Harmonic Persistent Homology for Disentangling Multiway Interaction in Data

Explore the concept of Harmonic Persistent Homology and its application in analyzing multi-omics data in this one-hour lecture. Delve into the process of associating concrete subspaces of cycles to each homology class through harmonic representatives. Gain insights into the relationship between essential simplices and harmonic representatives weights. Learn how to apply a computational pipeline to multi-omics data, uncovering hidden patterns that highlight relationships between different omic profiles. Discover how this approach enables disease subtyping and biomarker identification for similar latent biological pathways associated with complex diseases. The lecture covers joint work by Davide Gurnari, Aldo Guzmán-Sáenz, Filippo Utro, Saugata Basu, and Laxmi Parida, presented as part of the Applied Algebraic Topology Network series.