3 papers
math.AT2024
Integral Betti signature confirms the hyperbolic geometry of brain, climate, and financial networks
Luigi Caputi, Anna Pidnebesna, Jaroslav Hlinka
This paper extends the possibility to examine the underlying curvature of data through the lens of topology by using the Betti curves, tools of Persistent Homology, as key topologi…
math.AT2024
The weak categorical quiver minor theorem and its applications: matchings, multipaths, and magnitude cohomology
Luigi Caputi, Carlo Collari, Eric Ramos
Building upon previous works of Proudfoot and Ramos, and using the categorical framework of Sam and Snowden, we extend the weak categorical minor theorem from undirected graphs to…
math.CO2022
On the homotopy type of multipath complexes
Luigi Caputi, Carlo Collari, Sabino Di Trani +1
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph is the simplicial complex whose faces are the multipaths of ${\tt…