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Edge connectivity of a neutrosophic graph

Neutrosophic Sets and Systems 2025年 81卷 729-740页

作者： Tripathy, Aparna Panada, Amaresh Chandra Behera, Siva Prasad Mohanty, Bhabani S. Department of Mathematics C.V. Raman Global University Odisha Bhubaneswar752054 India Department of Statistics and Applied Mathematics Central University of Tamil Nadu India

Neutosophic graphs are an extension of fuzzy and intuitionistic fuzzy graphs by including the uncertainty, vagueness, and indeterminacy that are normal in the real world. This paper looks into the edge connectivity of a neutrosophic graph, which is a basic parameter that shows how strong and fault-tolerant networks are that are modelled by these graphs. Edge connectivity, which is the smallest number of edges that need to be taken away from a graph to make it trivial or disconnected, is a key concept in figuring out how strong and resilient networks are in many situations. This paper also addresses computational challenges related to determining edge connectivity in neutrosophic graphs. We develop efficient algorithms that minimize computational overhead and ensure accuracy in identifying the critical edge sets. We analyze the performance of these algorithms through both theoretical complexity assessments and empirical evaluations on benchmark datasets. Some of the most important things that the study found were critical edges that, when removed, have a big effect on how connected the graph is and how indeterminacy affects the strength of networks. The research underscores the importance of incorporating neutrosophic parameters into graph connectivity studies to better model and analyse systems characterized by uncertainty and partial knowledge. © 2025, University of New Mexico. All rights reserved.

关键词： consensus algorithm

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Event-triggered State consensus of Heterogeneous Uncertain Second-order Nonlinear Multi-agent Systems

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Zidonghua Xuebao/Acta Automatica Sinica 2025年第4期51卷 804-812页

作者： Li, Zhen-Xing Zhuang, Jiao-Jiao Yang, Cheng-Dong Qiu, Jian-Long Cao, Jin-De School of Automation and Electrical Engineering Linyi University Linyi276000 China School of Mechanical and Vehicle Engineering Linyi University Linyi276000 China School of Information Science and Engineering Linyi University Linyi276000 China School of Mathematics Southeast University Nanjing211189 China

This paper studies event-triggered state consensus of heterogeneous uncertain second-order nonlinear multi-agent systems. Firstly, to deal with the uncertain parameter of each agent dynamics, parameter observers are designed for each agent to asymptotically estimate uncertain parameters, these observers can estimate exact values of uncertain parameters. Secondly, distributed parameter observers are designed for each follower agent to asymptotically estimate uncertain parameters of leader agent, and each agent use its neighbors＇sampled information at the trigger instant to estimate its neighbors＇states. Based on estimated parameters and neighbors＇states, an event-triggered consensus algorithm is proposed, which does not rely on any continuous information transmission among agents. Furthermore, it is proved that multi-agent systems can reach state consensus under the proposed algorithm, and there is no Zeno-behavior. Finally, a multi-pendulum system is given to verify event-triggered consensus algorithm. The simulation experiment results show that the position and velocity of follower agents can track that of leader agent asymptotically, and the average trigger number of overall multi-agent systems is 8.825 per second, comparison simulation experiment shows that the proposed event-triggered consensus algorithm can effectively reduce event-triggered number. © 2025 Science Press. All rights reserved.

关键词： consensus algorithm

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Inversion algorithm determining sharp boundaries in electrical resistivity tomography

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Geophysics 2025年第3期90卷 WA221-WA233页

作者： Ishizu, Keiichi Goto, Tada-Nori Fukahata, Yukitoshi Koike, Katsuaki Vachiratienchai, Chatchai Siripunvaraporn, Weerachai University of Hyogo Graduate School of Science Himeji Japan Kyushu University Department of Earth Resources Engineering Fukuoka Japan University of Hyogo Graduate School of Science Himeji Japan Kyoto University Disaster Prevention Research Institute Kyoto Japan Kyoto University Graduate School of Engineering Kyoto Japan Curl-E Geophysics Co. Ltd. Nakhon Pathom Thailand Mahidol University Department of Physics Faculty of Science Bangkok Thailand

Blurred resistivity boundaries resulting from smoothness-regularized inversions of electrical resistivity tomography (ERT) data can lead to inaccurate interpretations of sharp boundary structures. To address this issue, various ERT inversion algorithms have introduced localized adjustments (localized discontinuities) in the regularization operator at positions where sharp boundaries are anticipated. Current approaches rely on prior information about sharp boundary locations, obtained from complementary geophysical, geologic, and drilling data, to determine the positions and weights for these regularization adjustments. However, such prior information is frequently insufficient, limiting the application of localized regularization adjustments. Accordingly, we develop a sharp boundary inversion (SBI) algorithm using the Akaike Bayesian information criterion (ABIC) that determines the optimal positions and weights for localized regularization adjustments by testing various configurations and selecting the one that minimizes ABIC. A synthetic modeling study demonstrates that the SBI algorithm correctly delineated the sharp boundaries of a conductor. Its application to field data demonstrates that it delineated the sharp boundaries of a utility tunnel, and the size and horizontal position of the recovered tunnel were consistent with the estimated dimensions from the blueprint. As it does not rely heavily on prior information, the SBI algorithm can be applied to a wide range of geophysical survey data, even when prior knowledge of sharp boundary locations is limited. © 2025 The Authors.

关键词： consensus algorithm

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The Coherence and Robustness Analysis for a Family of Unbalanced Networks

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2025年 11卷 378-387页

作者： Liu, Jia-Bao Wang, Xu Hua, Liang Cao, Jinde Chen, Liping Anhui Jianzhu Univ Sch Math & Phys Hefei 230601 Peoples R China Anhui Jianzhu Univ Sch Elect & Informat Engn Hefei 230601 Peoples R China Nantong Univ Sch Elect Engn Nantong 226019 Jiangsu Peoples R China Southeast Univ Sch Math Nanjing 211189 Peoples R China Purple Mt Labs Nanjing 211111 Peoples R China Hefei Univ Technol Sch Elect Engn & Automat Hefei 230009 Peoples R China

This study focuses on the coherence in a class of unbalanced networks, emphasizing the investigation of the impact of leader selection and network parameters on coherence. We discuss three different categories of consensus algorithms: leaderless algorithms of first and second orders, and first-order leader-follower algorithm. Firstly, we derive exact solutions for leaderless network coherence in the first and second orders. Secondly, we design various leader allocation schemes for the first-order leader-follower networks, obtaining expressions correlated with the network scale N, the double-ring cardinalities p and q, and the number of leaders k. Thirdly, we conduct numerical simulations and robustness analyses to explore the impact of leader quantity and topology structure on network coherence. Specifically, the conclusions are as follows: (1) When N decreases, an increase in k demonstrates improved network coherence. (2) The smaller the difference between p and q, the better the coherence. (3) The smaller the sum of p and q, the stronger the robustness. (4) Uniform distribution of k1 and k2 leads to optimal coherence. Finally, the Laplacian energy and Kirchhoff index of the network are analyzed.

关键词： Coherence Robustness Laplace equations Topology Eigenvalues and eigenfunctions Symmetric matrices Numerical simulation consensus algorithm Vectors Stability analysis Unbalanced networks coherence leader selection robustness

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ITERATIVE algorithmS WITH SELF-ADAPTIVE RULE AND KM METHOD FOR SOLVING SPLIT FIXED POINT PROBLEMS

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UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 2025年第1期87卷 15-28页

作者： Zheng, Lu Gogoasa, Alexandru Department of Business Administration Personnel Management Cheongju University Korea Republic of Department of Mathematics and Informatics National University of Science and Technology Politehnica Bucharest Bucharest060042 Romania

In this paper, we investigate the split fixed point problem regarding pseudocontractive operators and demicontractive operators in Hilbert spaces. We propose an iterative algorithm with self-adaptive rule and the Krasnoselskii-Mann method for finding a solution of this split problem. The self-adaptive rule does not require the a priori knowledge of the Lipschitz constant of pseudocontractive operators. Under several additional conditions, we prove that the presented algorithm converges strongly to a solution of the considered split problem. © 2025, Politechnica University of Bucharest. All rights reserved.

关键词： consensus algorithm

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NEW VISCOSITY algorithm WITH STRONG CONVERGENCE FOR QUASIMONOTONE VARIATIONAL INEQUALITIES

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UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 2025年第1期2025卷 77-90页

作者： Thong, Duong Viet Fundamental Sciences Faculty National Economics University Hanoi City Viet Nam

This paper investigates quasimonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. To address this problem, we propose a new iterative algorithm for finding an element of the solution set of the quasimonotone variational inequality problem. Our approach combines techniques from the inertial modified subgradient extragradient algorithm and the viscosity approximation method. Using a new self adaptive stepsize, we establish a strong convergence theorem for the sequence generated by the proposed algorithm under appropriate conditions. The results presented in this work improve upon and generalize some recent findings in this area. © 2025, Politechnica University of Bucharest. All rights reserved.

关键词： consensus algorithm

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TWO-FOLD BYZANTINE FAULT TOLERANCE algorithm: BYZANTINE consensus IN BLOCKCHAIN

arXiv

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arXiv 2025年

作者： Shakournia, Mohammad R. Jamshidi, Pooya Faragardi, Hamid Reza Yazdani, Nasser School of Electrical and Computer Engineering University of Tehran Tehran Iran Research Institute of Sweden Stockholm Sweden

Blockchain technology offers a decentralized and secure method for storing and authenticating data, rendering it well-suited for various applications such as digital currencies, supply chain management, and voting systems. However, the decentralized nature of blockchain also exposes it to vulnerabilities, particularly Byzantine faults, which arise when nodes in the network behave maliciously or encounter unexpected failures. Such incidents can result in inconsistencies within the blockchain and, in extreme scenarios, lead to a breakdown in consensus. Byzantine fault-tolerant consensus algorithms are crafted to tackle this challenge by ensuring that network nodes can agree on the blockchain’s state even in the presence of faulty or malicious nodes. To bolster the system’s resilience against these faults, it is imperative to detect them within the system. However, our examination of existing literature reveals a prevalent assumption: solutions typically operate under constraints regarding the number of faulty nodes. Such constraints confine the proposed solutions to ideal environments, limiting their practical applicability. In response, we propose a novel approach inspired by social paradigms, employing a trusted and fully monitored communication sub-process to detect Byzantine nodes. Upon detection, these nodes can be either disregarded in the consensus-building process, subjected to penalties, or undergo modifications as per the system’s policy. Finally, we statistically demonstrate that our approach achieves a detection probability that exceeds 95% for Byzantine nodes. In essence, our methodology ensures that if Byzantine nodes exhibit malicious behavior, healthy nodes can identify them with a confidence level of 95%. Copyright © 2025, The Authors. All rights reserved.

关键词： consensus algorithm

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Performance optimization of agricultural traceability blockchain based on sharding technology

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QUALITY ASSURANCE AND SAFETY OF CROPS & FOODS 2025年第2期17卷 213-231页

作者： Guo, Xiangdong Zhang, Yuting Yao, Jingfa Teng, Guifa Hebei Agr Univ Coll Mechatron & Elect Engn Baoding 071001 Peoples R China Hebei Agr Univ Coll Informat Sci & Technol Baoding 071001 Peoples R China Hebei Software Inst Software Engn Dept Baoding 071000 Peoples R China Hebei Coll Intelligent Interconnect Equipment & Mu Big Data Applicat Technol Res Dev Ctr Baoding 071000 Peoples R China Hebei Key Lab Agr Big Data Baoding 071001 Peoples R China Hebei Digital Agr Ind Technol Res Inst Shijiazhuang 056400 Peoples R China

With the increasing global concerns over food safety, ensuring the transparency and traceability of agricultural products throughout their entire production-to-consumption process has become a key issue of societal interest. Blockchain technology, due to its decentralized, immutable, and transparent nature, offers a novel solution for the traceability of agricultural products. However, traditional blockchain systems encounter performance bottlenecks when handling large-scale agricultural data, particularly under conditions of high data volume and frequent transactions, where issues such as processing delays and insufficient throughput commonly arise. Sharding technology, a critical approach for improving blockchain performance, has the potential to significantly enhance system throughput and response time by partitioning the blockchain network into multiple independent shards for parallel processing. However, the application of sharding technology in agricultural traceability systems faces several challenges, including shard load imbalance, communication delays between shards, and inefficiencies in consensus algorithms. To address these challenges, two innovative approaches were proposed in this study: firstly, to address the issue of uneven load distribution in sharding, a jump hash sharding algorithm was designed to optimize shard allocation strategies, thereby improving resource utilization and processing efficiency;secondly, to tackle the performance bottleneck of consensus algorithms, an enhanced consensus algorithm was introduced to improve consensus efficiency while maintaining security. Experimental results demonstrated that the proposed method significantly outperformed traditional blockchain-based traceability systems in terms of performance and scalability, providing a more efficient and reliable technological solution for the application of blockchain technology in the agricultural sector. This research not only offers a more efficient technological solu

关键词： agricultural product traceability blockchain consensus algorithm hump hash sharding algorithm performance optimization sharding technology

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Distributed Fixed-Time Dynamic Event-Triggered algorithm for Economic Dispatch in Smart Grids Over Directed Networks

IEEE Transactions on Industrial Cyber-Physical Systems

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IEEE Transactions on Industrial Cyber-Physical Systems 2025年 3卷 173-180页

作者： Ji, Lianghao Liu, Qi Zhang, Cuijuan Yang, Shasha Li, Huaqing Chongqing University of Posts and Telecommunications Chongqing Key Laboratory of Image Cognition Chongqing400065 China Southwest University Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing Chongqing400715 China

A fresh algorithm is presented for tackling the economic dispatch problem (EDP) in smart grids with directed network topology. This algorithm is based on distributed consensus and aims to minimize the total cost of power generation while maintaining the balance between power supply and demand and complying with generation capacity restrictions. Even with unknown and bounded disturbances, this algorithm can achieve optimal dispatch within a fixed time. In addition, an expected settling time can be calculated, which is a more accurate upper bound estimation that relies solely on the generators' initial conditions. Meanwhile, the dynamic event-triggered strategy is employed for reducing sampling frequency and network resource consumption. Finally, numerical simulations validate the effectiveness of the designed algorithm. © 2024 IEEE.

关键词： consensus algorithm

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Achieving local consensus over compact submanifolds

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IEEE Transactions on Automatic Control 2025年

作者： Hu, Jiang Zhang, Jiaojiao Deng, Kangkang University of California Department of Mathematics BerkeleyCA94720 United States KTH Royal Institute of Technology Division of Decision and Control Systems Stockholm Sweden National University of Defense Technology Department of Mathematics Changsha China

Decentralized optimization often relies on achieving consensus among disparate agents. This paper addresses the consensus problem in decentralized networks, focusing on the challenges posed by a nonconvex compact submanifold constraint. We identify conditions on network topology that facilitate local linear convergence to global consensus, where the achieved linear rate matches that of the Euclidean setting. Central to our analysis are the convex-like properties, specifically proximal smoothness and the restricted secant inequality, which form the foundation of our theoretical framework. These results will be useful for the design and analysis of decentralized manifold optimization algorithms. Numerical experiments are conducted to validate our theoretical findings. © 2025 IEEE.

关键词： consensus algorithm

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