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Artículo
Basis-independent partial matchings induced by morphisms between persistence modules
(Cornell University, 2020)
In this paper, we study how basis-independent partial matchings induced by morphisms between persistence modules (also called ladder modules) can be defined. Besides, we extend the notion of basis-independent partial ...
Artículo
Cubical cohomology ring of 3D photographs
(2011)
Cohomology groups and the cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. ...
Artículo
Persistent entropy for separating topological features from noise in vietoris-rips complexes
(Springer, 2019)
Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional ...
Artículo
Computational Topology in Image Context
(Elsevier, 2012)
Artículo
Characterizing Configurations of critical points through LBP Extended Abstract
(Universidad de Sevilla, 2015)
In this abstract we extend ideas and results submitted to [3] in which a new codification of Local Binary Patterns (LBP) is given using combinatorial maps and a method for obtaining a representative LBP image is developed ...
Artículo
Characterizing slope regions
(Springer, 2021)
This paper provides a theoretical characterization of monotonically connected image surface regions, called slope regions. The characterization is given by several topological properties described in terms of critical ...
Artículo
Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases
(MDPI, 2020-12-10)
This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational bases. The approximation is achieved by finding suitable weights and control points to fit the ...
Artículo
HPT and cocyclic operations
(International Press, 2005)
We reinterpret the classical theory of cocyclic operations in terms of permutations and homotopy equivalences of explicit chains. The essential tools we use are Homological Perturbation Theory and Eilenberg–Zilber ...
Artículo
Trainable and explainable simplicial map neural networks
(ELSEVIER SCIENCE INC, 2024)
Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, ...
Artículo
A new topological entropy-based approach for measuring similarities among piecewise linear functions
(Elsevier, 2017)
In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certi ed by the ...