3 papers
math.AT2026
Interval Decompositions for Multipersistence Modules over Finite Posets and Robustness of Sheaf Data on Simplicial Complexes
Pablo Hernández-García, Daniel Hernández Serrano, Darío Sánchez Gómez
We prove structure theorems for multipersistence modules indexed by finite posets that are not totally ordered. Specifically, we consider pointwise finite-dimensional modules over…
math.AT2025
From Persistence to Resilience: New Betti Numbers for Analyzing Robustness in Simplicial Complex Networks
Pablo Hernández-García, Daniel Hernández Serrano, Darío Sánchez Gómez
We show how persistence can be used to measure the robustness of cohomological cycles in finite simplicial complexes. We introduce two families of invariants: thick Betti numbers,…
cs.LG2024
Attending to Topological Spaces: The Cellular Transformer
Rubén Ballester, Pablo Hernández-García, Mathilde Papillon +6
Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks opera…