检索结果-内蒙古大学图书馆

Correction to: Optimal Error Estimates for Gegenbauer Approximations in Fractional Spaces

Journal of scientific computing 2025年第2期103卷 1-2页

作者： Xie, Ruiyi Liu, Wenjie Wang, Haiyong Wu, Boying School of Mathematics Harbin Institute of Technology Harbin People’s Republic of China Key Laboratory of Computing and Stochastic Mathematics Ministry of Education (LCSM) Changsha People’s Republic of China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan People’s Republic of China China and Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan People’s Republic of China

来源：评论

学校读者我要写书评

暂无评论

Defining myocardial fiber bundle architecture in atrial digital twins

引用

Computers in Biology and Medicine 2025年 188卷 109774-109774页

作者： Piersanti, Roberto Bradley, Ryan Ali, Syed Yusuf Quarteroni, Alfio Dede’, Luca Trayanova, Natalia A. MOX - Laboratory of Modeling and Scientific Computing Dipartimento di Matematica Politecnico di Milano Milano Italy ADVANCE - Alliance for Cardiovascular Diagnostic and Treatment Innovation Johns Hopkins University Baltimore United States Research Computing Lehigh University BethlehemPA United States Department of Biomedical Engineering Johns Hopkins University Baltimore United States Mathematics Institute École Polytechnique Fédérale de Lausanne Lausanne Switzerland

A key component in developing atrial digital twins (ADT) - virtual representations of patients’ atria — is the accurate prescription of myocardial fibers which are essential for the tissue characterization. Due to the difficulty of reconstructing atrial fibers from medical imaging, a widely used strategy for fiber generation in ADT relies on mathematical models. Existing methodologies utilize semi-automatic approaches, are tailored to specific morphologies, and lack rigorous validation against imaging fiber data. In this study, we introduce a novel atrial Laplace–Dirichlet-Rule-Based Method (LDRBM) for prescribing highly detailed myofiber orientations and providing robust regional annotation in bi-atrial morphologies of any complexity. The robustness of our approach is verified in eight extremely detailed bi-atrial geometries, derived from a sub-millimeter Diffusion-Tensor-Magnetic-Resonance Imaging (DTMRI) human atrial fiber dataset. We validate the LDRBM by quantitatively recreating each of the DTMRI fiber architectures: a comprehensive comparison with DTMRI ground truth data is conducted, investigating differences between electrophysiology (EP) simulations provided by either LDRBM and DTMRI fibers. Finally, we demonstrate that the novel LDRBM outperforms current state-of-the-art (LDRBMs and Universal Atrial Coordinates) fiber models, confirming the exceptional accuracy of our methodology and the critical importance of incorporating detailed fiber orientations in EP simulations. Ultimately, this work represents a fundamental step towards the development of physics-based digital twins of the human atria, establishing a new standard for prescribing fibers in ADT. © 2025 The Authors

关键词： Magnetic resonance imaging

来源：评论

学校读者我要写书评

暂无评论

Learning with Noisy Labels: the Exploration of Error Bounds in Classification

arXiv

引用

arXiv 2025年

作者： Liu, Haixia Li, Boxiao Yang, Can Wang, Yang School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan China Department of Mathematics The Hong Kong University of Science and Technology Clear Water Bay China

Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the presence of noisy labels is of considerable practical significance. In this paper, we focus on the error bounds of excess risks for classification problems with noisy labels within deep learning frameworks. We begin by exploring loss functions with noise-tolerant properties, ensuring that the empirical minimizer on noisy data aligns with that on the true data. Next, we estimate the error bounds of the excess risks, expressed as a sum of statistical error and approximation error. We estimate the statistical error on a dependent (mixing) sequence, bounding it with the help of the associated independent block sequence. For the approximation error, we first express the classifiers as the composition of the softmax function and a continuous function from [0, 1]d to RK. The main task is then to estimate the approximation error for the continuous function from [0, 1]d to RK. Finally, we focus on the curse of dimensionality based on the low-dimensional manifold assumption. Copyright © 2025, The Authors. All rights reserved.

关键词： Risk assessment

来源：评论

学校读者我要写书评

暂无评论

An automatic approach to develop the fourth-order and L2-stable lattice Boltzmann model for diagonal-anisotropic diffusion equations

arXiv

引用

arXiv 2025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 The State Key Laboratory of Intelligent Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China

This paper discusses how to develop a high-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the general d(≥ 1)-dimensional diagonal-anisotropic diffusion equation. Such an MRT-LB model considers the transformation matrix constructed in a natural way and the DdQ(2d2 + 1) [(2d2 + 1) discrete velocities in d-dimensional space] lattice structure. A key step in developing the high-order MRT-LB model is to determine the additional adjustable relaxation parameters and weight coefficients, which are used to eliminate the truncation errors at some certain orders of the MRT-LB model, while ensuring the stability of the MRT-LB model. In this work, we first present a unified MRT-LB model for the d-dimensional diagonal-anisotropic diffusion equation. Then, through the direct Taylor expansion, we analyze the macroscopic modified equations of the MRT-LB model up to fourth-order at the diffusive scaling, and further derive the conditions that ensure the MRT-LB model to be fourth-order consistent with the diagonal-anisotropic diffusion equation. In particular, when the diagonal-anisotropic diffusion equation is reduced to the isotropic type, we propose another MRT-LB model with the DdQ(2d+ 1) lattice structure [fewer discrete velocities than the DdQ(2d2 + 1) lattice structure], and the fourth-order conditions are similarly derived. Additionally, we also construct the fourth-order initialization scheme for the present LB method. After that, the condition which guarantees that the MRT-LB model can satisfy the stability structure is explicitly given, and we would like to point out that from a numerical perspective, once the stability structure is satisfied, the MRT-LB model must be L2 stable. In combination with the fourth-order consistent and L2 stability conditions, the relaxation parameters and weight coefficients of the MRT-LB model can be automatically given by a simple computer code. Finally, we perform numerical simulations of several benchmark problems, and f

关键词： Anisotropy

来源：评论

学校读者我要写书评

暂无评论

LOCAL SUPERCONVERGENCE OF CONTINUOUS GALERKIN SOLUTIONS FOR DELAY DIFFERENTIAL EQUATIONS OF PANTOGRAPH TYPE

引用

Journal of Computational Mathematics 2016年第2期34卷 186-199页

作者： Xiuxiu Xu Qiumei Huang Hongtao Chen Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen 361005 China

This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.

关键词： Pantograph delay differential equations Uniform mesh Continuous Galerkinmethods Supercloseness Superconvergence.

来源：评论

学校读者我要写书评

暂无评论

Numerical Investigations of a Class of Biological Models on Unbounded Domain

引用

Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 169-186页

作者： Qiumei Huang Dongfang Li Jiwei Zhang Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratoryof Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Beijing Computational Science Research Center Beijing1000193China

This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial *** overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)*** that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability *** delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically ***,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.

关键词： Biological models artificial boundary method absorbing boundary conditions finite difference method stability,convergence

来源：评论

学校读者我要写书评

暂无评论

MAP-based Problem-Agnostic Diffusion Model for Inverse Problems

arXiv

引用

arXiv 2025年

作者： Tao, Pingping Liu, Haixia Su, Jing Yang, Xiaochen Tan, Hongchen Shandong University Library No. 180 West Culture Road Shandong Weihai264209 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology No. 1037 Luoyu road Hubei Wuhan430074 China Dapartment of Basic Sciences Dalian University of Science and Technology No. 999-26 Harbor Road Liaoning Dalian116052 China School of Computer Science and Technology Harbin Institute of Technology No. 2 West Culture Road Shandong Weihai264209 China Institute of Future Technology Dalian University of Technology No. 2 Lingong Road Liaoning Dalian116081 China

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method for inverse problems. To leverage unconditionally pretrained diffusion models to address conditional generation tasks, we divide the conditional score function into two terms according to Bayes’ rule: an unconditional score function (approximated by a pretrained score network) and a guided term, which is estimated using a novel MAP-based method that incorporates a Gaussian-type prior of natural images. This innovation allows us to better capture the intrinsic properties of the data, leading to improved performance. Numerical results demonstrate that our method preserves contents more effectively compared to state-of-the-art methods—for example, maintaining the structure of glasses in super-resolution tasks and producing more coherent results in the neighborhood of masked regions during inpainting. Our numerical implementation is available at https://***/liuhaixias1/ MAP-DIFFUSION-IP. Copyright © 2025, The Authors. All rights reserved.

关键词： Inverse problems

来源：评论

学校读者我要写书评

暂无评论

A modular lattice boltzmann solver for GPU computing processors

引用

SeMA Journal 2012年第1期59卷 53-78页

作者： Astorino, M. Sagredo, J. Becerra Quarteroni, A. CMCS Chair of Modelling and Scientific Computing MATHICSE Mathematics Institute of Computational Science and Engineering École Polytechnique Fédérale de Lausanne Station 8 Lausanne CH-1015 Switzerland Department of Mathematics Politecnico di Milano MOX Modeling and Scientific Computing Via Bonardi 9 Milano 20133 Italy

During the past two decades, the lattice Boltzmann method (LBM) has been increasingly acknowledged as a valuable alternative to classical numerical techniques (e.g. finite elements, finite volumes, etc.) in fluid dynamics. A distinguishing feature of LBM is undoubtedly its highly parallelizable data structure. In this work we present a general parallel LBM framework for graphic processing units (GPUs) characterized by a high degree of modularity and memory efficiency, still preserving very good computational performance. After recalling the essential programming principles of the CUDA C language for GPUs, the details of the implementation will be provided. The data structure here presented takes into account the intrinsic properties of the Gauss-Hermite quadrature rules (on which the LBM is based) to guarantee a unique and flexible framework for two- and three-dimensional problems. In addition, a careful implementation of a memory efficient formulation of the LBM algorithm has allowed to limit the high memory consumption that typically affects this computational method. Numerical examples in two and three dimensions illustrate the reliability and the performance of the code. © 2012, Sociedad Española de Matemática Aplicada.

关键词： CUDA GPU programming lattice Boltzmann method Navier-Stokes equations parallel computing

来源：评论

学校读者我要写书评

暂无评论

Improved analysis of rectangular dielectric waveguides based on a legendre pseudospectral penalty scheme

Improved analysis of rectangular dielectric waveguides based...

引用

Integrated Photonics Research, Silicon and Nanophotonics, IPRSN 2010

作者： Chiang, Shun-Fan Lin, Bang-Yan Teng, Chun-Hao Chang, Hung-Chun Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics Graduate Institute of Communication Engineering National Taiwan University Taipei 10617 Taiwan Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu 30010 Taiwan

A Legendre pseudospectral method with penalty scheme is established in frequency domain for high-accuracy waveguide mode analysis. For a square dielectric waveguide, the calculated modal index is seen to converge to t... 详细信息

ISBN: (纸本)9781557528957

关键词： Frequency domain analysis

来源：评论

学校读者我要写书评

暂无评论

Deep Frequency Awareness Functional Maps for Robust Shape Matching

引用

IEEE Transactions on Visualization and Computer Graphics 2025年

作者： Luo, Feifan Li, Qinsong Hu, Ling Wang, Haibo Xu, Haojun Liu, Xinru Liu, Shengjun Chen, Hongyang Central South University School of Mathematics and Statistics Changsha China Zhejiang University College of Computer Science and Technology Hangzhou China Central South University Big Data Institute Changsha China Hunan First Normal University School of Mathematics and Statistics Changsha China Central South University Institute of Engineering Modeling and Scientific Computing School of Mathematics and Statistics Changsha China Zhejiang Lab Research Center for Data Hub and Security Hangzhou China

Traditional deep functional map frameworks are widely used for 3D shape matching;however, many methods fail to adaptively capture the relevant frequency information required for functional map estimation in complex scenarios, leading to poor performance, especially under significant deformations. To address these challenges, we propose a novel unsupervised learning-based framework, Deep Frequency Awareness Functional Maps (DFAFM), specifically designed to tackle diverse shape-matching problems. Our approach introduces the Spectral Filter Operator Preservation constraint, which ensures the preservation of critical frequency information. These constraints promote frequency awareness by learning a set of spectral filters and incorporating them as a loss function to jointly supervise the functional maps, pointwise maps, and spectral filters. The spectral filters are constructed using orthonormal Jacobi polynomials with learnable coefficients, enabling adaptive and efficient frequency representation. Furthermore, we propose a refinement strategy that leverages the learned spectral filters and constraints to enhance the accuracy of the final pointwise map. Extensive experiments conducted on multiple benchmark datasets demonstrate that our method outperforms state-of-the-art approaches, particularly in challenging scenarios involving non-isometric deformations and inconsistent topology. Our code is available at https://***/LuoFeifan77/DeepFAFM. © 1995-2012 IEEE.

关键词： Frequency estimation

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：