3 citations · 3 across the 6 of their papers we have counts for
8 papers
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…
Probability measures on graph trajectories
Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein
The aim of this note is to construct a probability measure on the space of trajectories in a continuous time Markov chain having a finite state diagram, or more generally which adm…
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…
MVF Designer: Design and Visualization of Morse Vector Fields
Youjia Zhou, Janis Lazovskis, Michael J. Catanzaro +2
Vector field design on surfaces was originally motivated by applications in graphics such as texture synthesis and rendering. In this paper, we consider the idea of vector field de…
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…