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Artículo
Topology-based representative datasets to reduce neural network training resources
(Springer, 2022)
One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of an iterative change of parameters trying to minimize a loss function. ...
Artículo
Continuous Well-Composedness Implies Digital Well-Composedness in n-D
(Springer, 2022)
In this paper, we prove that when a n-D cubical set is continuously well-composed (CWC), that is, when the boundary of its continuous analog is a topological (n- 1) -manifold, then it is digitally well-composed (DWC), which ...
Artículo
Two-hidden-layer feed-forward networks are universal approximators: A constructive approach
(ScienceDirect, 2020-11)
It is well-known that artificial neural networks are universal approximators. The classical existence result proves that, given a continuous function on a compact set embedded in an n-dimensional space, there exists a ...
Artículo
Simplicial-Map Neural Networks Robust to Adversarial Examples
(MDPI [Commercial Publisher], 2021-01-15)
Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data point produces a change on the output label assigned by the model. Such adversarial examples represent ...
Artículo
Making Sullivan Algebras Minimal Through Chain Contractions
(Springer, 2021)
In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, taking as input a (nonminimal) Sullivan algebra A with an ordered finite set of generators preserving ...
Artículo
Optimizing the Simplicial-Map Neural Network Architecture
(MDPI, 2021)
Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial complexes. It has been proved that simplicial-map neural networks are universal approximators ...
Artículo
Approximating lower-star persistence via 2D combinatorial map simplification
(Elsevier, 2020)
Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in the associated persistence diagrams. In this paper, we propose a filtration simplification algorithm ...
Artículo
Emotion recognition in talking-face videos using persistent entropy and neural networks
(American Institute of Mathematical Sciences (AIMS), 2022)
The automatic recognition of a person’s emotional state has become a very active research field that involves scientists specialized in different areas such as artificial intelligence, computer vi sion, or psychology, ...
Artículo
Digitization
(Springer, 2020)
Artículo
Strong Euler well-composedness
(Springer, 2021)
In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed ...