拓扑图持久性

IF 0.3 Q4 MATHEMATICS

Communications in Applied and Industrial Mathematics Pub Date : 2017-07-30 DOI:10.2478/caim-2020-0005

Mattia G. Bergomi, M. Ferri, Lorenzo Zuffi

{"title":"拓扑图持久性","authors":"Mattia G. Bergomi, M. Ferri, Lorenzo Zuffi","doi":"10.2478/caim-2020-0005","DOIUrl":null,"url":null,"abstract":"Abstract Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological constructions can be used to gain information otherwise concealed by the low-dimensional nature of graphs. We do this by extending previous work in homological persistence, and proposing novel graph-theoretical constructions. Beyond cliques, we use independent sets, neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"11 1","pages":"72 - 87"},"PeriodicalIF":0.3000,"publicationDate":"2017-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Topological graph persistence\",\"authors\":\"Mattia G. Bergomi, M. Ferri, Lorenzo Zuffi\",\"doi\":\"10.2478/caim-2020-0005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological constructions can be used to gain information otherwise concealed by the low-dimensional nature of graphs. We do this by extending previous work in homological persistence, and proposing novel graph-theoretical constructions. Beyond cliques, we use independent sets, neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.\",\"PeriodicalId\":37903,\"journal\":{\"name\":\"Communications in Applied and Industrial Mathematics\",\"volume\":\"11 1\",\"pages\":\"72 - 87\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2017-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/caim-2020-0005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/caim-2020-0005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 5

摘要

摘要图是现代数据表示的一种基本工具。图中包含的拓扑信息的丰富性远远超出了它作为一维单纯复形的解释。我们展示了拓扑结构如何被用来获得被图的低维性质所掩盖的信息。我们通过扩展先前在同源持久性方面的工作来做到这一点，并提出了新的图论构造。除了派系之外，我们使用独立的集合、社区、无飞地的集合和拉姆齐启发的扩展持久性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Topological graph persistence

Abstract Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological constructions can be used to gain information otherwise concealed by the low-dimensional nature of graphs. We do this by extending previous work in homological persistence, and proposing novel graph-theoretical constructions. Beyond cliques, we use independent sets, neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.