Examinando por Autor "Vélez, M."
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Ítem Biomedical computer vision using computer algebra: Analysis of a case of rhinocerebral mucormycosis in a diabetic boy(Springer Science + Business Media, 2010-01-01) Vélez, M.; Ospina, J.; Vélez, M.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónComputer algebra is applied to biomedical computer vision. Specifically certain biomedical images resulting from a case of rhinocerebral mucormysocis in a diabetic boy are analyzed using techniques in computational geometry and in algebraic-geometric topology. We apply convolution and deblurring via diffusion equation from the side of computational geometry and knot theory, graph theory and singular homology form the side of algebraic-geometric topology. Our strategy consists in to represent the biomedical images using algebraic structures in such way that the peculiarities of the images are represented using algebraic complexities. With our strategy we obtain an automatic procedure for the analysis and the diagnostic based on biomedical images. © 2010 Springer-Verlag Berlin Heidelberg.Ítem Possible topological quantum computation via khovanov homology: D-brane topological quantum computer(SPIE-INT SOC OPTICAL ENGINEERING, 2009-01-01) Vélez, M.; Ospina, J.; Vélez, M.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA model of a D-Brane Topological Quantum Computer (DBTQC) is presented and sustained. The model isbased on four-dimensional TQFTs of the Donaldson-Witten and Seiber-Witten kinds. It is argued that the DBTQC is able to compute Khovanov homology for knots, links and graphs. The DBTQC physically incorporates the mathematical process of categorification according to which the invariant polynomials for knots, links and graphs such as Jones, HOMFLY, Tutte and Bollobás-Riordan polynomials can be computed as the Euler characteristics corresponding to special homology complexes associated with knots, links and graphs. The DBTQC is conjectured as a powerful universal quantum computer in the sense that the DBTQC computes Khovanov homology which is considered like powerful that the Jones polynomial. © 2009 SPIE.Ítem Quantum hypercomputation based on the dynamical algebra su(1, 1)(IOP PUBLISHING LTD, 2006-10-06) Sicard, A.; Ospina, J.; Vélez, M.; Sicard, A.; Ospina, J.; Vélez, M.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónAn adaptation of Kieu's hypercomputational quantum algorithm (KHQA) is presented. The method that was used was to replace the Weyl-Heisenberg algebra by other dynamical algebra of low dimension that admits infinite-dimensional irreducible representations with naturally defined generalized coherent states. We have selected the Lie algebra , because this algebra possesses the necessary characteristics to realize the hypercomputation and also because such algebra has been identified as the dynamical algebra associated with many relatively simple quantum systems. In addition to an algebraic adaptation of KHQA over the algebra , we presented an adaptation of KHQA over some concrete physical referents: the infinite square well, the infinite cylindrical well, the perturbed infinite cylindrical well, the Pöschl-Teller potentials, the Holstein-Primakoff system and the Laguerre oscillator. We conclude that it is possible to have many physical systems within condensed matter and quantum optics in which it is possible to consider an implementation of KHQA. © 2006 IOP Publishing Ltd.Ítem Two qutrits universal quantum gates from the nine-dimensional unitary solutions of the Yang-Baxter equation(SPIE-INT SOC OPTICAL ENGINEERING, 2007-04-25) Vélez, M.; Ospina, J.; Vélez, M.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónUsing the Kauffman-Lomonaco method, some two-qutrits universal quantum gates are derived from the nine-dimensional unitary solutions of the Yang-Baxter equations associated with algebraic structures like the partial transpose operator and the dihedral group, which admit three dimensional representations. The Yang-Baxterization method given by Zhang-Kauffman-Ge is continuously used to obtain two-qutrits quantum gates and certain Hamiltonians for the evolution of the quantum gates are obtained, being such Hamiltonians interpreted as physical Hamiltonians of chain of particles of spin 1. Finally, the generalization for systems of two qudits is presented in the case of Yang-Baxterization of representations of braided monoidal algebra like the BH algebra and the bicolored Birman-Wenzl-Muraki algebra For these algebras the corresponding two-qudits quantum gates are constructed jointly with the associated Hamiltonians interpreted like physical chains of particles with spin d . It is conjectured that the derived two-qdits quantum gates and the Hamiltonians may be implemented over bi-dimensional lattice systems like anyons systems or more generally over any physical systems ruled by the Yang-Baxter equations.