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Papers Vol. 5 núm. 9 enero-junio 2009 by Jairo Villegas G
En este trabajo se describe un método para la detección de puntas epilépticas en un registro elec... more En este trabajo se describe un método para la detección de puntas epilépticas en un registro electroencefalográfico(EEG) de superficie tomando un solocanal. Se identificó un patrón al utilizar el análisis multirresolución con una wavelet biortogonal después de procesar y analizar con el Toolbox Wavelet de Matlab, 207 registros de puntas y 132 registros de artificios previamente clasificadas por el neurofisiólogo. Este patrón permitió diseñar un algoritmo para la detección de puntas en pacientes con epilepsia refractaria del lóbulo temporal, a partir de los máximos voltajes en cada uno de los seis niveles de reconstrucción usando la wavelet biortogonal 3.7. El algoritmo se aplicó sobre registros de pacientes con epilepsia, obteniéndose una sensibilidad del 92% y una especificidad del 80% en el diagnóstico de las puntas epilépticas.
PACS: 87.57.-s
MSC: 65T60, 42C40
Papers by Jairo Villegas G
Advanced Studies in Biology, 2013
In this paper we aim to extend a result of Hörmander’s, that Blocp;k(Ω) Cm(Ω) if (1+jj)m k 2 Lp0... more In this paper we aim to extend a result of Hörmander’s, that Blocp;k(Ω) Cm(Ω) if (1+jj)m k 2 Lp0, to the setting of vector valued local Hörmander-Beurling spaces, as well as to show that the space T1 j=1 Blocpj;kj (Ω;E) (1 pj 1, kj = ej!, j = 1; 2; : : : ) is topologically isomorphic to E!(Ω; E). Moreover, it is well known that the union of Sobolev spaces Hlocs (Ω) ( = Bloc2;(1+jj2)s=2 (Ω)) coincides with the space D0F (Ω) of nite order distributions on Ω. We show that this is also veried in the context of vector valued Beurling ultradistributions.
In order to find the approximate solution of the KdV equation, we use the finite element method o... more In order to find the approximate solution of the KdV equation, we use the finite element method of Taylor-Petrov-Galerkin, in which discretization in the time variable is carried out using Taylor series expansion and for discretization in space are considered as test functions cubic B-splines and Legendre polynomials as weight functions. These functions are adequate in that they satisfy continuity, integrability and orthogonality required to apply the method.
International Journal of Mathematical Analysis, 2016
In this paper we consider cardiac electrical activity through bidomain model, to describe the ele... more In this paper we consider cardiac electrical activity through bidomain model, to describe the electrical behavior of cardiac tissue, based on current flow, electric potential distribution and conservation of charge. So we use the finite volume scheme built on rectangular meshes. Discretizing will focus on existing algorithms for elliptic and parabolic equations, with convergence guaranteed by the classical theory.
![Research paper thumbnail of Los espacios de Hormander [B.sub.p,k] (E)](https://attachments.academia-assets.com/75443899/thumbnails/1.jpg)
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Scientia Et Technica, Jan 5, 2006
Turkish Journal of Mathematics, 2004
In this paper we aim to extend a result of Hörmander's, that B loc p,k (Ω) ⊂ C m (Ω) if (1+|•|) m... more In this paper we aim to extend a result of Hörmander's, that B loc p,k (Ω) ⊂ C m (Ω) if (1+|•|) m k ∈ L p , to the setting of vector valued local Hörmander-Beurling spaces, as well as to show that the space Ì ∞ j=1 B loc p j ,k j (Ω, E) (1 ≤ pj ≤ ∞, kj = e jω , j = 1, 2,. . .) is topologically isomorphic to Eω(Ω, E). Moreover, it is well known that the union of Sobolev spaces H loc s (Ω) (= B loc 2,(1+|•| 2) s/2 (Ω)) coincides with the space D F (Ω) of finite order distributions on Ω. We show that this is also verified in the context of vector valued Beurling ultradistributions.
Revista Universidad Eafit, Jul 4, 2012
Journal of Applied Analysis, 2007
For the treatment of certain cardiac disorders sometimes electrical currents are used as therapy,... more For the treatment of certain cardiac disorders sometimes electrical currents are used as therapy, as it happens when fibrillation. This phe-nomenon manifest itself with chaotic and accelerated heart rhythm, pre-venting the pumping of blood to the rest the organism. In considering this type of heart disease, introduce mathematical models to analyze the dynamics and behavior of these discharges, in particular, bidomain model is one of the most studied in order to understand the electrical process in cardiac tissue as a phenomenon that can be mathematically modeled .
The development of numerical techniques for obtaining approximate solutions of partial differenti... more The development of numerical techniques for obtaining approximate solutions of partial differential equations has very much increased in the last decades. Among these techniques are the finite element methods and finite difference. Recently, wavelet methods are applied to the numerical solution of partial differential equations, pioneer works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others. In this paper, we employ the wavelet-Petrov-Galerkin method to obtain the numerical solution of the Korteweg-de Vries (KdV) equation.
El estudio de sistemas de ecuaciones diferenciales lineales conlleva a problemas cuya solución no... more El estudio de sistemas de ecuaciones diferenciales lineales conlleva a problemas cuya solución no es fácil de obtener si no se tiene una sólida formación en álgebra lineal. Sin embargo es posible con un mínimo de teoría de matrices resolver ciertos problemas elementales de sistemas acoplados, los cuales aparecen en la formulación de modelos en sistemas mecánicos, problemas de mezclas, circuitos y en otras áreas de las ciencias.
En este trabajo se extienden al marco vectorial algunos resultados de Björck sobre espacios de Hö... more En este trabajo se extienden al marco vectorial algunos resultados de Björck sobre espacios de Hörmander B p,k utilizando la teoría de ultradistribuciones de Beurling.
Journal of Mathematical Analysis and Applications, 2010
In this paper we prove a number of results on sequence space representations and embedding theore... more In this paper we prove a number of results on sequence space representations and embedding theorems of Hörmander–Beurling spaces. As a consequence and using sharp results of Meise, Taylor and Vogt, a result of Kaballo on short sequences and hypoelliptic operators is extended to ω-hypoelliptic differential operators and to the vector-valued setting.
Papers Vol. 3 núm. 5 enero-junio 2007 by Jairo Villegas G
En este artículo se presenta la compresión de imágenes a través de la comparación entre el modelo... more En este artículo se presenta la compresión de imágenes a través de la comparación entre el modelo Wavelet y el modelo Fourier, utilizando la minimización de la función de error. El problema que se estudia es específico, consiste en determinar una base {ei} que minimice la función de error entre la imagen original y la recuperada después de la compresión. Es de resaltar que existen muchas aplicaciones, por ejemplo, en medicina o astronomía, en donde no es aceptable ningún deterioro de la imagen porque toda la información contenida, incluso la que se estima como ruido, se considera imprescindible.
MSC: 30H25, 65Txx, 65T60
En este trabajo se describe un método para la detección de puntas epilépticas en un registro elec... more En este trabajo se describe un método para la detección de puntas epilépticas en un registro electroencefalográfico(EEG) de superficie tomando un solocanal. Se identificó un patrón al utilizar el análisis multirresolución con una wavelet biortogonal después de procesar y analizar con el Toolbox Wavelet de Matlab, 207 registros de puntas y 132 registros de artificios previamente clasificadas por el neurofisiólogo. Este patrón permitió diseñar un algoritmo para la detección de puntas en pacientes con epilepsia refractaria del lóbulo temporal, a partir de los máximos voltajes en cada uno de los seis niveles de reconstrucción usando la wavelet biortogonal 3.7. El algoritmo se aplicó sobre registros de pacientes con epilepsia, obteniéndose una sensibilidad del 92% y una especificidad del 80% en el diagnóstico de las puntas epilépticas.
PACS: 87.57.-s
MSC: 65T60, 42C40
Advanced Studies in Biology, 2013
In this paper we aim to extend a result of Hörmander’s, that Blocp;k(Ω) Cm(Ω) if (1+jj)m k 2 Lp0... more In this paper we aim to extend a result of Hörmander’s, that Blocp;k(Ω) Cm(Ω) if (1+jj)m k 2 Lp0, to the setting of vector valued local Hörmander-Beurling spaces, as well as to show that the space T1 j=1 Blocpj;kj (Ω;E) (1 pj 1, kj = ej!, j = 1; 2; : : : ) is topologically isomorphic to E!(Ω; E). Moreover, it is well known that the union of Sobolev spaces Hlocs (Ω) ( = Bloc2;(1+jj2)s=2 (Ω)) coincides with the space D0F (Ω) of nite order distributions on Ω. We show that this is also veried in the context of vector valued Beurling ultradistributions.
In order to find the approximate solution of the KdV equation, we use the finite element method o... more In order to find the approximate solution of the KdV equation, we use the finite element method of Taylor-Petrov-Galerkin, in which discretization in the time variable is carried out using Taylor series expansion and for discretization in space are considered as test functions cubic B-splines and Legendre polynomials as weight functions. These functions are adequate in that they satisfy continuity, integrability and orthogonality required to apply the method.
International Journal of Mathematical Analysis, 2016
In this paper we consider cardiac electrical activity through bidomain model, to describe the ele... more In this paper we consider cardiac electrical activity through bidomain model, to describe the electrical behavior of cardiac tissue, based on current flow, electric potential distribution and conservation of charge. So we use the finite volume scheme built on rectangular meshes. Discretizing will focus on existing algorithms for elliptic and parabolic equations, with convergence guaranteed by the classical theory.
Scientia Et Technica, Jan 5, 2006
Turkish Journal of Mathematics, 2004
In this paper we aim to extend a result of Hörmander's, that B loc p,k (Ω) ⊂ C m (Ω) if (1+|•|) m... more In this paper we aim to extend a result of Hörmander's, that B loc p,k (Ω) ⊂ C m (Ω) if (1+|•|) m k ∈ L p , to the setting of vector valued local Hörmander-Beurling spaces, as well as to show that the space Ì ∞ j=1 B loc p j ,k j (Ω, E) (1 ≤ pj ≤ ∞, kj = e jω , j = 1, 2,. . .) is topologically isomorphic to Eω(Ω, E). Moreover, it is well known that the union of Sobolev spaces H loc s (Ω) (= B loc 2,(1+|•| 2) s/2 (Ω)) coincides with the space D F (Ω) of finite order distributions on Ω. We show that this is also verified in the context of vector valued Beurling ultradistributions.
Revista Universidad Eafit, Jul 4, 2012
Journal of Applied Analysis, 2007
For the treatment of certain cardiac disorders sometimes electrical currents are used as therapy,... more For the treatment of certain cardiac disorders sometimes electrical currents are used as therapy, as it happens when fibrillation. This phe-nomenon manifest itself with chaotic and accelerated heart rhythm, pre-venting the pumping of blood to the rest the organism. In considering this type of heart disease, introduce mathematical models to analyze the dynamics and behavior of these discharges, in particular, bidomain model is one of the most studied in order to understand the electrical process in cardiac tissue as a phenomenon that can be mathematically modeled .
The development of numerical techniques for obtaining approximate solutions of partial differenti... more The development of numerical techniques for obtaining approximate solutions of partial differential equations has very much increased in the last decades. Among these techniques are the finite element methods and finite difference. Recently, wavelet methods are applied to the numerical solution of partial differential equations, pioneer works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others. In this paper, we employ the wavelet-Petrov-Galerkin method to obtain the numerical solution of the Korteweg-de Vries (KdV) equation.
El estudio de sistemas de ecuaciones diferenciales lineales conlleva a problemas cuya solución no... more El estudio de sistemas de ecuaciones diferenciales lineales conlleva a problemas cuya solución no es fácil de obtener si no se tiene una sólida formación en álgebra lineal. Sin embargo es posible con un mínimo de teoría de matrices resolver ciertos problemas elementales de sistemas acoplados, los cuales aparecen en la formulación de modelos en sistemas mecánicos, problemas de mezclas, circuitos y en otras áreas de las ciencias.
En este trabajo se extienden al marco vectorial algunos resultados de Björck sobre espacios de Hö... more En este trabajo se extienden al marco vectorial algunos resultados de Björck sobre espacios de Hörmander B p,k utilizando la teoría de ultradistribuciones de Beurling.
Journal of Mathematical Analysis and Applications, 2010
In this paper we prove a number of results on sequence space representations and embedding theore... more In this paper we prove a number of results on sequence space representations and embedding theorems of Hörmander–Beurling spaces. As a consequence and using sharp results of Meise, Taylor and Vogt, a result of Kaballo on short sequences and hypoelliptic operators is extended to ω-hypoelliptic differential operators and to the vector-valued setting.
En este artículo se presenta la compresión de imágenes a través de la comparación entre el modelo... more En este artículo se presenta la compresión de imágenes a través de la comparación entre el modelo Wavelet y el modelo Fourier, utilizando la minimización de la función de error. El problema que se estudia es específico, consiste en determinar una base {ei} que minimice la función de error entre la imagen original y la recuperada después de la compresión. Es de resaltar que existen muchas aplicaciones, por ejemplo, en medicina o astronomía, en donde no es aceptable ningún deterioro de la imagen porque toda la información contenida, incluso la que se estima como ruido, se considera imprescindible.
MSC: 30H25, 65Txx, 65T60