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https://hdl.handle.net/10784/27664

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A Riemannian geometry in the q-exponential Banach manifold induced by q-divergences
(SPRINGER, 2013-01-01) Loaiza, G.; Quiceno, H.R.; Loaiza, G.; Quiceno, H.R.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
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 a-connections appears as special case of the q-connections ?(q). The main result is the expected one, namely the zero curvature of the manifold. © 2013 Springer-Verlag.
Hessian eigenfunctions for triangular mesh parameterization
(SciTePress, 2016-02-27) Mejia, D.; Ruiz OE; Cadavid, C.; Mejia, D.; Ruiz OE; Cadavid, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional H for Dimensionality Reduction (DR) of a sampled manifold M. This article presents a variation of classic HLLE for parameterization of 3D triangular meshes. Contrary to classic HLLE which estimates local Hessian nullspaces, the proposed approach follows intuitive ideas from Differential Geometry where the local Hessian is estimated by quadratic interpolation and a partition of unity is used to join all neighborhoods. In addition, local average triangle normals are used to estimate the tangent plane TxM at x ? M instead of PCA, resulting in local parameterizations which reflect better the geometry of the surface and perform better when the mesh presents sharp features. A high frequency dataset (Brain) is used to test our algorithm resulting in a higher rate of success (96.63%) compared to classic HLLE (76.4%). © Copyright 2016 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.
An approach to emotion recognition in single-channel EEG signals using stationarywavelet transform
(SPRINGER, 2017-01-01) Gómez, A.; Quintero, L.; López, N.; Castro, J.; Villa, L.; Mejía, G.; Gómez, A.; Quintero, L.; López, N.; Castro, J.; Villa, L.; Mejía, G.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
In this work, we perform an approach to emotion recognition from Electroencephalography (EEG) single channel signals extracted in four (4) mother-child dyads experiment in developmental psychology. Single channel EEG signals are decomposed by several types of wavelets and each subsignal are processed using several window sizes by performing a statistical analysis. Finally, three types of classifiers were used, obtaining accuracy rate between 50% to 87% for the emotional states such as happiness, sadness and neutrality. © Springer Nature Singapore Pte Ltd. 2017.
A Mixed-Integer Linear Programming Model for a Selective Vehicle Routing Problem
(Springer Verlag, 2018-01-01) Posada A.; Rivera J.C.; Palacio J.D.; Posada A.; Rivera J.C.; Palacio J.D.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
In this paper, we propose a new vehicle routing problem variant. The new problem is a type of selective vehicle routing model in which it is not necessary to visit all nodes, but to visit enough nodes in such a way that all clusters are visited and from which it is possible to cover all nodes. Here, a mixed-integer linear programming formulation (MILP) is proposed in order to model the problem. The MILP is tested by using adapted instances from the generalized vehicle routing problem (GVRP). The model is also tested on small size GVRP instances as a special case of our proposed model. The results allow to evaluate the impact of clusters configuration in solver efficacy. © 2018, Springer Nature Switzerland AG.
A Metaheuristic Approach for the Cumulative Capacitated Arc Routing Problem
(Springer Verlag, 2018-09-03) Rivera, Juan Carlos; Lenis, Sergio Andres; Rivera, Juan Carlos; Lenis, Sergio Andres; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
In this paper we propose a new variant of the capacitated arc routing problem (CARP). In this new problem the objective function becomes a cumulative objective computed as the traveled distance multiplied by the vehicle load. A metaheuristic approach is proposed which is based on the hybridization of three known procedures: GRASP, VND and Set covering model. The metaheuristic is tested with some benchmark instances from CARP. The results allow to evaluate the performance with the different metaheuristic components and to compare the solutions with the classical objective function. © 2018, Springer Nature Switzerland AG.
Consistent approximations of the control - Affine systems with bounded uncertainties: Application to the controlled lotka - Volterra dynamics
(Institute of Electrical and Electronics Engineers Inc., 2019-01-01) Azhmyakov V.; Londono C.; Osorio P.; Rojas A.; Puerta M.E.; Trujillo L.A.G.; Azhmyakov V.; Londono C.; Osorio P.; Rojas A.; Puerta M.E.; Trujillo L.A.G.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Our contribution is devoted to constructive approximations of a wide class of the modern control systems, namely, of the general control-affine dynamic models. We consider the generic tracking control problem associated with the control-affine systems in the presence of bounded uncertainties. The conventional linearization based solution approach to the tracking problem under consideration is finally refined and extended by a novel analytic errors estimation technique. Theoretic results developed in our contribution are applied to a practically motivated example of the controlled Lotka-Volterra system. © 2019 IEEE.
Mixed-Integer Linear Programming Models for One-Commodity Pickup and Delivery Traveling Salesman Problems
(Springer Verlag, 2019-01-01) Palacio J.D.; Rivera J.C.; Palacio J.D.; Rivera J.C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
This article addresses two different pickup and delivery routing problems. In the first one, called the one-commodity pickup and delivery traveling salesman problem, a known amount of a single product is supplied or demanded by a set of two different types of locations (pickup or delivery nodes). Therefore, a capacitated vehicle must visit each location once at a minimum cost. We also deal with the relaxed case where locations can be visited several times. In the last problem, the pickup or delivery operation can be split into several smaller pickups or deliveries, and also locations can be used as temporal storage points with the aim of reducing the cost of the route. To solve these problems, we present two mixed-integer linear programming models and we solve them via commercial solver. We analyze how several visits to a single location may improve solution quality and we also show that our simple strategy has a good performance for instances with up to 60 locations. © 2019, Springer Nature Switzerland AG.

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