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A Barzilai-Borwein conjugate gradient method

science China mathematics 2016年第8期59卷 1511-1524页

作者： DAI YuHong KOU CaiXia LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences School of Science Beijing University of Posts and Telecommunications

The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient method, however, heavily restricted the use of conjugate gradient method for largescale nonlinear optimization. This is, to the great extent, due to the requirement of a relatively exact line search at each iteration and the loss of conjugacy property of the search directions in various occasions. On the contrary, the limited-memory BFGS method and the Barzilai-Bowein gradient method share the so-called asymptotical one stepsize per line-search property, namely, the trial stepsize in the method will asymptotically be accepted by the line search when the iteration is close to the solution. This paper will focus on the analysis of the subspace minimization conjugate gradient method by Yuan and Stoer(1995). Specifically, if choosing the parameter in the method by combining the Barzilai-Borwein idea, we will be able to provide some efficient Barzilai-Borwein conjugate gradient(BBCG) methods. The initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches. This variant of the BBCG method might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization.

关键词： conjugate gradient method subspace minimization Barzilai-Bowein gradient method line search descent property global convergence

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Efficiently Verifiable Quantum Advantage on Near-Term Analog Quantum Simulators

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PRX Quantum 2025年第1期6卷 010341-010341页

作者： Zhenning Liu Dhruv Devulapalli Dominik Hangleiter Yi-Kai Liu Alicia J. Kollár Alexey V. Gorshkov Andrew M. Childs Joint Center for Quantum Information and Computer Science NIST/University of Maryland College Park Maryland 20742 USA Joint Quantum Institute NIST/University of Maryland College Park Maryland 20742 USA Department of Computer Science University of Maryland College Park Maryland 20742 USA Simons Institute for the Theory of Computing University of California at Berkeley California 94720 USA Applied and Computational Mathematics Division National Institute of Standards and Technology (NIST) Gaithersburg Maryland 20899 USA Department of Physics University of Maryland College Park Maryland 20742 USA Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 USA

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an O(λ2)-time classical computation, and the prover need only prepare O(1) samples of a history state and perform O(λ2) single-qubit measurements, for a security parameter λ. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

关键词： Quantum computers

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Security within Security: Attack Detection Model with Defenses Against Attacks Capability for Zero-trust Networks

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IEEE Journal on Selected Areas in Communications 2025年第6期43卷 2312-2327页

作者： Wang, Tingting Fang, Kai Cai, Jijing Wang, Lina Tian, Jinyu Feng, Hailin Li, Jianqing Guizani, Mohsen Wang, Wei Macau University of Science and Technology Faculty of Innovation Engineering School of Computer Science and Engineering Macau999078 China Zhejiang A&F University College of Mathematics and Computer Science Hangzhou311300 China Machine Learning Department United Arab Emirates Shenzhen MSU-BIT University Guangdong-Hong Kong-Macao Joint Laboratory for Emotion Intelligence and Pervasive Computing Artificial Intelligence Research Institute Shenzhen518172 China Beijing Institute of Technology School of Medical Technology Beijing100081 China

Traditional traffic anomaly-based attack detection methods in Zero-trust Networks (ZTN) suffer from inherent security vulnerabilities, as they neglect considerations regarding their security defenses. Compromising the attack detection model itself can result in the breakdown of normal attack detection capabilities. Ensuring the security of the attack detection model during runtime presents a novel challenge. To address these shortcomings, we propose a novel attack detection model, termed Security within Security: Attack Detection Model with Defenses Against Attacks Capability for Zero-Trust Networks (SWS), aimed at enhancing the security of ZTN. SWS focuses on achieving attack detection in non-secure detection environments, to maintain its detection capability even when under attack. By employing a soft thresholding method, SWS adapts to the dynamic changes in network traffic, thus reducing the interference of attack signals. The incorporation of an attention mechanism enables SWS to concentrate on analyzing the most indicative traffic features of attack behavior. Additionally, we integrate Residual Networks (ResNet) and Bidirectional Long Short-Term Memory (BiLSTM) to enhance the robustness of identifying complex network attack behaviors. The effectiveness of the SWS is validated through ablation studies, model comparisons, experiments conducted over different training epochs, and experiments conducted on various components of the dataset. Experimental results demonstrate that compared to existing attack detection models, SWS achieves improvements in detection accuracy and recall rate by 13.4% and 10.6%, respectively, while reducing the False Positive Rate (FPR) by 16.9%. © 1983-2012 IEEE.

关键词： Economic and social effects

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Interaction of Magnesium Ion and Acetate Anion in Bulk Water:Toward High-Level Machine Learning Potential

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Chinese Journal of Chemical Physics 2025年第1期38卷 95-101,I0056页

作者： Jiaying Gu Jin Xiao Xingyu Wu Xi Zhu Huimin Chen John ZHZhang Tong Zhu Ya Gao Zhixiang Yin School of Mathematics Physics and StatisticsShanghai University of Engineering ScienceShanghai 201620China Shanghai Engineering Research Center of Molecular Therapeutics&New Drug Development School of Chemistry and Molecular EngineeringEast China Normal UniversityShanghai 200062China CAS Key Laboratory of Quantitative Engineering Biology Shenzhen Institute of Synthetic BiologyShenzhen Institutes of Advanced TechnologyChinese Academy of SciencesShenzhen 518055China NYU-ECNU Center for Computational Chemistry at NYU Shanghai Shanghai 200062China Department of Chemistry New York UniversityNew York 10003USA Collaborative Innovation Center of Extreme Optics Shanxi UniversityTaiyuan 030006China Shanghai Frontiers Science Research Center for Druggability of Cardiovascular Noncoding RNA Shanghai 201620China

Metal ions play crucial roles in various biologi-cal functions,in-cluding maintain-ing homeostasis,regulating mus-cle contraction,and facilitating enzyme ***,accurately simulating the interaction between metal ions and amino acid side chain analogs using high-level wave function theories remains challenging due to the significant computational costs *** this study,deep potential molecular dynamics(DeePMD)simulation was employed to investigate the solvation structure of the Mg^(2+)-Ac^(−)ion pair in aqueous *** address the computational bottleneck associated with expensive quan-tum mechanics(QM)methods,the Deep Kohn-Sham(DeePKS)approach was utilized,which allows us to generate highly accurate self-consistent energy functionals while significantly re-ducing computational *** root mean square error and mean absolute error of energies and atomic forces indicate close agreement between DeePKS predictions and QM strongly constrained and appropriately normed(SCAN)***,the neural network potential(NNP)generated using the SCAN-level dataset predicted by DeePKS exhibits high-er accuracy compared to previous work,which employed a moderate BLYP *** potential of mean force for the Mg^(2+)-Ac−system was further examined,revealing a prefer-ence for monodentate coordination of Mg^(2+)with a~5.8 kcal/mol energy barrier between bidentate and monodentate ***,this work provides a comprehensive,precise,and reliable methodology for investigating metal ions’properties in aqueous solutions.

关键词： Molecular dynamics simulation Umbrella sampling Neural network potential Machine learning

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Heat transfer optimization on convective flow of various fluids inside an enclosure with curved heat source

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ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 2025年第5期105卷

作者： Venkatadri, K. Rajeswari, V. Raja Santhosh, N. Leung, Ho-Hon Kamalov, Firuz Prasad, V. Ramachandra Sivaraj, R. AP Tirupati India Department of Electronics and Communication Engineering School of Engineering and Technology Sri Padmavati Mahila Visvavidyalayam Tirupati India Department of Mathematics and Statistics School of Applied Science and Humanities Vignan's Foundation For Science Technology and Research vadlamudi Andhra Pradesh Guntur India Department of Mathematical Sciences United Arab Emirates University Al Ain United Arab Emirates Department of Electrical Engineering Canadian University Dubai Dubai United Arab Emirates Department of Mathematics School of Advanced Sciences Vellore Institute of Technology Vellore India Department of Mathematics and Computing Dr B. R. Ambedkar National Institute of Technology Punjab Jalandhar India

In this work, the efficiency of thermo-fluidic thermal performance is numerically extrapolated on the incompressible natural convection flow of three fluids (mercury, air, and water) inside an enclosure with a curved heat source. The governing equations are presented in the Cartesian coordinate system and solved using the stream function-vorticity technique with second-order finite difference approach. The fluid movement and thermal transport features are represented in terms of local and average Nusselt numbers, as well as streamlines and isotherms for the considered fluids with various strengths of buoyancy force. Results explore that water with high buoyancy force produce the highest local and mean heat transmission rates. When the strength of buoyancy force is low, the local Nusselt number enhances linearly for all the considered fluids, whereas the variation is nonlinear when the strength of buoyancy force is high. When the strength of buoyancy force is high (Formula presented.), the mean heat transfer rate within the enclosure can be enhanced up to (Formula presented.) by replacing the working fluid mercury with water. The best heat transfer efficiency can be achieved with water among mercury, air, and water. © 2025 Wiley-VCH GmbH.

关键词： Natural convection

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Deep Learning Classification of Subtypes of Luminal Breast Cancer from Immunohistochemistry Slides 5th

Deep Learning Classification of Subtypes of Luminal Breast C...

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5th International Conference on computing and Network Communications, CoCoNet 2023

作者： Shaji, Vishnu Sharma, Mridul Mathew, Merin Malavika, K. Louis, Dhanya Mary Vijaykumar, Dehannathparambil Kottarathil Nair, Lakshmi Malavika George, Archana Gutjahr, Georg Department of Computer Science and Engineering Amrita School of Computing Amrita Vishwa Vidyapeetham Amritapuri India Department of Mathematics Amrita Vishwa Vidyapeetham Amritapuri Kerala Kollam India Department of Pharmacy Practice Amrita School of Pharmacy Amrita Institute of Medical Sciences And Research Centre Kerala Kochi India Department of Breast Oncology Amrita Institute of Medical Sciences And Research Center Amrita Vishwa Vidyapeetham Kerala Kochi India Department of Pathology Amrita Institute of Medical Sciences And Research Center Amrita Vishwa Vidyapeetham Kerala Kochi India Amrita Vishwa Vidyapeetham Amritapuri Kerala Kollam India

ISBN: (纸本)9789819747108

This paper proposes deep-learning models to assist in classifying subtypes of luminal breast cancer from immunohistochemistry slides. The classification has traditionally been done by pathologists who evaluate Ki67 indexes by manually counting positive and negative cells that are dyed in different colors in the immunohistochemistry slides. This manual process is error-prone and time-consuming. Therefore, this paper explores the possibility of automatically classifying immunohistochemistry slides. The performances of 4 pre-trained, deep convolutional networks are compared. Based on the good performance of the models, we conclude that the task of Ki67 classification for determining subtypes of luminal breast cancer is well-suited for deep learning models and that for this reason, manual counting of Ki67-positive cells are neither needed nor desirable. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Convolutional neural networks

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An incompressibility, div\bm{B}=0 preserving, current density, helicity, energy-conserving finite element method for incompressible MHD systems B = 0 preserving, current density, helicity, energy-conserving finite element method for incompressible MHD systems

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Journal of computational Physics 2025年

作者： Shipeng Mao Ruijie Xi Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science School of Mathematical Science NCMIS LSEC University of Chinese Academy of Sciences Chinese Academy of Sciences Beijing 100190 China

In this paper, we propose a novel structure-preserving finite element scheme for the three-dimensional incompressible magnetohydrodynamic (MHD) equations. The contribution of our research is three-fold. Firstly, the proposed scheme exactly preserves critical physical properties, including the incompressibility condition, the solenoidal condition of magnetic field, current density conservation, energy conservation and magnetic/fluid helicity conservation in their respective physical limits. To the best of our knowledge, this is the first numerical method that preserves all these properties simultaneously. Secondly, it introduces the first linear scheme that upholds the helicity-preserving property for MHD, thus eliminating the necessity for fixed-point iterations as seen in existing literature. Last but not least, for the resulting large linear systems, we develop efficient block preconditioners that remain robust at high fluid and magnetic Reynolds numbers by incorporating techniques such as the augmented Lagrangian method and mass augmentation. Finally, a series of numerical experiments demonstrate that our method is accurate, stable, robust under extreme physical parameters and capable of preserving all the stated physical properties, including benchmark problems of Orszag Tang vortex and driven magnetic reconnection with fluid and magnetic Reynolds numbers up to 10 5 – 10 6 .

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Reconfiguration and Optimal Positioning of Multiple-Point Capacitors in a High-Voltage Distribution Network Using the NSGAII

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Open Journal of Applied sciences 2025年第2期15卷 501-516页

作者： Arouna Oloulade Richard Gilles Agbokpanzo Maurel Richy Aza-Gnandji Hassane Ousseyni Ibrahim Moussa Gonda Eméric Tokoudagba Juliano Sétondji François-Xavier Fifatin Adolphe Moukengue Imano Abomey-Calavi Polytechnic School Electrical Engineering Department (EPAC) Electronics Telecommunications and Applied Computing Laboratory (LETIA) University of Abomey-Calavi Cotonou Benin Electrical Engineering Department National University of Science Technology Engineering and Mathematics Lokossa Benin Laboratory of Rural Engineering National University of Agriculture Porto-Novo Benin Polytech Maradi Electrical Engineering Department University Dan Dicko of Dankoulodo of Maradi Maradi Niger University Institute of Technology Electrical Engineering Department University of Douala Douala Cameroun

The distribution networks sometimes suffer from excessive losses and voltage violations in densely populated areas. The aim of the present study is to improve the performance of a distribution network by successively applying mono-capacitor positioning, multiple positioning and reconfiguration processes using GA-based algorithms implemented in a Matlab environment. From the diagnostic study of this network, it was observed that a minimum voltage of 0.90 pu induces a voltage deviation of 5.26%, followed by active and reactive losses of 425.08 kW and 435.09 kVAR, respectively. Single placement with the NSGAII resulted in the placement of a 3000 kVAR capacitor at node 128, which proved to be the invariably neuralgic point. Multiple placements resulted in a 21.55% reduction in losses and a 0.74% regression in voltage profile performance. After topology optimization, the loss profile improved by 65.08% and the voltage profile improved by 1.05%. Genetic algorithms are efficient and effective tools for improving the performance of distribution networks, whose degradation is often dynamic due to the natural variability of loads.

关键词： Reconfiguration Capacitor Bank NSGA II Dynamic Network Degradation Distribution Network Reliability

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Quantum Hamiltonian Descent for Non-smooth Optimization

arXiv

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arXiv 2025年

作者： Leng, Jiaqi Zheng, Yufan Jia, Zhiyuan Fan, Lei Zhao, Chaoyue Peng, Yuxiang Wu, Xiaodi Simons Institute for the Theory of Computing University of California Berkeley United States Department of Mathematics University of California Berkeley United States Department of Computer Science University of Maryland College Park United States Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Applied Mathematics University of Washington United States Department of Engineering Technology University of Houston United States Department of Electrical and Computer Engineering University of Houston United States Department of Industrial and Systems Engineering University of Washington United States Artephi Computing Inc United States

Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed, scalability, and parameter tuning, particularly in high-dimensional and non-convex settings. In this paper, we explore how quantum mechanics can be leveraged to overcome these limitations. Specifically, we investigate the theoretical properties of the Quantum Hamiltonian Descent (QHD) algorithm for non-smooth optimization in both continuous and discrete time. First, we propose continuous-time variants of the general QHD algorithm and establish their global convergence and convergence rate for non-smooth convex and strongly convex problems through a novel Lyapunov function design. Furthermore, we prove the finite-time global convergence of continuous-time QHD for non-smooth non-convex problems under mild conditions (i.e., locally Lipschitz). In addition, we propose discrete-time QHD, a fully digitized implementation of QHD via operator splitting (i.e., product formula). We find that discrete-time QHD exhibits similar convergence properties even with large time steps. Finally, numerical experiments validate our theoretical findings and demonstrate the computational advantages of QHD over classical non-smooth non-convex optimization algorithms. Copyright © 2025, The Authors. All rights reserved.

关键词： Continuous time systems

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Methods for wave equation prestack depth migration and numerical experiments

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science China mathematics 2004年第z1期47卷 111-120页

作者： ZHANG Guanquan ZHANG Wensheng Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

In this paper the methods of wave theory based prestack depth migration and their implementation are studied. Using the splitting of wave operator, the wavefield extrapolation equations are deduced and the numerical schemes are presented. The numerical tests for SEG/EAEG model with MPI are performed on the PC-cluster. The numerical results show that the methods of single-shot (common-shot) migration and synthesized-shot migration are of practical values and can be applied to field data processing of 3D prestack depth migration.

关键词： wave operator splitting, 3D prestack depth migration, SEG/EAEG model, synthesized-shot, finite-difference method, factorization method, hybrid method, MPI.

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