3 citations · 3 across the 6 of their papers we have counts for
5 papers · 1 filter
The Persistence Landscapes of Affine Fractals
Michael J. Catanzaro, Lee Przybylski, Eric S. Weber
We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of af…
Harmonic Representatives in Homology over Arbitrary Fields
Michael J. Catanzaro, Brantley Vose
We introduce a notion of harmonic chain for chain complexes over fields of positive characteristic. A list of conditions for when a Hodge decomposition theorem holds in this settin…
Hypercurrents
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
We introduce the notion of a protocol, which consists of a space whose points are labeled by real numbers indexed by the set of cells of a fixed CW complex in prescribed degrees, w…
Moduli Spaces of Morse Functions for Persistence
Michael J. Catanzaro, Justin Curry, Brittany Terese Fasy +5
We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classe…
Kirchhoff's theorems in higher dimensions and Reidemeister torsion
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
Using ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an appli…