Abstract
dc:description.abstractThis thesis presents a general background on discrete Morse theory, as developed by Robin Forman, as well as an introduction to computability and computational complexity. Since general point-set data equipped with a smooth structure can admit a triangulation, discrete Morse theory finds numerous applications in data analysis which can range from traffic control to geographical interpretation. Currently, there are various methods which convert point-set data to simplicial complexes or piecewise-smooth manifolds; however, this is not the focus of the thesis. Instead, this thesis will show that the Morse homology of such data is computable in the classical sense of Turing decidability, bound the complexity of finding the Morse homology of a given simplicial complex, and provide a measure for when this is more efficient than simplicial homology.
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2019
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Dare, Christopher Edward
- Chair dc:contributor.committeechair
-
- Floyd, William J.
- Committee members dc:contributor.committeemember
-
- Mihalcea, Constantin Leonardo
- Kay, Leslie D.
- Haskell, Peter E.
Subjects
dc:subject × 1Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:20267
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/90397