Publications & Preprints

Here is a list of submitted manuscripts and published articles I have worked on.

My google scholar page

Topological data analysis

• Catanzaro, Michael J.; Rizzo, Sam; Kopchick, John; Chodury, Asadur; Rosenberg, David R.; Bubenik, Peter; Diwadkar, Vaibhav A. Topological Data Analysis Captures Task-Driven fMRI Profiles in Individual Participants: A Classification Pipeline Based on Persistence, Neuroinformatics. (2023), DOI https://doi.org/10.1007/s12021-023-09645-3.

• Smith, Abraham D.; Catanzaro, Michael J.; Angeloro, Gabrielle; Patel, Nirav; Bendich, Paul. Topological Parallax: A Geometric Specification for Deep Perception Models, Accepted to Neurips 2023. Available on the arXiv at https://arxiv.org/abs/2306.11835.

• Catanzaro, Michael J.; Przybylski, Lee; Weber, Eric S. Persistence Landscapes of Affine Fractals. Demonstratio Mathematica, 55 (2022), 163–192. Available on the arXiv at arXiv:2201.02552.

• Catanzaro, Michael J.; Vose, Brantley. Harmonic Representatives in homology over arbitrary fields, J Appl. and Comput. Topology. 7 (2023), 643–670, DOI https://doi.org/10.1007/s41468-023-00117-w. Available on the arXiv at https://arxiv.org/abs/2110.10885.

Multiparameter persistence

• Bubenik, Peter; Catanzaro, Michael J. Multiparameter persistent homology via generalized Morse theory. Available on the arXiv at arXiv:2107.08856. Accepted to Fields Institute Communications.

Exploring moduli spaces of Morse functions

• Zhou, Youjia; Lazovskis, Janis; Catanzaro, Michael J.; Zabka, Matthew; Wang, Bei. Combinatorial Exploration of Morse–Smale Functions on the Sphere via Interactive Visualization. Accepted to IEEE Workshop on Topological Data Analysis and Visualization 2023.
• Catanzaro, Michael J.; Curry, Justin; Fasy, Brittany Terese; Lazovskis, Janis; Malen, Greg; Riess, Hans; Wang, Bei; Zabka, Matthew. Moduli Spaces of Morse Functions for Persistence. Journal of Applied and Computational Topology, 4 (2020), 353–385. Available on the arXiv at arXiv:1909.10623.

Random chain complexes

• Catanzaro, Michael J.; Zabka, Matthew J. A Model for Random Chain Complexes. Abh. Math. Semin. Univ. Hambg. 91 (2021), 335-344. Available on the arXiv at arXiv:1901.00964.

Stochastic Currents and Markov CW chains

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R., Fluctuations of cycles in a finite CW complex, Isr. J. Math. 248 (2022), 315–354, DOI https://doi.org/10.1007/s11856-022-2303-9. https://arxiv.org/abs/1710.07995.

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Hypercurrents. Available on the arXiv at arXiv:2010.06783.

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Probability measures on graph trajectories. Available on the arXiv at arXiv:2104.13566.

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting, Chemical Physics, 481 (2016), 5–18. Available on the arXiv at arXiv:1609.00336.

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Stochastic dynamics of extended objects in driven systems II: Current quantization in the low-temperature limit, Chemical Physics, 481 (2016), 19–27. Available on the arXiv at arXiv:1609:00334.

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. A higher Boltzmann distribution, Journal of Applied and Computational Topology 1 (2017), 215–240. Available on the arXiv at arXiv:1506.06775.

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Kirchhoff’s theorems in higher dimensions and Reidemeister torsion, Homology, Homotopy, and Applications 17 (2015), 165–189. Available on the arXiv at arxiv:1206.6783.

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; and Klein, John R. On Kirchhoff’s theorems with coefficients in a line bundle, Homology, Homotopy, and Applications 15 (2013), 267–280. Available on the arXiv at arxiv:1207.2822.

Exciton Scattering

• Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R. Exciton Scattering via Algebraic Topology. Journal of Topology and Analysis 11 (2019), 251–272. Available on the arXiv at arXiv:1505.02365.

• Li, Hao; Catanzaro, Michael J.; Tretiak, Sergei; Chernyak, Vladimir. Excited-state structure modifications due to molecular substituents and exciton scattering in conjugated molecules, Journal of Physical Chemistry Letters 5 (2014), 641–647. Available on the arXiv at arxiv:1612.03523.

Topology and music theory

• Catanzaro, Michael J. Generalized Tonnetze, J. Math. Music 5 (2011), 117–139. Available on the arXiv at arxiv:1612.03519.

Theses

• Catanzaro, Michael J. “A Topological Study of Stochastic Dynamics on CW Complexes” (2016). Wayne State University Dissertations, 1433.

• Catanzaro, Michael J. Finitely Presented Modules over the Steenrod Algebra in Sage”. Wayne State University Theses, 602. December 2011.

Expository

The following is an expository paper I wrote explaining the types of stochastic processes I am interested in studying.

• Catanzaro, Michael J. A user’s guide: Dynamics and fluctuations of cellular cycles on CW complexes.