From the 1 of 3 linked papers with an AI index.
3 papers
Interval Decompositions for Multipersistence Modules over Finite Posets and Robustness of Sheaf Data on Simplicial Complexes
Pablo Hernández-GarcÃa, Daniel Hernández Serrano, DarÃo Sánchez Gómez
The paper establishes conditions under which multipersistence modules indexed by finite posets can be broken down into direct sums of interval modules, and applies these results to…
From Persistence to Resilience: New Betti Numbers for Analyzing Robustness in Simplicial Complex Networks
Pablo Hernández-GarcÃa, Daniel Hernández Serrano, DarÃo 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,…
Attending to Topological Spaces: The Cellular Transformer
Rubén Ballester, Pablo Hernández-GarcÃa, 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…