Revista de Matemáticas 10(1 y 2)
URI permanente para esta colecciónhttps://hdl.handle.net/10669/12862
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Ítem An enumerative procedure for identifying maximal covers(2009-02-20 00:00:00) Muñoz, SusanaIn this paper we present an enumerative procedure for identifying all maximalcovers from the set of covers implied by a 0-1 knapsack constraint. The inequalitiesinduced by these maximal covers are not dominated by the inequality induced by anyother cover implied by the knapsack constraint. Thus, their identification can help totighten 0-1 models. On the other hand, we present an improvement on a proceduretaken from the literature for identifying certain maximal covers. Some comparativecomputational experiments where both procedures have been applied to randomlygenerated knapsack constraints are also reported.Keywords: Maximal covers, tighter formulations, knapsack constraints, dominated inequalitiesÍtem Problemas matemáticos sugeridos por la genética y la ecología de poblaciones(2009-02-20 00:00:00) Gómez Alcaraz, GuillermoThe main goal of the present work is to show a paralellism between the equationsin Physics and Mathematics, and some problems generated in another branch whichcould be called Mathematical Biology. The article is divided in two parts; in the firstone we discuss a behavior problem of a population disseminated in a certain area,and in the second part we try to develop numerical methods in continuous integrals,solution of problems of that type.Keywords: Biomathemaics, population genetics, numerical methods.Ítem El problema del conjunto independiente en la selección de horarios de cursos(2009-02-20 00:00:00) López Bracho, Rafael; Gutiérrez Andrade, Miguel Ángel; Ortuño Sánchez, María Paula; Ramírez Rodríguez, JavierRegistration process at the Universidad Aut´onoma Metropolitana is such thatevery student is free to choose his/her own subjects and schedule. Success of thissystem, based in the percentage of students that obtain a place in the lectures chosen, depends principally on the characteristics of the supply of scheduled lectures, relativesto quantity and variety of timetables, as well as the oportunity of the students todo an adequate selection of lectures. An adequate selection of lectures is a subset ofthe lectures set with pairwise different subjects and timetables. The Choose LecturesProblem is to find the maximal adequate selection of lectures. A Graph Theory modelof the problem and an algorithm to solve it will be shown.Keywords: Graph Theory, Independent Set, Operations Research, Educational Timetabling.Ítem El problema del multicubrimiento: una aplicación para la selección de paradas en la red de transporte de la Ciudad de México(2009-02-20 00:00:00) Gutiérrez Andrade, Miguel Ángel; de los Cobos Silva, Sergio Gerardo; Pérez Salvador, Blanca Rosa; Goddard Close, JohnIn this paper an heuristic algorithm is developed. Its implementation is developedas well, in order to solve a sampling problem in the urban transportation network in Mexico City. The problem consist of the selection of at least 2 points (stops) on each ofthe 236 routes in the study comprising a total of 8390 stops. This problem is presentedas a multicover problem subject to 236 restrictions and 8390 binary variables. Giventhat this an NP-hard problem, it was implemented an heuristic algorithm to determinethe sampling points.Keywords: Multicover problem, heuristic methods, greedy algorithms, combinatorial optimization.Ítem Una variante del método que utiliza la simulación de un proceso de difusión para la caracterización de formas de figuras planas(2009-02-20 00:00:00) Skliar, Osvaldo; Láscaris Comneno, Tatiana; Medina, Víctor; Poveda, José S.This is a variation of a previously presented method [1] for characterizing the shapesof plane figures. In addition to retaining the advantages of the original method, thisvariant includes one more: it is no longer necessary to halt a (simulated) diffusionprocess during the transient stage; that is, before arriving at an equilibrium. Onthe contrary, the longer the process takes, the more noticeable the difference becomesbetween the concave parts and the convex parts of the contours of the figures analyzed.Keywords: shape characterization, contours of plane figures, diffusion process, concavities,convexities.Ítem Un método para la caracterización exhaustiva de formas de figuras planas, tanto simple como múltiplemente conexas(2009-02-20 00:00:00) Skliar, Osvaldo; Medina, Víctor; Poveda, José S.This article presents a method with which the shapes of plane figures may becharacterized exhaustively by using descriptive mathematical entities obtained fromthese figures. They may be either simply or multiply connected. Thus the particularfigures may be reconstructed from these mathematical entities which will be known asthe ”characteristic curves” of the corresponding figures. Once what is understood by the ”distance” between any two pixels has been specified, each of these characteristiccurves is generated as a function of the elements belonging to the two sets of distancesbetween particular pixels.The characteristic curves of the figures considered are independent of the positionsof these figures with regard to any reference system. In other words, they are invariableeven when the figures are subjected to displacements or rotations.Keywords: shape characterization, contours of plane figures, triangulation method, centerof mass, pattern recognitionÍtem Herramientas matemáticas para la valoración de la ampliación de una infraestructura portuaria(2009-02-20 00:00:00) Casasús, Trinidad; Crespo, Enric; Juan, C.; Olmos, F.; Pérez, Juan C.infraestructuraportuaria ya consolidada, que conlleva unas inversiones a largo plazo.Para ello hay que recurrir a medios de an´alisis capaces de recoger, en la medidade lo posible, la incertidumbre sobre la futura evoluci´on de los tr´aficos de mercanc´?as,sobre el efecto de la competencia entre puertos, etc., y que los m´etodos tradicionales noaproximan en toda su dimensi´on. Existe, adem´as, un problema de decisi´on de pol´?tica´optima de gesti´on del proyecto que depende de variables de decisi´on que modelizanlas opciones presentes en el mismo.Las oportunidades de inversi´on han sido tratadas como una colecci´on de opcionesamericanas sobre activos reales. Nosotros hemos optado por una variaci´on del m´etodode Monte Carlo para la obtenci´on del Valor Actual Neto estoc´astico. Para la toma dedecisiones se plantea un problema de control ´optimo.El procedimiento genera unos escenarios que incrementan la informaci´on sobre eltr´afico y les asocia un VAN esperado as´? como la probabilidad de que ´este sea positivoo negativo. Adem´as de esta distribuci´on de probabilidad proporciona la de los flujos de caja (posible indicador del riesgo) y del VAN asociado.Los c´alculos asociados a cada escenario son muy costosos y resulta imposible examinar todas las posibilidades de porcentajes de participaci´on del capital privado y de fecha ´optima para cada inversi´on, o su desestimaci´on. Proponemos un m´etodo basadoen el Scatter Search para tomar estas decisiones.Palabras clave: Ecuaciones estoc´asticas, m´etodos de Monte Carlo, m´etodos metaheur´?sticos.Ítem Los valores del juego de parada óptima para medias aritméticas de variables de Bernoulli(2009-02-20 00:00:00) Lobo Segura, Jaime; Cambronero, SantiagoWe study optimal stopping problems for generalized averages of identically distributedBernoulli variables, taking values in the set D = {d0, d1}. We obtain a recurrentformula in the finite horizon case, which gives the value of the game in terms ofassociated problems of smaller horizon. This allows us to create algorithms for computingthe value of the game, as well as the optimal stopping time in these cases.Moreover, we present a series of aplicattions to the study of properties of the value asa function of the parameters.Keywords: Stopping times problems, generalized means, stopping times decomposition,sufficient class of stopping times, recurrence formulas, Bernoulli variables.Ítem Sobre el problema inverso de difusión(2009-02-20 00:00:00) Mercado Escalante, José Roberto; Aldama R., Álvaro Alberto; Brambila P., F.Infiltration is physically described in order to model it as a diffusion stochasticprocess. Theorem M-B 1 is enunciated; whose main objective is the inverse diffusionproblem. The theorem is demonstrated in the specific context of solution injectability,and it is applied to solve the inverse diffusion problem in the presence of Boltzmann’sgroup. The inverse problem of the similarity exponent is solved following group analysismethods. The dispersion of a water drop in a three-dimensional porous medium isapplied; a result which in turn is applicable to drop irrigation.Keywords: inverse problems, group analysis of differential equations, similarity, fractals,diffusion, porous medium.Ítem A comparison of approximations to percentiles of the noncentral chi2-distribution(2009-02-20 00:00:00) Sahai, Hardeo; Ojeda, Mario MiguelVarious approximations to percentiles of the noncentral 2-distribution are examinedfor their accuracy over a wide range of values of the parameters of the distribution.Keywords: Probability distribution, percentiles, numerical approximation.Ítem Estrategia para la selección de modelos gráficos en tablas de contingencia no estructuradas(2009-02-20 00:00:00) González Debén, Adalberto; Alfonso Sagué, KarenLoglinear models are frequently utilized in the analysis of association patterns betweenvariables in a multidimensional contingency table. Discrete graphical modelsare fashionable. They are a subset of the hierarchical loglinear models and its conditionalindependence structures are represented by a graph. Because of that they canbe more easily interpreted. In this work four models selection methods are describedand compared: stepwise selection (backward, forward and in two steps) and the EHprocedure.A strategy for model selection is proposed.Keywords: graphical models, contingency tables, model selection methodsÍtem Metodología estadística: bases para el establecimiento de políticas adecuadas para el manejo del arbolado urbano en la Ciudad de México(2009-02-20 00:00:00) Aldama Ojeda, Alejandro; Vázquez, Héctor J.; Grabinsky, Jaime; Chacalo, AliciaAn Exploratory analysis using arboricultural and ecological statistical approachesof a representative sample of Mexico City’s street trees were followed by a confirmatorystudy through Path Analysis to test hypothesis stating causal relationships amongdifferent variables. All this in order to evaluate and to manage the quality of MexicoCity’s Urban Forest.Keywords: factor analysis, principal components, correspondence analysis, cluster analysis,measures of association, path analysis, urban trees.Ítem Método heurístico para particionamiento óptimo(2009-02-20 00:00:00) de los Cobos Silva, Sergio Gerardo; Trejos Zelaya, Javier; Pérez Salvador, Blanca Rosa; Gutiérrez Andrade, Miguel ÁngelMany data analysis problems deal with non supervised partitioning of a data set,in non empty clusters well separated between them and homogeneous within the clusters.An ideal partitioning is obtained when any object can be assigned a class without ambiguity. The present paper has two main parts; first, we present different methodsand heuristics that find the number of clusters for optimal partitioning of a set; afterwards,we propose a new heuristic and we perform different comparisons in orderto evaluate the advantages on well known data sets; we end the paper with someconcluding remarks.Keywords: Optimal partitioning, clustering, classification, heuristics.Ítem Métodos de optimización del stress. Comparaciones usando disimilitudes tipo intervalo(2009-02-20 00:00:00) Castillo Elizondo, William; González, Jorge; Rodríguez Rojas, OldemarBy the use of simulated annealing it is defined the algorithm MDSI-SS for the optimization of Stress defined by Donoeux and Masson [6] for interval-type dissimilarities.On three data sets it is compared the value of stress obtained by MDSI-SS and INTERSCAL (the later is the algorithm proposed by Rodríguez et al. [12]).