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Mostrando ítems 1-10 de 98
Capítulo de Libro
Extending the notion of AT-Model for integer homology computation
(2007)
When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing (co)homology, representative (co)cycles of (co)homology generators and the cup product on cohomology of ...
Capítulo de Libro
A Graph-with-Loop Structure for a Topological Representation of 3D Objects
(2007)
Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the height function), we construct a graph G h (K) which is an extension of the Reeb graph R h (|K|). ...
Capítulo de Libro
Gait-based gender classification using persistent homology
(2013)
In this paper, a topological approach for gait-based gender recognition is presented. First, a stack of human silhouettes, extracted by background subtraction and thresholding, were glued through their gravity centers, ...
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 ...
Ponencia
Separating Topological Noise from Features Using Persistent Entropy
(Springer, 2016)
Topology is the branch of mathematics that studies shapes and maps among them. From the algebraic definition of topology a new set of algorithms have been derived. These algorithms are identified with “computational ...
Capítulo de Libro
Towards Minimal Barcodes
(2013)
In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a ...
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. ...