Outputs (3)

Topological Data Analysis of Monopole Current Networks in U(1) Lattice Gauge Theory (2024)
Journal Article
Crean, X., Giansiracusa, J., & Lucini, B. (2024). Topological Data Analysis of Monopole Current Networks in U(1) Lattice Gauge Theory. SciPost Physics, 17(4), Article 100. https://doi.org/10.21468/SciPostPhys.17.4.100

In 4-dimensional pure compact U(1) lattice gauge theory, we analyse topological aspects of the dynamics of monopoles across the deconfinement phase transition. We do this using tools from Topological Data Analysis (TDA). We demonstrate that observabl... Read More about Topological Data Analysis of Monopole Current Networks in U(1) Lattice Gauge Theory.

Ladder Decomposition for Morphisms of Persistence Modules (2024)
Journal Article
Giansiracusa, J., & Urbančič, Ž. (online). 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.