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A comparison framework for interleaved persistence modules and applications of persistent homology to problems in fluid dynamics
Descriptive
TitleInfo
Title
A comparison framework for interleaved persistence modules and applications of persistent homology to problems in fluid dynamics
Name
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Levanger
NamePart
(type = given)
Rachel
NamePart
(type = date)
1982-
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Rachel Levanger
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author
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Mischaikow
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Konstantin
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Konstantin Mischaikow
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Advisory Committee
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chair
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Weibel
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Charles
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Charles Weibel
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Advisory Committee
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internal member
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Ferry
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Stephen
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Stephen Ferry
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Advisory Committee
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internal member
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Kondic
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Lou
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Lou Kondic
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Advisory Committee
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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school
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Text
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theses
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2017
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2017-05
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2017
Place
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xx
Language
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eng
Abstract
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We prove an algebraic stability theorem for interleaved persistence modules that is more general than any formulations currently in the literature. We show how this generalization leads to a framework that may be used to compare persistence modules locally, enabling the computation of non-uniform error bounds for persistence diagrams. We give several examples of how to use this comparison framework, and also address an open problem on non-uniform sublevel set filtrations. We also give two applications of persistent homology to problems in fluid dynamics. Our first application examines the structure of the dynamics of a time-evolving system on a two-dimensional domain, where we give examples for studying fixed points and periodic orbits. Our second application uses persistent homology in conjunction with techniques in computer vision to study pattern defects in the spiral defect chaos regime of Rayleigh-Bénard convection.
Subject
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Topic
Mathematics
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Rutgers University Electronic Theses and Dissertations
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ETD_7974
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electronic resource
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application/pdf
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Extent
1 online resource (vii, 179 p. : ill.)
Note
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Ph.D.
Note
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Includes bibliographical references
Subject
(authority = ETD-LCSH)
Topic
Homology theory
Subject
(authority = ETD-LCSH)
Topic
Fluid dynamics
Subject
(authority = ETD-LCSH)
Topic
Rayleigh-Bénard convection
Note
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by Rachel Levanger
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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Identifier
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doi:10.7282/T3057JSD
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ETD doctoral
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Rights
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The author owns the copyright to this work.
RightsHolder
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Name
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Levanger
GivenName
Rachel
Role
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Permission or license
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2017-04-10 13:33:49
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Rachel Levanger
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Affiliation
Rutgers University. Graduate School - New Brunswick
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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2017-04-11T11:30:58
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2017-04-11T11:30:58
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