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Monotone projected gradient methods for large-scale box-constrained quadratic programming

Science China Mathematics 2006年第5期49卷 688-702页

作者： ZHOU Bin, GAO Li & DAI Yuhong School of mathematical Sciences and LMAM, Peking University, Beijing 100871, China state key laboratory of Scientific and engineering computing, Institute of Computational Mathematics and Scientific/engineering computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China School of Mathematical Sciences LMAM Peking University Beijing 100871 China State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics Scientific/Engineering Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China

Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.

关键词： projected gradients, monotone gradient methods, box-constrained quadratic programming, large-scale problems.

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Algebraic structure and Poisson＇s theory of mechanico-electrical systems

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Chinese Physics B 2006年第8期15卷 1653-1661页

作者：刘鸿基唐贻发傅景礼 Department of Physics Shangqiu Teachers College Shangqiu 476000 China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing 100080 China Institute of Mathematical Physics Zhejiang Sci-Tech University Hangzhou 310018 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.

关键词： algebraic structure Poisson integral method mechanico-electrical system

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Backlund Transformations for the Initial Problems of Nizhnich and Nizhnich-Novikov-Veselov Equations

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理论物理通讯(英文版) 2003年第7期40卷 15-18页

作者： SU Hong-Liang WANG Ming-Liang QIN Meng-Zhao State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scien-tific/Engineering Computing Academy of Mathematics and System Science the Chinese Academy of Sciences Beijing 100080 China Mathematical Department Luoyang Institute of Technology Luoyang 471039 China

The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the initialproblem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initialproblems of Nizhnich and the Nizhnich-Novikov-Veselov equations are solved by using this approach.

关键词： Backlund transformation initial problem Nizhnick equation Nizhnich Novikov-Veselov equation homogeneous balance method

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Fractal phenomena in powder injection molding process

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中国有色金属学会会刊：英文版 2003年第5期13卷 1112-1118页

作者：郑洲顺曲选辉李云平雷长明段柏华 State Key Laboratory for Powder Metallurgy Central South University Changsha 410083ChinaSchool of Mathematical Science and Computing TechnologyCentral South UniversityChangsha 410083 China State Key Laboratory for Powder Metallurgy Central South University Changsha 410083ChinaSchool of Materials Science and Engineering University of Science and Technology BeijingBeijing 100083China State Key Laboratory for Powder Metallurgy Central South University Changsha 410083China

The complicated characteristics of the powder were studied by fractal theory. It is illustrated that powder shape, binder structure, feedstock and mold filling flow in powder injection molding process possess obvious fractal characteristics. Based on the result of SEM, the fractal dimensions of the projected boundary of carbonylic iron and carbonylic nickel particles were determined to be 1.074±0.006 and 1.230±0.005 respectively by box counting measurement. The results show that the fractal dimension of the projected boundary of carbonylic iron particles is close to smooth curve of one dimension, while the fractal dimension of the projected boundary of carbonylic nickel particle is close to that of trisection Koch curve, indicating that the shape characteristics of carbonylic nickel particles can be described and analyzed by the characteristics of trisection Koch curve. It is also proposed that the fractal theory can be applied in the research of powder injection molding in four aspects.

关键词：粉末注射成型不规则破碎理论 PIM Navier-Stokes方程

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THE RELAXING SCHEMES FOR HAMILTON-JACOBI EQUATIONS

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计算数学(英文版) 2001年第3期19卷 231-240页

作者： Hua-zhong Tang Hua-zhong Tang Hua-mu Wu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems SciencesChinese Academy of Sciences Beijing 100080 China School of Mathematical Sciences Peking University Beijing 100871 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems SciencesChinese Academy of Sciences Beijing 100080 China

Hamilton-Jacobiequation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference approximations for Hamilton-Jacobi equation and hyperbolic conservation laws. In this paper we present the relaxing system for HamiltonJacobiequations in arbitrary space dimensions, and high resolution relaxing schemes for Hamilton-Jacobi equation, based on using the local relaxation approximation. The schemes are numerically tested on a variety of 1D and 2D problems, including a problem related to optimal control problem. High-order accuracy in smooth regions, good resolution of discontinuities, and convergence to viscosity solutions are observed.

关键词： The relaxing scheme The relaxing systems Hamilton-Jacobi equation Hyperbolic conservation laws.

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Elastic property of single double-stranded DNA molecules: Theoretical study and comparison with experiments

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Physical Review E 2000年第1期62卷 1045-1045页

作者： Haijun Zhou Yang Zhang Zhong-can Ou-Yang Institute of Theoretical Physics Academia Sinica P.O. Box 2735 Beijing 100080 China State Key Laboratory of Scientific and Engineering Computing Beijing 100080 China Institute for Advanced Study Tsinghua University Beijing 100084 China

This paper aims at a comprehensive understanding of the novel elastic property of double-stranded DNA (dsDNA) discovered very recently through single-molecule manipulation techniques. A general elastic model for double-stranded biopolymers is proposed, and a structural parameter called the folding angle φ is introduced to characterize their deformations. The mechanical property of long dsDNA molecules is then studied based on this model, where the base-stacking interactions between DNA adjacent nucleotide base pairs, the steric effects of base pairs, and the electrostatic interactions along DNA backbones are taken into account. Quantitative results are obtained by using a path integral method, and excellent agreement between theory and the observations reported by five major experimental groups are attained. The strong intensity of the base stacking interactions ensures the structural stability of DNA, while the short-ranged nature of such interactions makes externally stimulated large structural fluctuations possible. The entropic elasticity, highly extensibility, and supercoiling property of DNA are all closely related to this account. The present work also suggests the possibility that negative torque can induce structural transitions in highly extended DNA from the right-handed B form to left-handed configurations similar to the Z-form configuration. Some formulas concerned with the application of path integral methods to polymeric systems are listed in the Appendixes.

关键词： .base pairs double-stranded Elastic supercoiling backbones Deformations torque Ou-Yang base-stacking folding angle dsDNA molecules

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Bending and Base-Stacking Interactions in Double-Stranded DNA

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Physical Review Letters 1999年第22期82卷 4560-4560页

作者： Zhou Haijun Zhang Yang Ou-Yang Zhong-can Institute of Theoretical Physics Academia Sinica P.O. Box 2735 Beijing 100080 China State Key Laboratory of Scientific and Engineering Computing Beijing 100080 China Center for Advanced Study Tsinghua University Beijing 100084 China

An elastic model for double-stranded polymers is constructed to study the recently observed DNA entropic elasticity, cooperative extensibility, and supercoiling property. With the introduction of a new structural parameter (the folding angle ϕ), bending deformations of sugar-phosphate backbones, steric effects of nucleotide base pairs, and base-stacking interactions are considered. The comprehensive agreements between theory and experiments both on torsionally relaxed DNA and on negatively supercoiled DNA strongly indicate that base-stacking interactions, although short-ranged in nature, dominate the elasticity of DNA and, hence, are of vital biological significance.

关键词： .parameter negatively extensibility supercoiling backbones relaxed supercoiled dsDNA Ou-Yang torsionally base-stacking folding angle steric effects nucleotide base

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Uniform Graph Pre-training and Prompting for Transferable Recommendation

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ACM Transactions on Information Systems 1000年

作者： Qing Yu Lixin Zou Xiangyang Luo Xiangyu Zhao Chenliang Li Wuhan University China State Key Lab of Mathematical Engineering and Advanced Computing China City University of Hong Kong China

Recently, the paradigm of pre-training and fine-tuning has achieved impressive performance owing to their ability to transfer general knowledge from pre-trained domain to target domain. Meanwhile, Graph Neural Networks (GNNs) have gained prominence in recommender systems. However, there is a lack of unified pre-training and fine-tuning paradigms in graph-based recommendation systems. Applying pre-training and fine-tuning in graph-based recommendation is challenging due to the unique characteristics of recommendation data, including the non-uniform representation, negative transfer effects, and skewed data distributions. To overcome these challenges, we introduce ProRec (Pre-training and prompting Recommendation), a novel model that synergizes uniform graph pre-training with prompt-tuning for recommendation systems. Specifically, to address the challenge of inconsistent features across different recommendation datasets, ProRec constructs unified input features at the subgraph level and uses a Graph Auto-Encoder for pre-training, laying the foundation for uniform knowledge transfer from the pre-trained domain to the downstream domain. Additionally, ProRec employs prompt-tuning during the fine-tuning phase, which, in a parameter-efficient manner, enhancing the generalization of pre-trained knowledge to downstream tasks and thereby reducing negative transfer effects. Furthermore, a cross-layer contrastive learning strategy is adopted to eliminate uneven data distribution, promoting more evenly distributed and informative representations. Finally, extensive benchmark comparisons have demonstrated that ProRec outperforms the latest state-of-the-art methods. The source code necessary for replication is available at https://***/Code2Q/ProRec.

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Multi-Agent Reinforcement Learning based Edge Content Caching for Connected Autonomous Vehicles in IoV

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ACM Transactions on Autonomous and Adaptive Systems 1000年

作者： Xiaolong Xu Linjie Gu Muhammad Bilal Maqbool Khan Yiping Wen Guoqiang Liu Yuan Yuan School of Software Jiangsu Province Engineering Research Center of Advanced Computing and Intelligent Services Nanjing University of Information Science and Technology China Changwang School of Honors Nanjing University of Information Science and Technology China Department of Computer and Electronics Systems Engineering Hankuk University of Foreign Studies Korea Department of IT and Computer Science Pak-Austria Fachhochschule-Institute of Applied Sciences and Technology Pakistan School of Computer Science and Engineering Hunan University of Science and Technology China School of Software Nanjing University of Information Science and Technology China School of Computer Science and Engineering Beihang University State Key Laboratory of Software Development Environment Zhongguancun Laboratory China

Connected Autonomous Vehicle (CAV) Driving, as a data-driven intelligent driving technology within the Internet of Vehicles (IoV), presents significant challenges to the efficiency and security of real-time data management. The combination of Web3.0 and edge content caching holds promise in providing low-latency data access for CAVs’ real-time applications. Web3.0 enables the reliable pre-migration of frequently requested content from content providers to edge nodes. However, identifying optimal edge node peers for joint content caching and replacement remains challenging due to the dynamic nature of traffic flow in IoV. Addressing these challenges, this article introduces GAMA-Cache, an innovative edge content caching methodology leveraging Graph Attention Networks (GAT) and Multi-Agent Reinforcement Learning (MARL). GAMA-Cache conceptualizes the cooperative edge content caching issue as a constrained Markov decision process. It employs a MARL technique predicated on cooperation effectiveness to discern optimal caching decisions, with GAT augmenting information extracted from adjacent nodes. A distinct collaborator selection mechanism is also developed to streamline communication between agents, filtering out those with minimal correlations in the vector input to the policy network. Experimental results demonstrate that, in terms of service latency and delivery failure, the GAMA-Cache outperforms other state-of-the-art MARL solutions for edge content caching in IoV.

关键词： Content Caching Reinforcement Learning Connected Autonomous Driving

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Transactions on Data Hiding and Multimedia Security IX 1

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丛书名： Lecture Notes in Computer Science

1000年

作者： Yun Q. Shi Feng Liu Weiqi Yan

ISBN: (数字)9783642550461

ISBN: (纸本)9783642550454

Since the mid 1990s, data hiding has been proposed as an enabling technology for securing multimedia communication and is now used in various applications including broadcast monitoring, movie fingerprinting, steganography, video indexing and retrieval and image authentication. Data hiding and cryptographic techniques are often combined to complement each other, thus triggering the development of a new research field of multimedia security. Besides, two related disciplines, steganalysis and data forensics, are increasingly attracting researchers and becoming another new research field of multimedia security. This journal, LNCS Transactions on Data Hiding and Multimedia Security, aims to be a forum for all researchers in these emerging fields, publishing both original and archival research results. The seven papers included in this special issue were carefully reviewed and selected from 21 submissions. They address the challenges faced by the emerging area of visual cryptography and provide the readers with an overview of the state of the art in this field of research.

关键词： Cryptology Systems and Data Security Coding and Information Theory Image Processing and Computer Vision

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