Examinando por Autor "Ospina, Juan"
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Ítem Analytical solution for transient flow of a generalized bingham fluid with memory in a movable tube using computer algebra(SPRINGER, 2007-01-01) Ospina, Juan; Velez, Mario; Ospina, Juan; Velez, Mario; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA rheological linear model for a certain generalized Bingham fluid with rheological memory, which flows in a movable tube is proposed and analytically solved. The model is a system of two linear and coupled partial differential equations with integral memory. We apply the Laplace transform method making the inverse transform by means of the Bromwich integral and the theorem of residues and the analytical solution are obtained using computer algebra. We deduce the explicit forms of the velocity and stress profiles for the generalized Bingham fluid in terms of Bessel and Struve functions. Various limit cases are obtained and the standard Hagen-Poiseuille and Buckingham-Reiner equations are recovered from more general equations. This works shows the powerful of Maple to solve complex rheological problems in an analytical form as it is presented here by the first time. © Springer-Verlag Berlin Heidelberg 2007.Ítem Dynamic analysis and performance evaluation of the BIAcore surface plasmon resonance biosensor(SPIE-INT SOC OPTICAL ENGINEERING, 2015-01-01) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónSolution procedures were proposed to analyze nonlinear mass transport through an optical biosensor. A generalized collocation technique was applied to predict the dynamic behavior of an analyte along the flow chamber as a result of convection, diffusion and chemical reaction. The method estimated the effective time constants for reaching average steady-state concentrations of the free and bound analytes in the cell. When diffusion in the direction of flow was neglected, a closed-form solution, based on double Laplace transforms, was obtained after linearizing the original system. In both models, an increase in the sample diffusion coefficient lowered the effective time constant. This approach may help researchers evaluate the performance of biosensors and meet specific design criteria. © 2015 SPIE.Ítem A FIRST-ORDER TIME CONSTANT ESTIMATION FOR NONLINEAR DIFFUSION PROBLEMS(TAYLOR & FRANCIS INC, 2014-06-03) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA Laplace transform-based procedure was proposed to calculate the effective time constant for a class of nonlinear diffusion problems. The governing mathematical representation was first estimated with a linear model by omitting the nonlinear term. The solution to this problem was later introduced into the original equation, which was solved with Laplace transforms, resulting in a first-order approximation of the real system's behavior. A time constant was calculated using frequency-domain expressions. Two case studies were considered to illustrate the methodology. As the rate of heat supplied to a rod is raised, the speed at which the temperature reached an equilibrium value decreased. Increasing the maximum velocity in reaction-diffusion transport by a factor of three lowered the time constant by only 1.7%. The applications of this method range from biosensor dynamics to process control. © 2014 Copyright Taylor and Francis Group, LLC.Ítem Gravitational topological quantum computation(SPRINGER, 2007-01-01) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA new model in topological quantum computing, named Gravitational Topological Quantum Computing (GTQC), is introduced as an alternative respect to the Anyonic Topological Quantum Computing and DNA Computing. In the new model the quantum computer is the quantum space-time itself and the corresponding quantum algorithms refer to the computation of topological invariants for knots, links and tangles. Some applications of GTQC in quantum complexity theory and computability theory are discussed, particularly it is conjectured that the Khovanov polynomial for knots and links is more hard than #P-hard; and that the homeomorphism problem, which is noncomputable, maybe can be computed after all via a hyper-computer based on GTQC. © Springer-Verlag Berlin Heidelberg 2007.Ítem Mackendrick: A Maple Package oriented to symbolic computational epidemiology(SPRINGER, 2006-01-01) Ospina, Juan; Hincapie, Doracelly; Ospina, Juan; Hincapie, Doracelly; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA Maple Package named Mackendrick is presented. Such package is oriented to symbolic computational epidemiology. © Springer-Verlag Berlin Heidelberg 2006.Ítem Mathematical modeling of Chikungunya fever control(SPIE-INT SOC OPTICAL ENGINEERING, 2015-01-01) Hincapie-Palacio, Doracelly; Ospina, Juan; Hincapie-Palacio, Doracelly; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónChikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures. © 2015 SPIE.Ítem Poschl-Teller potentials based solution to Hilbert's tenth problem(Universidad EAFIT, 2006-12-01) Sicard, Andrés; Ospina, Juan; Universidad EAFITÍtem Possible quantum algorithm for the Lipshitz-Sarkar-Steenrod square for Khovanov homology(SPIE-INT SOC OPTICAL ENGINEERING, 2013-01-01) Ospina, Juan; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónRecently the celebrated Khovanov Homology was introduced as a target for Topological Quantum Computation given that the Khovanov Homology provides a generalization of the Jones polynomal and then it is possible to think about of a generalization of the Aharonov.-Jones-Landau algorithm. Recently, Lipshitz and Sarkar introduced a space-level refinement of Khovanov homology. which is called Khovanov Homotopy. This refinement induces a Steenrod square operation Sq?2 on Khovanov homology which they describe explicitly and then some computations of Sq?2 were presented. Particularly, examples of links with identical integral Khovanov homology but with distinct Khovanov homotopy types were showed. In the presente work we will introduce possible quantum algorithms for the Lipshitz-Sarkar-Steenrod square for Khovanov Homolog and their possible simulations using computer algebra. © 2013 SPIE.Ítem Possible universal quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant(SPIE-INT SOC OPTICAL ENGINEERING, 2012-01-01) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónPossible quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant are proposed. Such algorithms are resulting from adaptations of the recently proposed Kauffmans` algorithm for the standard Khovanov homology. The method that was applied consists in to write the relevant quantum invariant as the trace of a certain unitary operator and then to compute the trace using the Hadamard test. We apply such method to the quantum computation of the Jones polynomial, HOMFLY polynomial, Chromatic polynomial, Tutte polynomial and Bollobàs-Riordan polynomial. These polynomials are quantum topological invariants for knots, links, graphs and ribbon graphs respectively. The Jones polynomial is categorified by the standard Khovanov homology and the others polynomials are categorified by generalized Khovanov homologies, such as the Khovanov-Rozansky homology and the graph homologies. The algorithm for the Rasmussen's invariant is obtained using the gauge theory; and the recently introduced program of homotopyfication is linked with the super-symmetric quantum mechanics. It is claimed that a new program of analytification could be development from the homotopyfication using the celebrated Atiyah-Singer theorem and its super-symmetric interpretations. It is hoped that the super-symmetric quantum mechanics provides the hardware for the implementation of the proposed quantum algorithms. © 2012 SPIE.Ítem Possible universal quantum algorithms for generalized Turaev-Viro invariants(SPIE-INT SOC OPTICAL ENGINEERING, 2011-01-01) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónAn emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological invariants for knots and links (Jones polynomials, HOMFLY polynomials, Khovanov polynomials); topological invariants for graphs (Tutte polynomial and Bollobás-Riordan polynomial); topological invariants for 3-manifolds (Reshetiskin-Turaev, Turaev-Viro and Turaer-Viro-Ocneanu invariants) and topological invariants for 4-manifolds (Crane-Yetter invariants). In a few words, TQC is concerned with the formulation of quantum algorithms for the computation of these topological invariants in quantum topology. Given that one of the fundamental achievements of quantum topology was the discovery of strong connections between monoidal categories and 3-dimensional manifolds, in TQC is possible and necessary to exploit such connections with the purpose to formulate universal quantum algorithms for topological invariants of 3-manifolds. In the present work we make an exploration of such possibilities. Specifically we search for universal quantum algorithms for generalized Turaev-Viro invariants of 3-manifolds such as the Turaev-Viro-Ocneanu invariants, the Kashaev-Baseilhac-Benedetti invariants of 3-manifolds with links and the Geer-Kashaev-Turaev invariants of 3-manifolds with a link and a principal bundle. We also look for physical systems (three dimensional topological insulators and three-dimensional gravity) over which implement the resulting universal topological quantum algorithms.Ítem Quantum algorithms for virtual Jones polynomials via thistlethwaite theorems(SPIE-INT SOC OPTICAL ENGINEERING, 2010-01-01) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónRecently a quantum algorithm for the Jones polynomial of virtual links was proposed by Kauffman and Dye via the implementation of the virtual braid group in anyonic topological quantum computation when the virtual crossings are considered as generalized swap gates. Also recently, a mathematical method for the computation of the Jones polynomial of a given virtual link in terms of the relative Tuttle polynomial of its face (Tait) graph with some suitable variable substitutions was proposed by Diao and Hetyei. The method of Diao and Hetyei is offered as an alternative to the ribbon graph approach according to which the Tutte polynomial of a given virtual link is computed in terms of the Bollobás- Riordan polynomial of the corresponding ribbon graph. The method of Diao and Hetyei can be considered as an extension of the celebrated Thistlethwaite theorem according to which invariant polynomials for knots and links are derived from invariant polynomials for graphs. Starting from these ideas we propose a quantum algorithm for the Jones polynomial of a given virtual link in terms of the generalized Tutte polynomials by exploiting the Thistlethwaite theorem and the Kauffman algorithm. Our method is claimed as the quantum version of the Diao-Hetyei method. Possible supersymmetric implementations of our algortihm are discussed jointly with its formulations using topological quantum lambda calculus. © 2010 SPIE.Ítem Topological and geometrical quantum computation in cohesive Khovanov homotopy type theory(SPIE-INT SOC OPTICAL ENGINEERING, 2015-05-21) Ospina, Juan; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónThe recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a formal, logical approach to concepts like smoothness, cohomology and Khovanov homology; and such approach permits to clarify the quantum algorithms in the context of Topological and Geometrical Quantum Computation. In particular we consider the so-called a "open-closed stringy topological quantum computera" which is a theoretical topological quantum computer that employs a system of open-closed strings whose worldsheets are open-closed cobordisms. The open-closed stringy topological computer is able to compute the Khovanov homology for tangles and for hence it is a universal quantum computer given than any quantum computation is reduced to an instance of computation of the Khovanov homology for tangles. The universal algebra in this case is the Frobenius Algebra and the possible open-closed stringy topological quantum computers are forming a symmetric monoidal category which is equivalent to the category of knowledgeable Frobenius algebras. Then the mathematical design of an open-closed stringy topological quantum computer is involved with computations and theorem proving for generalized Frobenius algebras. Such computations and theorem proving can be performed automatically using the Automated Theorem Provers with the TPTP language and the SMT-solver Z3 with the SMT-LIB language. Some examples of application of ATPs and SMT-solvers in the mathematical setup of an open-closed stringy topological quantum computer will be provided. © 2015 SPIE.Ítem Topological quantum computation of the Dold-Thom functor(SPIE-INT SOC OPTICAL ENGINEERING, 2014-05-22) Ospina, Juan; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA possible topological quantum computation of the Dold-Thom functor is presented. The method that will be used is the following: a) Certain 1+1-topological quantum field theories valued in symmetric bimonoidal categories are converted into stable homotopical data, using a machinery recently introduced by Elmendorf and Mandell; b) we exploit, in this framework, two recent results (independent of each other) on refinements of Khovanov homology: our refinement into a module over the connective k-theory spectrum and a stronger result by Lipshitz and Sarkar refining Khovanov homology into a stable homotopy type; c) starting from the Khovanov homotopy the Dold-Thom functor is constructed; d) the full construction is formulated as a topological quantum algorithm. It is conjectured that the Jones polynomial can be described as the analytical index of certain Dirac operator defined in the context of the Khovanov homotopy using the Dold-Thom functor. As a line for future research is interesting to study the corresponding supersymmetric model for which the Khovanov-Dirac operator plays the role of a supercharge. © 2014 SPIE.Ítem Tutte polynomials and topological quantum algorithms in social network analysis for epidemiology, bio-surveillance and bio-security(SPRINGER, 2008-01-01) Velez, Mario; Ospina, Juan; Hincapie, Doracelly; Velez, Mario; Ospina, Juan; Hincapie, Doracelly; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónThe Tutte polynomial and the Aharonov-Arab-Ebal-Landau algorithm are applied to Social Network Analysis (SNA) for Epidemiology, Biosurveillance and Biosecurity. We use the methods of Algebraic Computational SNA and of Topological Quantum Computation. The Tutte polynomial is used to describe both the evolution of a social network as the reduced network when some nodes are deleted in an original network and the basic reproductive number for a spatial model with bi-networks, borders and memories. We obtain explicit equations that relate evaluations of the Tutte polynomial with epidemiological parameters such as infectiousness, diffusivity and percolation. We claim, finally, that future topological quantum computers will be very important tools in Epidemiology and that the representation of social networks as ribbon graphs will permit the full application of the Bollobás-Riordan-Tutte polynomial with all its combinatorial universality to be epidemiologically relevant. © 2008 Springer Berlin Heidelberg.Ítem Two-dimensional description of absorption in humans after dermal exposure to volatile organic compounds(TAYLOR & FRANCIS INC, 2017-06-03) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA two-dimensional diffusion model was developed to predict the absorption of chemicals in humans following dermal contact. A firstorder evaporation rate equation was applied to the skin surface while a perfect-sink boundary condition was imposed at the stratum corneum/viable epidermis interface. Initially, there was a certain amount of the substance present within the stratum corneum at the end of the exposure period. Laplace transform techniques were implemented to solve the governing equations and to derive an expression for the time elapsed before reaching 90% of the final amount of chemical absorbed by the body. This index was 0.43, 2.67, 6.91, and 36.9 h for ethanol, diphenylamine, p-nitroaniline, and benzyl butyl-phthalate, respectively. Simulations show that surface evaporation is important for highly volatile compounds. A large fraction of the amount of poorly volatile compounds, available in the skin after exposure, was absorbed into the bloodstream. © Taylor & Francis Group, LLC.Ítem Two-dimensional transport analysis of transdermal drug absorption with a non-perfect sink boundary condition at the skin-capillary interface(ELSEVIER SCIENCE INC, 2013-07-01) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónA transient percutaneous drug absorption model was solved in two dimensions. Clearance of the topically-applied pharmaceutical occured at the skin-capillary boundary. Timolol penetration profiles in the dermal tissue were produced revealing concentration gradients in the directions normal and parallel to the skin surface. Ninety-eight percent of the steady-state flux was reached after 85. h or four time constants. The analytical solution procedure agreed with published results. As the clearance rate increased relative to diffusion, the delivery rate and amount of drug absorbed into the bloodstream increased while the time to reach the equilibrium flux decreased. Researchers can apply the closed-form expressions to simulate the process, estimate key parameters and design devices that meet specific performance requirements. © 2013 Elsevier Inc.Ítem Universal quantum gates Via Yang-baxterization of dihedral quantum double(SPRINGER, 2007-01-01) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónThe recently discovered Yang-Baxterization process for the quantum double of the dihedral group algebra, is presented keeping on mind the quantum computation. The products resultant from Yang-Baxterization process are interpreted as universal quantum gates using the Bryslinski's theorem. Results are obtained for two-qubits and two-qutrits gates. Using the Zhang-Kauffman-Ge method (ZKGM), certain Hamiltonians responsible for the quantum evolution of the quantum gates are obtained. Possible physical systems such as anyons systems are mentioned as referents for practical implementation. © Springer-Verlag Berlin Heidelberg 2007.Ítem Using computer algebra for Yang-Baxterization applied to quantum computing(SPIE-INT SOC OPTICAL ENGINEERING, 2006-05-12) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónUsing Computer Algebra Software (Mathematica and Maple), the recently introduced topic of Yang-Baxterization applied to quantum computing, is explored from the mathematical and computational views. Some algorithms of computer algebra were elaborated with the aim to make the calculations to obtain some of results that were originally presented in the paper by Shang-Kauffman-Ge. Also certain new results about computational Yang-baxterization are presented. We obtain some Hamiltonians for hypothetical physical systems which can be realized within the domain of spin chains and certain diffusion process. We conclude that it is possible to have real physical systems on which implement, via Yang-baxterization, the standard quantum gates with topological protection. Finally some lines for future research are deligned.