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Topological Tools for Understanding ...

Feng, Michelle Hsiao-Chin.

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Topological Tools for Understanding Complex Systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Topological Tools for Understanding Complex Systems./
Author:	Feng, Michelle Hsiao-Chin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	140 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-11, Section: A.
Contained By:	Dissertations Abstracts International81-11A.
Subject:	Applied mathematics. -
Online resource:	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.
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500 $a Source: Dissertations Abstracts International, Volume: 81-11, Section: A.
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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).
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