Papers by Antonio Giraldo
Rakhmanov's theorem establishes a result about the asymptotic behavior of the elements of the... more Rakhmanov's theorem establishes a result about the asymptotic behavior of the elements of the Jacobi matrix associated with a measure µ which is defined on the interval I = [−1, 1] with µ > 0 almost everywhere on I. In this work we give a weak version of this theorem, for a measure with support on a connected finite union of Jordan arcs on the complex plane, in terms of the Hessenberg matrix, the natural generalization of the tridiagonal Jacobi matrix to the complex plane.
Discrete Geometry for Computer Imagery, 2009
In a recent paper we have introduced a notion of continuity in digital spaces which extends the u... more In a recent paper we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued maps, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterized the deletion of simple points, one of the most important processing operations in digital topology, as a particular kind of retraction. In this work we give a simpler algorithm to define the retraction associated to the deletion of a simple point and we use this algorithm to characterize some well known parallel thinning algorithm as a particular kind of multivalued retraction, with the property that each point is retracted to its neighbors.
Pattern Recognition Letters, 2000
In some recent papers we have introduced a notion of continuity in digital spaces which extends t... more In some recent papers we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued maps, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points and some well known parallel thinning algorithm as a particular type of retractions, called (N,k)(N,k)-retractions.In this paper we give a full characterization of the thinning algorithms that can be modeled as (N,k)(N,k)-retractions. This class agrees, with minor modifications, with the class of thinning algorithms satisfying Ronse sufficient conditions for preservation of topology.► We consider retractions defined by digitally continuous multivalued maps. ► A special kind of retractions, called (N,k)(N,k)-retractions, is considered. ► Deletion of simple points and many thinning algorithms are (N,k)(N,k)-retractions. ► We characterize thinning algorithms that can be modeled as (N,k)(N,k)-retractions. ► Characterization in terms of Ronse-like conditions for topology preservation.
Se presentan ideas para el desarrollo de prácticas con técnicas y algoritmos Fractales. Estas téc... more Se presentan ideas para el desarrollo de prácticas con técnicas y algoritmos Fractales. Estas técnicas tienen especial interés en el tratamiento de imágenes, tanto en la generación y simulación como en la compresión.
ACM Sigcse Bulletin, 2008
In this work we will expose some proposals directed to the development of horizontal skills in th... more In this work we will expose some proposals directed to the development of horizontal skills in the first year courses of Mathematics for Computer Science, with the purpose of stimulating the curiosity and the interest of the students by means of collaborative work. Our experience is based on the planning of multidisciplinary activities following projects based learning (PBL) pedagogies, included
Fuel and Energy Abstracts, 2011
In this work, we introduce an algebraic operation between bounded Hessenberg matrices and we anal... more In this work, we introduce an algebraic operation between bounded Hessenberg matrices and we analyze some of its properties. We call this operation mm-sum and we obtain an expression for it that involves the Cholesky factorization of the corresponding Hermitian positive definite matrices associated with the Hessenberg components.This work extends a method to obtain the Hessenberg matrix of the sum of measures from the Hessenberg matrices of the individual measures, introduced recently by the authors for subnormal matrices, to matrices which are not necessarily subnormal.Moreover, we give some examples and we obtain the explicit formula for the mm-sum of a weighted shift. In particular, we construct an interesting example: a subnormal Hessenberg matrix obtained as the mm-sum of two not subnormal Hessenberg matrices.► We introduce an algebraic operation, mm-sum, between bounded Hessenberg matrices. ► The mm-sum is obtained from sums of Hermitian positive definite matrices associated. ► The mm-sum expression involves the Cholesky factors of the associated HPD matrices. ► We analyze some properties of the mm-sum as subnormality or hyponormality. ► We obtain the explicit formula for the mm-sum of a weighted shift.
We consider a Jordan arc \Gamma in the complex plane \mathbb{C} and a regular measure \mu whose s... more We consider a Jordan arc \Gamma in the complex plane \mathbb{C} and a regular measure \mu whose support is \Gamma . We denote by D the upper Hessenberg matrix of the multiplication by z operator with respect to the orthonormal polynomial basis associated with \mu . We show in this work that, if the Hessenberg matrix D is uniformly asymptotically Toeplitz, then the symbol of the limit operator is the restriction to the unit circle of the Riemann mapping function \phi(z) which maps conformally the exterior of the unit disk onto the exterior of the support of the measure \mu . We use this result to show how to approximate the Riemann mapping function for the support of \mu from the entries of the Hessenberg matrix D.
Discrete Geometry for Computer Imagery, 2008
We introduce in this paper a notion of continuity in digital spaces which extends the usual notio... more We introduce in this paper a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach uses multivalued maps. We show how the multivalued approach provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterize the deletion of simple points, one of the most important processing operations in digital topology, as a particular kind of retraction.
Journal of Mathematical Imaging and Vision, 2000
In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes... more In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes in Computer Science, vol. 4992, pp. 81–92, 2008) we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued functions, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In this work we develop properties of this family of continuous functions, now concentrating on morphological operations and thinning algorithms. We show that our notion of continuity provides a suitable framework for the basic operations in mathematical morphology: erosion, dilation, closing, and opening. On the other hand, concerning thinning algorithms, we give conditions under which the existence of a retraction F:X⟶X∖D guarantees that D is deletable. The converse is not true, in general, although it is in certain particular important cases which are at the basis of many thinning algorithms.
International Conference on Advanced Learning Technologies, 2008
The goal of this work is the design and construction of adaptive tutorials based on the applicati... more The goal of this work is the design and construction of adaptive tutorials based on the application of algorithms for the automatic resolution of problems which can be used to automatically generate texts of a formative character, practical exercises or tests and to evaluate them.
Proceedings of the fifteenth annual conference on Innovation and technology in computer science education - ITiCSE '10, 2010
Abstract In this work we describe the design and outcomes of a Starting-Out Project, which was co... more Abstract In this work we describe the design and outcomes of a Starting-Out Project, which was conducted at the Universidad Politécnica de Madrid's School of Computing before students started their courses, as a welcoming and guidance activity. One goal is to ...
2008 Eighth IEEE International Conference on Advanced Learning Technologies, 2008
The goal of this work is the design and construction of adaptive tutorials based on the applicati... more The goal of this work is the design and construction of adaptive tutorials based on the application of algorithms for the automatic resolution of problems which can be used to automatically generate texts of a formative character, practical exercises or tests and to evaluate them.
Lecture Notes in Computer Science, 2009
... Carmen Escribano, Antonio Giraldo, and Marıa Asunción Sastre ⋆ Departamento de Matemática Apl... more ... Carmen Escribano, Antonio Giraldo, and Marıa Asunción Sastre ⋆ Departamento de Matemática Aplicada, Facultad de Informática Universidad Politécnica de Madrid, Campus de Montegancedo Boadilla del Monte, 28660 Madrid, Spain Abstract. ...
Lecture Notes in Computer Science, 2008
Page 1. Digitally Continuous Multivalued Functions Carmen Escribano, Antonio Giraldo,⋆ and Marıa ... more Page 1. Digitally Continuous Multivalued Functions Carmen Escribano, Antonio Giraldo,⋆ and Marıa Asunción Sastre Departamento de Matemática Aplicada, Facultad de Informática Universidad Politécnica, Campus de Montegancedo Boadilla del Monte, 28660 Madrid, Spain ...
Lecture Notes in Computer Science, 2012
ABSTRACT In a recent paper we have introduced a notion of multivalued continuity in digital space... more ABSTRACT In a recent paper we have introduced a notion of multivalued continuity in digital spaces which extends the usual notion of digital continuity and allows to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points in 2-D, one of the most important processing operations in digital topology, as a particular kind of retraction. In this work we extend some of these results to 3-dimensional digital sets.
ACM Sigcse Bulletin, 2008
We present here a java applet, accessible through the World Wide Web, which allows to apply to a ... more We present here a java applet, accessible through the World Wide Web, which allows to apply to a binary digital image a series of topological algorithms for image processing.
Journal of Mathematical Imaging and Vision, 2012
In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes... more In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes in Computer Science, vol. 4992, pp. 81–92, 2008) we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued functions, provides a better framework to define topological notions, like retractions, in a far
Advances in Computational Mathematics, 2013
We show in this paper that, if µ is a regular measure whose support is a Jordan arc or a connecte... more We show in this paper that, if µ is a regular measure whose support is a Jordan arc or a connected finite union of Jordan arcs in the complex plane C, then the limits of the elements of the diagonals of the Hessenberg matrix D of µ, whenever those limits exist, determine the coefficients of the Laurent series expansion of the Riemann mapping φ(z) which maps conformally the exterior of the unit disk onto the exterior of the support of the measure µ. Moreover, in the case of an arc of the unit circle, we use this result to show how to approximate the Riemann mapping of the support of µ from the entries of the Hessenberg matrix D.
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Papers by Antonio Giraldo