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Capturing Changes in Combinatorial Dynamical Systems Via Persistent Homology- [electronic resource]
Capturing Changes in Combinatorial Dynamical Systems Via Persistent Homology- [electronic resource]
상세정보
- 자료유형
- 학위논문
- Control Number
- 0016932816
- International Standard Book Number
- 9798379846268
- Dewey Decimal Classification Number
- 500
- Main Entry-Personal Name
- Slechta, Ryan.
- Publication, Distribution, etc. (Imprint
- [S.l.] : Purdue University., 2022
- Publication, Distribution, etc. (Imprint
- Ann Arbor : ProQuest Dissertations & Theses, 2022
- Physical Description
- 1 online resource(105 p.)
- General Note
- Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
- General Note
- Advisor: Dey, Tamal K.
- Dissertation Note
- Thesis (Ph.D.)--Purdue University, 2022.
- Restrictions on Access Note
- This item must not be sold to any third party vendors.
- Summary, Etc.
- 요약Recent innovations in combinatorial dynamical systems permit them to be studied with algorithmic methods. One such method from topological data analysis, called persistent homology, allows one to summarize the changing homology of a sequence of simplicial complexes. This dissertation explicates three methods for capturing and summarizing changes in combinatorial dynamical systems through the lens of persistent homology. The first places the Conley index in the persistent homology setting. This permits one to capture the persistence of salient features of a combinatorial dynamical system. The second shows how to capture changes in combinatorial dynamical systems at different resolutions by computing the persistence of the Conley-Morse graph. Finally, the third places Conley's notion of continuation in the combinatorial setting and permits the tracking of isolated invariant sets across a sequence of combinatorial dynamical systems.
- Subject Added Entry-Topical Term
- Decomposition.
- Subject Added Entry-Topical Term
- Dynamical systems.
- Subject Added Entry-Topical Term
- Neighborhoods.
- Subject Added Entry-Topical Term
- Permits.
- Subject Added Entry-Topical Term
- Bar codes.
- Subject Added Entry-Topical Term
- Mathematics.
- Added Entry-Corporate Name
- Purdue University.
- Host Item Entry
- Dissertations Abstracts International. 85-01B.
- Host Item Entry
- Dissertation Abstract International
- Electronic Location and Access
- 로그인을 한후 보실 수 있는 자료입니다.
- Control Number
- joongbu:643781
MARC
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■020 ▼a9798379846268
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■035 ▼a(MiAaPQ)Purdue19611564
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a500
■1001 ▼aSlechta, Ryan.
■24510▼aCapturing Changes in Combinatorial Dynamical Systems Via Persistent Homology▼h[electronic resource]
■260 ▼a[S.l.]▼bPurdue University. ▼c2022
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2022
■300 ▼a1 online resource(105 p.)
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-01, Section: B.
■500 ▼aAdvisor: Dey, Tamal K.
■5021 ▼aThesis (Ph.D.)--Purdue University, 2022.
■506 ▼aThis item must not be sold to any third party vendors.
■520 ▼aRecent innovations in combinatorial dynamical systems permit them to be studied with algorithmic methods. One such method from topological data analysis, called persistent homology, allows one to summarize the changing homology of a sequence of simplicial complexes. This dissertation explicates three methods for capturing and summarizing changes in combinatorial dynamical systems through the lens of persistent homology. The first places the Conley index in the persistent homology setting. This permits one to capture the persistence of salient features of a combinatorial dynamical system. The second shows how to capture changes in combinatorial dynamical systems at different resolutions by computing the persistence of the Conley-Morse graph. Finally, the third places Conley's notion of continuation in the combinatorial setting and permits the tracking of isolated invariant sets across a sequence of combinatorial dynamical systems.
■590 ▼aSchool code: 0183.
■650 4▼aDecomposition.
■650 4▼aDynamical systems.
■650 4▼aNeighborhoods.
■650 4▼aPermits.
■650 4▼aBar codes.
■650 4▼aMathematics.
■690 ▼a0405
■71020▼aPurdue University.
■7730 ▼tDissertations Abstracts International▼g85-01B.
■773 ▼tDissertation Abstract International
■790 ▼a0183
■791 ▼aPh.D.
■792 ▼a2022
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16932816▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
■980 ▼a202402▼f2024
