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IAENG International Journal of Computer Science 2025年第1期52卷 46-51页

作者： Wang, Jingya Wen, Bin Liu, Yong School of Mathematics and Statistics Changshu Institute of Technology Jiangsu Suzhou215500 China School of Mathematics and Statistics Changshu Institute of Technology Jiangsu Suzhou215500 China School of Mathematics and Statistics Changshu Institute of Technology Jiangsu Suzhou215500 China

The augmented Kaczmarz algorithm is devised to solve an inconsistent linear system by employing the classical Kaczmarz algorithm on a parameterized augmented linear system derived from the original inconsistent linear system. The convergence of the resulting algorithm is proved. Numerical results show that our algorithm exhibits superior performance compared to the greedy randomized augmented Kaczmarz algorithm in relation to the number of iterations and computational durations for ill-conditioned linear inconsistent systems. © (2025), (International Association of Engineers). All rights reserved.

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Solving the shortest path Problem in an interval-valued Neutrosophic Pythagorean environment using an enhanced A* search algorithm

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Neutrosophic Sets and Systems 2025年 76卷 360-374页

作者： Raut, Prasanta Kumar Satapathy, Sakya Singh Behera, Siva Prasad Broumi, Said Sahoo, Ajay Kumar Department of Mathematics C.V. Raman Global University Odisha Bhubaneswar India Department of Mathematics Trident Academy of Technology Odisha Bhubaneswar India Laboratory of Information Processing Faculty of Science Ben M’Sik University Hassan II Casablanca Morocco Department of Mathematics Indira Gandhi Institute of Technology Dhenkanal Odisha Sarang759146 India

The A* search algorithm is widely utilized to evaluate the shortest path in a given network. However, in a traditional A* search algorithm, the nodes are assumed to have crisp values, i.e., a single value. This assumption may not hold in many real-world scenarios where uncertainty or ambiguity is involved. In such cases, an interval-valued Neutrosophic Pythagorean (IVNP) environment can provide a more sound and accurate representation. Interval-valued Neutrosophic Pythagorean sets (IVNPS) are an effective way to model vague and imprecise data, which is prevalent in executive problems. These sets provide a more flexible way to capture uncertainty by allowing the values of nodes in the graph to vary within certain intervals rather than having fixed values. This interval representation can effectively handle imprecise or incomplete information and is a powerful tool in executive processes. In this research paper, we proposed an improved A* search algorithm that takes advantage of the interval-valued neutrosophic Pythagorean environment. This algorithm aims to evaluate the shortest path in a graph under uncertainty and ambiguity. The proposed algorithm incorporates the IVNPS theory into the A* search framework to handle the uncertainty in node values and edge weights. It utilizes the concept of neutrosophic Pythagorean distance to calculate the heuristic function and make informed decisions on the next node to expand. © 2025, University of New Mexico. All rights reserved.

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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.

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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.

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Informatica (Slovenia)

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Informatica (Slovenia) 2025年第13期49卷 13-32页

作者： Tian, Chuan Wan, Huan Wu, Ye Department of Economic Management Jiangxi Tourism & Commerce Vocational College Nanchang330100 China

In the field of user feature segmentation, the currently adopted segmentation methods have the defect of low segmentation accuracy. To address this problem, the study introduces the K-prototypes algorithm for user feature segmentation to improve the segmentation accuracy of user feature segmentation. The study first improves the traditional K-prototypes algorithm using fuzzy similarity matrix. The improved K-prototypes algorithm can effectively select the initial clustering center and fuzzy coefficients and weight coefficients, and pre-set the number of clusters in order to realize the accurate segmentation of user feature. After that, user feature segmentation model is constructed based on the improved K-prototypes algorithm to plan the best marketing methods for users with different characteristics. The study selected 605, 3200, and 684 data objects from the R15, D13, and credit approval datasets as experimental subject. Moreover, it compared the improved K-prototypes algorithm with the fuzzy C-means clustering algorithm and the density peak clustering algorithm in terms of clustering accuracy, root mean square error, mean absolute error, and clustering recall rate to evaluate the performance of the three algorithms. The performance advantages and disadvantages of the three algorithms were evaluated by accuracy, root mean square error, mean absolute error, and recall. The accuracy of the improved K-prototypes algorithm reached 0.9438, which was significantly higher than the other two algorithms. Moreover, the mean square error and mean absolute error of this algorithm were significantly lower than the other two algorithms, indicating that the clustering effect of this algorithm was significantly better than the other two algorithms. The recall of the improved K-prototypes algorithm reached 0.953, and the variation of recall was small, indicating the efficiency of this algorithm in dividing user features. All three algorithms were able to select the correct initial

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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.

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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.

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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.

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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.

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Computationally Light Privacy Preservation of Matrix-Weighted Average consensus

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IEEE Transactions on Control of Network Systems 2025年

作者： Wang, Peng Shao, Haibin Pan, Lulu Yan, Weiwu Li, Ning Shanghai Jiao Tong University Department of Automation Shanghai200240 China

Multi-agent consensus algorithms have emerged as foundational tools across a spectrum of applications and matrix-weighted consensus ones are capable of characterizing cross-dimensional interdependence. Yet, their potential is often shadowed by a pressing concern: the privacy of agents' initial values, which frequently represent sensitive data or proprietary information. A computationally light privacy-preserving mechanism for matrix-weighted average consensus (MAC) algorithms is proposed in response to the concern of agents' privacy. In the mechanism, agents' states are first perturbed and then multiplied by the matrix weights before being sent to their neighbors. Both the perturbation and the matrix weight are neighbor-dependent, i.e., they may be selected to be different for different neighbors, and they can be selected independently to mask the true state of an agent. The proposed mechanism can simultaneously guarantee the privacy of initial values and accurate average consensus. The additional computational burden that an agent bears is only the addition of vectors in the same dimension as its state compared to the original MAC algorithm. Through practical case studies with a peer-to-peer transactive energy system, we demonstrate the tangible implications of safeguarding initial value privacy with the proposed mechanism. © 2014 IEEE.

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