Las matemáticas del color

El articulo resume como modelizar matemáticamente la percepción humana del color a través de los espacios de color más habituales como el RGB y el XYZ.Sanabria Codesal, E. (2023). Las matemáticas del color. Universitat Politècnica de València. http://hdl.handle.net/10251/19383

Generalización de la Carta de Smith

La generalización de la Carta de Smith al espacio tridimensional es un ejemplo de como las materias básicas de un grado aportan herramientas interesantes en la formación integral de un graduado. En este caso, conceptos matemáticos básicos consiguen mejorar la clásica carta de Smith, una herramienta muy útil en el análisis y diseño de circuitos.Sanabria Codesal, E. (2018). Generalización de la Carta de Smith. http://hdl.handle.net/10251/105652DE

Computational Cost Reduction for N+2 Order Coupling Matrix Synthesis Based on Desnanot-Jacobi Identity

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works[EN] Matrix inversion is routinely performed in computational engineering, with coupling matrix filter synthesis considered here as just one of many example applications. When calculating the elements of the inverse of a matrix, the determinants of the submatrices are evaluated. The recent mathematical proof of the Desnanot-Jacobi (also known as the “Lewis Carol”) identity shows how the determinant of an N+2 order square matrix can be directly computed from the determinants of the N+1 order principal submatrices and N order core submatrix. For the first time, this identity is applied directly to an electrical engineering problem, simplifying N+2 order coupled matrix filter synthesis (general case, which includes lossy and asymmetrical filters). With the general two-port network theory, we prove the simplification using the Desnanot-Jacobi identity and show that the N+2 coupling matrix can be directly extracted from the zeros of the admittance parameters (given by N+1 order determinants) and poles of the impedance parameters (given by the N order core matrix determinant). The results show that it is possible to decrease the computational complexity (by eliminating redundancy), reduce the associated cost function (by using less iterations), and under certain circumstances obtain different equivalent solutions. Nevertheless, the method also proves its practical usefulness under constrained optimizations when the user desires specific coupling matrix topologies and constrained coefficient values (e.g, purely real/imaginary/positive/negative). This can lead to a direct coupling matrix constrained configuration where other similar methods fail (using the same optimization algorithms).A. A. Muller would like to thank Prof. Janos Pinter and Dr. Frank Kampas for the very helpful discussions on the use of their Nelder Mead algorithm-based optimizer tool and to Dr. R. J. Cameron for the private communication on his method of enclosuresMüller, A.; Sanabria-Codesal, E.; Lucyszyn, S. (2016). Computational Cost Reduction for N+2 Order Coupling Matrix Synthesis Based on Desnanot-Jacobi Identity. IEEE Access. 4:10042-10050. doi:10.1109/ACCESS.2016.2631262S1004210050

Realization of graphs by fold Gauss maps

Work partially supported by CNPq (200921/2012) and FAPEMIG (APQ-00715-14). Work partially supported by DGCYT grant no MTM2015-64013-P.Mendes De Jesus, C.; Sanabria-Codesal, E. (2018). Realization of graphs by fold Gauss maps. Topology and its Applications. 234:248-258. https://doi.org/10.1016/j.topol.2017.11.016S24825823

Coupling matrix filter synthesis based on reflection matrices

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The paper introduces the concept of reflection matrices in the coupling matrix filter reconfiguration. It is shown that reflection matrices are complementary to rotation matrices a useful concept that can be used alternatively to rotation matrices in the similarity transformations that are applied in order to transform the coupling matrix to a suitable form. A cross-coupled filter example is given where both concepts are used.This work has been founded by SIWTUNE Marie Curie CIG no 322162 and DGCYT MTM2012-33073 grants.Müller, A.; Favennec, J.; Sanabria-Codesal, E. (2015). Coupling matrix filter synthesis based on reflection matrices. IEEE. https://doi.org/10.1109/APMC.2015.741179

A Hyperbolic Compact Generalized Smith Chart

[EN] The Smith chart was introduced by Philip Hagar Smith in 1939 and then refined and extended several years before becoming an icon of microwave engineering. To have a finite and practical size, the classical 2D Smith Chart is constrained to the unit circle. Hence, loads with reflection coefficient magnitude greater than one cannot be plotted. In 2011, the 3D Smith chart was published by A.A. Muller, P. Soto, D. Dascalu, D. Neculoiu and V. E. Boria. The 3D Smith chart unifies the design of active and passive circuits with any magnitude of the voltage reflection coefficient on the sphere by keeping all the circle forms of the classical Smith chart unchanged, but its handling requires a spherical surface and thus a CAD tool (www.3dsmithchart.com) was developed in order to utilize it.The authors wish to thank to the Marie Curie CIG grant Siwtune 322162 for their support.Müller, A.; Sanabria Codesal, E. (2016). A Hyperbolic Compact Generalized Smith Chart. Microwave Journal. 59(8):90-94. http://hdl.handle.net/10251/84254S909459

Colour image smoothing through a soft-switching mechanism using a graph model

[EN] In this study, the authors propose a soft-switching ¿lter to improve the performance of recent colour image smoothing ¿lters when processing homogeneous image regions. The authors use a recent ¿lter mixed with the classical arithmetic mean ¿lter (AMF). The recent method is used to process image pixels close to edges, texture and details and the AMF is only used to process homogeneous regions. To this end, the authors propose a method based on the graph theory to distinguish image details and homogeneous regions and to perform a soft switching between the two ¿lters. Experimental results show that the proposed method provides improved results which supports the appropriateness of the graph theory-based method and suggests that the same structure can be used to improve the performance of other non-linear colour image smoothing methods.The authors acknowledge the support of Spanish Ministry of Science and Innovation under grant MTM2009-12872-C02-01, Spanish Ministry of Science and Technology under grant MTM2010-18539 and DGCYT under grant MTM2009-08933Jordan Lluch, C.; Morillas, S.; Sanabria Codesal, E. (2012). Colour image smoothing through a soft-switching mechanism using a graph model. IET Image Processing. 6(9):1293-1298. doi:10.1049/IET-IPR.2011.0164S129312986

Social network analysis by means of Markov chains

[EN] The main aim of this paper is shown a mathematical model about the social networks that enhances the interest of the Mathematics' students that are in rst course. This model is based on Markov chains. Its approach and resolution permit to illustrate the applicability of the discrete equation systems and toemphasize the concepts studied about eigenvalue problems and diagonalization. Furthermore, all results are computed with the Mathematica software.[ES] El objetivo de este trabajo es mostrar un modelo matemático sencillo, aplicado al análisis de las redes sociales, que potencie el interés de los alumnos en la asignatura Matemáticas I. El planteamiento y la resolución de este modelo, basado en las cadenas de Markov, nos permiten ilustrar la aplicabilidad los sistemas de ecuaciones discretas y reforzar los conceptos de autovalores, autovectores y diagonalización. Utilizaremos el software de cálculo Mathematica, al que tienen acceso los estudiantes de la asignatura, para resolver el problema, lo que facilitará trabajar con diversos modelos y dimensiones grandes.Este trabajo ha sido parcialmente subvencionado por el Ministerio de Economía y Competitividad bajo los proyectos BES-2015-072901 y MTM2015-64013-P.Carreño Sanchez, A.; Sanabria Codesal, E. (2019). Análisis de redes sociales mediante cadenas de Markov. Modelling in Science Education and Learning. 12(1):21-30. https://doi.org/10.4995/msel.2019.10938SWORD213012

Piedra, Papel, Tijera y sus generalizaciones

[EN] In this paper we show how modeling helps us to motivate the Graph Theory's students. We use the well-known game of “rock, paper, scissors” and its generalizations to show the applicability of mathematical concepts studied.[ES] En este artículo mostramos como la modelización nos ayuda a motivar a los alumnos en un curso de teoría de grafos. Utilizamos el conocido juego de\piedra, papel y tijera" y sus generalizaciones para mostrar la aplicabilidad de los conceptos matemáticos estudiados.Trabajo parcialmente nanciado por el proyecto PID-DMA 2012.Jordán Lluch, C.; Sanabria-Codesal, E. (2013). Piedra, Papel, Tijera y sus generalizaciones. Modelling in Science Education and Learning. 6(2):145-153. doi:10.4995/msel.2013.1942SWORD1451536

An algorithm for self-organization of driverless vehicles of a car-rental service

[EN] The solution of fleet assignment problems is one of the core points in the management of a car-rental company. These problems arise from the restrictions imposed by the acceptance of reservations of the customers and from the necessity of an arrangement of the cars at the different depots for attending these bookings. However, with the coming of driverless cars, the rearrangement of vehicles among the depots can be simplified since no staff must be responsible of these tasks. In this note, we show a heuristic algorithm that permits to minimize the number of cars that have to be subcontracted from an external provider in order to attend a list of reservations from customers. Its efficacy is shown in comparison with the solution given by the integer linear programming method. These results can be of interest for other autonomous systems that need to be controlled.The first author is supported by MEC Project MTM2013-47093-P. The third author is supported by MEC Project MTM2012-33073. When adapting the paper to the template we missed out the acknowledgements to the research projects that support our research.Conejero, JA.; Jordan-Lluch, C.; Sanabria-Codesal, E. (2016). An algorithm for self-organization of driverless vehicles of a car-rental service. Nonlinear Dynamics. 84(1):107-114. https://doi.org/10.1007/s11071-015-2237-4S107114841Abara, J.: Applying integer linear programming to the fleet assignment problem. Interfaces 19(4), 20–28 (1989)Ahuja, R.K., Magnati, T.L., Orlin, J.B.: Networks Flows: Theory, Algorithms, and Applications. Prentice Hall, Englewood Cliffs (1993)Bodin, L., Golden, B., Assad, A., Ball, M.: Routing and scheduling of vehicles and crews: the state of the art. Comput. Oper. Res. 10, 63–212 (1983)Cacchiani, V., Caprara, A., Toth, P.: A Lagrangian heuristic for a train-unit assignment problem. Discrete Appl. Math. 161, 1707–1718 (2013)Cacchiani, V., Caprara, A., Toth, P.: Solving a real-world train unit assignment problem. Math. Program. Ser. B 124, 207–231 (2010)CNN. Driverless car tech gets serious at CES http://edition.cnn.com/2014/01/09/tech/innovation/self-driving-cars-ces/ . Last visit on June 18th, 2015Conejero, J.A., Jordan, C., Sanabria-Codesal, E.: An iterative algorithm for the management of an electric-car-rental service. J. Appl. Math. 2014, Article ID 483734, 11 (2014)DARPA Grand Challenge. http://en.wikipedia.org/wiki/2005_DARPA_Grand_Challenge#2005_Grand_Challenge . Last visit on June 18th, 2015Fraile, A., Larrod, E., Magren, A., Sicilia, J.A.: Decision model for siting transport and logistic facilities in urban environments: A methodological approach. J. Comput. Appl. Math. doi: 10.1016/j.cam.2014.12.012Evans, J.R., Minieka, E.: Optimization Algorithms for Networks and Graphs. Dekker, USA (1992)Fink, A., Reiners, T.: Modeling and solving the short-term car rental logistics problem. Transp. Res. Part E 42, 272–292 (2006)Google driverless cars http://en.wikipedia.org/wiki/Google_driverless_car . Last visit on June 18th, (2015)Heikkilä, S.: Mobility as a service A proposal for action for the public administration. Case Helsinki. Master Thesis. School of Engineering. Aalto UniversityHertz, A., Schindl, D., Zufferey, N.: A solution method for a car fleet management problem with maintenance constraints. J. Heuristics 15, 425–450 (2009)Kennington, J.L., Helgason, R.V.: Algorithms for Network Programming. Wiley, New York (1980)Lohatepanont, M., Barnhart, C.: Airline schedule planning: integrated models and algorithms for schedule design and fleet assignment. Transp. Sci. 38, 19–32 (2004)Mobincity Project. http://www.mobincity.eu/ . Last visit on June 18th, (2015)RelayRides. https://relayrides.com/ Last visit on June 18th, (2015)ROADEF Challenge. Description of the problem. http://www.prism.uvsq.fr/~vdc/ROADEF/CHALLENGES/1999/ (1999) Last visit on June 18th, (2015)Superhub Project: SUstainable and PERsuasive Human Users moBility in future cities. http://superhub-project.eu/ . Last visit on June, 18th (2015)Yan, S., Chen, C.H.: Optimal flight scheduling models for cargo airlines under alliances. J. Sched. 11, 175–186 (2008)Yan, S., Tang, C.H., Lee, M.C.: A flight scheduling model for Taiwan airlines under market competitions. Omega 35, 175–186 (2007)Yan, S., Tseng, C.H.: A passenger demand based model for airline flight scheduling. Comput. Oper. Res. 29, 1559–1581 (2002)Yang, Y., Jin, W., Hao, X.: Car rental logistics problem: A review of literature. IEEE International Conference on Service Operations and Logistics, and Informatics, pp. 2815 - 2819. E-ISBN: 978-1-4244-2013-1 (2008