Explores higher-order interactions in brain networks using simplicial complexes and information theory, analyzing data from fMRI, financial time-series, and infectious diseases.
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.
Covers CNNs, RNNs, SVMs, and supervised learning methods, emphasizing the importance of tuning regularization and making informed decisions in machine learning.
Introduces the construction of quasi-categories from Kan enriched categories through defining simplicially enriched categories and constructing the simplicial nerve functor.
Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.