In this paper we explain at the theoretical level how discrete Morse theory can provide us a more efficient approach to compute persistent homologies. In achieving so we also provide a framework for discrete Morse theory to be applied to persistent homology for other purposes.
This is a Ph.D. dissertation for a study conducted at OSU/Horticulture. The main objective of this study was dissecting the genetic background for white mold resistance in common (snap) bean. Tow main approaches were followed to achieve the goal. The first approach was using the classical quantitative trait loci (QTL)...