Examinando por Autor "Quiceno, H. R."

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    A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
    (Springer, 2013) Quiceno, H. R.; Loaiza, Gabriel; Universidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones; Gabriel Loaiza (gloaiza@eafit.edu.co)
    For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears as special case of the q −connections ∇ (q). The main result is the expected one, namely the zero curvature of the manifold.
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    Analysis of the stability and dispersion for a Riemannian acoustic wave equation
    (ELSEVIER SCIENCE INC, 2019-01-15) Quiceno, H. R.; Arias, C.; Quiceno, H. R.; Arias, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    The construction of images of the Earth's interior using methods as reverse time migration (RTM) or full wave inversion (FWI) strongly depends on the numerical solution of the wave equation. A mathematical expression of the numerical stability and dispersion for a particular wave equation used must be known in order to avoid unbounded numbers of amplitudes. In case of the acoustic wave equation, the Courant–Friedrich–Lewy (CFL) condition is a necessary but is not a sufficient condition for convergence. Thus, we need to search other types of expression for stability condition. In seismic wave problems, the generalized Riemannian wave equation is used to model their propagation in domains with curved meshes which is suitable for zones with rugged topography. However, only a heuristic version of stability condition was reported in the literature for this equation. We derived an expression for stability condition and numerical dispersion analysis for the Riemannian acoustic wave equation in a two-dimensional medium and analyzed its implications in terms of computational cost. © 2018 Elsevier Inc.
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    A q-exponential statistical Banach manifold
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2013-02-15) Loaiza, G.; Quiceno, H. R.; Loaiza, G.; Quiceno, H. R.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    Let µ be a given probability measure and Mµ the set of µ-equivalent strictly positive probability densities. In this paper we construct a Banach manifold on Mµ, modeled on the space L 8(p{dot operator}µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis's deformed exponential), where 0<q<1 is any real number. This family is characterized by the fact that when q?1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space. The coordinate mappings of the manifold are given in terms of Csiszár's F-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score function. © 2012 Elsevier Ltd.