4 citations · 6 across the 4 of their papers we have counts for
5 papers
L-fuzzy simplicial homology
Javier Perera-Lago, Alvaro Torras-Casas, Rocio Gonzalez-Diaz
Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this articl…
The Induced Matching Distance: A Novel Topological Metric with Applications in Robotics
Javier Perera-Lago, Álvaro Torras-Casas, Jérôme Guzzi +1
This paper introduces the induced matching distance, a novel topological metric designed to compare discrete structures represented by a symmetric non-negative function. We apply t…
Properties and Stability of Persistence Matching Diagrams
Alvaro Torras-Casas, Rocio Gonzalez-Diaz
We introduce persistence matching diagrams induced by set mappings of metric spaces, based on 0-persistent homology of Vietoris-Rips filtrations. Also, we present a geometric defin…
Additive Partial Matchings Induced by Persistence Maps
R. Gonzalez-Diaz, M. Soriano-Trigueros, A. Torras-Casas
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linea…
Distributing Persistent Homology via Spectral Sequences
Álvaro Torras Casas
We set up the theory for a distributed algorithm for computing persistent homology. For this purpose we develop linear algebra of persistence modules. We present bases of persisten…