Methods and applications of topological data analysis
Abstract/Contents
- Abstract
- The focus of this dissertation is the development of methods for topological analysis as well as the application of topological tools to real world problems. The first half of the dissertation focuses on an algorithm for de-noising high-dimensional data for topological data analysis. This method significantly extends the applicability of many topological data analysis methods. In particular, this method extends the use of persistent homology, a generalized notion of homology for discrete data points, to data sets that were previously inaccessible because of noise. The second half of this dissertation focuses on a method for using topology to simplify complex chemical structures and to define a metric to quantify similarity for use in screening large databases of chemical compounds. This method has shown very promising initial results in locating new materials for efficiently separating carbon dioxide from the exhaust of coal-burning power plants.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2010 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Kloke, Jennifer Novak |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Kerckhoff, Steve |
| Thesis advisor | Mazzeo, Rafe |
| Advisor | Kerckhoff, Steve |
| Advisor | Mazzeo, Rafe |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jennifer Novak Kloke. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Ph. D. Stanford University 2010 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2010 by Jennifer Novak Kloke
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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