東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Topological Tools for Understanding ...

Feng, Michelle Hsiao-Chin.

FindBook

Google Book

Amazon

博客來

Topological Tools for Understanding Complex Systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Topological Tools for Understanding Complex Systems./
作者:	Feng, Michelle Hsiao-Chin.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	140 p.
附註:	Source: Dissertations Abstracts International, Volume: 81-11, Section: A.
Contained By:	Dissertations Abstracts International81-11A.
標題:	Applied mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27960587
ISBN:	9798645426286

Topological Tools for Understanding Complex Systems.
Feng, Michelle Hsiao-Chin.

Topological Tools for Understanding Complex Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 140 p.

Source: Dissertations Abstracts International, Volume: 81-11, Section: A.

Thesis (Ph.D.)--University of California, Los Angeles, 2020.

This item must not be sold to any third party vendors.

The behavior of complex systems is often influenced by their structure. In mathematics, the field of algebraic topology has been especially useful for characterizing mathematical structures. Topological data analysis (TDA) is a growing field in which methods from algebraic topology are applied to studying the structure of data. TDA has been used in a variety of applications, including biological data, granular materials, and demography. Social interactions are heavily informed by space and have complex structure due to patterns in the way humans arrange themselves geographically. Consequently, social applications can benefit from the application of TDA.In this dissertation, I develop topological methods for studying spatial networks and apply them to a wide variety of data sets. In particular, I study methods for building topological spaces (specifically, simplicial complexes) based on data. I present two novel simplicial-complex constructions, the adjacency complex and the level-set complex, for spatial data. I apply both constructions to random networks, cities, voting, and scientific images, gaining insights into the structure of these systems. I also propose a novel simplicial complex construction for studying patterns of neighborhood formation based on combining demographic and spatial data. I present case studies in neighborhood segregation for two U.S. cities. In addition to my topological research, I discuss two projects in the study of social systems using methods from network analysis. I present an extension to multilayer networks of the Hegselmann--Krause model for opinion dynamics and discuss preliminary findings on its convergence properties. I also present a framework for estimating homelessness underreporting in California Local Education agencies (LEAs).

ISBN: 9798645426286Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Applied mathematics

Topological Tools for Understanding Complex Systems.
LDR:02946nmm a2200361 4500 001 2277315
005 20210521101655.5
008 220723s2020 ||||||||||||||||| ||eng d
020 $a 9798645426286
035 $a (MiAaPQ)AAI27960587
035 $a AAI27960587
040 $a MiAaPQ $c MiAaPQ
100 1 $a Feng, Michelle Hsiao-Chin. $3 3555628
245 1 0 $a Topological Tools for Understanding Complex Systems.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 140 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-11, Section: A.
500 $a Advisor: Porter, Mason A.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a The behavior of complex systems is often influenced by their structure. In mathematics, the field of algebraic topology has been especially useful for characterizing mathematical structures. Topological data analysis (TDA) is a growing field in which methods from algebraic topology are applied to studying the structure of data. TDA has been used in a variety of applications, including biological data, granular materials, and demography. Social interactions are heavily informed by space and have complex structure due to patterns in the way humans arrange themselves geographically. Consequently, social applications can benefit from the application of TDA.In this dissertation, I develop topological methods for studying spatial networks and apply them to a wide variety of data sets. In particular, I study methods for building topological spaces (specifically, simplicial complexes) based on data. I present two novel simplicial-complex constructions, the adjacency complex and the level-set complex, for spatial data. I apply both constructions to random networks, cities, voting, and scientific images, gaining insights into the structure of these systems. I also propose a novel simplicial complex construction for studying patterns of neighborhood formation based on combining demographic and spatial data. I present case studies in neighborhood segregation for two U.S. cities. In addition to my topological research, I discuss two projects in the study of social systems using methods from network analysis. I present an extension to multilayer networks of the Hegselmann--Krause model for opinion dynamics and discuss preliminary findings on its convergence properties. I also present a framework for estimating homelessness underreporting in California Local Education agencies (LEAs).
590 $a School code: 0031.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mathematics. $3 515831
650 4 $a Demography. $3 614991
653 $a Applied mathematics
653 $a Applied topology
653 $a Computational social science
653 $a Topological data analysis
690 $a 0364
690 $a 0405
690 $a 0938
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 2096468
773 0 $t Dissertations Abstracts International $g 81-11A.
790 $a 0031
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27960587