Publications & Submitted Articles

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

My google scholar page

Topological data analysis

• 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. Submitted.

• Catanzaro, Michael J.; Vose, Brantley. Harmonic Representatives in Homology over Arbitrary Fields. Available on the arXiv at arXiv:2110.10885. Submitted.

• Bubenik, Peter; Catanzaro, Michael J. Multiparameter persistent homology via generalized Morse theory. Available on the arXiv at arXiv:2107.08856. Submitted.

• Salch A, Regalski A, Abdallah H, Suryadevara R, Catanzaro MJ, Diwadkar VA. From mathematics to medicine: A practical primer on topological data analysis (TDA) and the development of related analytic tools for the functional discovery of latent structure in fMRI data. PLoS ONE 16 (2021).

Exploring moduli spaces of Morse functions

• 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.

• Catanzaro, Michael J.; Wang, Bei; Zabka, Matthew; Zhou, Youjia. MVF Designer: Design and Visualization of Morse Vector Fields. Available on the arXiv at arXiv:1912.09580. Submitted.

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. On fluctuations of cycles in a finite CW complex. Israel Journal of Mathematics 248 (2022), 315–354. Available on the arXiv at arXiv:1710.07995. Submitted.

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

• 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.