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Computational connection matrix theory
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TitleInfo
Title
Computational connection matrix theory
Name (type = personal)
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Spendlove
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Kelly
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Kelly Spendlove
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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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internal member
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Woodward
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Christopher
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Christopher Woodward
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Advisory Committee
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internal member
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Van der Vorst
NamePart (type = given)
Robert
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Robert Van der Vorst
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Advisory Committee
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outside member
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Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
School of Graduate Studies
Role
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school
TypeOfResource
Text
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theses
OriginInfo
DateCreated (encoding = w3cdtf); (keyDate = yes); (qualifier = exact)
2019
DateOther (encoding = w3cdtf); (qualifier = exact); (type = degree)
2019-10
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Abstract (type = abstract)
We develop a computational and categorical framework for connection matrix theory. In terms of computations, we give an algorithm for computing the connection matrix based on algebraic-discrete Morse theory. The makes the connection matrix available, for the first time, as a computational tool within applied topology and dynamics. In addition, the algorithm provides a straightforward constructive proof of the existence of connection matrices. In terms of categories, our formulation resolves the non-uniqueness of the connection matrix, as well as relates the connection matrix to persistent homology.

We extend existing computational Conley theory to incorporate connection matrix theory. This is done by developing a setting, which we call transversality models, in which discrete approximations to continuous flows can be used to compute connection matrices for the underlying continuous system. We make applications to a Morse theory on spaces of braid diagrams.

Finally, we provide an implicit discrete Morse pairing for cubical complexes. This enables the computation of connection matrices in high-dimensional cubical complexes. We benchmark our algorithm on a set of such examples.
Subject (authority = RUETD)
Topic
Mathematics
Subject (authority = local)
Topic
Connection matrix
Subject (authority = LCSH)
Topic
Index theorems
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
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ETD_10064
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application/pdf
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Extent
1 online resource (x, 141 pages) : illustrations
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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NjNbRU
Identifier (type = doi)
doi:10.7282/t3-kh58-md25
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Spendlove
GivenName
Kelly
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2019-05-26 10:32:04
AssociatedEntity
Name
Kelly Spendlove
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
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Name
Author Agreement License
Detail
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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Technical

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2019-05-26T14:18:18
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2019-05-26T14:18:18
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