Relationship to the fibered barcode in multiparamet
8
Decomposing a PD bundle into simpler parts
9
Stratifying the base space
10
Sections of PD bundles
11
How can we compute PD bundles?
12
Review: Computing vineyards
13
Algorithm for computing PD bundles
14
Future Applications
Description:
Explore the multidimensional generalization of vineyards in topological data analysis through a comprehensive lecture on Persistence Diagram Bundles. Delve into the challenges of analyzing evolving data sets with multiple parameters and discover how Persistence Diagram (PD) bundles overcome the limitations of traditional vineyards and multiparameter persistent homology. Learn about the concept, efficient computation algorithms, and unique properties of PD bundles, including their ability to exhibit monodromy. Gain insights into the potential applications of this innovative approach in analyzing complex, time-evolving point clouds with additional system parameters.
Persistence Diagram Bundles- A Multidimensional Generalization of Vineyards