Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text

Gráfico de controle modificado para processos com estruturas complexas de autocorrelação

This work proposes a modified control chart incorporating concepts of time series analysis. Specifically, we considerer Gaussian mixed transition distribution (GMTD) models. The GMTD models are a more general class than the autorregressive (AR) family, in the sense that the autocorrelated processes may present flat stretches, bursts or outliers. In this scenario traditional Shewhart charts are no longer appropriate tools to monitoring such processes. Therefore, Vasilopoulos and Stamboulis (1978) proposed a modified version of those charts, considering proper control limits based on autocorrelated processes. In order to evaluate the efficiency of the proposed technique a comparison with a traditional Shewhart chart (which ignores the autocorrelation structure of the process), a AR(1) Shewhart control chart and a GMTD Shewhart control chart was made. An analytical expression for the process variance, as well as control limits were developed for a particular GMTD model. The ARL was used as a criteria to measure the efficiency of control charts. The comparison was made based on a series generated according to a GMTD model. The results point to the direction that the modified Shewhart GMTD charts have a better performance than the AR(1) Shewhart and the traditional Shewhart.

Estimação e previsão no processo INARCH(2)

In the last decades the study of integer-valued time series has gained notoriety due to its broad applicability (modeling the number of car accidents in a given highway, or the number of people infected by a virus are two examples). One of the main interests of this area of study is to make forecasts, and for this reason it is very important to propose methods to make such forecasts, which consist of nonnegative integer values, due to the discrete nature of the data. In this work, we focus on the study and proposal of forecasts one, two and h steps ahead for integer-valued second-order autoregressive conditional heteroskedasticity processes [INARCH (2)], and in determining some theoretical properties of this model, such as the ordinary moments of its marginal distribution and the asymptotic distribution of its conditional least squares estimators. In addition, we study, via Monte Carlo simulation, the behavior of the estimators for the parameters of INARCH(2) processes obtained using three di erent methods (Yule- Walker, conditional least squares, and conditional maximum likelihood), in terms of mean squared error, mean absolute error and bias. We present some forecast proposals for INARCH(2) processes, which are compared again via Monte Carlo simulation. As an application of this proposed theory, we model a dataset related to the number of live male births of mothers living at Riachuelo city, in the state of Rio Grande do Norte, Brazil.

Estimação e previsão no processo INARCH(2)

In the last decades the study of integer-valued time series has gained notoriety due to its broad applicability (modeling the number of car accidents in a given highway, or the number of people infected by a virus are two examples). One of the main interests of this area of study is to make forecasts, and for this reason it is very important to propose methods to make such forecasts, which consist of nonnegative integer values, due to the discrete nature of the data. In this work, we focus on the study and proposal of forecasts one, two and h steps ahead for integer-valued second-order autoregressive conditional heteroskedasticity processes [INARCH (2)], and in determining some theoretical properties of this model, such as the ordinary moments of its marginal distribution and the asymptotic distribution of its conditional least squares estimators. In addition, we study, via Monte Carlo simulation, the behavior of the estimators for the parameters of INARCH(2) processes obtained using three di erent methods (Yule- Walker, conditional least squares, and conditional maximum likelihood), in terms of mean squared error, mean absolute error and bias. We present some forecast proposals for INARCH(2) processes, which are compared again via Monte Carlo simulation. As an application of this proposed theory, we model a dataset related to the number of live male births of mothers living at Riachuelo city, in the state of Rio Grande do Norte, Brazil.

Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.

Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.

Avaliação e correções de testes de hipóteses em modelos de sobrevivência com fração de cura

Survival models deals with the modelling of time to event data. In certain situations, a share of the population can no longer be subjected to the event occurrence. In this context, the cure fraction models emerged. Among the models that incorporate a fraction of cured one of the most known is the promotion time model. In the present study we discuss hypothesis testing in the promotion time model with Weibull distribution for the failure times of susceptible individuals. Hypothesis testing in this model may be performed based on likelihood ratio, gradient, score or Wald statistics. The critical values are obtained from asymptotic approximations, which may result in size distortions in nite sample sizes. This study proposes bootstrap corrections to the aforementioned tests and Bartlett bootstrap to the likelihood ratio statistic in Weibull promotion time model. Using Monte Carlo simulations we compared the nite sample performances of the proposed corrections in contrast with the usual tests. The numerical evidence favors the proposed corrected tests. At the end of the work an empirical application is presented.

Um estudo sobre polinômios matriciais

This research work aims to make a study of the algebraic theory of matrix monic polynomials, as well as the definitions, concepts and properties with respect to block eigenvalues, block eigenvectors and solvents of P(X). We investigte the main relations between the matrix polynomial and the Companion and Vandermonde matrices. We study the construction of matrix polynomials with certain solvents and the extention of the Power Method, to calculate block eigenvalues and solvents of P(X). Through the relationship between the dominant block eigenvalue of the Companion matrix and the dominant solvent of P(X) it is possible to obtain the convergence of the algorithm for the dominant solvent of the matrix polynomial. We illustrate with numerical examples for diferent cases of convergence.

Modelos flexíveis de sobrevivência com fração de cura: implementação computacional

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

CV-Muzar - Um ambiente de suporte a comunidades virtuais para apoio à aprendizagem em museus

Este artigo tem como objetivo mostrar que é possível incentivar a aprendizagem em museus através da construção de comunidades virtuais, com base em repositórios de objetos de aprendizagem (OA), ferramentas comunicacionais e produção de OA por parte dos visitantes. O enfoque é incentivar a aprendizagem no sentido de motivar a participação/envolvimento do visitante nas atividades da comunidade virtual. Nesta perspectiva, partimos do pressuposto de que a informação, a comunicação, a interação e a colaboração são essenciais para o processo de aprender no contexto informal dos museus. Acreditamos que a interação e a colaboração são partes integrantes do processo de aprendizagem proporcionado por comunidades virtuais e que o principal recurso de aprendizagem oferecido nessas comunidades são os objetos de aprendizagem. Assim sendo, por meio de um entendimento do aprender baseado na comunicação e na linguagem, percebemos os museus interativos como espaços discursivos em que os visitantes mergulham e por eles são modificados. Neste sentido, argumentamos que as comunidades virtuais de aprendizagem, com a possibilidade de virtualizar a linguagem, são excelentes mecanismos para ampliar o poder comunicacional dos museus, criando novas estratégias comunicativas. Para atingir o objetivo, foi necessário reunir quatro conceitos técnicos da área de informática, são eles: comunidades virtuais de aprendizagem; objetos de aprendizagem; metadados e mapas de tópicos. A junção destes conceitos permitiu a construção do ambiente de comunidade virtual, denominada CV-Muzar. Diante do exposto, de modo a identificar os meios pelos quais se podem motivar os visitantes a realmente produzirem novos conhecimentos durante sua visita informal ao museu, examinando essa questão tanto do ponto de vista quantitativo, como também qualitativamente, foi realizada uma experimentação do ambiente com um grupo de pessoas convidadas segundo suas áreas de formação.

Simulación en tiempo acelerado de una red de autobuses metropolitana usando un CAS

Se ha realizado una aplicación para simular en tiempo acelerado una red de autobuses metropolitana y de metro usando un CAS. Con esta aplicación se pretende optimizar estos medios de transporte de forma que el uso de estos sea la primera posibilidad a elegir y no la última alternativa. Esta aplicación permite la representación de cualquier mapa descrito por el usuario, para ello se han desarrollado una serie de algoritmos capaces de representarlos y registrar la información necesaria para el correcto movimiento de los autobuses y del metro. La generación de personas en las paradas de autobuses y metro, modificación del tiempo que se tarda en recorrer la distancia entre dos paradas en función del tráfico que exista y la generación de posibles averías tanto en los autobuses como en los metros se ha realizado usando funciones de distribución como la Exponencial, Poisson y Normal. Estas funciones varían dependiendo de los parámetros que se introduzcan mediante la interfaz de usuario. El CAS encargado de realizar la simulación es Maxima y tanto para la representación gráfica de la simulación como para mostrar los resultados se ha usado JAVA.

Mejoras en los proyectos de simulación de flujo de tráfico en tiempo acelerado

Se han desarrollado cuatro mejoras en los proyectos de simulación de flujo de tráfico en tiempo acelerado. Los proyectos [1] y [2] realizan una simulación de flujo de tráfico en un CAS, Maxima, y usan Java, para realizar la GUI. Ambos usan Jacomax para realizar la comunicación Java-Maxima. La primera ha sido implementar un algoritmo Dijkstra difuso en [2] que simule (de forma más real que el algoritmo Dijkstra), el camino que sigue un vehículo entre un origen y un destino, dentro de un mapa (un grafo) que representa una zona de Málaga. Además, se ha personalizado el grafo inicial asociando uno ponderado a cada vehículo, en el cual, las aristas (las calles) tienen un peso calculado con una uniforme o una normal. Para ganar en rendimiento en [1] y [2], se ha permitido al usuario decidir cada cuantos pasos en Maxima se comunica con Java, eliminando así muchas comunicaciones que resultaban lentas. Además, se ha creado un programa con Java, el cual crea un paquete Maxima con las funciones de distribución, densidad, masa, variables aleatorias, que el usuario desee, dando la posibilidad de elegir entre las más usuales ya implementadas. Este paquete puede ser cargado en [1] y [2] permitiendo al usuario elegir la función de distribución que más se asemeje al fenómeno que se desea simular. La última ha sido conseguir que funcionen los proyectos [1] y [2] en una máquina Mac.

Aplicación de modelos multivariantes en la construcción de indicadores sintéticos de calidad ambiental para zonas urbanas de El Salvador

Uno de los actuales retos en nuestro país es la generación de información estadísticas relevante y oportuna para la toma de decisiones de las políticas públicas. Los indicadores estadísticos, constituyen una de las herramientas indispensables para el logro de estas acciones, y una de las tareas para la Dirección General de Estadísticas y Censos (DIGESTYC) y el Ministerio de Medio Ambiente y Recursos Naturales (MARN) es fomentar la cultura estadística para su correcto uso y aplicación. Es importante conocer lo que son los indicadores, sus características, utilidad, tipos y limitaciones para, enmarcar la importancia que tienen y los retos que imponen a los generadores de estadísticas del país

Comparación entre el análisis discriminante y la regresión logística en la clasificación de una colonia de cangrejos herradura (Limulus polyphemus)

El problema planteado en este trabajo consiste en estudiar la efectividad de clasificación entre los métodos “Análisis Discriminante”, que consiste en ubicar a los individuos en una determinada población con base a características medibles y observadas en los individuos; y la “Regresión Logística”, que se utiliza para estimar las probabilidades de que un individuo pertenezca a un determinado grupo dado que las características del individuo han tomado ciertos valores concretos. El objetivo fundamental de este trabajo es ver la efectividad de los métodos “Análisis Discriminante” y la “Regresión Logística” clasificando el cangrejo herradura hembra con o sin individuos satélites, partiendo de características como el peso, el ancho de caparazón, el color y el estado de las espinas del cangrejo herradura hembra.

O problema da supressão na protecção de informação confidencial: formalizações e algoritmos.

Doutoramento em Matemática Aplicada à Economia e à Gestão.