检索结果-内蒙古大学图书馆

arXiv 2024年

作者： Chen, Ying Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

In this work, we first develop a unified Bhatnagar-Gross-Krook lattice Boltzmann (BGK-LB) model for the d(d ≥ 1)-dimensional linear hyperbolic equation (L-HE), where the natural moments and the DdQ(2d2 + 1) [(2d2 + 1) discrete velocities in d-dimensional space] lattice structure are considered. Subsequently, at the acoustic scaling, we conduct an accuracy analysis on the developed BGK-LB model by the direct Taylor expansion (DTE) method, and present the second- and third-order moments of the equilibrium distribution functions (EDFs) to ensure that the BGK-LB model can be fourth-order consistent with the L-HE. And on this basis, when considering the Dirichlet boundary condition, the fourth-order full-way and half-way boundary schemes are proposed to approximate the unknown distribution functions to ensure that the BGK-LB model can be overall fourth-order accurate. Thereafter, based on the kinetic entropy theory, we derive the conditions that the fourth-order moments of the EDFs should satisfy to ensure the microscopic entropy stability of the BGK-LB model. In addition, with the aid of the von Neumann stability analysis, we also discuss the L2 stability of the BGK-LB model and numerically plot the stability regions. In particular, from a numerical perspective, we find that the region of microscopic entropy stability is identical to that of L2 stability. Finally, we carry out some numerical experiments to test the accuracy and stability of the BGK-LB model, and the numerical results are in agreement with our theoretical analysis. In addition, we compare the developed full-way and half-way boundary schemes for the Dirichlet boundary condition, which shows that the full-way boundary scheme is more stable. Copyright © 2024, The Authors. All rights reserved.

关键词： Entropy

来源：评论

学校读者我要写书评

暂无评论

A phase-field-based lattice Boltzmann method for two-phase flows with the interfacial mass/heat transfer

arXiv

引用

arXiv 2024年

作者： Chen, Baihui Zhan, Chengjie Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

In this work, we develop a phase-field-based lattice Boltzmann (LB) method for a two-scalar model of the two-phase flows with interfacial mass/heat transfer. Through the Chapman–Enskog analysis, we show that the present LB method can correctly recover the governing equations for phase field, flow field and concentration/temperature field. In particular, to derive the two-scalar equations for the mass/heat transfer, we propose a new LB model with an auxiliary source distribution function to describe the extra flux terms, and the discretizations of some derivative terms can be avoided. The accuracy and efficiency of the present method is also tested through several benchmark problems, and the influence of mass/heat transfer on the fluid viscosity is further considered by introducing an exponential relation. The numerical results show that the present LB method is suitable for the two-phase flows with interfacial mass/heat transfer. © 2024, CC BY.

关键词： Distribution functions

来源：评论

学校读者我要写书评

暂无评论

Regularized Lattice Boltzmann Method Based Maximum Principle and Energy Stability Preserving Finite-Difference Scheme for the Allen-Cahn Equation

SSRN

引用

SSRN 2024年

作者： Chen, Ying Liu, Xi Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

The Allen-Cahn equation (ACE) inherently possesses two crucial properties: the maximum principle and the energy dissipation law. Preserving these two properties at the discrete level is also necessary in the numerical methods for the ACE. In this paper, unlike the traditionally top-down macroscopic numerical schemes which discretize the ACE directly, we first propose a novel bottom-up mesoscopic regularized lattice Boltzmann method based macroscopic numerical scheme for d (=1, 2, 3)-dimensional ACE, where the DdQ(2d+1) [(2d+1) discrete velocities in d-dimensional space] lattice structure is adopted. In particular, the proposed macroscopic numerical scheme has a second-order accuracy in space, and can also be viewed as an implicit-explicit finite-difference scheme for the ACE, in which the nonlinear term is discretized semi-implicitly, the temporal derivative and dissipation term of the ACE are discretized by using the explicit Euler method and second-order central difference method, respectively. Then we demonstrate that the proposed scheme can preserve the maximum bound principle and the original energy dissipation law at the discrete level under some conditions. Finally, some numerical experiments are conducted to validate our theoretical analysis. © 2024, The Authors. All rights reserved.

关键词： Maximum principle

来源：评论

学校读者我要写书评

暂无评论

Subspace method based on neural networks for eigenvalue problems

arXiv

引用

arXiv 2024年

作者： Dai, Xiaoying Fan, Yunying Sheng, Zhiqiang LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China

With the rapid development of machine learning, numerical discretization methods based on deep neural networks have been widely used in many fields, especially in solving high-dimensional problems where traditional methods face bottlenecks. However, for low-dimensional problems, existing machine learning methods are not as accurate and efficient as traditional methods. In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. Our basic idea is to use neural network based basis functions to span a subspace, then calculate the parameters of the neural network based basis functions through appropriate training, and finally calculate the Galerkin projection of the eigenvalue problem onto the subspace and obtain an approximate solution. In addition, we reduce the dimension of the subspace by applying some dimensionality reduction technique, which can improve the accuracy of the approximate solution in further. Numerical experiments show that we can obtain approximate eigenvalues with accuracy of 10−11 but with less then 400 epochs, which is significantly superior to other existing neural network based *** Codes 65N25, 65L15, 68T07 Copyright © 2024, The Authors. All rights reserved.

关键词：

来源：评论

学校读者我要写书评

暂无评论

Intelligent Solution System for Cloud Security Based on Equity Distribution:Model and Algorithms

引用

Computers, Materials & Continua 2024年第1期78卷 1461-1479页

作者： Sarah Mustafa Eljack Mahdi Jemmali Mohsen Denden Mutasim Al Sadig Abdullah M.Algashami Sadok Turki Department of Computer Science and Information College of Science at ZulfiMajmaah UniversityAl-Majmaah11952Saudi Arabia Department of Computer Science College of Computing and InformaticsUniversity of SharjahSharjahUnited Arab Emirates Higher Institute of Computer Science and Mathematics University of MonastirMonastir5000Tunisia Mars Laboratory University of SousseSousseTunisia Department of Logistic and Maintenance UFR MIM at MetzUniversity of LorraineMetzFrance Department of Computer and Information Technologies College of Telecommunicationand Information Riyadh CTITechnical and Vocational Training Corporation TVTCRiyadh12464Saudi Arabia Department of Computer Science Higher Institute of Applied Sciences of SousseSousse UniversitySousse4000Tunisia

In the cloud environment,ensuring a high level of data security is in high *** planning storage optimization is part of the whole security process in the cloud *** enables data security by avoiding the risk of data loss and data *** development of data flow scheduling approaches in the cloud environment taking security parameters into account is *** our work,we propose a data scheduling model for the cloud *** is made up of three parts that together help dispatch user data flow to the appropriate *** first component is the Collector Agent whichmust periodically collect information on the state of the network *** second one is the monitoring agent which must then analyze,classify,and make a decision on the state of the link and finally transmit this information to the *** third one is the scheduler who must consider previous information to transfer user data,including fair distribution and reliable *** should be noted that each part of the proposedmodel requires the development of its *** this article,we are interested in the development of data transfer algorithms,including fairness distribution with the consideration of a stable link *** algorithms are based on the grouping of transmitted files and the iterative *** proposed algorithms showthe performances to obtain an approximate solution to the studied problem which is an NP-hard(Non-Polynomial solution)*** experimental results show that the best algorithm is the half-grouped minimum excluding(HME),with a percentage of 91.3%,an average deviation of 0.042,and an execution time of 0.001 s.

关键词： Cyber-security cloud computing cloud security algorithms heuristics

来源：评论

学校读者我要写书评

暂无评论

GBFRS: Robust Fuzzy Rough Sets via Granular-ball computing

arXiv

引用

arXiv 2025年

作者： Xia, Shuyin Lian, Xiaoyu Sang, Binbin Wang, Guoyin Gao, Xinbo Chongqing Key Laboratory of Computational Intelligence Key Laboratory of Big Data Intelligent Computing Key Laboratory of Cyberspace Big Data Intelligent Security Ministry of Education Chongqing University of Posts and Telecommunications Chongqing400065 China College of Computer and Information Science the National Center for Applied Mathematics in Chongqing Chongqing Normal University Chongqing401331 China

Fuzzy rough set theory is effective for processing datasets with complex attributes, supported by a solid mathematical foundation and closely linked to kernel methods in machine learning. Attribute reduction algorithms and classifiers based on fuzzy rough set theory exhibit promising performance in the analysis of high-dimensional multivariate complex data. However, most existing models operate at the finest granularity, rendering them inefficient and sensitive to noise, especially for high-dimensional big data. Thus, enhancing the robustness of fuzzy rough set models is crucial for effective feature selection. Muiti-garanularty granular-ball computing, a recent development, uses granular-balls of different sizes to adaptively represent and cover the sample space, performing learning based on these granular-balls. This paper proposes integrating multi-granularity granular-ball computing into fuzzy rough set theory, using granular-balls to replace sample points. The coarse-grained characteristics of granular-balls make the model more robust. Additionally, we propose a new method for generating granular-balls, scalable to the entire supervised method based on granular-ball computing. A forward search algorithm is used to select feature sequences by defining the correlation between features and categories through dependence functions. Experiments demonstrate the proposed model’s effectiveness and superiority over baseline methods. The source codes and datasets are both available on the public link: https://***/lianxiaoyu724/GBFRS Copyright © 2025, The Authors. All rights reserved.

关键词： Granular computing

来源：评论

学校读者我要写书评

暂无评论

Matching extension and matching exclusion via the size or the spectral radius of graphs

arXiv

引用

arXiv 2023年

作者： Miao, Shujing Li, Shuchao Wei, Wei Hubei Key Laboratory of Mathematical Science Faculty of Mathematics and Statistics Central China Normal University Wuhan430079 China Center of Intelligent Computing and Applied Statistics School of Mathematics Physics and Statistics Shanghai University of Engineering Science Shanghai201620 China

A graph G is said to be k-extendable if every matching of size k in G can be extended to a perfect matching of G, where k is a positive integer. We say G is 1-excludable if for every edge e of G, there exists a perfect matching excluding e. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G is k-extendable. Then we determine a lower bound on the size (resp. the spectral radius) of G to guarantee that G is 1-excludable. All the corresponding extremal graphs are characterized. Copyright © 2023, The Authors. All rights reserved.

关键词： Matrix algebra

来源：评论

学校读者我要写书评

暂无评论

THE LATENT VARIABLE PROXIMAL POINT ALGORITHM FOR VARIATIONAL PROBLEMS WITH INEQUALITY CONSTRAINTS

arXiv

引用

arXiv 2025年

作者： Dokken, Jørgen S. Farrell, Patrick E. Keith, Brendan Papadopoulos, Ioannis P.A. Surowiec, Thomas M. Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Oslo Norway Mathematical Institute University of Oxford Oxford United Kingdom Mathematical Institute Faculty of Mathematics and Physics Charles University Prague Czech Republic Division of Applied Mathematics Brown University ProvidenceRI United States Weierstrass Institute Berlin Germany

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides;in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. In this paper, we describe the LVPP algorithm in a general form and apply it to twelve problems from across mathematics. © 2025, CC BY.

关键词： Consensus algorithm

来源：评论

学校读者我要写书评

暂无评论

Enhancing Electrocardiography Data Classification Confidence: A Robust Gaussian Process Approach (MuyGPs)

arXiv

引用

arXiv 2024年

作者： Nnyaba, Ukamaka V. Shemtaga, Hewan M. Collins, David W. Muyskens, Amanda L. Priest, Benjamin W. Billor, Nedret Department of Mathematics and Statistics Auburn University AuburnAL36849 United States Department of Mathematics and Statistics Auburn University AuburnAL36849 United States Computational Engineering Division Lawrence Livermore National Laboratory LivermoreCA94550 United States Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States

Analyzing electrocardiography (ECG) data is essential for diagnosing and monitoring various heart diseases. The clinical adoption of automated methods requires accurate confidence measurements, which are largely absent from existing classification methods. In this paper, we present a robust Gaussian Process classification hyperparameter training model (MuyGPs) for discerning normal heartbeat signals from the signals affected by different arrhythmias and myocardial infarction. We compare the performance of MuyGPs with traditional Gaussian process classifier as well as conventional machine learning models, such as, Random Forest, Extra Trees, k-Nearest Neighbors and Convolutional Neural Network. Comparing these models reveals MuyGPs as the most performant model for making confident predictions on individual patient ECGs. Furthermore, we explore the posterior distribution obtained from the Gaussian process to interpret the prediction and quantify uncertainty. In addition, we provide a guideline on obtaining the prediction confidence of the machine learning models and quantitatively compare the uncertainty measures of these models. Particularly, we identify a class of less-accurate (ambiguous) signals for further diagnosis by an expert. © 2024, CC BY.

关键词： Convolutional neural networks

来源：评论

学校读者我要写书评

暂无评论

PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval

arXiv

引用

arXiv 2023年

作者： Liu, Aoxu Fan, Xiaohong Yang, Yin Zhang, Jianping The School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University the Key Laboratory of Intelligent Computing & Information Processing the Ministry of Education Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University the National Center for Applied Mathematics in Hunan Xiangtan411105 China

The problem of phase retrieval (PR) involves recovering an unknown image from limited amplitude measurement data and is a challenge nonlinear inverse problem in computational imaging and image processing. However, many of the PR methods are based on black-box network models that lack interpretability and plug-and-play (PnP) frameworks that are computationally complex and require careful parameter tuning. To address this, we have developed PRISTA-Net, a deep unfolding network (DUN) based on the first-order iterative shrinkage thresholding algorithm (ISTA). This network utilizes a learnable nonlinear transformation to address the proximal-point mapping sub-problem associated with the sparse priors, and an attention mechanism to focus on phase information containing image edges, textures, and structures. Additionally, the fast Fourier transform (FFT) is used to learn global features to enhance local information, and the designed logarithmic-based loss function leads to significant improvements when the noise level is low. All parameters in the proposed PRISTA-Net framework, including the nonlinear transformation, threshold parameters, and step size, are learned end-to-end instead of being manually set. This method combines the interpretability of traditional methods with the fast inference ability of deep learning and is able to handle noise at each iteration during the unfolding stage, thus improving recovery quality. Experiments on Coded Diffraction Patterns (CDPs) measurements demonstrate that our approach outperforms the existing state-of-the-art methods in terms of qualitative and quantitative evaluations. Our source codes are available at https://***/liuaxou/PRISTA-Net. Copyright © 2023, The Authors. All rights reserved.

关键词： Mapping

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：