检索结果-南通市图书馆

Uncovering Patterns Beneath the Surface:A Glimpse into the Applications of algebraic topology

Journal of Contemporary Educational Research 2023年第12期7卷 282-289页

作者： Chenyu Bai Yixuan Chen Beijing 101 High School International Department Beijing 100091China The Experimental High School Attached to Beijing Normal University Beijing 100032China

This paper explores the significant impact of algebraic topology on diverse real-world *** with an introduction to the historical development and essence of algebraic topology,it delves into its applications in neuroscience,physics,biology,engineering,data analysis,and Geographic Information Systems(GIS).Remarkable applications incorporate the analysis of neural networks,quantum mechanics,materials science,and disaster management,showcasing its boundless *** computational challenges,this study outlines prospects,emphasizing the requirement for proficient algorithms,noise robustness,multi-scale analysis,machine learning integration,user-friendly tools,and interdisciplinary *** essence,algebraic topology provides a transformative lens for uncovering stowed-away topological structures in complex data,offering solutions to perplexing problems in science,engineering,and society,with vast potential for future exploration and innovation.

关键词： algebraic topology Applications Data analysis Geographic Information Systems

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Application of topology-based structure features for machine learning in materials science

引用

Chinese Journal of Structural Chemistry 2023年第7期42卷 47-53页

作者： Shisheng Zheng Haowen Ding Shunning Li Dong Chen Feng Pan School of Advanced Materials Peking University Shenzhen Graduate SchoolShenzhenGuangdong518055PR China Department of Mathematics Michigan State UniversityEast Lansing MIUSA

Structure features play an important role in machine learning models for the materials ***,two topology-based features for the representation of material structure,specifically structure graph and algebraic topology,are *** present the fundamental mathematical concepts underlying these techniques and how they encode material ***,we discuss the practical applications and enhancements of these features made in specific material predicting *** review may provide suggestions on the selection of suitable structural features and inspire creativity in developing robust descriptors for diverse applications.

关键词： Machine learning Structure feature Structure graph algebraic topology

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Computational Tools in Weighted Persistent Homology

引用

Chinese Annals of Mathematics,Series B 2021年第2期42卷 237-258页

作者： Shiquan REN Chengyuan WU Jie WU Yau Mathematical Sciences Center Tsinghua UniversityBeijing 100084China Department of Mathematics National University of SingaporeSingapore 119076Singapore Institute of High Performance Computing A*STARSingapore 138632Singapore School of Mathematical Sciences Hebei Normal UniversityShijiazhuang 050024China Center for topology and Geometry based Technology Hebei Normal University050024China.

In this paper, the authors study further properties and applications of weighted homology and persistent homology. The Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology are introduced. For applications, the authors show an algorithm to construct a filtration of weighted simplicial complexes from a weighted network. They also prove a theorem to calculate the mod p^(2) weighted persistent homology provided with some information on the mod p weighted persistent homology.

关键词： algebraic topology Persistent homology Weighted persistent homology Bockstein spectral sequence

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

TANGENT UNIT-VECTOR FIELDS:NONABELIAN HOMOTOPY INVARIANTS AND THE DIRICHLET ENERGY

引用

Acta Mathematica Scientia 2010年第5期30卷 1357-1399页

作者： A.Majumdar J.M.Robbins M.Zyskin Mathematical Institute University of Oxford24-29 St.GilesOxford OX1 3LBUK School of Mathematics University of BristolUniversity WalkBristol BS8 1TWUK Department of Mathematics SETB 2.454-80 Fort BrownBrownsvilleTX 78520USA

Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we compute the infimum Dirichlet energy 6（H） for continuous maps satisfying tangent boundary conditions of arbitrary homotopy type H. The expression for C（H） involves a topological invariant - the spelling length - associated with the （non-abelian） fundamental group of the n-times punctured two-sphere, π1（S2 - {s1,..., sn}, ＊）. The lower bound for C（H） is obtained from combinatorial group theory arguments, while the upper bound is obtained by constructing explicit representatives which, on all but an arbitrarily small subset of O, are alternatively locally conformal or anticonformal. For conformal and anticonformal classes （classes containing wholly conformal and anticonformal representatives respectively）, the expression for C（H） reduces to a previous result involving the degrees of a set of regular values sl,…… sn in the target 82 space. These degrees may be viewed as invariants associated with the abelianization of vr1（S2 - {s1,..., sn}, ＊）. For nonconformal classes, however, ε（H） may be strictly greater than the abelian bound. This stems from the fact that, for nonconformal maps, the number of preimages of certain regular values may necessarily be strictly greater than the absolute value of their degrees. This work is motivated by the theoretical modelling of nematic liquid crystals in confined polyhedral geometries. The results imply new lower and upper bounds for the Dirichlet energy （one-constant Oseen-Frank energy） of reflection-symmetric tangent unitvector fields in a rectangular prism.

关键词： harmonic maps conformal maps algebraic topology non-abelian homotopy invariants eombinatorics liquid crystals

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Cohomology in 3D Magneto-Quasistatics Modeling

引用

Communications in Computational Physics 2013年第6期14卷 48-76页

作者： Pawel Dlotko Ruben Specogna Institute of Computer Science Jagiellonian Universityul.St.Łojasiewicza 630-348 KrakowPoland Universita di Udine Dipartimento di Ingegneria ElettricaGestionale e MeccanicaVia delle Scienze 20833100 UdineItaly

Electromagnetic modeling provides an interesting context to present a link between physical phenomena and homology and cohomology *** the past twenty-five years,a considerable effort has been invested by the computational electromagnetics community to develop fast and general techniques for defining *** magneto-quasi-static discrete formulations based on magnetic scalar potential are employed in problems which involve conductive regions with holes,cuts are needed to make the boundary value problem well *** an intimate connection with homology theory has been quickly recognized,heuristic definitions of cuts are surprisingly still dominant in the *** aim of this paper is first to survey several definitions of cuts together with their ***,cuts are defined as generators of the first cohomology group over integers of a finite *** provably general definition has also the virtue of providing an automatic,general and efficient algorithm for the computation of *** counter-examples show that heuristic definitions of cuts should be *** use of cohomology theory is not an option but the invaluable tool expressly needed to solve this problem.

关键词： algebraic topology (co)homology computational electromagnetics cuts

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

欢迎您,

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

在线全文

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

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

在线全文

在线全文

在线全文

在线全文

在线全文

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：