413 citations · 934 across the 23 of their papers we have counts for
10 papers · 1 filter
Computing homology of -complexes from their quotients
Christine Escher, Chad Giusti, Chung-Ping Lai
In this paper, we investigate the question of how one can recover the homology of a simplicial complex equipped with a regular action of a finite group from the structure o…
Persistent Extension and Analogous Bars: Data-Induced Relations Between Persistence Barcodes
Iris H. R. Yoon, Robert Ghrist, Chad Giusti
A central challenge in topological data analysis is the interpretation of barcodes. The classical algebraic-topological approach to interpreting homology classes is to build maps t…
U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology
Haibin Hang, Chad Giusti, Lori Ziegelmeier +1
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in…
Signatures, Lipschitz-free spaces, and paths of persistence diagrams
Chad Giusti, Darrick Lee
Paths of persistence diagrams provide a summary of the dynamic topological structure of a one-parameter family of metric spaces. These summaries can be used to study and characteri…
Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide
Lu Li, Connor Thompson, Gregory Henselman-Petrusek +2
Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creat…
Mod-two cohomology rings of alternating groups
Chad Giusti, Dev Sinha
We calculate the mod-two cohomology of all alternating groups together, with both cup and transfer product structures, which in particular determines the additive structure and rin…