Date of Award
2006
Degree Name
Mathematics
College
College of Science
Type of Degree
M.A.
Document Type
Thesis
First Advisor
Peter Saveliev
Second Advisor
Ralph Oberste-Vorth
Third Advisor
Scott Sarra
Fourth Advisor
Philippe Georgel
Fifth Advisor
Jo Fuller
Abstract
Homology is a field of topology that classifies objects based on the number of n- dimensional holes (cuts, tunnels, voids, etc.) they possess. The number of its real life ap- plications is quickly growing, which requires development of modern computational meth- ods. In my thesis, I will present methods of calculation, algorithms, and implementations of simplicial homology, alpha shapes, and persistent homology.
The Alpha Shapes method represents a point cloud as the union of balls centered at each point, and based on these balls, a complex can be built and homology computed. If the balls are allowed to grow, one can compute the persistent homology, which gives a better understanding of the shape of the object represented by the point cloud by eliminating noise.
These methods are particularly well suited for studying biological molecules. I will test the hypothesis that persistent homology can describe some important features of a protein's shape.
Subject(s)
Homology theory.
Topology.
Triangulation.
Recommended Citation
Johnson, Christopher Aaron, "Applications of Computational Homology" (2006). Theses, Dissertations and Capstones. 672.
https://mds.marshall.edu/etd/672
