检索结果-内蒙古大学图书馆

arXiv 2020年

作者： Lei, Huan Wu, Lei Weinan, E. Department of Computational Mathematics Science & Engineering Department of Statistics & Probability Michigan State University MI48824 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Polymer solution is used as an example to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the micro-scale model and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a new form of the objective tensor derivative. Numerical results demonstrate the accuracy of DeePN2. Copyright © 2020, The Authors. All rights reserved.

关键词： Viscous flow

来源：评论

学校读者我要写书评

暂无评论

Parallel Multicore CSB Format and Its Sparse Matrix Vector Multiplication

引用

Advances in Linear Algebra & Matrix Theory 2014年第1期4卷 1-8页

作者： Bing Yang Shuo Gu Tong-Xiang Gu Cong Zheng Xing-Ping Liu Graduate School of Chinese Academy of Engineering Physics Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics BeijingChina School of Electronic Engineering University of Electronic Science and Technology of China Chengdu China

Sparse Matrix Vector Multiplication (SpMV) is one of the most basic problems in scientific and engineering computations. It is the basic operation in many realms, such as solving linear systems or eigenvalue problems. Nowadays, more than 90 percent of the world’s highest performance parallel computers in the top 500 use multicore architecture. So it is important practically to design the efficient methods of computing SpMV on multicore parallel computers. Usually, algorithms based on compressed sparse row (CSR) format suffer from a number of nonzero elements on each row so hardly as to use the multicore structure efficiently. Compressed Sparse Block (CSB) format is an effective storage format which can compute SpMV efficiently in a multicore computer. This paper presents a parallel multicore CSB format and SpMV based on it. We carried out numerical experiments on a parallel multicore computer. The results show that our parallel multicore CSB format and SpMV algorithm can reach high speedup, and they are highly scalable for banded matrices.

关键词： SpMV Multicore Parallel Computers Parallel Multicore CSB Format

来源：评论

学校读者我要写书评

暂无评论

Hyperuniformity of quasicrystals

引用

Physical Review B 2017年第5期95卷 054119-054119页

作者： Erdal C. Oğuz Joshua E. S. Socolar Paul J. Steinhardt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

Hyperuniform systems, which include crystals, quasicrystals, and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of the spectral intensity is dense and discontinuous. We employ the integrated spectral intensity Z(k) to quantitatively characterize the hyperuniformity of quasicrystalline point sets generated by projection methods. The scaling of Z(k) as k tends to zero is computed for one-dimensional quasicrystals and shown to be consistent with independent calculations of the variance, σ2(R), in the number of points contained in an interval of length 2R. We find that one-dimensional quasicrystals produced by projection from a two-dimensional lattice onto a line of slope 1/τ fall into distinct classes determined by the width of the projection window. For a countable dense set of widths, Z(k)∼k4; for all others, Z(k)∼k2. This distinction suggests that measures of hyperuniformity define new classes of quasicrystals in higher dimensions as well.

关键词： Microstructure Structural properties

来源：评论

学校读者我要写书评

暂无评论

Towards Trajectory Planning for a 6-Degree-of-Freedom Robot Manipulator Considering the Orientation of the End-effector Using Computer Algebra 10

Towards Trajectory Planning for a 6-Degree-of-Freedom Robot ...

引用

10th International Symposium on Symbolic Computation in Software science - Work in Progress Workshop, SCSS 2024 WiP

作者： Okazaki, Takumu Terui, Akira Mikawa, Masahiko Master's Program in Mathematics Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan Institute of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Institute of Library Information and Media Science University of Tsukuba Tsukuba305-8550 Japan

We consider the trajectory planning of a 6-Degree-of-Freedom (DOF) robot manipulator using computer algebra, with controlling the orientation of the end-effector. As a first step towards the objective, we present a solution to the inverse kinematics problem of the manipulator such that the orientation of the end-effector remains constant using computer algebra. © 2024 CEUR-WS. All rights reserved.

关键词： End effectors

来源：评论

学校读者我要写书评

暂无评论

Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning

arXiv

引用

arXiv 2020年

作者： Weinan, E. Han, Jiequn Jentzen, Arnulf Department of Mathematics Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Faculty of Mathematics and Computer Science University of Münster Germany

In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are potentially free of the curse of dimensionality for many different applications and have been proven to be so in the case of some nonlinear Monte Carlo methods for nonlinear parabolic PDEs. In this paper, we review these numerical and theoretical advances. In addition to algorithms based on stochastic reformulations of the original problem, such as the multilevel Picard iteration and the Deep BSDE method, we also discuss algorithms based on the more traditional Ritz, Galerkin, and least square formulations. We hope to demonstrate to the reader that studying PDEs as well as control and variational problems in very high dimensions might very well be among the most promising new directions in mathematics and scientific computing in the near *** Codes 65C05, 65K10, 65M75, 90C06 Copyright © 2020, The Authors. All rights reserved.

关键词： Monte Carlo methods

来源：评论

学校读者我要写书评

暂无评论

GLOBAL SOLUTION AND ITS LONG TIME BEHAVIOR FOR THE GENERALIZED LONG-SHORT WAVE EQUATIONS

引用

Journal of Partial Differential Equations 2005年第3期18卷 206-218页

作者： Zhang Ruifeng Guo Boling College of Mathematics and Information Science Henan University Kaifeng 475001 Beijing Graduate School of Chinese Academy of Engineering Physics Beijing 100088 China Beijing Institute of Applied Physics and Computational Mathematics Beijing 100088 China

The long time behavior of the solutions of the generalized long-short wave equations with dissipation term is studied. The existence of global attractor of the initial periodic boundary value is proved by means of a u... 详细信息

关键词： The generalized long-short wave equations a uniform priori esti-mate global attractor Hausdorff dimension fractal dimension.

来源：评论

学校读者我要写书评

暂无评论

An Optimized Path Planning of Manipulator with Spline Curves Using Real Quantifier Elimination Based on Comprehensive Gröbner Systems 10

An Optimized Path Planning of Manipulator with Spline Curves...

引用

10th International Symposium on Symbolic Computation in Software science - Work in Progress Workshop, SCSS 2024 WiP

作者： Shirato, Yusuke Oka, Natsumi Terui, Akira Mikawa, Masahiko Master's Program in Mathematics Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan Institute of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Institute of Library Information and Media Science University of Tsukuba Tsukuba305-8550 Japan

This paper presents an advanced method for addressing the inverse kinematics and optimal path planning challenges in robot manipulators. The inverse kinematics problem involves determining the joint angles for a given position and orientation of the end-effector. Furthermore, the path planning problem seeks a trajectory between two points. Traditional approaches in computer algebra have utilized Gröbner basis computations to solve these problems, offering a global solution but at a high computational cost. To overcome the issue, the present authors have proposed a novel approach that employs the Comprehensive Gröbner System (CGS) and CGS-based quantifier elimination (CGS-QE) methods to efficiently solve the inverse kinematics problem and certify the existence of solutions for trajectory planning. This paper extends these methods by incorporating smooth curves via cubic spline interpolation for path planning and optimizing joint configurations using shortest path algorithms to minimize the sum of joint configurations along a trajectory. This approach significantly enhances the manipulator's ability to navigate complex paths and optimize movement sequences. © 2024 CEUR-WS. All rights reserved.

关键词： Inverse kinematics

来源：评论

学校读者我要写书评

暂无评论

Towards Trajectory Planning of a Robot Manipulator with Computer Algebra using Bézier Curves for Obstacle Avoidance 10

Towards Trajectory Planning of a Robot Manipulator with Comp...

引用

10th International Symposium on Symbolic Computation in Software science - Work in Progress Workshop, SCSS 2024 WiP

作者： Hatakeyama, Ryo Terui, Akira Mikawa, Masahiko Master's Program in Mathematics Graduate School of Science and Technology University of Tsukuba Tsukuba305-8571 Japan Institute of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Institute of Library Information and Media Science University of Tsukuba Tsukuba305-8550 Japan

This paper discusses the trajectory planning of a robot manipulator with computer algebra. In the operation of robot manipulators, it is important to make the trajectory of the end effector so that it does not collide with obstacles. For this purpose, we have proposed a method of generating a method of trajectory planning using cubic spline curves. However, the method has the disadvantage that the trajectory may not be included in the feasible region of the manipulator, thus an extra test for the inclusion of the curve is needed. In this paper, we propose a new method of generating a trajectory using Bézier curves, which is guaranteed to be included in the feasible region. © 2024 CEUR-WS. All rights reserved.

关键词： Trajectories

来源：评论

学校读者我要写书评

暂无评论

Optimal Complexity in Non-Convex Decentralized Learning over Time-Varying Networks

arXiv

引用

arXiv 2022年

作者： Huang, Xinmeng Yuan, Kun Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Center for Machine Learning Research Peking University China

Decentralized optimization with time-varying networks is an emerging paradigm in machine learning. It saves remarkable communication overhead in large-scale deep training and is more robust in wireless scenarios especially when nodes are moving. Federated learning can also be regarded as decentralized optimization with time-varying communication patterns alternating between global averaging and local updates. While numerous studies exist to clarify its theoretical limits and develop efficient algorithms, it remains unclear what the optimal complexity is for non-convex decentralized stochastic optimization over time-varying networks. The main difficulties lie in how to gauge the effectiveness when transmitting messages between two nodes via time-varying communications, and how to establish the lower bound when the network size is fixed (which is a prerequisite in stochastic optimization). This paper resolves these challenges and establish the first lower bound complexity. We also develop a new decentralized algorithm to nearly attain the lower bound, showing the tightness of the lower bound and the optimality of our algorithm. Copyright © 2022, The Authors. All rights reserved.

关键词： Time varying networks

来源：评论

学校读者我要写书评

暂无评论

Social distancing and COVID-19: Randomization inference for a structured dose-response relationship

arXiv

引用

arXiv 2020年

作者： Zhang, Bo Heng, Siyu Ye, Ting Small, Dylan S. Department of Statistics The Wharton School University of Pennsylvania Graduate Group in Applied Mathematics and Computational Science School of Arts and Sciences University of Pennsylvania

Social distancing is widely acknowledged as an effective public health policy combating the novel coronavirus. But extreme forms of social distancing like isolation and quarantine have costs and it is not clear how much social distancing is needed to achieve public health effects. In this article, we develop a design-based framework to test the causal null hypothesis and make inference about the dose-response relationship between reduction in social mobility and COVID-19 related public health outcomes. We first discuss how to embed observational data with a time-independent, continuous treatment dose into an approximate randomized experiment, and develop a randomization-based procedure that tests if a structured dose-response relationship fits the data. We then generalize the design and testing procedure to accommodate a time-dependent treatment dose in a longitudinal setting. Finally, we apply the proposed design and testing procedures to investigate the effect of social distancing during the phased reopening in the United States on public health outcomes using data compiled from sources including Unacast™, the United States Census Bureau, and the County Health Rankings and Roadmaps program. We rejected a primary analysis null hypothesis that stated the social distancing from April 27, 2020, to June 28, 2020, had no effect on the COVID-19-related death toll from June 29, 2020, to August 2, 2020 (p-value © 2020, CC0.

关键词： Random processes

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：