Now showing items 1-4 of 4
Simplicial homotopy group model for K2 of a ring, A
Contributor:Whitfield, JaDon Saeed
We construct an isomorphism between the group K2(R) from classical, algebraic K-Theory for a ring R and a simplicial homotopy group constructed using simplicial homotopy theory based on that same ring R. First I describe ...
Exploiting geometry, topology, and optimization for knowledge discovery in big data
Contributor:Ziegelmeier, Lori Beth
In this dissertation, we consider several topics that are united by the theme of topological and geometric data analysis. First, we consider an application in landscape ecology using a well-known vector quantization algorithm ...
D-neighborhood complex of a graph, The
The Neighborhood complex of a graph, G, is an abstract simplicial complex formed by the subsets of the neighborhoods of all vertices in G. The construction of this simplicial complex can be generalized to use any subset ...
Patterns in dynamics
Contributor:Motta, Francis Charles
In this paper we introduce and explore the idea of persistent homology (PH) and discuss several applications of this computational topology tool beyond its intended purpose. In particular we apply persistence to data ...