Outputs (6)

Ladder Decomposition for Morphisms of Persistence Modules (2024)
Journal Article
Giansiracusa, J., & Urbančič, Ž. (2024). Ladder Decomposition for Morphisms of Persistence Modules. Journal of Applied and Computational Topology, https://doi.org/10.1007/s41468-024-00174-9

The output of persistent homology is an algebraic object called a persistence module. This object admits a decomposition into a direct sum of interval persistence modules described entirely by the barcode invariant. In this paper we investigate when... Read More about Ladder Decomposition for Morphisms of Persistence Modules.

Algebraic Dynamical Systems in Machine Learning (2024)
Journal Article
Jones, I., Swan, J., & Giansiracusa, J. (2024). Algebraic Dynamical Systems in Machine Learning. Applied Categorical Structures, 32(1), Article 4. https://doi.org/10.1007/s10485-023-09762-9

We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures for dynam... Read More about Algebraic Dynamical Systems in Machine Learning.

A general framework for tropical differential equations (2023)
Journal Article
Giansiracusa, J., & Mereta, S. (2024). A general framework for tropical differential equations. manuscripta mathematica, 173(3-4), 1273-1304. https://doi.org/10.1007/s00229-023-01492-5

We construct a general framework for tropical differential equations based on idempotent semirings and an idempotent version of differential algebra. Over a differential ring equipped with a non-archimedean norm enhanced with additional differential... Read More about A general framework for tropical differential equations.

Probing center vortices and deconfinement in SU(2) lattice gauge theory with persistent homology (2023)
Journal Article
Sale, N., Lucini, B., & Giansiracusa, J. (2023). Probing center vortices and deconfinement in SU(2) lattice gauge theory with persistent homology. Physical Review D, 107(3), Article 034501. https://doi.org/10.1103/physrevd.107.034501

We investigate the use of persistent homology, a tool from topological data analysis, as a means to detect and quantitatively describe center vortices in SU(2) lattice gauge theory in a gaugeinvariant manner. We provide evidence for the sensitivity o... Read More about Probing center vortices and deconfinement in SU(2) lattice gauge theory with persistent homology.

The universal tropicalization and the Berkovich analytification (2022)
Journal Article
Giansiracusa, J., & Giansiracusa, N. (2022). The universal tropicalization and the Berkovich analytification. Kybernetika (Prague. On-line), 58(5), 790-815. https://doi.org/10.14736/kyb-2022-5-0790

Given an integral scheme X over a non-archimedean valued field k, we construct a universal closed embedding of X into a k-scheme equipped with a model over the field with one element F1 (a generalization of a toric variety). An embedding into such an... Read More about The universal tropicalization and the Berkovich analytification.

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology (2022)
Journal Article
Sale, N., Giansiracusa, J., & Lucini, B. (2022). Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology. Physical Review E, 105(2), https://doi.org/10.1103/physreve.105.024121

We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a topological latti... Read More about Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology.