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30 pages, 4522 KiB  
Review
Mapping Scientific Knowledge on Patents: A Bibliometric Analysis Using PATSTAT
by Fernando Henrique Taques
FinTech 2025, 4(3), 32; https://doi.org/10.3390/fintech4030032 - 18 Jul 2025
Viewed by 757
Abstract
The digital economy has amplified the role of technological innovation in transforming financial services and business models. Patent data offer valuable insights into these dynamics, especially within the growing FinTech ecosystem. This study conducts a bibliometric analysis of academic research that utilizes PATSTAT, [...] Read more.
The digital economy has amplified the role of technological innovation in transforming financial services and business models. Patent data offer valuable insights into these dynamics, especially within the growing FinTech ecosystem. This study conducts a bibliometric analysis of academic research that utilizes PATSTAT, a global database managed by the European Patent Office, focusing on its application in studies related to digital innovation, finance, and economic transformation. A systematic mapping of publications indexed in Scopus, Web of Science, Wiley, Emerald, and Springer Nature is carried out using Biblioshiny and Bibliometrix in RStudio 2025.05.0, complemented by graph-based visualizations via VOSviewer 1.6.20. The findings reveal a growing body of research that leverages PATSTAT to explore technological trajectories, intellectual property strategies, and innovation systems, particularly in areas such as blockchain technologies, AI-driven finance, digital payments, and smart contracts. This study contributes to the literature by highlighting the strategic value of patent analytics in the FinTech landscape and offers a reference point for researchers and decision-makers aiming to understand emerging trends in financial technologies and the digital economy. Full article
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41 pages, 1006 KiB  
Article
A Max-Flow Approach to Random Tensor Networks
by Khurshed Fitter, Faedi Loulidi and Ion Nechita
Entropy 2025, 27(7), 756; https://doi.org/10.3390/e27070756 - 15 Jul 2025
Viewed by 233
Abstract
The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. [...] Read more.
The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. These can be regarded as specific probabilistic models for tensors with particular geometry dictated by a graph (or network) structure. First, we introduce a model of RTN obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). The entanglement spectrum of the resulting random state is analyzed along a given bipartition of the local Hilbert spaces. The limiting eigenvalue distribution of the reduced density operator of the RTN state is provided in the limit of large local dimension. This limiting value is described through a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, an explicit formula for the limiting eigenvalue distribution is provided using classical and free multiplicative convolutions. The physical implications of these results are discussed, allowing the analysis to move beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN. Full article
(This article belongs to the Section Quantum Information)
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31 pages, 423 KiB  
Article
The Behavior of Tree-Width and Path-Width Under Graph Operations and Graph Transformations
by Frank Gurski and Robin Weishaupt
Algorithms 2025, 18(7), 386; https://doi.org/10.3390/a18070386 - 25 Jun 2025
Viewed by 454
Abstract
Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width under various unary and binary graph transformations. For [...] Read more.
Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width under various unary and binary graph transformations. For considered transformations, we provide upper and lower bounds for the tree-width and path-width of the resulting graph in terms of those of the initial graphs or argue why such bounds are impossible to specify. Among the studied unary transformations are vertex addition, vertex deletion, edge addition, edge deletion, subgraphs, vertex identification, edge contraction, edge subdivision, minors, powers of graphs, line graphs, edge complements, local complements, Seidel switching, and Seidel complementation. Among the studied binary transformations, we consider the disjoint union, join, union, substitution, graph product, 1-sum, and corona of two graphs. Full article
(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)
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18 pages, 2689 KiB  
Article
Blockchain-Enabled, Nature-Inspired Federated Learning for Cattle Health Monitoring
by Lakshmi Prabha Ganesan and Saravanan Krishnan
Informatics 2025, 12(3), 57; https://doi.org/10.3390/informatics12030057 - 20 Jun 2025
Viewed by 543
Abstract
Traditional cattle health monitoring systems rely on centralized data collection, posing significant challenges related to data privacy, network connectivity, model reliability, and trust. This study introduces a novel, nature-inspired federated learning (FL) framework for cattle health monitoring, integrating blockchain to ensure model validation, [...] Read more.
Traditional cattle health monitoring systems rely on centralized data collection, posing significant challenges related to data privacy, network connectivity, model reliability, and trust. This study introduces a novel, nature-inspired federated learning (FL) framework for cattle health monitoring, integrating blockchain to ensure model validation, system resilience, and reputation management. Inspired by the fission–fusion dynamics of elephant herds, the framework adaptively forms and merges subgroups of edge nodes based on six key parameters: health metrics, activity levels, geographical proximity, resource availability, temporal activity, and network connectivity. Graph attention networks (GATs) enable dynamic fission, while Density-Based Spatial Clustering of Applications with Noise (DBSCAN) supports subgroup fusion based on model similarity. Blockchain smart contracts validate model contributions and ensure that only high-performing models participate in global aggregation. A reputation-driven mechanism promotes reliable nodes and discourages unstable participants. Experimental results show the proposed framework achieves 94.3% model accuracy, faster convergence, and improved resource efficiency. This adaptive and privacy-preserving approach transforms cattle health monitoring into a more trustworthy, efficient, and resilient process. Full article
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29 pages, 1086 KiB  
Article
Economic Logistics Optimization in Fire and Rescue Services: A Case Study of the Slovak Fire and Rescue Service
by Martina Mandlikova and Andrea Majlingova
Logistics 2025, 9(2), 74; https://doi.org/10.3390/logistics9020074 - 12 Jun 2025
Viewed by 803
Abstract
Background: Economic logistics in fire and rescue services is a critical determinant of operational readiness, fiscal sustainability, and resilience to large-scale emergencies. Despite its strategic importance, logistics remains under-researched in Central and Eastern European contexts, where legacy governance structures and EU-funded modernization [...] Read more.
Background: Economic logistics in fire and rescue services is a critical determinant of operational readiness, fiscal sustainability, and resilience to large-scale emergencies. Despite its strategic importance, logistics remains under-researched in Central and Eastern European contexts, where legacy governance structures and EU-funded modernization coexist with systemic inefficiencies. This study focuses on the Slovak Fire and Rescue Service (HaZZ) as a case to explore how economic logistics systems can be restructured for greater performance and value. Objective: The objective of this paper was to evaluate the structure, performance, and reform potential of the logistics system supporting HaZZ, with a focus on procurement efficiency, lifecycle costing, digital integration, and alignment with EU civil protection standards. Methods: A mixed-methods design was applied, comprising the following: (1) Institutional analysis of governance, budgeting, and legal mandates based on semi-structured expert interviews with HaZZ and the Ministry of Interior officers (n = 12); (2) comparative benchmarking with Germany, Austria, the Czech Republic, and the Netherlands; (3) financial analysis of national logistics expenditures (2019–2023) using Total Cost of Ownership (TCO) principles, completed with the visualization of cost trends and procurement price variance through original heat maps and time-series graphs. Results: The key findings are as follows: (1) HaZZ operates a formally centralized but practically fragmented logistics model across 51 district units, lacking national coordination mechanisms and digital infrastructure; (2) Maintenance costs have risen by 42% between 2019 and 2023 despite increasing capital investment due to insufficient lifecycle planning and asset heterogeneity; (3) Price variance for identical equipment categories across regions exceeds 30%, highlighting the inefficiencies in decentralized procurement; (4) Slovakia lacks a national Logistics Information System (LIS), unlike peer countries which have deployed integrated digital platforms (e.g., CELIS in the Czech Republic); (5) Benchmarking reveals high-impact practices in centralized procurement, lifecycle-based contracting, regional logistics hubs, and performance accountability—particularly in Austria and the Netherlands. Impacts: Four high-impact, feasible reforms were proposed: (1) Establishment of a centralized procurement framework; (2) national LIS deployment to unify inventory and asset tracking; (3) adoption of lifecycle-based and performance-based contracting models; (4) development of regional logistics hubs using underutilized infrastructure. This study is among the first to provide an integrated economic and institutional analysis of the Fire and Rescue Service logistics in a post-socialist EU member state. It offers a structured, transferable reform roadmap grounded in comparative evidence and adapted to Slovakia’s hybrid governance model. The research bridges gaps between modernization policy, procurement law, and digital public administration in the context of emergency services. Full article
(This article belongs to the Special Issue Current & Emerging Trends to Achieve Sustainable Supply Trends)
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20 pages, 1081 KiB  
Article
Smart Contract Security in Decentralized Finance: Enhancing Vulnerability Detection with Reinforcement Learning
by Jose Juan de Leon, Cenchuan Zhang, Christos-Spyridon Koulouris, Francesca Medda and Rahul
Appl. Sci. 2025, 15(11), 5924; https://doi.org/10.3390/app15115924 - 24 May 2025
Viewed by 1329
Abstract
The growing interest in decentralized finance (DeFi), driven by advancements in blockchain technologies such as Ethereum, highlights the crucial role of smart contracts. However, the inherent openness of blockchains creates an extensive attack surface, exposing participants’ funds to undetected security flaws. In this [...] Read more.
The growing interest in decentralized finance (DeFi), driven by advancements in blockchain technologies such as Ethereum, highlights the crucial role of smart contracts. However, the inherent openness of blockchains creates an extensive attack surface, exposing participants’ funds to undetected security flaws. In this work we investigated the use of deep reinforcement learning techniques, specifically Deep Q-Network (DQN) and Proximal Policy Optimization (PPO), for detecting and classifying vulnerabilities in smart contracts. This approach utilizes control flow graphs (CFGs) generated through EtherSolve to capture the semantic features of contract bytecode, enabling the reinforcement learning models to recognize patterns and make more accurate predictions. Experimental results from extensive public datasets of smart contracts revealed that the PPO model performs better than DQN and demonstrates effectiveness in identifying unchecked-call vulnerability. The PPO model exhibits more stable and consistent learning patterns and achieves higher overall rewards. This research introduces a machine learning method for enhancing smart contract security, reducing financial risks for users, and contributing to future developments in reinforcement learning applications. Full article
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35 pages, 467 KiB  
Article
SCH-Hunter: A Taint-Based Hybrid Fuzzing Framework for Smart Contract Honeypots
by Haoyu Zhang, Baotong Wang, Wenhao Fu and Leyi Shi
Information 2025, 16(5), 405; https://doi.org/10.3390/info16050405 - 14 May 2025
Viewed by 694
Abstract
Existing smart contract honeypot detection approaches exhibit high false negatives and positives due to (i) their inability to generate transaction sequences triggering order-dependent traps and (ii) their limited code coverage from traditional fuzzing’s random mutations. In this paper, we propose a hybrid fuzzing [...] Read more.
Existing smart contract honeypot detection approaches exhibit high false negatives and positives due to (i) their inability to generate transaction sequences triggering order-dependent traps and (ii) their limited code coverage from traditional fuzzing’s random mutations. In this paper, we propose a hybrid fuzzing framework for smart contract honeypot detection based on taint analysis, SCH-Hunter. SCH-Hunter conducts source-code-level feature analysis of smart contracts and extracts data dependency relationships between variables from the generated Control Flow Graph to construct specific transaction sequences for fuzzing. A symbolic execution module is also introduced to resolve complex conditional branches that fuzzing alone fails to penetrate, enabling constraint solving. Furthermore, real-time dynamic taint propagation monitoring is implemented using taint analysis techniques, leveraging taint flow information to optimize seed mutation processes, thereby directing mutation resources toward high-value code regions. Finally, by integrating EVM (Ethereum Virtual Machine) code instrumentation with taint information flow analysis, the framework effectively identifies and detects security-sensitive operations, ultimately generating a comprehensive detection report. Empirical results are as follows. (i) For code coverage, SCH-Hunter performs better than the state-of-art tool, HoneyBadger, achieving higher average code coverage rates on both datasets, surpassing it by 4.79% and 17.41%, respectively. (ii) For detection capabilities, SCH-Hunter is not only roughly on par with HoneyBadger in terms of precision and recall rate but also capable of detecting a wider variety of smart contract honeypot techniques. (iii) For the evaluation of components, we conducted three ablation studies to demonstrate that the proposed modules in SCH-Hunter significantly improve the framework’s detection capability, code coverage, and detection efficiency, respectively. Full article
(This article belongs to the Topic Software Engineering and Applications)
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24 pages, 3146 KiB  
Article
Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction
by Kanyuta Poochinapan, Sompop Moonchai, Tanadon Chaobankoh and Phakdi Charoensawan
Mathematics 2025, 13(10), 1569; https://doi.org/10.3390/math13101569 - 9 May 2025
Viewed by 417
Abstract
A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular [...] Read more.
A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular instances in the setting of integral equations and differential equations. We also describe how a class of third-order boundary value problems satisfying the present contraction can be solved iteratively. To support our findings, we conduct a series of numerical experiments with various third-order boundary value problems. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
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20 pages, 2779 KiB  
Article
Effects of Policy Communication Changes on Social Media: Before and After Policy Adjustment
by Zenglei Yue and Guang Yu
Systems 2025, 13(4), 248; https://doi.org/10.3390/systems13040248 - 2 Apr 2025
Viewed by 754
Abstract
The structure of a policy communication network shows the effect of policy communication on social media. Policies need to be dynamically adjusted during the implementation process, which may affect the policy’s interaction on social media. Based on the Policy Network Theory, this study [...] Read more.
The structure of a policy communication network shows the effect of policy communication on social media. Policies need to be dynamically adjusted during the implementation process, which may affect the policy’s interaction on social media. Based on the Policy Network Theory, this study explores the effects of policy communication changes on social media before and after the adjustment of China’s Mass Entrepreneurship and Innovation (MEI) Policy using Exponential Random Graph Models (ERGMs) analysis and community analysis. The study reveals that after the policy adjustment, the communication network structure indicated a significant increase in triangular configurations, yet the formation of edges remained constrained. Meanwhile, cross-community connections in the communication network decreased, with communities exhibiting localized contraction, and emotional polarization becoming more pronounced. These phenomena occurred because policy adjustments have boosted interaction levels through new incentive mechanisms, whereas the content and delivery methods of policy communication remain insufficiently engaging, which constrains relationship-building. Additionally, the policy’s evolution from a mobilization–participation model to a vertical governance paradigm has systematically reconfigured inter-community interaction patterns, resulting in structural transformations in cross-group information flows. To enhance the dissemination of policies on social media, it is recommended to intervene in the policy communication network structure through role embedding, shift from a reactive public sentiment management paradigm to proactive emotional governance, and strengthen policy communication strategies that emphasize emotional resonance. These measures can improve the effectiveness of policy communication and help address the challenges posed by emotional polarization and network fragmentation. Full article
(This article belongs to the Section Systems Practice in Social Science)
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17 pages, 3036 KiB  
Article
Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators
by Nijia Ye and Zhengwei Geng
Mathematics 2025, 13(7), 1076; https://doi.org/10.3390/math13071076 - 25 Mar 2025
Viewed by 253
Abstract
To address the complexity of constructing traditional topological contracted graphs due to the significant increase in the types and quantities of basic links during the synthesis of complex parallel mechanisms, this paper introduces a novel concept termed “Simplified Contraction Graph (SCG)”. The SCG [...] Read more.
To address the complexity of constructing traditional topological contracted graphs due to the significant increase in the types and quantities of basic links during the synthesis of complex parallel mechanisms, this paper introduces a novel concept termed “Simplified Contraction Graph (SCG)”. The SCG achieves a deeper level of simplification by omitting the consideration of ternary links on the basis of traditional contracted graphs. Firstly, this paper defines the application of characteristic strings to express the construction rules of SCG, thereby transforming the construction process into an automated generation problem of characteristic strings. Building on this, to mitigate the interference of link arrangement in the construction of conventional SCGs, this paper further proposes the concept of a simplified SCG and investigates its isomorphism properties. A program is designed based on the criteria for generating characteristic strings and isomorphism judgment, successfully generating several special SCGs. Finally, this paper introduces the edge-adding method, which enables the reconstruction of special SCGs into ordinary SCGs and contracted graphs, providing an effective tool for the topological synthesis of parallel mechanisms. Full article
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25 pages, 18192 KiB  
Article
AML-Based Multi-Dimensional Co-Evolution Approach Supported by Blockchain: Architecture Design and Case Study on Intelligent Production Lines for Industry 4.0
by Kai Ding, Detlef Gerhard and Liuqun Fan
Information 2025, 16(3), 243; https://doi.org/10.3390/info16030243 - 18 Mar 2025
Cited by 1 | Viewed by 648
Abstract
Based on Automation ML (AML), Intelligent Production Lines (IPLs) for Industry 4.0 can effectively organize multi-dimensional data and models. However, this process requires interdisciplinary and multi-team contributions, which often involve the dual pressures of private data encryption and public data sharing. As a [...] Read more.
Based on Automation ML (AML), Intelligent Production Lines (IPLs) for Industry 4.0 can effectively organize multi-dimensional data and models. However, this process requires interdisciplinary and multi-team contributions, which often involve the dual pressures of private data encryption and public data sharing. As a transparent decentralized network, blockchain’s compatibility with the challenges of AML collaboration processes, data security, and privacy is not ideal. This paper proposes a new method to enhance the collaborative evolution of IPLs. Its innovations are, firstly, developing a comprehensive two-layer management model, combining blockchain with the Interplanetary File System (IPFS) to build an integrated solution for private and public hybrid containers based on a collaborative model; secondly, designing a version co-evolution management method by combining smart contract workflows and AML multi-dimensional modeling processes; meanwhile, introducing a specially designed conflict resolution mechanism based on the graph model to maintain consistency in version multi-batch management and; finally, using the test cases established in the lab’s I5Blocks for verification. Full article
(This article belongs to the Special Issue Blockchain and AI: Innovations and Applications in ICT)
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21 pages, 632 KiB  
Article
MVCG-SPS: A Multi-View Contrastive Graph Neural Network for Smart Ponzi Scheme Detection
by Xiaofang Jiang and Wei-Tek Tsai
Appl. Sci. 2025, 15(6), 3281; https://doi.org/10.3390/app15063281 - 17 Mar 2025
Viewed by 806
Abstract
Detecting fraudulent activities such as Ponzi schemes within smart contract transactions is a critical challenge in decentralized finance. Existing methods often fail to capture the heterogeneous, multi-faceted nature of blockchain data, and many graph-based models overlook the contextual patterns that are vital for [...] Read more.
Detecting fraudulent activities such as Ponzi schemes within smart contract transactions is a critical challenge in decentralized finance. Existing methods often fail to capture the heterogeneous, multi-faceted nature of blockchain data, and many graph-based models overlook the contextual patterns that are vital for effective anomaly detection. In this paper, we propose MVCG-SPS, a Multi-View Contrastive Graph Neural Network designed to address these limitations. Our approach incorporates three key innovations: (1) Meta-Path-Based View Construction, which constructs multiple views of the data using meta-paths to capture different semantic relationships; (2) Reinforcement-Learning-Driven Multi-View Aggregation, which adaptively combines features from multiple views by optimizing aggregation weights through reinforcement learning; and (3) Multi-Scale Contrastive Learning, which aligns embeddings both within and across views to enhance representation robustness and improve anomaly detection performance. By leveraging a multi-view strategy, MVCG-SPS effectively integrates diverse perspectives to detect complex fraudulent behaviors in blockchain ecosystems. Extensive experiments on real-world Ethereum datasets demonstrated that MVCG-SPS consistently outperformed state-of-the-art baselines across multiple metrics, including F1 Score, AUPRC, and Rec@K. Our work provides a new direction for multi-view graph-based anomaly detection and offers valuable insights for improving security in decentralized financial systems. Full article
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22 pages, 2442 KiB  
Article
Generator-Level Transient Stability Assessment in Power System Based on Graph Deep Learning with Sparse Hybrid Pooling
by Jiyu Huang, Lin Guan, Yinsheng Su, Zihan Cai, Liukai Chen, Yongzhe Li and Jinyang Zhang
Electronics 2025, 14(6), 1180; https://doi.org/10.3390/electronics14061180 - 17 Mar 2025
Viewed by 373
Abstract
Aimed at increasingly challenging operation conditions in modern power systems, online pre-fault transient stability assessment (TSA) acts as a significant tool to detect latent stability risks and provide abundant generator-level information for preventive controls. Distinguished from “system-level” to describe terms concerning the whole [...] Read more.
Aimed at increasingly challenging operation conditions in modern power systems, online pre-fault transient stability assessment (TSA) acts as a significant tool to detect latent stability risks and provide abundant generator-level information for preventive controls. Distinguished from “system-level” to describe terms concerning the whole system, here “generator-level” describes those concerning a generator. Due to poor topology-related expressive power, existing deep learning-based TSA methods can hardly predict generator-level stability indexes, unless they adopt the generator dynamics during and after faults by time-domain simulation (TDS) as the model input. This makes it difficult to fully leverage the speed advantages of deep learning. In this paper, we propose a generator-level TSA (GTSA) scheme based on topology-oriented graph deep learning which no longer requires time-domain simulation to provide the dynamic features. It integrates two modules to extract the network-dominated interaction trends from only the steady-state information. A sparse Edge Contraction-based Attention Pooling (ECAP) scheme is designed to dynamically simplify the network structure by feature aggregation, where the generator-specific information and key area features are kept. A Global Attention Pooling (GAP) module works to generate the interaction features among generators across the system. Hence, the constructed ECAP&GAP-GTSA scheme can not only output the system stability category but also provide the dominant generators and inter-generator oscillation severity. The performance as well as interpretability and generalization of our scheme are validated on the IEEE 39-bus system and the IEEE 300-bus system under various operation topologies and generator scales. The averaging inference time of a sample on the IEEE 39-bus system and IEEE 300-bus system is merely 1/671 and 1/149 of that of TDS, while the accuracy reaches about 99%. Full article
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13 pages, 563 KiB  
Article
Stability-Optimized Graph Convolutional Network: A Novel Propagation Rule with Constraints Derived from ODEs
by Liping Chen, Hongji Zhu and Shuguang Han
Mathematics 2025, 13(5), 761; https://doi.org/10.3390/math13050761 - 26 Feb 2025
Cited by 1 | Viewed by 524
Abstract
The node representation learning capability of Graph Convolutional Networks (GCNs) is fundamentally constrained by dynamic instability during feature propagation, yet existing research lacks systematic theoretical analysis of stability control mechanisms. This paper proposes a Stability-Optimized Graph Convolutional Network (SO-GCN) that enhances training stability [...] Read more.
The node representation learning capability of Graph Convolutional Networks (GCNs) is fundamentally constrained by dynamic instability during feature propagation, yet existing research lacks systematic theoretical analysis of stability control mechanisms. This paper proposes a Stability-Optimized Graph Convolutional Network (SO-GCN) that enhances training stability and feature expressiveness in shallow architectures through continuous–discrete dual-domain stability constraints. By constructing continuous dynamical equations for GCNs and rigorously proving conditional stability under arbitrary parameter dimensions using nonlinear operator theory, we establish theoretical foundations. A Precision Weight Parameter Mechanism is introduced to determine critical Frobenius norm thresholds through feature contraction rates, optimized via differentiable penalty terms. Simultaneously, a Dynamic Step-size Adjustment Mechanism regulates propagation steps based on spectral properties of instantaneous Jacobian matrices and forward Euler discretization. Experimental results demonstrate SO-GCN’s superiority: 1.1–10.7% accuracy improvement on homophilic graphs (Cora/CiteSeer) and 11.22–12.09% enhancement on heterophilic graphs (Texas/Chameleon) compared to conventional GCN. Hilbert–Schmidt Independence Criterion (HSIC) analysis reveals SO-GCN’s superior inter-layer feature independence maintenance across 2–7 layers. This study establishes a novel theoretical paradigm for graph network stability analysis, with practical implications for optimizing shallow architectures in real-world applications. Full article
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16 pages, 312 KiB  
Article
New Fixed-Point Results in Controlled Metric Type Spaces with Applications
by Nizar Souayah and Lotfi Hidri
Axioms 2025, 14(2), 85; https://doi.org/10.3390/axioms14020085 - 24 Jan 2025
Viewed by 866
Abstract
In this manuscript, we present several novel results in fixed-point theory for a complete controlled metric space. The first presented result is inspired from the Caristi contraction where we explore the existence and uniqueness of fixed points under specific conditions. Furthermore, we propose [...] Read more.
In this manuscript, we present several novel results in fixed-point theory for a complete controlled metric space. The first presented result is inspired from the Caristi contraction where we explore the existence and uniqueness of fixed points under specific conditions. Furthermore, we propose a graphical form of it by endowing the considered space with a graph and develop a new fixed-point theorem, which is illustrated by two examples. Also, we establish a theorem for the α-admissible mapping. To demonstrate its effectiveness, the last theorem proposes an approach to solve a second-order differential equation. Full article
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