35 citations · 35 across the 8 of their papers we have counts for
9 papers
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.…
Simplicial degree in complex networks. Applications of Topological Data Analysis to Network Science
Daniel Hernández Serrano, Juan Hernández Serrano, Darío Sánchez Gómez
Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social,…
Topological recursion, topological quantum field theory and Gromov-Witten invariants of BG
Daniel Hernández Serrano
The purpose of this paper is to give a twisted version of the Eynard-Orantin topological recursion by a 2D Topological Quantum Field Theory. We define a kernel for a 2D TQFT and us…
Mirror symmetry for orbifold Hurwitz numbers
Vincent Bouchard, Daniel Hernandez Serrano, Xiaojun Liu +1
We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be e…