set to assign labels to query samples, inherently leverages the symmetry between support and query processing. Although these methods have achieved remarkable results, they still face challenges such as the misjudging of noisy samples or outliers, as well as distinguishing semantic similarity relations. To address the aforementioned challenges, we propose a novel semantic enhanced prototype network, which can integrate the semantic information of relations more effectively to promote more expressive representations of instances and relation prototypes, so as to improve the performance of the few-shot RE. Firstly, we design a prompt encoder to uniformly process different prompt templates for instance and relation information, and then utilize the powerful semantic understanding and generation capabilities of large language models (LLMs) to obtain precise semantic representations of instances, their prototypes, and conceptual prototypes. Secondly, graph attention learning techniques are introduced to effectively extract specific-relation features between conceptual prototypes and isomorphic instances while maintaining structural symmetry. Meanwhile, a prototype-level contrastive learning strategy with bidirectional feature symmetry is proposed to predict query instances by integrating the interpretable features of conceptual prototypes and the intra-class shared features captured by instance prototypes. In addition, a clustering loss function was designed to guide the model to learn a discriminative metric space with improved relational symmetry, effectively improving the accuracy of the model’s relationship recognition. Finally, the experimental results on the FewRel1.0 and FewRel2.0 datasets show that the proposed approach delivers improved performance compared to existing advanced models in the task of few-shot RE. Full article

Road-surface distress poses a serious threat to traffic safety and imposes a growing burden on urban maintenance budgets. While modern detectors based on convolutional networks and Vision Transformers achieve strong frame-level performance, they often overlook an essential property of road environments—structural symmetry within road networks and damage patterns. We present Graph-MambaRoadDet (GMRD), a symmetry-aware and lightweight framework that integrates dynamic graph reasoning with state–space modeling for accurate, topology-informed, and real-time road damage detection. Specifically, GMRD employs an EfficientViM-T1 backbone and two DefMamba blocks, whose deformable scanning paths capture sub-pixel crack patterns while preserving geometric symmetry. A superpixel-based graph is constructed by projecting image regions onto OpenStreetMap road segments, encoding both spatial structure and symmetric topological layout. We introduce a Graph-Generating State–Space Model (GG-SSM) that synthesizes sparse sample-specific adjacency in $\mathcal{O}\left(M\right)$ time, further refined by a fusion module that combines detector self-attention with prior symmetry constraints. A consistency loss promotes smooth predictions across symmetric or adjacent segments. The full INT8 model contains only 1.8 M parameters and 1.5 GFLOPs, sustaining 45 FPS at 7 W on a Jetson Orin Nano—eight times lighter and 1.7× faster than YOLOv8-s. On RDD2022, TD-RD, and RoadBench-100K, GMRD surpasses strong baselines by up to +6.1 mAP_50:95 and, on the new RoadGraph-RDD benchmark, achieves +5.3 G-mAP and +0.05 consistency gain. Qualitative results demonstrate robustness under shadows, reflections, back-lighting, and occlusion. By explicitly modeling spatial and topological symmetry, GMRD offers a principled solution for city-scale road infrastructure monitoring under real-time and edge-computing constraints. Full article

The integrity parameter in vulnerability refers to a set of removed vertices and the maximum number of connected components that remain functional. A bipolar fuzzy graph (BFG) assigns membership values to both positive and negative attributes. A new parameter, integrity, is defined and discussed using an example of a BFG. The integrity value of a special type of graph is determined, and the node strength sequence (NSS) for BFG is introduced. Specific NSS values are used to discuss the integrity values of paths and cycles. The integrity of the union, join, and Cartesian product of two BFGs is presented. This parameter is then applied to a road network with both positive and negative attributes, and the findings are discussed with a conclusion. Full article

Aperiodic tessellations of polykite unitiles, such as hats and turtles, and the recently introduced hares, red squirrels, and gray squirrels, have attracted significant interest due to their structural and combinatorial properties. Our primary objective here is to learn how we could build a self-assembling polyhedron that would have an aperiodic tessellation of its surface using only a single type of polykite unitile. Such a structure would be analogous to some viral capsids that have been reported to have a quasicrystal configuration of capsomeres. We report on our use of a graph–theoretic approach to examine the adjacency and symmetry constraints of these unitiles in tessellations because by using graph theory rather than the usual geometric description of polykite unitiles, we are able (1) to identify which particular vertices and/or edges join one another in aperiodic tessellations; (2) to take advantage of being scale invariant; and (3) to use the deformability of shapes in moving from the plane to the sphere. We systematically classify their connectivity patterns and structural characteristics by utilizing Hamiltonian cycles of vertex degrees along the perimeters of the unitiles. In addition, we applied Blumeyer’s 2 × 2 classification framework to investigate the influence of chirality and periodicity, while Heesch numbers of corona structures provide further insights into tiling patterns. Furthermore, we analyzed the distribution of polykite unitiles with Voronoi tessellations and their Delaunay triangulations. The results of this study contribute to a better understanding of self-assembling structures with potential applications in biomimetic materials, nanotechnology, and synthetic biology. Full article

In this work, the concept of equitable partition is applied to molecular graphs to define quantitative descriptors of the symmetry and complexity of molecules, with the ultimate goal of shedding new light on the structure–property relationships of chemical compounds and materials. The ways in which symmetry is reflected in these descriptors and their correlations with molecular properties are demonstrated using simple examples, and their potential for the prediction of properties of complex molecules is underscored. Full article

Accurate correspondence of complex neuroanatomical surfaces under non-rigid deformations remains a formidable challenge in computational neuroimaging, owing to inter-subject topological variability, partial occlusions, and non-isometric distortions. Here, we introduce the Dynamic Graph Analyzer (DGA), a unified hybrid framework that integrates simplified structural descriptors with spatial constraints and formulates matching as a global linear assignment. Structurally, the DGA computes node-level metrics, degree weighted by betweenness centrality and local clustering coefficients, to capture essential topological patterns at a low computational cost. Spatially, it employs a two-stage scheme that combines global maximum distances and local rescaling of adjacent node separations to preserve geometric fidelity. By embedding these complementary measures into a single cost matrix solved via the Kuhn–Munkres algorithm followed by a refinement of weak correspondences, the DGA ensures a globally optimal correspondence. In benchmark evaluations on the FAUST dataset, the DGA achieved a significant reduction in the mean geodetic reconstruction error compared to spectral graph convolutional netwworks (GCNs)—which learn optimized spectral descriptors akin to classical approaches like heat/wave kernel signatures (HKS/WKS)—and traditional spectral methods. Additional experiments demonstrate robust performance on partial matches in TOSCA and cross-species alignments in SHREC-20, validating resilience to morphological variation and symmetry ambiguities. These results establish the DGA as a scalable and accurate approach for brain shape correspondence, with promising applications in biomarker mapping, developmental studies, and clinical morphometry. Full article

This work addresses the broken symmetry in syntactic–semantic representations for Aspect-Based Sentiment Analysis, where advancements have been driven by the use of pre-trained language models to achieve contextual understanding and graph neural networks capturing aspect–opinion dependencies using syntactic trees. However, long-distance aspect–opinion pairs pose challenges: the structural noise in dependency trees often causes erroneous associations, while the discrete structure of the constituent trees leads to constituent fragmentation. In this paper, we propose DySynGAT and introduce a Localized Graph Attention Network (LGAT) to fuse bi-gram syntactic and semantic information from both dependency and constituent trees, effectively mitigating interference from dependency tree noise. A dynamic semantic enhancement module efficiently integrates local and global semantics, alleviating constituent fragmentation caused by constituent trees. An aspect–context interaction graph (ACIG), built upon minimal semantic segmentation and jointly enhanced features, filters out noisy cross-clause edges. Spatial reduction attention (SRA) with mean pooling compresses the redundant sequential features, reducing the noise under long-range dependencies. Experiments on foods and beverages, electronics, and user review datasets demonstrate F1 score improvements of 0.55%, 3.55%, and 1.75% over SAGAT-BERT, demonstrating strong cross-domain robustness. Full article

Structured knowledge representation is of great significance for constructing a knowledge graph of coal mine equipment safety. However, traditional methods encounter substantial difficulties when handling the complex semantics and domain-specific terms in technical texts. To tackle this challenge, we propose a knowledge extraction framework that integrates large language models (LLMs) with prompt engineering to achieve the efficient joint extraction of information. This framework strengthens the traditional triple structure by introducing symmetric entity-type information encompassing the head entity type and the tail entity type. Furthermore, it enables simultaneous entity recognition and relation extraction within a unified model. Experimental results demonstrate that the proposed knowledge extraction framework significantly outperforms the traditional step-by-step approach of first extracting entities and then relations. To meet the requirements of actual industrial production, we verified the impacts of different prompt strategies, as well as small lightweight models and large complex models, on the extraction task. Through multiple sets of comparative experiments, we found that the Chain-of-Thought (CoT) prompting strategy can effectively improve performance across different models, and the choice of model architecture has a significant impact on task performance. Our research provides an accurate and scalable solution for knowledge graph construction in the coal mine equipment safety domain, and its symmetry-aware design exhibits great potential for cross-domain knowledge transfer. Full article

Cloud imagery analysis from terrestrial observation points represents a fundamental capability within contemporary atmospheric monitoring infrastructure, serving essential functions in meteorological prediction, climatic surveillance, and hazard alert systems. However, traditional ground-based cloud image segmentation methods have fundamental limitations, particularly their inability to effectively model the graph structure and symmetry in cloud data. To address this, we propose G-CLIP, a ground-based cloud image segmentation method based on graph symmetry. G-CLIP synergistically integrates four innovative modules. First, the Prototype-Driven Asymmetric Attention (PDAA) module is designed to reduce complexity and enhance feature learning by leveraging permutation invariance and graph symmetry principles. Second, the Symmetry-Adaptive Graph Convolution Layer (SAGCL) is constructed, modeling pixels as graph nodes, using cosine similarity to build a sparse discriminative structure, and ensuring stability through symmetry and degree normalization. Third, the Multi-Scale Directional Edge Optimizer (MSDER) is developed to explicitly model complex symmetric relationships in cloud features from a graph theory perspective. Finally, the Uncertainty-Driven Loss Optimizer (UDLO) is proposed to dynamically adjust weights to address foreground–background imbalance and provide uncertainty quantification. Extensive experiments on four benchmark datasets demonstrate that our method achieves state-of-the-art performance across all evaluation metrics. Our work provides a novel theoretical framework and practical solution for applying graph neural networks (GNNs) to meteorology, particularly by integrating graph properties with uncertainty and leveraging symmetries from graph theory for complex spatial modeling. Full article

Micro-expressions, characterized by brief and subtle facial muscle movements, are essential for conveying nuanced emotions in digital humans, yet existing rendering techniques often produce rigid or emotionally monotonous animations due to the inadequate modeling of temporal dynamics and action unit interdependencies. This paper proposes a graph-driven framework for micro-expression rendering that generates emotionally diverse and lifelike expressions. We employ a 3D-ResNet-18 backbone network to perform joint spatio-temporal feature extraction from facial video sequences, enhancing sensitivity to transient motion cues. Action units (AUs) are modeled as nodes in a symmetric graph, with edge weights derived from empirical co-occurrence probabilities and processed via a graph convolutional network to capture structural dependencies and symmetric interactions. This symmetry is justified by the inherent bilateral nature of human facial anatomy, where AU relationships are based on co-occurrence and facial anatomy analysis (as per the FACS), which are typically undirected and symmetric. Human faces are symmetric, and such relationships align with the design of classic spectral GCNs for undirected graphs, assuming that adjacency matrices are symmetric to model non-directional co-occurrences effectively. Predicted AU activations and timestamps are interpolated into continuous motion curves using B-spline functions and mapped to skeletal controls within a real-time animation pipeline (Unreal Engine). Experiments on the CASME II dataset demonstrate superior performance, achieving an F1-score of 77.93% and an accuracy of 84.80% (k-fold cross-validation, k = 5), outperforming baselines in temporal segmentation. Subjective evaluations confirm that the rendered digital human exhibits improvements in perceptual clarity, naturalness, and realism. This approach bridges micro-expression recognition and high-fidelity facial animation, enabling more expressive virtual interactions through curve extraction from AU values and timestamps. Full article