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Ítem Algebraic analysis of social networks for bio-surveillance: the cases of SARS-Beijing-2003 and AH1N1 influenza-Mexico-2009.(SPRINGER-VERLAG BERLIN, 2011-01-01) Hincapié D; Ospina J; Hincapié D; Ospina J; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónAlgebraic analysis of social networks exhibited by SARS-Beijing-2003 and AH1N1 flu-Mexico-2009 was realized. The main tools were the Tutte polynomials and Maple package Graph-Theory. The topological structures like graphs and networks were represented by invariant polynomials. The evolution of a given social network was represented like an evolution of the algebraic complexity of the corresponding Tutte polynomial. The reduction of a given social network was described like an involution of the algebraic complexity of the associated Tutte polynomial. The outbreaks of SARS and AH1N1 Flu were considered like represented by a reduction of previously existing contact networks via the control measures executed by health authorities. From Tutte polynomials were derived numerical indicators about efficiency of control measures.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 Characterization of the Colombian web(Universidad EAFIT, 2009) Molina Ramírez, Alejandro; Lalinde Pulido, Juan GuillermoÍtem Computing Tutte polynomials of contact networks in classrooms(SPIE-INT SOC OPTICAL ENGINEERING, 2013-01-01) Hincapié, D.; Ospina, J.; Hincapié, D.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónObjective: The topological complexity of contact networks in classrooms and the potential transmission of an infectious disease were analyzed by sex and age. Methods: The Tutte polynomials, some topological properties and the number of spanning trees were used to algebraically compute the topological complexity. Computations were made with the Maple package GraphTheory. Published data of mutually reported social contacts within a classroom taken from primary school, consisting of children in the age ranges of 4-5, 7-8 and 10-11, were used. Results: The algebraic complexity of the Tutte polynomial and the probability of disease transmission increases with age. The contact networks are not bipartite graphs, gender segregation was observed especially in younger children. Conclusion: Tutte polynomials are tools to understand the topology of the contact networks and to derive numerical indexes of such topologies. It is possible to establish relationships between the Tutte polynomial of a given contact network and the potential transmission of an infectious disease within such network. © 2013 SPIE.Ítem Dual aspect model for failure forecasting in cyber-physical systems(TU-Delft, 2014-05-23) Mejía Gutiérrez, Ricardo; Opiyo, Eliab Z.; Horvath, Imre; Ruíz Arenas, Santiago; Universidad EAFIT. Departamento de Ingeniería de Diseño; Ricardo Mejia (rmejiag@eafit.edu.co); Imre Horváth (i.horvath@TUDelft.nl); Santiago Ruiz (s.ruizarenas@tudelft.nl); Eliab Z. Opiyo (e.z.opiyo@tudelft.nl); Ingeniería de Diseño - GRIDCyber physical systems (CPSs) are complex systems whose performance depends on the interactions between heterogeneous subsystems, the external environment, and the interrelations among natural systems and its cyber-physical augmentations -- Any fault that occur during these diverse and interrelated interactions may cause failure or a malfunction of the entire system -- The traditional multi-aspects modelling techniques developed for analysing complex systems performance can to some extent fundamentally be used in the analysis of CPSs -- The problem, however, is that these modelling techniques do not consider the consequences of the integration of natural systems and cyber-physical augmentations -- In this article, we propose a novel dual-aspect modelling technique that integrates natural and CPSs functional systems -- This modeling technique includes natural systems such as plants and humans as integral parts of the system, and therefore allow us to study their interactions, influences and effects -- A cyber-physical greenhouse case study is presented to demonstrate the applicability of the proposed modelling technique -- The proposed dual aspect modelling technique will be used in the subsequent stages of our research to analyse the interactions between natural systems and CPS augmentations with a view to identify influential factors of failure in system operation as well as the cause and types or modes failuresÍtem Funciones de Morse minimales en el espacio dodecaédrico de Poincaré, vía la Ecuación del Calor(Universidad EAFIT, 2014) Bernal Vera, Jhon Willington; Cadavid Moreno, Carlos AlbertoLet (M,g) be a compact, connected, without boundary riemannian manifold that is homogeneous, i.e. each pair of points p, q 2M have isometric neighborhoods -- This thesis is a another step towards an understanding of the extent to which it is true that for each “generic” initial condition f0, the solution to @f/@t = gf, f (·, 0) = f0 is such that for sufficiently large t, f (·, 0) is a minimal Morse function, i.e., a Morse function whose total number of critical points is the minimal possible on M -- In this thesis we show that for the Poincaré dodecahedral space this seems to hold if one allows a generic small perturbation of the metric -- Concretely, we consider an approximation of the spherical Poincaré dodecahedral space by a suitably weighted graph, calculate the eigenvalues and eigenvectors of its laplacian oparator, and study the critical point structure of eigenvectors of some of the first nonzero eigenvalues, and observe that they have the least possible number of critical pointsÍtem Geodesic-based manifold learning for parameterization of triangular meshes(Springer Verlag, 2014) Acosta, Diego A.; Ruíz, Óscar E.; Arroyave, Santiago; Ebratt, Roberto; Cadavid, Carlos; Londono, Juan J.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEReverse Engineering (RE) requires representing with free forms (NURBS, Spline, Bézier) a real surface which has been pointsampled -- To serve this purpose, we have implemented an algorithm that minimizes the accumulated distance between the free form and the (noisy) point sample -- We use a dualdistance calculation point to / from surfaces, which discourages the forming of outliers and artifacts -- This algorithm seeks a minimum in a function that represents the fitting error, by using as tuning variable the control polyhedron for the free form -- The topology (rows, columns) and geometry of the control polyhedron are determined by alternative geodesicbased dimensionality reduction methods: (a) graphapproximated geodesics (Isomap), or (b) PL orthogonal geodesic grids -- We assume the existence of a triangular mesh of the point sample (a reasonable expectation in current RE) -- A bijective composition mapping allows to estimate a size of the control polyhedrons favorable to uniformspeed parameterizations -- Our results show that orthogonal geodesic grids is a direct and intuitive parameterization method, which requires more exploration for irregular triangle meshes -- Isomap gives a usable initial parameterization whenever the graph approximation of geodesics on be faithful -- These initial guesses, in turn, produce efficient free form optimization processes with minimal errors -- Future work is required in further exploiting the usual triangular mesh underlying the point sample for (a) enhancing the segmentation of the point set into faces, and (b) using a more accurate approximation of the geodesic distances within , which would benefit its dimensionality reductionÍtem Geometry generation for computer aided engineering. Study cases in meshing and ceramics modeling(Universidad EAFIT, 2009) Serrano Salazar, Ricardo; Ruíz Salguero, Óscar EduardoÍtem Identificação de clusters industriais na Colômbia baseados na teoria de grafos(Elsevier, 2009-01-01) Duque, J.C.; Rey, S.J.; Gómez, D.A.; Universidad EAFIT. Departamento de Economía y Finanzas; Research in Spatial Economics (RISE)This paper presents a new way to identify and understand the industry clusters in the Colombian economy. The analysis relies on a recent methodology proposed by Duque and Rey (2008) where intricate input-output linkages between industries are simplified using network analysis. In addition to other techniques for cluster identification available in the literature, this novel methodology allows us not only to classify each industry in a given cluster, but also to understand how industries are related to each other within their clusters. This methodology offers a conciliatory approach to two radically different views about the economic unit from which policy makers should design their strategies for resource allocation: Porter's cluster strategy versus Hausmann's industrial targeting.Ítem Identifying industry clusters in Colombia based on graph theory(Elsevier, 2009-01-01) Duque, J.C.; Rey, S.J.; Gómez, D.A.; Universidad EAFIT. Departamento de Economía y Finanzas; Research in Spatial Economics (RISE)This paper presents a new way to identify and understand the industry clusters in the Colombian economy. The analysis relies on a recent methodology proposed by Duque and Rey (2008) where intricate input-output linkages between industries are simplified using network analysis. In addition to other techniques for cluster identification available in the literature, this novel methodology allows us not only to classify each industry in a given cluster, but also to understand how industries are related to each other within their clusters. This methodology offers a conciliatory approach to two radically different views about the economic unit from which policy makers should design their strategies for resource allocation: Porter's cluster strategy versus Hausmann's industrial targeting.Ítem Instalación, implementación y uso de las librerías Boost y su aplicación para el Centro de Computación Científica Apolo(Universidad EAFIT, 2013) Monsalve Castañeda, Sergio Andrés; Lalinde Pulido, Juan GuillermoÍtem Multi-layer Graph Theory Utilisation for Improving Traceability and Knowledge Management in Early Design Stages(Elsevier, 2017-01-01) Ríos-Zapata, D.; Pailhès, J.; Mejía-Gutiérrez, R.Decision making processes in design often challenges designers to prioritise specifications and variables in order to develop solutions that are closer to the product's requirement goals. Concerning to support their decisions, different tools and methods are used by engineers and designers allowing to reduce uncertainty in design. Nevertheless, many of these decision support systems are focused in late design stages, such as detailed design and manufacturing design, even if the possibility to influence a new product is higher in early stages. The issues regarding to those situations are often associated to design processes related to multi-physics design, where the modification of geometric-related variables might affect the performance of the solution, and the analysis of tracking the influence of the modifications might generate reprocessing and loses of time, specially when those relations are tricky and are not easily identifiable by analysing equations and a manual analysis of requirements must be performed. This article is centred in proposing a traceability model for early design stages based in graph theory. The proposal supports the information generated in design, from the input requirements (linguistic field) up to mathematical modelling and variables definition (real numbers field). This information is arranged into different layers, allowing a multilevel approach in terms of information management. The model also features a novel solution for weighting vertex in graph model, featuring a model that balances the direction of improvement, the importance and flexibility of any specification and how its behaviour will affect the design variables associated to it. The goal of the proposed model is to offer to designers, since the conceptual design stage, a method that can show automatically the level of correlation between any pair variables and specifications by the use of information trees and featuring chains that can connect them whether there is or not a connection via equations. © 2017 The Authors.Ítem On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface(2012-05-30) Cadavid, Carlos A.; Osorno, María C.; Ruíz, Óscar E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEWe develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold -- The method is applied to a closed hyperbolic surface of genus two -- The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolic surface of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifoldsÍtem Possible quantum algorithms for the Bollobás-Riordan-Tutte polynomial of a ribbon graph(SPIE-INT SOC OPTICAL ENGINEERING, 2008-01-01) Velez, M.; Ospina, J.; Velez, M.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónThree possible quantum algorithms, for the computation of the Bollobás-Riordan-Tutte polynomial of a given ribbon graph, are presented and discussed. The first possible algorithm is based on the spanning quasi-trees expansion for generalized Tutte polynomials of generalized graphs and on a quantum version of the Binary Decision Diagram (BDD) for quasi-trees . The second possible algorithm is based on the relation between the Kauffman bracket and the Tutte polynomial; and with an application of the recently introduced Aharonov-Arad-Eban-Landau quantum algorithm. The third possible algorithm is based on the relation between the HOMFLY polynomial and the Tutte polynomial; and with an application of the Wocjan-Yard quantum algorithm. It is claimed that these possible algorithms may be more efficient that the best known classical algorithms. These three algorithms may have interesting applications in computer science at general or in computational biology and bio-informatics in particular. A line for future research based on the categorification project is mentioned.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 Propuesta curricular para el cambio de enfoque en la enseñanza de las matemáticas en la Media Técnica en Desarrollo de Software(Universidad EAFIT, 2014) Narváez Berrío, Alexander de Jesús; Lalinde Pulido, Juan GuillermoCon el transcurso de los tiempos, las matemáticas se han constituido en uno de los aprendizajes de mayor fuerza en los procesos de transformación curricular en la Educación Básica y Media -- Hoy, cuando la Educación Superior se enfrenta a las demandas cambiantes del medio y del mundo laboral, es necesario resignificar los ambientes de enseñanza, para que todos los procesos que se tejen en la escuela, apunten a la significación y la transformación -- Este proyecto busca ser una apuesta a la transformación en los modos de enseñar, apostándole a una matemática aplicada a contextos informáticos, que hacen más comprensible los procesos de enseñanza universitaria y formar en competencias necesarias para hacer parte de una profesión indispensable en el mundo real donde todo está mediado por la tecnologíaÍtem Solving stochastic epidemiological models using computer algebra(SPIE-INT SOC OPTICAL ENGINEERING, 2011-01-01) Hincapie, D.; Ospina, J.; Hincapie, D.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónMathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).Ítem Surveillance Camera Location Models on a Public Transportation Network(Universidad EAFIT, 2017-04-24) Solano-Pinzón, Nathaly; Pinzón-Marroquín, David; Guerrero, William Javier; Escuela Colombiana de Ingeniería Julio Garavito