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Application of gradient descent algorithms based on geodesic distances

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Science China(Information Sciences) 2020年第5期63卷 176-186页

作者： Xiaomin DUAN huafei sun Linyu PENG School of Science Dalian Jiaotong University School of Mathematics and Statistics Beijing Institute of Technology Waseda Institute for Advanced Study Waseda University

In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the objective function. The first proposed problem is the control for positive definite Hermitian matrix systems whose outputs only depend on their inputs. The geodesic distance is adopted as the difference of the output matrix and the target matrix. The controller to adjust the input is obtained such that the output matrix is as close as possible to the target matrix. We show the trajectory of the control input on the manifold using the Riemannian gradient algorithm. The second application is to compute the Karcher mean of a finite set of given Toeplitz positive definite Hermitian matrices, which is defined as the minimizer of the sum of geodesic distances. To obtain more efficient iterative algorithm than traditional ones, a natural gradient algorithm is proposed to compute the Karcher mean. Illustrative simulations are provided to show the computational behavior of the proposed algorithms.

关键词： system control Riemannian gradient algorithm natural gradient algorithm Karcher mean Toeplitz positive definite Hermitian matrix

A NATURAL GRADIENT ALGORITHM FOR THE SOLUTION OF LYAPUNOV EQUATIONS BASED ON THE GEODESIC DISTANCE

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Journal of Computational Mathematics 2014年第1期32卷 93-106页

作者： Xiaomin Duan huafei sun Zhenning Zhang School of Mathematics Bcijing Institute of Technology Beijing 100081 China School of Science Dalian Jiaotong University Dalian 116028 China College of Applied Scienees Beijing University of Technology Beijing 100123 China

A new framework based on the curved Riemannian manifold is proposed to calculate the numerical solution of the Lyapunov matrix equation by using a natural gradient descent algorithm and taking the geodesic distance as the objective function. Moreover, a gradient descent algorithm based on the classical Euclidean distance is provided to compare with this natural gradient descent algorithm. Furthermore, the behaviors of two proposed algorithms and the conventional modified conjugate gradient algorithm are compared and demonstrated by two simulation examples. By comparison, it is shown that the convergence speed of the natural gradient descent algorithm is faster than both of the gradient descent algorithm and the conventional modified conjugate gradient algorithm in solving the Lyapunov equation.

关键词： Lyapunov equation Geodesic distance Natural gradient descent algorithm.

Principal whitened gradient-projection algorithm for distribution control

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Science China(Information Sciences) 2013年第3期56卷 202-209页

作者： ZHANG ShiCheng sun huafei LI ChunHui School of Mathematics Xuzhou Normal University Department of Mathematics Beijing Institute of Technology

In this paper,we use an information geometric algorithm to solve the distribution control *** new designed algorithm is called principal whitened gradient-projection *** the principal natural gradient step,we use principal whitened gradient algorithm to obtain an optimal trajectory of the weight vector on the B-spline manifold from the viewpoint of information *** the projection step,we project the selected points on B onto *** coordinates of the projections on M give the trajectory of the control input u.

关键词： principal whitened gradient distribution control Kullback divergence

Optimal control on special Euclidean group via natural gradient algorithm

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Science China(Information Sciences) 2016年第11期59卷 63-72页

作者： Chunhui LI Erchuan ZHANG Lin JIU huafei sun School of Mathematics and Statistics Beijing Institute of Technology School of Mathematics and Statistics University of Western Australia Department of Mathematics Tulane University School of Mathematics and Statistics and Beijing Key Laboratory on MCAACI Beijing Institute of Technology

Considering the optimal control problem about the control system of the special Euclidean group whose output only depends on its input is meaningful in practical applications. The optimal control considered here is described as the output matrix is as close as possible to the target matrix by adjusting the system *** geodesic distance is adopted as the measure of the difference between the output matrix and the target matrix, and the trajectory of the control input obtained in the process is achieved. Furthermore, some numerical simulations are shown to illustrate our outcomes based on the natural gradient descent algorithm for optimizing the control system of the special Euclidean group.

关键词： system control natural gradient special Euclidean group geodesic distance numerical simulation

Heisenberg Uncertainty Principle for n-Dimen-sional Linear Canonical Transforms

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Journal of Beijing Institute of Technology 2021年第3期30卷 249-253页

作者： Yonggang Li Chuan Zhang huafei sun School of Science Zhengzhou University of AeronauticsZhengzhou 450000China 11th Research Institute of China Electronics Technology Group Corporation Beijing 100015China School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal *** linear canonical transformation has been widely used in various fields of signal processing recently and Heisenberg uncertainty principle has been endowed with new expressive meaning in linear canonical transforms domain,in this manuscript,an improved Heisenberg uncertainty principle is obtained in linear canonical trans-forms domain.

关键词： Heisenberg uncertainty principle linear canonical transforms Pitt inequality

LIE-TROTTER FORMULA FOR THE HADAMARD PRODUCT

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Acta Mathematica Scientia 2020年第3期40卷 659-669页

作者： Jing WANG Yonggang LI huafei sun School of Information Beijing Wuzi UniversityBeijing 101149China College of Science Zhengzhou University of AeronauticsZhengzhou 450015China School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China Beijing Key Laboratory on MCAACI Beijing 100081China

Suppose that A and B are two positive-definite matrices,then,the limit of(A^p/2B^pA^p/2)1/p as p tends to 0 can be obtained by the well known Lie-Trotter *** this article,we generalize the usual product of matrices to the Hadamard product denoted as*which is commutative,and obtain the explicit formula of the limit(A^p*B^p)^1/p as p tends to ***,the existence of the limit of(A^p*B^p)^1/p as p tends to+∞is proved.

关键词： Lie-Trotter formula reciprocal Lie-Trotter formula Hadamard product positive-definite matrix

Numerical analysis of the failure process of soil-rock mixtures through computed tomography and PFC3D models

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International Journal of Coal Science & Technology 2018年第2期5卷 126-141页

作者： Yang Ju huafei sun Mingxu Xing Xiaofei Wang Jiangtao Zheng State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and Technology No. 1 University Avenue Xuzhou 221116 China State Key Laboratory of Coal Resources and Safe Mining China University of Mining and Technology D11 Xueyuan Road Beijing 100083 China School of Mechanics and Civil Engineering China University of Mining and Technology D 11 Xueyuan Road Beijing 100083 China State Intellectual Property Bureau of China No. 6 Xitucheng Road Beijing 100088 China

Soil-rock mixture （SRM） is a unique type of geomaterial characterized by a heterogeneous composition and a complicated structure. It is intractable for the continuum-based soil and rock mechanics theories to accurately characterize and predict the SRM＇s mechanical properties. This study reports a novel numerical method incorporating microfocus computed tomography and PFC3D codes to probe the deformation and failure processes of SRM. The three-dimensional （3D） PFC models that represent the SRM＇s complex structures were built. By simulating the entire failure process in PFC3D, the SRM＇s strength, elastic modulus and crack growth were obtained. The influence of rock ratios on the SRM＇s strength, deformation and failure processes, as well as its internal mesoscale mechanism, were analyzed. By comparing simulation results with experimental data, it was verified that the 3D PFC models were in good agreement with SRM＇s real structure and the SRM＇s compression process, deformation and failure patterns; its intrinsic mesomechanism can be effectively analyzed based on such 3D PFC models.

关键词： Soil-rock mixture (SRM) - PFC3D model Three-dimensional structure Microfocus computed tomography (μCT) Failure mechanism Crack growth

Numerical simulations of seepage flow in rough single rock fractures

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Petroleum 2015年第3期1卷 200-205页

作者： Qingang Zhang Yang Ju Wenbo Gong Liang Zhang huafei sun School of Mechanics and Civil Engineering China University of Mining and TechnologyBeijing 10083China State Key Laboratory for Geomechanics and Deep Underground Engineering China University of Mining and TechnologyXuzhou 221116China State Key Laboratory of Coal Resources and Safe Mining China University of Mining and TechnologyBeijing 100083China

To investigate the relationship between the structural characteristics and seepage flow behavior of rough single rock fractures,a set of single fracture physical models were produced using the WeierstrasseMandelbrot functions to test the seepage flow *** single fractures,with various surface roughnesses characterized by fractal dimensions,were built using COMSOL multiphysics *** fluid flow behavior through the rough fractures and the influences of the rough surfaces on the fluid flow behavior was then *** numerical simulation indicates that there is a linear relationship between the average flow velocity over the entire flow path and the fractal dimension of the rough *** is shown that there is good agreement between the numerical results and the experimental data in terms of the properties a of the fluid flowing through the rough single rock fractures.

关键词： Seepage flow Single fracture Rough surface Fractal dimension Fractured rock

高职院校体育教师教学能力培养方式的实践研究

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当代体育科技 2023年第12期13卷 81-84页

作者：孙华飞芜湖职业技术学院体育教学部安徽芜湖241003

历经13年发展的全国职业院校教师教学能力大赛,现已成为推动我国高等职业院校师资队伍建设,促进教师教学能力提升的重要引擎。研究以体育课程团队4年参加大赛的参赛历程为研究对象,阐述在“以赛促教”视角下提升教师课程思政意识,探索... 详细信息

历经13年发展的全国职业院校教师教学能力大赛,现已成为推动我国高等职业院校师资队伍建设,促进教师教学能力提升的重要引擎。研究以体育课程团队4年参加大赛的参赛历程为研究对象,阐述在“以赛促教”视角下提升教师课程思政意识,探索“基础+专业”模式,提高混合式教学能力,深化“三教改革”,构建高水平教师团队等高职体育教师教学能力的提升路径,还提出基于大赛的三维模块化TRCOT闭环模式,让大赛成果反哺课堂教学,探索适合职业院校体育教师教学能力提升的可持续发展之路。

关键词：高职院校体育师资队伍教学能力培养方式