35 citations · 35 across the 8 of their papers we have counts for
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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…
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,…
Centrality measures in simplicial complexes: applications of Topological Data Analysis to Network Science
Daniel Hernández Serrano, Darío Sánchez Gómez
Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions.…