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On the vanishing dissipation limit for the incompressible MHD equations on bounded domains

science China mathematics 2022年第1期65卷 31-50页

作者： Qin Duan Yuelong Xiao Zhouping Xin Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China The Institute of Mathematical Sciences The Chinese University of Hong KongHong Kong 999077China

In this paper,we investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded *** the boundary,the velocity field fulfills a Navier-slip condition,while the magnetic field satisfies the insulating *** is shown that the initial boundary value problem has a global weak solution for a general smooth *** importantly,for a flat domain,we establish the uniform local well-posedness of the strong solution with higher-order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD equation as the dissipations tend to zero.

关键词： MHD equations initial boundary value problem vanishing dissipation limit

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Optimal Second-Order Rates for Quantum Soft Covering and Privacy Amplification

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IEEE Transactions on Information Theory 2024年第7期70卷 5077-5091页

作者： Shen, Yu-Chen Gao, Li Cheng, Hao-Chung National Taiwan University Department of Electrical Engineering Taipei10617 Taiwan University of Houston Department of Mathematics HoustonTX77204 United States Graduate Institute of Communication Engineering Department of Mathematics Institute of Applied Mathematical Sciences Center for Quantum Science and Engineering National Taiwan University Department of Electrical Engineering Taipei10617 Taiwan Physics Division National Center for Theoretical Sciences Taipei10617 Taiwan Quantum Computing Center New Taipei City23678 Taiwan

We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to extract uniform and independent randomness against quantum adversaries. For both tasks, we use trace distance to measure the closeness between the processed state and the ideal target state. We show that the minimal amount of samples for achieving an \varepsilon -covering is given by the (1-\varepsilon ) -hypothesis testing information (with additional logarithmic additive terms), while the maximal extractable randomness for an \varepsilon -secret extractor is characterized by the conditional (1-\varepsilon ) -hypothesis testing entropy. When performing independent and identical repetitions of the tasks, our one-shot characterizations lead to tight asymptotic expansions of the above-mentioned operational quantities. We establish their second-order rates given by the quantum mutual information variance and the quantum conditional information variance, respectively. Moreover, our results extend to the moderate deviation regime, which are the optimal asymptotic rates when the trace distances vanish at sub-exponential speed. Our proof technique is direct analysis of trace distance without smoothing. © 1963-2012 IEEE.

关键词： Hash functions

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An Iterative Thresholding Method for the Minimum Compliance Problem

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Communications in computational Physics 2023年第4期33卷 1189-1216页

作者： Luyu Cen Wei Hu Dong Wang Xiaoping Wang Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew JerseyUSA School of Science and Engineering The Chinese University of Hong KongShenzhenGuangdong 518172China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big DataGuangdong 518172China

In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary *** prove that the energy is decreasing in each *** effective continuation schemes are proposed to avoid trapping into the local *** results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

关键词： Minimum compliance convolution thresholding linear elasticity

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Topological properties of Sb(111)surface:A first-principles study

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Chinese Physics B 2022年第4期31卷 603-607页

作者： Shuangxi Wang Ping Zhang Department of Materials Science and Engineering China University of PetroleumBeijing 102249China Institute of Applied Physics and Computational Mathematics Beijing 100088China Center for Applied Physics and Technology Peking UniversityBeijing 100871China

First-principles calculations based on the density functional theory were performed to systematically study the electronic properties of the thin film of antimony in(111)*** considering the spin-orbit interaction,for stoichiometric surface,the topological states keep robust for six-bilayer case,and can be recovered in the three-bilayer film,which are guaranteed by time-reversal symmetry and inverse *** reduced surface doped by non-magnetic Bi or magnetic Mn atom,localized three-fold symmetric features can be ***,band structures show that the non-trivial topological states stand for non-magnetic substitutional Bi atom,while can be eliminated by adsorbed or substitutional magnetic Mn atom.

关键词： first-principles study antimony topological states

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Urban Slum Mapping Using Homogeneous Urban Patches 3

Urban Slum Mapping Using Homogeneous Urban Patches

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3rd IEEE International Conference on Intelligent Techniques in Control, Optimization and Signal Processing, INCOS 2024

作者： Prabhu, R. Priya, M. Sangeetha Dayana, R. Suresh, M. School of Computing Srm Institute of Science and Technology Department of Networking and Communications Kattankulathur Campus Chennai India Saveetha Engineering College Department of Computer Science and Engineering Thandalam Chennai India Jeppiaar Institute of Technology Department of Computer Science and Engineering Sriperumbudur Chennai India R.M.D. Engineering College Kavaraipettai Department of Mathematics Thiruvallur India

ISBN: (纸本)9798350361186

Slums (Informal Settlements) are the most dynamic areas whose geographical locations are inaccurate according to official statistics and maps because of the exponential expansion of urbanization strategies. As a result, a method has to be developed to distinguish between informal settlements and track their spatial patterns. This paper presents an integrated method for detecting slums from satellite images that employs homogeneous urban patches (HUP) and grey level co-occurrence matrix (GLCM)-based image segmentation. In order to extract meaningful spatial features, urban patches are segmented according to their homogeneity and GLCM analysis provides useful texture information about slum areas. The combination of both these GLCM and HUP features allows for the creation of a classification map that accurately identifies and maps slum areas. We utilized WorldView-2 (1.84m) satellite imagery of Madurai to test the effectiveness of proposed HUP approach. The validation process includes rigorous testing against ground truth data, with careful consideration given to the selection of training and testing datasets. The effectiveness of the proposed method is evaluated using metrics including overall accuracy, user accuracy, and producer accuracy Furthermore, the proposed algorithm outperformed existing GLCM-based approaches in terms of accuracy. © 2024 IEEE.

关键词： Image segmentation

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Industrial Control Anomaly Detection Based on Distributed Linear Deep Learning

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Computers, Materials & Continua 2025年第1期82卷 1129-1150页

作者： Shijie Tang Yong Ding Huiyong Wang School of Computer Science and Information Security Guilin University of Electronic TechnologyGuilin541004China School of Electronic Engineering and Automation Guilin University of Electronic TechnologyGuilin541004China Guangxi Engineering Research Center of Industrial Internet Security and Blockchain Guilin University of Electronic TechnologyGuilin541004China Institute of Cyberspace Technology HKCT Institute for Higher EducationHong Kong999077China School of Mathematics&Computing Science Guilin University of Electronic TechnologyGuilin541004China

As more and more devices in Cyber-Physical Systems(CPS)are connected to the Internet,physical components such as programmable logic controller(PLC),sensors,and actuators are facing greater risks of network attacks,and fast and accurate attack detection techniques are *** key problem in distinguishing between normal and abnormal sequences is to model sequential changes in a large and diverse field of time *** address this issue,we propose an anomaly detection method based on distributed deep *** method uses a bilateral filtering algorithm for sequential sequences to remove noise in the time series,which can maintain the edge of discrete *** use a distributed linear deep learning model to establish a sequential prediction model and adjust the threshold for anomaly detection based on the prediction error of the validation *** method can not only detect abnormal attacks but also locate the sensors that cause *** conducted experiments on the Secure Water Treatment(SWAT)and Water Distribution(WADI)public *** experimental results show that our method is superior to the baseline method in identifying the types of attacks and detecting efficiency.

关键词： Anomaly detection CPS deep learning MLP(multi-layer perceptron)

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A study of geometry teaching mode based on Van Hiele theory and NetPad 23

A study of geometry teaching mode based on Van Hiele theory ...

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7th International Conference on Education and Multimedia Technology, ICEMT 2023

作者： Gao, Jinghui Wang, Ying Ding, Qianhui Xu, Zhangtao Guan, Hao Institute of Computing Science and Technology Guangzhou University China Software Engineering Institute of Guangzhou Guangzhou China School of Mathematics and Statistics of CCNU Central China Normal University China

ISBN: (纸本)9798400709142

It is one of the main goals of the mathematics curriculum reform to cultivate and develop geometric thinking in junior high school students. Geometric thinking skills have a very profound impact on middle school students learning of mathematics. Van Hiele's theory is dedicated to reducing the gap between the level of difficulty defined by the material and the thinking of the students. It provides strong theoretical support for analyzing the development process of students' geometric thinking and evaluating their level of geometric thinking. With the combination of dynamic geometry software (NetPad) and Van Hiele theory, this study proposes a geometry teaching mode for junior high school students' geometric thinking cultivation, which includes five teaching sessions of Interview, Direct Orientation, Explication, Activities, and Integration. An effective teacher-led, student inquiry-based teaching process, it helps students discover geometric patterns, understand geometric properties, and improve their geometric thinking. The effectiveness of the mode was verified by seventh graders using NetPad to explore Euler's theorem. The results verified the effectiveness of this geometry teaching model to a certain extent. On the other hand, it proves that this model can help improve teaching efficiency. The teaching practice provides a program reference for teachers to design a scientific and reasonable geometry lesson. © 2023 ACM.

关键词： Geometry

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Exploration-Aided Downstream Graph Learning Tasks: A Survey on Exploratory Graph Learning

Exploration-Aided Downstream Graph Learning Tasks: A Survey ...

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International Conference on Information and Communication Technology Convergence (ICTC)

作者： Yu Hou Won-Yong Shin School of Mathematics and Computing (Computational Science and Engineering) Yonsei University Seoul Republic of Korea

Graph learning is crucial for extracting meaningful information from graph-structured data, enabling effective solutions to various downstream tasks. However, existing methods for solving downstream graph learning tasks often rely on the availability of the graph structure, which may not always be accessible in real-world applications. To overcome this limitation, recent approaches have introduced exploratory learning techniques, which aim to tackle graph learning tasks on graphs with unknown topology. In this article, we provide a comprehensive overview of exploratory graph learning applied to two widely studied graph learning tasks: 1) influence maximization and 2) community detection. We delve into the problem formulation of both tasks concerning graphs with unknown topological information. Additionally, we explore the application of exploratory learning techniques to address these problems effectively.

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On Measures Resulting from the Choquet Integration 20th

On Measures Resulting from the Choquet Integration

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20th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2024

作者： Ontkovičová, Zuzana Torra, Vicenç Department of Computing Science Umeå University Umeå Sweden Institute of Information Engineering Automation and Mathematics Faculty of Chemical and Food Technology Slovak University of Technology in Bratislava Bratislava Slovakia

ISBN: (纸本)9783031739996

In this paper, we study measures arising as a result of the Choquet integration with respect to a particular class of measures. The initial insight is provided with several classes of additive and fuzzy measures. It can be seen that some classes are closed regarding the integration, e.g. probabilities, while some are not, such as distorted Lebesgue measures. Knowing both an integration measure and a resulting measure after the Choquet integration directly leads to a fuzzy analogue of the Radon-Nikodym derivatives. For them, a completely different possible approach to their existence is presented for a specific pair of measures. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Integration

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A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics

A Scalable Real-Time Data Assimilation Framework for Predict...

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2024 Workshops of the International Conference for High Performance computing, Networking, Storage and Analysis, SC Workshops 2024

作者： Yin, Junqi Liang, Siming Liu, Siyan Bao, Feng Chipilski, Hristo G. Lu, Dan Zhang, Guannan Oak Ridge National Laboratory National Center for Computational Science Oak RidgeTN United States Florida State University Department of Mathematics TallahasseeFL United States Oak Ridge National Laboratory Computational Science and Engineering Division Oak RidgeTN United States Florida State University Department of Scientific Computing TallahasseeFL United States Oak Ridge National Laboratory Computer Science and Mathematics Division Oak RidgeTN United States

ISBN: (纸本)9798350355543

AI-based foundation models like FourCastNet, GraphCast, ClimaX, and Pangu-Weather are revolutionizing weather and climate predictions but are not yet ready for operational use. Their limitation lies in the absence of a data assimilation system to incorporate real-time Earth system observations, crucial for accurately forecasting events like tropical cyclones and atmospheric rivers. To overcome these obstacles, we introduce a generic real-time data assimilation framework and demonstrate its end-to-end performance on the Frontier supercomputer. This framework comprises two primary modules: an ensemble score filter (EnSF), which significantly outperforms the state-of-the-art data assimilation method, e.g., the Local Ensemble Transform Kalman Filter (LETKF);and a vision transformer-based surrogate capable of real-time adaptation through the integration of observational data. We demonstrate both the strong and weak scaling of our framework up to 1024 GPUs on the Exascale supercomputer, Frontier. Our results not only illustrate the framework's exceptional scalability on high-performance computing systems, but also demonstrate the importance of supercomputers in real-time data assimilation for weather and climate predictions. Even though the proposed framework is tested only on a benchmark surface quasi-geostrophic (SQG) turbulence system, it has the potential to be combined with existing AI-based foundation models, making it suitable for future operational implementations. © 2024 IEEE.

关键词： data assimilation Diffusion models foundation models generative AI high-performance computing uncertainty quantification

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