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Okutan-Thesis.pdf (3.65 MB)
ETD Abstract Container
Abstract Header
Persistence, Metric Invariants, and Simplification
Author Info
Okutan, Osman Berat
ORCID® Identifier
http://orcid.org/0000-0003-0149-8624
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1559312147225384
Abstract Details
Year and Degree
2019, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
Given a metric space, a natural question to ask is how to obtain a simpler and faithful approximation of it. In such a situation two main concerns arise: How to construct the approximating space and how to measure and control the faithfulness of the approximation. In this dissertation, we consider the following simplification problems: Finite approximations of compact metric spaces, lower cardinality approximations of filtered simplicial complexes, tree metric approximations of metric spaces and finite metric graph approximations of compact geodesic spaces. In each case, we give a simplification construction, and measure the faithfulness of the process by using the metric invariants of the original space, including the Vietoris-Rips persistence barcodes.
Committee
Memoli Facundo (Advisor)
Kahle Matthew (Committee Member)
Lafont Jean-Francois (Committee Member)
Brown Philip (Other)
Pages
183 p.
Subject Headings
Mathematics
Keywords
metric simplification
;
metric approximation
;
Vietoris-Rips
;
persistence
;
barcode
;
metric graph
;
metric tree
;
Reeb graph
;
Gromov-Hausdorff
;
hyperbolicity
;
interleaving
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Citations
Okutan, O. B. (2019).
Persistence, Metric Invariants, and Simplification
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1559312147225384
APA Style (7th edition)
Okutan, Osman.
Persistence, Metric Invariants, and Simplification.
2019. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1559312147225384.
MLA Style (8th edition)
Okutan, Osman. "Persistence, Metric Invariants, and Simplification." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1559312147225384
Chicago Manual of Style (17th edition)
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Document number:
osu1559312147225384
Download Count:
513
Copyright Info
© 2019, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.