Explores higher-order interactions in brain networks using simplicial complexes and information theory, analyzing data from fMRI, financial time-series, and infectious diseases.
Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.
Explores the role of higher-order topological properties in complex networks using topological data analysis for structural break and price anomaly detection.
Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.