The theory of persistent homology (PH), introduced by Edelsbrunner, Letscher, and Zomorodian in , provides a framework for extracting topological information from experimental data. This framework was then expanded by Carlsson and Zomorodian in  to allow for multiple parameters of analysis with the theory of multidimensional persistent homology (MPH). This particular generalization is considerably more difficult to compute and to apply than its predecessor. We introduce an intermediate theory, coordinated persistent homology (CPH), that allows for multiple parameters while still preserving the clarity and coherence of PH. In addition to introducing the basic theory, we provide a polynomial time algorithm to compute CPH for time series and prove several important theorems about the nature of CPH. We also describe an application of the theory to a problem in seismology.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Callor, Nickolas Brenten, "Coordinated Persistent Homology and an Application to Seismology" (2019). Theses and Dissertations. 9115.
persistent homology, multidimensional persistent homology, coordinated persistent homology, multiltrations, time series