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Unbiased weighing matrices of weight 9

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arXiv 2025年

作者： Araya, Makoto Harada, Masaaki Kharaghani, Hadi Suda, Sho Yu, Wei-Hsuan Department of Computer Science Shizuoka University Hamamatsu432–8011 Japan Research Center for Pure and Applied Mathematics Graduate School of Information Sciences Tohoku University Sendai980–8579 Japan Department of Mathematics and Computer Science University of Lethbridge LethbridgeABT1K 3M4 Canada Department of Mathematics National Defense Academy of Japan Kanagawa Yokosuka239–8686 Japan Mathematics Department National Central University Taoyuan32001 Taiwan

We investigate unbiased weighing matrices of weight 9 and provide a construction method using mutually suitable Latin squares. For n ≤ 16, we determine the maximum size among sets of mutually unbiased weighing matrices of order n and weight 9. Notably, our findings reveal that 13 is the smallest order where such pairs exist, and 16 is the first order for which a maximum class of unbiased weighing matrices is *** Codes 05B20 © 2025, CC BY.

关键词： Matrix algebra

Fundamental Limit of Angular Resolution in Partly Calibrated Arrays with Position Errors

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arXiv 2025年

作者： Zhang, Guangbin Wang, Yan Huang, Tianyao Eldar, Yonina C. Yangtze Delta Region Academy Beijing Institute of Technology Zhejiang Jiaxing China Radar Research Laboratory School of Information and Electronics Beijing Institute of Technology Beijing China School of Computer and Communication Engineering University of Science and Technology Beijing Beijing China Department of Computer Science and Applied Mathematics Weizmann Institute of Science Israel

We consider high angular resolution detection using distributed mobile platforms implemented with so-called partly calibrated arrays, where position errors between subarrays exist and the counterparts within each subarray are ideally calibrated. Since position errors between antenna arrays affect the coherent processing of measurements from these arrays, it is commonly believed that its angular resolution is influenced. A key question is whether and how much the angular resolution of partly calibrated arrays is affected by the position errors, in comparison with ideally calibrated arrays. To address this fundamental problem, we theoretically illustrate that partly calibrated arrays approximately achieve high angular resolution. Our analysis uses a special characteristic of Cramér-Rao lower bound (CRB) w.r.t. the source separation: When the source separation increases, the CRB first declines rapidly, then plateaus out, and the turning point is close to the angular resolution limit. This means that the turning point of CRB can be used to indicate angular resolution. We then theoretically analyze the declining and plateau phases of CRB, and explain that the turning point of CRB in partly calibrated arrays is close to the angular resolution limit of distributed arrays without errors, demonstrating high resolution ability. This work thus provides a theoretical guarantee for the high-resolution performance of distributed antenna arrays in mobile platforms. Copyright © 2025, The Authors. All rights reserved.

关键词： Source separation

Investigating Mitochondrial Calcium-Phosphate Dissolution Fractional Order System with Robust Control

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International Journal of applied and Computational mathematics 2025年第3期11卷 1-17页

作者： Partohaghighi, Mohammad Ahmad, Shabir Akram, Tayyaba Electrical Engineering and Computer Science Department University of California Merced Merced United States Department of Mathematics and Physics University of Campania “Luigi Vanvitelli” Caserta 81100 Italy Department of Mathematics King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia Interdisciplinary Research Center for Biosystems and Machines King Fahd University of Petroleum and Minerals Dhahran Saudi Arabia

Mitochondrial calcium-dissociation gathers inside the mitochondria of vascular soft tissue cells and is able to interrupt phosphate resolution for up to an hour. In this study, we study the fractional model of mitochondrial calcium-phosphate dissolution (MCD) a system utilizing the Caputo-Fabrizio operator equipped by order α. Furthermore, the theory of the existence of solutions is demonstrated to ensure there exists at least single solution to the considered model. The Picard-Lindelof approach and Banach fixed point theorem are adopted to explore the existence of the solution of the proposed model. Additionally, numerical outcomes of the system are achieved by the three-step Adams-Bashforth method. Graphs of approximate solutions are simulated to show complex behavior of the mitochondrial calcium-dissociation model for a few fractional orders and initial conditions. Some theoretical results of the robust control are obtained to control chaos dynamics. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.

关键词： Mathematical modelling Mitochondrial calcium-phosphate dissolution system Numerical method Numerical simulation

Discrete-Time Uncertain Event-Triggered H∞ Control for Slow Sampling Markov Jump Systems With Strictly Dissipativity

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Mathematical Methods in the applied Sciences 2025年

作者： Kchaou, Mourad Syed Ali, M. Vigneshwar, B. Sanober, Sumaya Ibrahim, Tarek F. D Alanazi, Faizah Electrical Department College of Engineering University of Hail Kingdom Saudi Arabia Complex Systems and Networked Science Research Laboratory Department of Mathematics Thiruvalluvar University Tamil Nadu Vellore India Department of Computer Science Old Dominion University NorfolkVA United States Department of Mathematics Sciences College King Khalid University Abha Saudi Arabia Department of Mathematics Faculty of Sciences Mansoura University Mansoura Egypt Department of Mathematics College of Science Northern Border University Arar Saudi Arabia

This paper investigates the (Formula presented.) control problem for discrete-time uncertain slow sampling Markov jump systems under the event-triggered scheme. Discrete-time Markov jumps are controlled using an event-triggered scheme. An event-based strategy is addressed to reduce the data communication and improve the control efficiency. By applying a switched Lyapunov functional and linear matrix inequalities (LMIs), we derive sufficient conditions for (Formula presented.) -dissipativity of the resulting system. An event-triggered scheme is introduced into LMIs approaches in order to solve the dissipative control problem. The control strategy is implemented by combining the disturbance output with state feedback control law in order to achieve asymptotically stable closed-loop systems. Convex combination approach is utilized to handle slow sampling input, while parameter uncertainty and external disturbances are both included, and the robustness (Formula presented.) performance is analyzed. The developed methods are illustrated with two examples that illustrate their flexibility and applicability. © 2025 John Wiley & Sons Ltd.

关键词： Markov processes

Nonlinear normalized fractional electroosmotic spacelike fluid model

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International Journal of Thermofluids 2025年 26卷

作者： Körpinar, Talat Körpinar, Zeliha Akgül, Ali Al-Mdallal, Qasem Muş Alparslan University Department of Mathematics Muş49250 Turkey Muş Alparslan University Department of Administration Muş49250 Turkey Department of Electronics and Communication Engineering Saveetha of Engineering SIMATS Tamilnadu Chennai India Siirt University Art and Science Faculty Department of Mathematics Siirt56100 Turkey Department of Computer Engineering Biruni University Istanbul Topkapı34010 Turkey Near East University Mathematics Research Center Department of Mathematics Near East Boulevard PC: 99138 Nicosia/Mersin 10 Turkey Department of Mathematical Sciences P.O. Box 17551 UAE University Al-Ain United Arab Emirates

In this paper, we present optical recursively fractional SKμ−electroosmotic fractional recursivelySKμ−energy. Also, we have spacelike microfluidicsfractional SKμ− electroosmotic recursively tension energy. Moreover, we construct main Katugampola recursive-normal hyperbolic fractional KFα−tension field in hyperbolic space. Finally, we characterize spacelike radiative recursively fractional SKμ− phase in hyperbolic space. © 2025 The Authors

关键词： Fluid energy Spacelike fractional flow Microfluidics

Singular networks and ultrasensitive terminal behaviors

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arXiv 2025年

作者： Franci, Alessio Besselink, Bart van der Schaft, Arjan Department of Electrical Engineering and Computer Science University of Liege Liege Belgium WEL Research Institute Wavre Belgium Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence University of Groningen Groningen Netherlands University of Groningen Netherlands

Negative conductance elements are key to shape the input-output behavior at the terminals of a network through localized positive feedback amplification. The balance of positive and negative differential conductances creates singularities at which rich, intrinsically nonlinear, and ultrasensitive terminal behaviors emerge. Motivated by neuromorphic engineering applications, in this note we extend a recently introduced nonlinear network graphical modeling framework to include negative conductance elements. We use this extended framework to define the class of singular networks and to characterize their ultra-sensitive input/output behaviors at given terminals. Our results are grounded in the Lyapunov-Schmidt reduction method, which is shown to fully characterize the singularities and bifurcations of the input-output behavior at the network terminals, including when the underlying input-output relation is not explicitly computable through other reduction methods. Copyright © 2025, The Authors. All rights reserved.

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Evaluating Gaussianity of heterogeneous fractional Brownian motion

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arXiv 2025年

作者： Balcerek, Michal Pacheco-Pozo, Adrian Wylomańska, Agnieszka Krapf, Diego Department of Electrical and Computer Engineering School of Biomedical Engineering Colorado State University Fort CollinsCO80523 United States Faculty of Pure and Applied Mathematics Hugo Steinhaus Center Wroclaw University of Science and Technology Wroclaw50-370 Poland

Heterogeneous diffusion processes are prevalent in various fields, including the motion of proteins in living cells, the migratory movement of birds and mammals, and finance. These processes are often characterized by time-varying dynamics, where interactions with the environment evolve, and the system undergoes fluctuations in diffusivity. Moreover, in many complex systems anomalous diffusion is observed, where the mean square displacement (MSD) exhibits non-linear scaling with time. Among the models used to describe this phenomenon, fractional Brownian motion (FBM) is a widely applied stochastic process, particularly for systems exhibiting long-range temporal correlations. Although FBM is characterized by Gaussian increments, heterogeneous processes with FBM-like characteristics may deviate from Gaussianity. In this article, we study the non-Gaussian behavior of switching fractional Brownian motion (SFBM), a model in which the diffusivity of the FBM process varies while temporal correlations are maintained. To characterize non-Gaussianity, we evaluate the kurtosis, a common tool used to quantify deviations from the normal distribution. We derive exact expressions for the kurtosis of the considered heterogeneous anomalous diffusion process and investigate how it can identify non-Gaussian behavior. We also compare the kurtosis results with those obtained using the Hellinger distance, a classical measure of divergence between probability density functions. Through both analytical and numerical methods, we demonstrate the potential of kurtosis as a metric for detecting non-Gaussianity in heterogeneous anomalous diffusion processes. © 2025, CC BY.

关键词： Brownian movement

Generative AI-Enabled Quantum Encryption Algorithm for Securing IoT-Based Healthcare Application Using Blockchain

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IEEE Internet of Things Journal 2025年

作者： Prajapat, Sunil Kumar, Pankaj Das, Ashok Kumar Muhammad, Ghulam Central University of Himachal Pradesh Srinivasa Ramanujan Department of Mathematics Dharamshala176215 India International Institute of Information Technology Center for Security Theory and Algorithmic Research Hyderabad500 032 India Korea University College of Informatics Department of Computer Science and Engineering Anam-ro Seoul145 Korea Republic of King Saud University College of Computer and Information Sciences Department of Computer Engineering Riyadh11543 Saudi Arabia

The integration of Artificial Intelligence (AI) with the Internet of Things (IoT) has transformed numerous domains through the AI of Things (AIoT). Nonetheless, AIoT encounters issues related to energy usage and carbon emissions as mobile technology continues to progress. Generative AI (GAI) possesses significant potential to mitigate carbon emissions associated with AIoT, owing to its higher reasoning and generative powers. Conventional security protocols frequently encounter issues with computational efficiency, latency, and overall security comprehensiveness. Blockchain technology, characterized by its decentralized and immutable properties, is a viable approach for improving electronic healthcare data transmission and node authentication in IoT networks. This research examines secure data transmission and node encryption in IoT systems, with a particular emphasis on data management. Conventional approaches encounter constraints in computational efficiency, latency, and comprehensive security. This study presents a novel protocol that combines GAI and blockchain technology with quantum encryption to enhance authentication and ensure secure data transmission. The algorithm comprises multiple consecutive processes, including the encoding and transmission of node requests, followed by the authentication process utilizing hash functions and digital signatures. The authentication approach utilizes a challenge-response technique, guaranteeing that only nodes with authentic credentials can advance. Thereafter, a dynamic key exchange protocol and quantum encryption method provide secure data delivery. The results indicate the procedure’s effectiveness in ensuring secure and regulated access to patient data, underscoring its significance in medical facilities. The system’s functionalities are augmented by a thorough evaluation employing machine learning. The findings indicate that the system exhibits an accuracy of 99.4%, precision of 99.10%, recall of 98.66%, F1-score of

关键词： Quantum computers

DP2Unlearning: An Efficient and Guaranteed Unlearning Framework for LLMs

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arXiv 2025年

作者： Mahmud, Tamim Al Jebreel, Najeeb Domingo-Ferrer, Josep Sánchez, David Universitat Rovira i Virgili Department of Computer Engineering and Mathematics CYBERCAT-Center for Cybersecurity Research of Catalonia Av. Països Catalans 26 Catalonia Tarragona43007 Spain

Large language models (LLMs) have recently revolutionized language processing tasks but have also brought ethical and legal issues. LLMs have a tendency to memorize potentially private or copyrighted information present in the training data, which might then be delivered to end users at inference time. When this happens, a naive solution is to retrain the model from scratch after excluding the undesired data. Although this guarantees that the target data have been forgotten, it is also prohibitively expensive for LLMs. Approximate unlearning offers a more efficient alternative, as it consists of ex post modifications of the trained model itself to prevent undesirable results, but it lacks forgetting guarantees because it relies solely on empirical evidence. In this work, we present DP2Unlearning, a novel LLM unlearning framework that offers formal forgetting guarantees at a significantly lower cost than retraining from scratch on the data to be retained. DP2Unlearning involves training LLMs on textual data protected using ϵdifferential privacy (DP), which later enables efficient unlearning with the guarantees against disclosure associated with the chosen ϵ. Our experiments demonstrate that DP2Unlearning achieves similar model performance post-unlearning, compared to an LLM retraining from scratch on retained data –the gold standard exact unlearning– but at approximately half the unlearning cost. In addition, with a reasonable computational cost, it outperforms approximate unlearning methods at both preserving the utility of the model post-unlearning and effectively forgetting the targeted information. The code of our experiments is available at https://***/tamimalmahmud/DP2unlearning/. Copyright © 2025, The Authors. All rights reserved.

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