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2D Shape similarity as a complement for Voronoi-Delone methods in shape reconstruction
(Elsevier, 2005) Ruíz S., Óscar E.; Cadavid, Carlos A.; Granados, Miguel; Peña, Sebastián; Vásquez, Eliana; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In surface reconstruction from planar slices it is necessary to build surfaces between corresponding 2D regions in consecutive levels -- The problem has been traditionally attacked with (i) direct reconstruction based on local geometric proximity between the regions, and (ii) classification of topological events between the slices, which control the evolution of the cross cuts -- These approaches have been separately applied with mixed success -- In the case (i), the results may be surfaces with over-stretched or unnatural branches, resulting from a local contour proximity which does not correspond to global similarity between regions -- In (ii), the consequences from topological events upon the actual surface realization have not been drawn -- In this paper an integration of (i) and (ii) is presented, which uses a criteria of similarity between composed 2D regions in consecutive slices to: (a) decide if a surface should actually relate those regions, (b) identify the topological transitions between levels and (c) construct the local surface for the related regions -- The method implemented hinders over-stretched and unnatural branches, therefore rendering a surface which adjusts to geometrically-sound topological events -- This is a good alternative when the surface reconstructed needs to be topologically faithful (for example in flow simulation) in addition to represent the a rough geometrical space (for example in radiation planning)
A Local Stochastic Strategy for Rubik´s Cube,
(2013-06-01) Vélez, Juan Diego; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
A model for solving vehicle scheduling problems: a case study
(IMPRENTA UNIV ANTIOQUIA, 2018-09-01) Gulnara Baldoquin, Maria; Jose Rengifo-Campo, Alvaro; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
In this work we formulate a model to solve a type of vehicle scheduling problem, derived from the operation of the mass transit system (MIO) in Cali city, Colombia. Four companies operate the system with 3 types of buses and four depots. Two kinds of tasks should be assigned to operators' buses. A task is a sequence of consecutive travels of a route between two stations: initial and final. Each task should start and should finish in a depot, not necessarily the same. There are two main objectives defined by the operators. One objective is to minimize the total deadhead kilometers between depots and stations where tasks should start or end. The other objective is to minimize the maximum deviation of kilometers (commercial and deadhead) assigned to the operators regarding the ideal quantity of kilometers that they should have, according to the number of their buses in the fleet. We have implemented the proposed model in AMPL using Gurobi solver and we validate it using nine representative instances, generated with real data obtained from the system operation. The results obtained, in all cases, improve the solutions proposed by the company. Model variations are proposed to deal with new desirable constraints for the company.
A multi-start evolutionary local search for the one-commodity pickup and delivery traveling salesman problem
(Springer Netherlands, 2020-01-01) Palacio J.D.; Rivera J.C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
This article addresses the one-commodity pickup and delivery traveling salesman problem (1-PDTSP), which is a generalization of the well-known traveling salesman problem. The 1-PDTSP aims to find a Hamiltonian tour in which a set of supply points (pickup locations), demand points (delivery locations) are visited and, the total traveled distance is minimized. We propose a hybrid metaheuristic based on multi-start evolutionary local search and variable neighborhood descent to solve the 1-PDTSP. To test the performance of our algorithm, we solve instances with up to 500 nodes available in the literature and we demonstrate that our approach is able to provide competitive results when comparing to other existing strategies. Since a direct application of the 1-PDTSP arises as the bicycle repositioning problem, we also use our metaheuristic algorithm to solve a set of real-case instances based on EnCicla, the bicycle sharing system in the Aburrá Valley (Antioquia, Colombia). © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem
(Springer Netherlands, 2015-05-01) Rivera, Juan Carlos; Christian Prins; H. Murat Afsar; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
A q-exponential statistical Banach manifold
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2013-02-15) 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.
A Remark on the Heat Equation and Minimal Morse Functions on Tori and Spheres
(Fondo Editorial Universidad EAFIT, 2013-04-01) Vélez, Juan Diego; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
A unified model framework for the multiattribute consistent periodic vehicle routing problem
(Public Library of Science, 2020-01-01) Baldoquin M.G.; Martine J.A.; Diaz-Ramirez J.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Modeling real-life transportation problems usually require the simultaneous incorporation of different variants of the classical vehicle routing problem (VRP). The periodic VRP (PVRP) is a classical extension in which routes are determined for a planning period of several days and each customer has an associated set of allowable visit schedules. This work proposes a unified model framework for PVRP that consists of multiple attributes or variants not previously addressed simultaneously, such as time-windows, time-dependence, and consistency-which guarantees the visits to customer by the same vehicle-, together with three objective functions that respond to the needs of practical problems. The numerical experimentation is focused on the effects of three factors: frequency, depot centrality, and the objective function on the performance of a general-purpose MILP solver, through the analysis of the achieved relative gaps. Results show higher sensitivity to the objective functions and to the problem sizes. © 2020 Baldoquin et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Accelerated Thermal Simulation for Three-Dimensional Interactive Optimization of Computer Numeric Control Sheet Metal Laser Cutting
(American Society of Mechanical Engineers (ASME), 2017-12-21) Mejía, D.; Moreno, Aitor; Arbelaiz, Ander; Posada, Jorge; Ruiz, O.; Chopitea, Raúl; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Accelerated Thermal Simulation for Three-Dimensional Interactive Optimization of Computer Numeric Control Sheet Metal Laser Cutting
(American Society of Mechanical Engineers (ASME), 2018-03-01) Mejia D.; Moreno A.; Arbelaiz A.; Posada J.; Ruiz-Salguero O.; Chopitea R.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In the context of computer numeric control (CNC)-based sheet metal laser cutting, the problem of heat transfer simulation is relevant for the optimization of CNC programs. Current physically based simulation tools use numeric or analytic algorithms which provide accurate but slow solutions due to the underlying mathematical description of the model. This paper presents: (1) an analytic solution to the laser heating problem of rectangular sheet metal for curved laser trajectories and convective cooling, (2) a graphics processing unit (GPU) implementation of the analytic solution for fast simulation of the problem, and (3) an integration within an interactive environment for the simulation of sheet metal CNC laser cutting. This analytic approach sacrifices the material removal effect of the laser cut in the favor of an approximated real-time temperature map on the sheet metal. The articulation of thermal, geometric, and graphic feedback in virtual manufacturing environments enables interactive redefinition of the CNC programs for better product quality, lower safety risks, material waste, and energy usage among others. The error with respect to finite element analysis (FEA) in temperature prediction descends as low as 3.5%. Copyright © 2018 by ASME.
ADOMIAN DECOMPOSITION METHOD AND TAYLOR SERIES METHOD IN ORDINARY DIFFERENTIAL EQUATIONS
(2013-08-01) Sanchez, Jose Albeiro; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Adomian Decomposition Method for a Class of Nonlinear Problems
(Hindawi Publishing Corporation, 2011-01-01) Cano, JAS; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
The Adomian decomposition method together with some properties of nested integrals is used to provide a solution to a class of nonlinear ordinary differential equations and a coupled system
Algebraic Geometry and Group Theory in Geometric Constraint Satisfaction for Computer Aided Design and Assembly Planning
(1996-01-01) RUIZ, OSCAR EDUARDO; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
(Taylor & Francis, 1996) Ruíz, Óscar E.; Ferreira, Placid M.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Mechanical design and assembly planning inherently involve geometric constraint satisfaction or scene feasibility (GCS/SF) problems -- Such problems imply the satisfaction of proposed relations placed between undefined geometric entities in a given scenario -- If the degrees of freedom remaining in the scene are compatible with the proposed relations or constraints, a set of entities is produced that populate the scenario satisfying the relations -- Otherwise, a diagnostic of inconsistency of the problem is emitted -- This problem appears in various forms in assembly planning (assembly model generation), process planning, constraint driven design, computer vision, etc -- Previous attempts at solution using separate numerical, symbolic or procedural approaches suffer serious shortcomings in characterizing the solution space, in dealing simultaneously with geometric (dimensional) and topological (relational) inconsistencies, and in completely covering the possible physical variations of the problem -- This investigation starts by formulating the problem as one of characterizing the solution space of a set of polynomials -- By using theories developed in the area of algebraic geometry, properties of Grobner Bases are used to assess the consistency and ambiguity of the given problem and the dimension of its solution space -- This method allows for die integration of geometric and topological reasoning -- The high computational cost of Grobner Basis construction and the need for a compact and physically meaningful set of variables lead to the integration of known results on group theory -- These results allow the characterization of geometric constraints in terms of the subgroups of the Special Group of Euclidean displacements in E^3, SE(3) -- Several examples arc developed which were solved with computer algebra systems (MAPLE and Mathematica) -- They are presented to illustrate the use of the Euclidean group-based variables, and to demonstrate the theoretical completeness of the algebraic geometry analysis over the domain of constraints expressible as polynomials
An alternative model to explain the vectorial capacity using as example Aedes aegypti case in dengue transmission
(Elsevier BV, 2019-01-01) Catano-Lopez A.; Rojas-Diaz D.; Laniado H.; Arboleda-Sánchez S.; Puerta-Yepes M.E.; Lizarralde-Bejarano D.P.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Vectorial capacity (VC), as a concept that describes the potential of a vector to transmit a pathogen, has had historical problems related to lacks in dimensional significance and high error propagation from parameters that take part in the model to output. Hence, values estimated with those equations are not sufficiently reliable to consider in control strategies or vector population study. In this paper, we propose a new VC model consistent at dimensional level, i.e., the definition and the equation of VC have same and consistent units, with a parameter estimation method and mathematical structure that reduces the uncertainty in model output, using as a case of study an Aedes aegypti population of the municipality of Bello, Colombia. After a literature review, we selected one VC equation following biological, measurability and dimensional criteria, then we rendered a local and global sensitivity analysis, identifying the mortality rate of mosquitoes as a target component of the equation. Thus, we studied the Weibull and Exponential distributions as probabilistic models that represent the expectation of mosquitoes infective life, intending to include the best distribution in a selected VC structure. The proposed mortality rate estimation method includes a new parameter that represents an increase or decrease in vector mortality, as it may apply. We noticed that its estimation reduces the uncertainty associated with the expectation of mosquitoes' infective life expression, which also reduces the output range and variance in almost a half. Virology; Applied mathematics; Health sciences; Epidemiology; Infectious disease; Mortality; Uncertainty analysis; Vectorial capacity; Sensitivity analysis; Dengue © 2019 The Authors
An Application of Hensel's Lemma and Puiseaux series to the problem of the existence of limits of quotients of real analytic functions
(ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2012-10-01) Vélez, Juan Diego; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
An approach to emotion Recognition in Single-channel EEG Signals using Stationary Wavelet Transform
(SPRINGER, 2017-04-01) MEJIA, GUSTAVO ANTONIO; QUINTERO, OLGA LUCIA; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
An implicit class of continuous dynamical system with data-sample outputs: a robust approach
(Oxford University Press, 2020-06-01) Juarez, Raymundo; Azhmyakov, Vadim; Espinoza, A. Tadeo; Salas, Francisco G.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this manuscript is created by application of an extended version of the conventional invariant ellipsoid method. Moreover, we also apply some specific Lyapunov-based descriptor techniques from the stability theory of continuous systems. The above combination of the modified invariant ellipsoid approach and descriptor method makes it possible to obtain the robustness of the designed control and to establish some well-known stability properties of dynamical systems under consideration. Finally, the applicability of the proposed method is illustrated by a computational example. A brief discussion on the main implementation issue is also included.
Analysis of the stability and dispersion for a Riemannian acoustic wave equation
(ELSEVIER SCIENCE INC, 2019-01-15) 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.
Analysis with wavelets of electrocardiographic alterations in chronic Chagas patients
(BOARD, 2013-01-01) Riveros, Fernando; Jairo A Villegas G; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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