6 papers
Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain and Field Choice in Persistent Homology
Jiajie Luo, Gregory Henselman-Petrusek
We study pointwise free and finitely-generated persistence modules over a principal ideal domain, indexed by a (possibly infinite) totally-ordered poset category. We show that such…
A U-match Algorithm for Persistent Relative Homology
Christian Lentz, Gregory Henselman-Petrusek, Lori Ziegelmeier
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persisten…
Interval Decomposition of Persistence Modules over a Principal Ideal Domain
Jiajie Luo, Gregory Henselman-Petrusek
The study of persistent homology has contributed new insights and perspectives into a variety of interesting problems in science and engineering. Work in this domain relies on the…
Tracking the topology of neural manifolds across populations
Iris H. R. Yoon, Gregory Henselman-Petrusek, Yiyi Yu +3
Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from…
Stability for Inference with Persistent Homology Rank Functions
Qiquan Wang, Inés GarcÃa-Redondo, Pierre Faugère +2
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds,…
Network Preference Dynamics using Lattice Theory
Hans Riess, Gregory Henselman-Petrusek, Michael C. Munger +3
Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume,…