Search Results (123)

This research evaluates the suitability of Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT) for improving financial return predictions across 15 major worldwide stock indices. The proposed method uses graph modeling to represent financial index relationships which enables the detection of symmetric market dependencies including mutual spillover effects and bidirectional influence patterns. The symmetric network structures become most important during financial instability because market interdependencies strengthen at such times. The evaluation process compares these models against XGBoost and Multi-Layer Perceptron (MLP) and Support Vector Machine (SVM) traditional forecasting approaches. The results of 30 time-series cross-validation experiments show that GNN models produce lower RMSE and MAE values, especially during financial crises and recovery phases and volatile market periods. The models show reduced advantages when markets remain stable. The research demonstrates that graph-based forecasting models which incorporate symmetry effectively detect complex financial relationships which leads to important implications for investment strategies and financial risk management and global economic forecasting. Full article

Let G be a connected graph. The Steiner k-Wiener index $S{W}_k\left(G\right)$ of graph G is defined as $S{W}_k\left(G\right)={\displaystyle \sum _{S\subseteq V\left(G\right),\left|S\right|=k}}{d}_G\left(S\right)$, where $d_G\left(S\right)$ represents the minimum size of a connected subgraph of G that connects S. Using some graph operations, we obtain the minimum value and the second minimum value of the Steiner k-Wiener index for cacti with order n and t cycles, and we characterize the corresponding extremal graphs by exploiting structural symmetries. Full article

Traditional educational assessment systems suffer from inefficient question selection strategies that fail to optimally probe student knowledge while requiring extensive testing time. We present a novel hierarchical probabilistic neural framework that integrates Bayesian inference with symmetric deep neural architectures to enable adaptive, efficient knowledge assessment. Our method models student knowledge as latent representations within a graph-structured concept dependency network, where probabilistic mastery states, updated through variational inference, are encoded by symmetric graph properties and symmetric concept representations that preserve structural equivalences across similar knowledge configurations. The system employs a symmetric dual-network architecture: a concept embedding network that learns scale-invariant hierarchical knowledge representations from assessment data and a question selection network that optimizes symmetric information gain through deep reinforcement learning with symmetric reward structures. We introduce a novel uncertainty-aware objective function that leverages symmetric uncertainty measures to balance exploration of uncertain knowledge regions with exploitation of informative question patterns. The hierarchical structure captures both fine-grained concept mastery and broader domain understanding through multi-scale graph convolutions that preserve local graph symmetries and global structural invariances. Our symmetric information-theoretic method ensures balanced assessment strategies that maintain diagnostic equivalence across isomorphic concept subgraphs. Experimental validation on large-scale educational datasets demonstrates that our method achieves 76.3% diagnostic accuracy while reducing the question count by 35.1% compared to traditional assessments. The learned concept embeddings reveal interpretable knowledge structures with symmetric dependency patterns that align with pedagogical theory. Our work generalizes across domains and student populations through symmetric transfer learning mechanisms, providing a principled framework for intelligent tutoring systems and adaptive testing platforms. The integration of probabilistic reasoning with symmetric neural pattern recognition offers a robust solution to the fundamental trade-off between assessment efficiency and diagnostic precision in educational technology. Full article

Salient object detection is a challenging task in the field of computer vision. The graph-based model has attracted lots of research attention and achieved remarkable progress in this task, which constructs graphs to formulate the intrinsic structure of any image. Nevertheless, the existing graph-based salient object detection methods still have certain limitations and face two major challenges: (1) Previous graphs are constructed by the Gaussian kernel, but they are often corrupted by original noise. (2) They fail to capture common representations and complementary diversity of multi-view features. Both of these degrade saliency performance. In this paper, we propose a novel method, called multi-scale pure graphs with multi-view subspace clustering for salient object detection. Its main contribution is a new, two-stage graph, constructed and constrained by multi-view subspace clustering with sparsity and low rank. One of the advantages is that the multi-scale pure graphs upgrade the saliency performance from the propagation of noise in the graph matrix. Another advantage is that the multi-scale pure graphs exploit consistency and complementary information among multi-view features, which can effectively boost the capability of the graphs. In addition, to verify the impact of the symmetry of the multi-scale pure graphs on the salient object detection performance, we compared the proposed two-stage graphs, which included cases considering the multi-scale pure graphs and those not considering the multi-scale pure graphs. The experimental results were derived using several RGB benchmark datasets and several state-of-the-art algorithms for comparison. The results demonstrate that the proposed method outperforms the state-of-the-art approaches in terms of multiple standard evaluation metrics. This paper reveals that multi-view subspace clustering is beneficial in promoting graph-based saliency detection tasks. Full article

Promoting the sustainable development of virtual water trade is of great significance to safeguarding China’s water resource security and balanced regional economic growth. This study analyzes the virtual water trade network among 31 Chinese provinces based on multi-regional input–output tables from 2012, 2015, and 2017, using total trade decomposition, social network analysis, and exponential random graph models. The key findings are as follows: (1) The total virtual water trade volume remains stable, with Xinjiang, Jiangsu, and Guangdong as the core regions, while remote areas such as Shaanxi and Gansu have lower trade volumes. The primary industry dominates, and it is driven by simple value chains. (2) Provinces such as Xinjiang, Heilongjiang, and Jiangsu form the network’s core. Network density and symmetry increased from 2012 to 2015 but declined slightly in 2017, with efficiency peaking and then dropping, and the clustering coefficient decreased annually. Four economic sectors exhibit distinct interactions: frequent two-way flows in Sector 1, significant inflows in Sector 2, prominent net spillovers in Sector 3, and key brokers in Sector 4. (3) The network evolved from a core-periphery structure with weak ties to a stable, heterogeneous, and resilient system. (4) Influencing factors, such asper capita water resources, economic development, and population, significantly impact trade. Similarities in economic levels, population, and water endowments promote trade, while spatial distance has a limited effect, with geographic proximity showing a significant negative impact on long-distance trade. Full article

To address issues commonly observed during the inference phase of large language models—such as inconsistent labels, formatting errors, or semantic deviations—a series of targeted strategies has been proposed. First, a relation label refinement strategy based on semantic similarity and syntactic structure has been designed to calibrate the model’s outputs, thereby improving the accuracy and consistency of label prediction. Second, to meet the contextual modeling needs of different types of instance bags, a multi-level contextual augmentation strategy has been constructed. For multi-sentence instance bags, a graph-based retrieval enhancement mechanism is introduced, which integrates intra-bag entity co-occurrence networks with document-level sentence association graphs to strengthen the model’s understanding of cross-sentence semantic relations. For single-sentence instance bags, a semantic expansion strategy based on term frequency-inverse document frequency is employed to retrieve similar sentences. This enriches the training context under the premise of semantic consistency, alleviating the problem of insufficient contextual information. Notably, the proposed multi-granularity framework captures semantic symmetry between entities and relations across different levels of context, which is crucial for accurate and balanced relation understanding. The proposed methodology offers practical advancements for semantic analysis applications, particularly in knowledge graph development. Full article

Many challenges in solving large graph coloring through parallel strategies remain unresolved. Previous algorithms based on Pregel-like frameworks, such as Apache Giraph, encounter parallelism bottlenecks due to sequential execution and the need for a full graph traversal in certain stages. Additionally, GPU-based algorithms face the dilemma of costly and time-consuming processing when moving complex graph applications to GPU architectures. In this study, we propose Spardex, a novel parallel and distributed graph coloring optimization algorithm designed to overcome and avoid these challenges. We design a symmetry-driven optimization approach wherein the EdgePartition1D strategy in GraphX induces partitioning asymmetry, leading to overlapping locally symmetric regions. This structure is leveraged through asymmetric partitioning and symmetric reassembly to reduce the search space. A two-stage pipeline consisting of partitioned repaint and core conflict detection is developed, enabling the precise correction of conflicts without traversing the entire graph as in previous algorithms. We also integrate symmetry principles from combinatorial optimization into a distributed computing framework, demonstrating that leveraging locally symmetric subproblems can significantly enhance the efficiency of large-scale graph coloring. Combined with Spark-specific optimizations such as AQE skew join optimization, all these techniques contribute to an efficient parallel graph coloring optimization in Spardex. We conducted experiments using the Aliyun Cloud platform. The results demonstrate that Spardex achieves a reduction of 8–72% in the number of colors and a speedup of 1.13–10.27 times over concurrent algorithms. Full article

As Advanced Persistent Threats (APTs) continue to evolve, constructing a dynamic cybersecurity knowledge graph requires precise extraction of entity–relationship triples from unstructured threat intelligence. Existing approaches, however, face significant challenges in modeling low-frequency threat associations, extracting multi-relational entities, and resolving overlapping entity scenarios. To overcome these limitations, we propose the Symmetry-Aware Prototype Contrastive Learning (SAPCL) framework for joint entity and relation extraction. By explicitly modeling syntactic symmetry in attack-chain dependency structures and its interaction with asymmetric adversarial semantics, SAPCL integrates dependency relation types with contextual features using a type-enhanced Graph Attention Network. This symmetry–asymmetry fusion facilitates a more effective extraction of multi-relational triples. Furthermore, we introduce a triple prototype contrastive learning mechanism that enhances the robustness of low-frequency relations through hierarchical semantic alignment and adaptive prototype updates. A non-autoregressive decoding architecture is also employed to globally generate multi-relational triples while mitigating semantic ambiguities. SAPCL was evaluated on three publicly available CTI datasets: HACKER, ACTI, and LADDER. It achieved F1-scores of 56.63%, 60.21%, and 53.65%, respectively. Notably, SAPCL demonstrated a substantial improvement of 14.5 percentage points on the HACKER dataset, validating its effectiveness in real-world cyber threat extraction scenarios. By synergizing syntactic–semantic multi-feature fusion with symmetry-driven dynamic representation learning, SAPCL establishes a symmetry–asymmetry adaptive paradigm for cybersecurity knowledge graph construction, thus enhancing APT attack tracing, threat hunting, and proactive cyber defense. Full article

The inherent symmetry in traffic flow patterns plays a fundamental role in urban transportation systems. This study proposes a Dynamic Graph Convolutional Recurrent Adaptive Network (DGCRAN) for traffic flow prediction, leveraging symmetry principles in spatial–temporal dependencies. Unlike conventional models relying on static graph structures that often break real-world symmetry relationships, our approach introduces two key innovations respecting the dynamic symmetry of traffic networks: First, a Dynamic Graph Convolutional Recurrent Network (DGCRN) is proposed that preserves and adapts to the time-varying symmetry in node associations, and an Adaptive Graph Convolutional Network (AGCN) that captures the symmetric and asymmetric patterns between nodes. The experimental results on PEMS03, PEMS04, and PEMS08 datasets demonstrate that DGCRAN maintains superior performance symmetry across metrics: reducing MAE, RMSE, and MAPE by average margins of 12.7%, 10.3%, and 14.2%, respectively, compared to 15 benchmarks. Notably, the model achieves maximum MAE reduction of 21.33% on PEMS08, verifying its ability to model the symmetric and asymmetric characteristics in traffic flow dependencies while significantly improving prediction accuracy and generalization capability. Full article

Entity alignment is a critical technique for integrating diverse knowledge graphs. Although existing methods have achieved impressive success in traditional entity alignment, they may struggle to handle the complexities arising from interactions and dependencies in multi-modal knowledge. In this paper, a novel multi-modal entity alignment model called ERMF is proposed, which leverages distinct modal characteristics of entities to identify equivalent entities across different multi-modal knowledge graphs. The symmetry in cross-modal interactions and hierarchical feature fusion is a core design principle of our approach. Specifically, we first utilize different feature encoders to independently extract features from different modalities. Concurrently, visual features and nearest neighbor negative sampling methods are incorporated to design a vision-guided negative sample generation strategy based on contrastive learning, ensuring a symmetric balance between positive and negative samples and guiding the model to learn effective relationship embeddings. Subsequently, in the feature fusion stage, we propose a multi-layer feature fusion approach that incorporates cross-attention and cross-modal attention mechanisms with symmetric processing of intra- and inter-modal correlations, thereby obtaining multi-granularity features. Extensive experiments were conducted on two public datasets, namely FB15K-DB15K and FB15K-YAGO15K. With 20% aligned seeds, ERMF improves Hits@1 by 8.4% and 26%, and MRR by 6% and 19.2% compared to the best baseline. The symmetric architecture of our model ensures the robust and balanced utilization of multi-modal information, aligning with the principles of structural and functional symmetry in knowledge integration. Full article

In this study, we define the $k$-Cullen, $k$-Cullen–Lucas, and Modified $k$-Cullen sequences, and certain terms in these sequences are given. Then, we obtain the Binet formulas, generating functions, summation formulas, etc. In addition, we examine the relations among the terms of the $k$-Cullen, $k$-Cullen–Lucas, Modified $k$-Cullen, Cullen, Cullen–Lucas, Modified Cullen, $k$-Woodall, $k$-Woodall–Lucas, Modified $k$-Woodall, Woodall, Woodall–Lucas, and Modified Woodall sequences. The generating functions were derived and analyzed, especially for cases where Fibonacci numbers were assigned to parameter $k.$ Graphical representations of the generating functions and their logarithmic transformations revealed interesting growth trends and convergence behavior. Further, by multiplying the generating functions with exponential expressions such as $e^k$, we explored the self-similar nature and mirrored dynamics among the sequences. Specifically, it was observed that the Modified Cullen sequence exhibited a symmetric and inverse-like resemblance to the Cullen and Cullen–Lucas sequences, suggesting the presence of deeper structural dualities. Additionally, indefinite integrals of the generating functions were computed and visualized over a range of Fibonacci-indexed k values. These integral-based graphs further reinforced the phenomenon of symmetry and self-similarity, particularly in the Modified Cullen sequence. A key insight of this study is the discovery of a structural duality between the Modified Cullen and standard Cullen-type sequences, supported both algebraically and graphically. This duality suggests new avenues for analyzing generalized recursive sequences through generating function transformations. This observation provides new insight into the structural behavior of generalized Cullen-type sequences. Full article

This study introduces a novel contrastive learning-based X-ray diffraction (XRD) analysis framework, an SE(3)-equivariant graph neural network (E3NN) based Atomic Cluster Expansion Neural Network (EACNN), which reduces the strong dependency on databases and initial models in traditional methods. By integrating E3NN with atomic cluster expansion (ACE) techniques, a dual-tower contrastive learning model has been developed, mapping crystal structures and XRD patterns to a continuous embedding space. The EACNN model retains hierarchical features of crystal systems through symmetry-sensitive encoding mechanisms and utilizes relationship mining via contrastive learning to replace rigid classification boundaries. This approach reveals gradual symmetry-breaking patterns between monoclinic and orthorhombic crystal systems in the latent space, effectively addressing the recognition challenges associated with low-symmetry systems and small sample space groups. Our investigation further explores the potential for model transfer to experimental data and multimodal extensions, laying the theoretical foundation for establishing a universal structure–property mapping relationship. Full article

Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering and matching strategies by decreasing redundancy and enhancing efficiency. Traditional influence graph models struggle to address such complexities. To address this gap, we present the novel concepts of covering and matching in intuitionistic fuzzy influence graphs (IFIGs) for modeling academic social networks. These graphs incorporate degrees of membership and non-membership to better reflect uncertainty in influence patterns. Thus, the main aim of this study is to initiate the concepts of covering and matching within the IFIG paradigm and provide its application in social networks. Initially, we establish some basic terms related to covering and matching with illustrative examples. We also investigate complete and complete bipartite IFIGs. To verify the practicality of this study, student interactions across subjects are analyzed using strong paths and strong independent sets. The proposed model is then evaluated using the TOPSIS method to rank participants based on their influence. Moreover, a comparative study is conducted to demonstrate that the proposed model not only handles uncertainty effectively but also performs better than the existing approaches. Full article

The concept of domination is introduced within the context of signed fuzzy graphs (signed-FGs), along with examples, as a novel metric to evaluate graph stability under varying conditions. This metric particularly focuses on dominant sets and integrity measures, providing a well-rounded approach to assessing the structural stability of signed- FGs. The necessity of fulfilling the domination integrity condition in evaluating the performance of signed-FGs is highlighted through a discussion on its formulation and an analysis of its upper and lower bounds. An algorithm for identifying strong arcs and classifying them is presented, along with an algorithm for identifying signed fuzzy trees. Furthermore, the role of symmetry in signed-FGs is explored, revealing that symmetrical structures often correspond to higher domination integrity, thus contributing to the improved stability and predictability of the graphs. The paper also establishes important connections with classical graph varieties, such as complete graphs and their variations, demonstrating that changes in domination integrity increase with certain parameters. Additionally, real-life scenarios where these concepts are applicable serve to complement the theoretical results. The case study findings illustrate the significance of domination integrity in practical contexts by emphasizing various instances where it can be determined and utilized. Such instances include identifying independent dominant sets in path and cycle diagrams, as well as estimating the lower bounds of domination integrity in these structures. The estimation of domination integrity using block graph methods is underscored as crucial for enhancing the efficiency of signed-FG applications. Full article

In the evolving landscape of healthcare, telemedicine has emerged as a transformative solution, effectively bridging gaps in medical service delivery across diverse geographic regions. Particularly in rural areas, where access to immediate and specialized care remains limited, store-and-forward telemedicine provides a powerful and practical approach. In rural emergency healthcare settings, resource limitations, specialist shortages, and unreliable connectivity frequently delay critical medical interventions. To address these challenges, this study proposes a store-and-forward telemedicine framework optimized through the use of queueing networks, aiming to enhance emergency response efficiency. The proposed model is structured as a four-node system comprising initial registration, consultation, diagnosis, and treatment. Each node operates as a service queue where patient data are sequentially collected, prioritized, and forwarded. By employing an open queueing network structure, the model devises steady-state probabilities for the number of patients at each node, facilitating a detailed performance analysis of patient flows. Symmetry plays a critical role in maintaining patient flow balance and system stability within the store-and-forward telemedicine model. When the routing probabilities between nodes are balanced, the queueing network exhibits probabilistic symmetry, ensuring consistent transition behavior. Moreover, the directed graph representation of the system demonstrates structural symmetry, reflecting identical service times at all nodes and uniform transition probabilities between nodes. Incorporating the concept of symmetry enables a simplified analytical approach, reduces computational complexity, and provides a more accurate approximation model for evaluating system performance. Full article