Relatórios de Pesquisa

12/2010 Range Control Charts Revisited: Simpler Tippett-like Formulae, It´s Practical Implementation and the Study of False Alarm
Emanuel P. Barbosa, Mario A. Gneri, Ariane Meneguetti

This paper presents simpler alternative formulae and procedures of implementation to deal with the relative range statistic (moments, distribution and quantiles) used in the construction of range control charts for process dispersion monitoring. The Tippett's integral formulae for sample relative range moments and distribution are revisited and simpler new alternative expressions are proposed together with an easy computational implementation procedure based on it's relation with the Tukey maximum studentized range statistic. Also, such proposed methods are applied in the assessment of the range chart performance considering false alarm comparison between exact control limits charts versus normal approximated versions (3-sigma Shewhart procedure), which show the serious drawbacks of such misplaced control limits. These much simple tools introduced here, we believe, will permit the presentation of R control charts more transparently and without unrealistic normal approximations or blind dependence on tables, avoiding the serious limitations of such \ad hoc" practice.

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11/2010 Average Sex Ratio and Population Maintenance Cost
Eduardo Garibaldi, Marcelo Sobottka

The ratio of males to females in a population is a meaningful characteristic of sexual species. The reason for this biological property be available to the observers of nature seems to be a question never asked. Introducing the notion of historically adapted populations as global minimizers of maintenance cost functions, we propose a theoretical explanation for the reported stability of this feature. This mathematical formulation suggests that sex ratio could be considered as an indirect result shaped by the antagonism between the size of the population and the finiteness of resources.

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10/2010 Global Behavior of the Ricci Flow on Homogeneous Manifolds with Two Isotropy Summands
Lino Grama, Ricardo M. Martins

In this paper we study the global behavior of the Ricci flow equation for two classes of homogeneous manifolds with two isotropy summands. Using methods of the qualitative theory of differential equations, we present the global phase portrait of such systems and derive some geometrical consequences on the structure of such manifolds under the action of the Ricci flow.

9/2010 Quadrados Mínimos Não-Lineares e Aplicações em Deformação de Objetos 2D
Matheus Souza, Maria A. Diniz-Ehrhardt

Nonlinear least squares problems arise in many applications, especially in curve fitting, but they may occur in a more general case as a overdetermined system of nonlinear equations. To solve these problems we use the Gauss{Newton Method, analysing not only its theoretical properties but also its computational performance. We apply these concepts to the study of 2D-Shape Deformation problems.

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8/2010 A Genetic Algorithm for Optimization Over a Simplex
Carlos H. Dias, Francisco A. M. Gomes Neto

Several combinatorial optimization problems require the minimization of a function over the standard n-dimensional simplex x1 +x2 +. . .+xn, x ≥ 0. Due to the high complexity of these problems, it is a common practice to solve them using metaheuristics, such as evolutionary algorithms. In this paper, we present a genetic algorithm based on a new chromosome representation that allows the direct generation of feasible solutions. With this representation, the solution space is discretized into hypercubes, and each hypercube is associated to an unique integer number that is stored in binary form to simplify the definition of the crossover and mutation operators. As an example, we use our approach to find the efficient frontier of some cardinality constrained portfolio optimization problems. Our experiments show that the new representation gives better results than the chromosomes built using the Cartesian coordinates on Rn.

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7/2010 An SLP Algorithm for Topology Optimization
Francisco A. M. Gomes Neto, T. A. Senne

Topology optimization problems, in general, and compliant mechanism design problems, in particular, are engineering applications that rely on nonlinear programming algorithms. Since these problems are usually huge, methods that do not require information about second derivatives are generally used for their solution. The most widely used of such methods are some variants of the method of moving asymptotes (MMA), proposed by Svanberg (1987), and sequential linear programming (SLP). Although showing a good performance in practice, most of the SLP algorithms used in topology optimization lack a global convergence theory. This paper introduces a globally convergent SLP method for nonlinear programming. The algorithm is applied to the solution of classic compliance minimization problems, as well as to the design of compliant mechanisms. Our numerical results suggest that the new algorithm is faster than the globally convergent version of the MMA method.

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6/2010 Cálculo Diferencial e Integral para funções fuzzy via extensão dos operadores de derivação e integração
Laécio C. Barros, Pedro Aladar Tonelli, Arthur Pires Julião

Na literatura há várias propostas de integração/derivação para a teoria de Cálculo Diferencial e Integral de funções fuzzy. Todas elas têm a preocupação de estender a teoria clássica de cálculo para funções reais. Nesse trabalho introduzimos novos conceitos para os operadores Integral e Diferencial a partir do Princípio de Extensão de Zadeh. Para isso, alguns espaços de funções fuzzy são definidos e estudos de inclusão entre eles são feitos. Nossa principal conclusão é que, sob algumas condições, os conceitos introduzidos aqui produzem a mesma teoria feita por Hüllermeier [14] para Equações Diferenciais Fuzzy (EDF). Ao contrário de Hüllermeier, que utiliza apenas o conceito de derivada parafunções clássicas, nós propomos o estudo de EDF a partir de derivada para funções fuzzy.

5/2010 On the Hamiltonian Structure of Normal Forms at Elliptic Equilibria of Reversible Vector Fields in $R^4$
Jeroen S. W. Lamb, Mauricio F. S. Lima, Ricardo M. Martins, Marco A. Teixeira, Jiazhong Yang

This paper addresses the question whether normal forms of smooth reversible vector fields in $R^4$ at an elliptic equilibrium possess a formal Hamiltonian structure. In the non-resonant case we establish a formal conjugacy between reversible and Hamiltonian normal forms. In the case of non-semisimple 1 : 1 resonance we establish a weaker form of equivalence, namely that of a formal orbital equivalence to a Hamiltonian normal form that involves an additional time-reparametrization of orbits.

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4/2010 On Estimation and Influence Diagnostics for Zero-Inflated Negative Binomial Regression Models
Aldo M. Garay, E. M. Hashimoto, E. M. M. Ortega, Víctor H. Lachos

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-inflated Poisson model. We consider a frequentist analysis, a jackknife estimator and non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models. In addition, an EM-type algorithm is developed to perform maximumlikelihood estimation. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform globalinfluence analysis. In order to study departures from the error assumption as well as the presence of outliers, we perform residual analysis based on the standardized Pearson residuals. The relevanceof the approach is illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data changes.

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3/2010 Statistical Diagnostics for Nonlinear Regression Models Based on Scale Mixtures of Skew-Normal Distributions
Aldo M. Garay, Filidor E. Vilca-Labra, Víctor H. Lachos

The purpose of this paper is to develop diagnostics analysis for nonlinear regression models under scale mixtures of skew-normal distributions (Branco and Dey, 2001). This novel class of models provides a useful generalization of the symmetrical nonlinear regression models (Vanegas and Cysneiros, 2010) since the random terms distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. The main virtue of considering the nonlinear regression model under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows an easy implementation of inference procedures. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented and the observed information matrix is derived analytically. We discuss a score test for testing the homogeneity of the scale parameter and its properties are investigated through Monte Carlo simulations. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. The newly developed procedures are illustrated considering a real data previously analyzed under normal and skew-normal nonlinear regression models.

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