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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
Cups products in Z2-cohomology of 3D polyhedral complexes
(2012)
Let I=(Z3,26,6,B) be a 3D digital image, let Q(I) be the associated cubical complex and let ∂Q(I) be the subcomplex of Q(I) whose maximal cells are the quadrangles of Q(I) shared by a voxel of B in the foreground -- the ...
Artículo
Computing Adem Cohomology Operations
(Cornell University, 2006)
We deal with the problem of obtaining explicit simplicial formu- lae defining the classical Adem cohomology operations at the cochain level. Having these formulae at hand, we design an algorithm for com- puting these ...
Artículo
Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images
(Springer, 2017)
A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted by Q(I ), whose basic building blocks are vertices, edges, square faces and cubes. In Gonzalez-Diaz et ...
Artículo
Representative Datasets: The Perceptron Case
(Cornell University, 2019)
One of the main drawbacks of the practical use of neural networks is the long time needed in the training process. Such training process consists in an iterative change of parameters trying to minimize a loss function. ...
Artículo
Simplification techniques for maps in simplicial topology
(2005)
This paper offers an algorithmic solution to the problem of obtaining “economical” formulae for some maps in Simplicial Topology, having, in principle, a high computational cost in their evaluation. In particular, maps of ...
Artículo
An entropy-based persistence barcode
(2015)
In persistent homology, the persistence barcode encodes pairs of simplices meaning birth and death of homology classes. Persistence barcodes depend on the ordering of the simplices (called a filter) of the given simplicial ...
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
Computing cup products in \(\mathbb {Z}_2\)-cohomology of 3D polyhedral complexes
(2014)
Let \(I=(\mathbb {Z}^3,26,6,B)\) be a three-dimensional (3D) digital image, let \(Q(I)\) be an associated cubical complex, and let \(\partial Q(I)\) be a subcomplex of \(Q(I)\) whose maximal cells are the quadrangles of ...
Artículo
A tool for integer homology computation: lambda-AT- model
(2011)
In this paper, we formalize the notion of lambda-AT-model (where λ is a non-null integer) for a given chain complex, which allows the computation of homological information in the integer domain avoiding using the Smith ...