Research Reports

18/2003 A SLLN for random closed sets
M. D. Jiménez-Gamero, Marko A. Rojas-Medar, Yurilev Chalco-Cano, M. D. Cubiles-de-la-Vega

In this paper we establish a strong law of large numbers for independent and identically nonempty random closed sets in Rp.


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17/2003 Analysis of Variance for Binary Data in Unbalanced Designs
Roberta de Souza, Hildete P. Pinheiro, Cibele Q. da Silva, Sérgio F. dos Reis

In the study of genetic divergence among organisms, generally the analysis is done directly from the DNA molecule. Therefore, a possible outcome is binary (dominant or recessive phenotype). Comparison of groups of molecular data is a great interest in molecular genetics and evolutionary biology. Some work have been done on analysis of variance for genetic data (Weir, 1990; Pinheiro et al., 2000; Pinheiro et al., 2001; Pinheiro et al., 2002 and others). Weir (1990) proposed a genetic diversity measure, the heterozygosity, and developed an analysis of variance for binary data in a balanced design.Here, we extend the work of Weir developing an analysis of variance for binary data with the purpose of comparing groups in unbalanced designs. In order to test the null hypothesis of homogeneity among groups, the asymptotic distribution of the test statistic was found. An application of the test to real data is illustrated using resampling methods such as the bootstrap to generate the empirical distribution of the test statistics.


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16/2003 A Bidimensional Phase-Field Model with Convection for ChangePhase of an Alloy
Gabriela Planas, José Luiz Boldrini

The article analyzes a two-dimensional phase-field model for a non-stationary process of solidification of a binary alloy with thermal properties. The model allows the occurrence of fluid flow in non-solid regions, which are a priori unknown, and is thusassociated to a free boundary value problem for a highly non-linear system of partial differential equations. These equations are the phase-field equation, the heat equation, the concentration equation and a modified Navier-Stokes equations obtained by the addition of a penalization term of Carman-Kozeny type, which accounts for the mushy effects, and also of a Boussinesq term to take in care of the effects of variations of temperature and concentration in the flow. A proof of existence of weak solutions for such system is given. The problem is firstly approximated and a sequence of approximate solutions is obtained by Leray-Schauder fixed point theorem. A solution is then found by using compactness argument.


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15/2003 Neale A. El-Dash, Luiz K. Hotta, Non-parametric Volatility Estimation in Continuous Time
Aluísio Pinheiro

The idea of volatility is fundamental to precise definition of risk and, hence, its estimation (or prediction) is a very important task in finance applications. We present some ideas on nonparamateric estimation of volatility function in diffusion models. A nonlinear wavelet estimate of the volatiltiy function is proposed and its performance is compared to three kernel estimators in both simulated and real data. Simulation is developed for eight volatility shapes and some interesting, but not unexpected, results are presented. Some issues such as online estimation and prediction, robustness to oversmoothing and performance under sudden changes in pattern of volatility are also discussed.


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14/2003 Dirac Equation in Riemannian Manifolds: An Explicit Analytical Solution in AdS(1, 2) Spacetime
R. Rocha Jr., Edmundo Capelas de Oliveira

We present and discuss the covariant spin-connection Dirac equation in riemannian manifolds. As a particular case we present the Anti-de Sitter n-spacetime, [AdS(n)], which is, together with the de Sitter and Minkowski, the most maximallysymmetric space with positive cosmological constant $\Lambda$. Some asymptotic properties are also discussed. We parameterize AdS(1,2) manifold with cartesian coordinates associated to tangent spaces and introduce the conformal time. After constructing a suitable 2-dimensional Dirac gamma matrices representation, we can separate the Dirac equation and solve it, obtaining a hypergeometric equation. We obtain the Dirac spinor in AdS(1,2) spacetime explicitly, as $\lambda_x$-periodic function of space and a hypergeometric function of time and the radius of AdS(1,2) spacetime.


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13/2003 Time Series Modeling and Forecasting With Feedforward Neural Networks: A Comparative Study Using the Resex Data
Silvia Joekes, Emanuel P. Barbosa

It is considered in this paper the modeling and forecasting, through feedforward neural networks, of a time series previouslystudied in the literature (Brubacher, 1974; Martin, 1980; Stahlbut, 1985; Allende, 1989) called RESEX series, which presentsseasonality and outliers. Some elements of the network architecture such as the input variables definition are suggestedby a previous time series analysis and other elements such as the number of intermediate layers and corresponding knots are defined through numerical methods. Not only traditional backpropagation based algorithms are used but also a robust learning algorithm is considered in order to deal more properly with the outliers. All models and methods (traditional and NN based) are then compared considering different predictive performance measures and theresults are discussed.


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12/2003 Sobre uma classe de integrais reais
Edmundo Capelas de Oliveira, Ary O. Chiacchio
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11/2003 Covering space for monotonic homotopy of trajectories of control systems
Fritz Colonius, Eyüp Kizil, Luiz A. B. San Martin

This paper considers monotonic (or causal) homotopy between trajectories of control systems. The main result is the construction of an analogue of the simply connected covering space. The constructed covering $\Gamma(\Sigma, x)$ has the structure of a manifold and satisfies the property that two trajectories are monotonic homotopic if and only if the end points of their liftings coincide.


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10/2003 Local Influence in Null Intercept Measurement Error Regression under a Student_t Model
Filidor E. Vilca-Labra, Reiko Aoki, Heleno Bolfarine

In this paper we discuss the application of local influence in measurement error regression model with null intercepts under a Student_t model with dependent populations. The Student_t distribution is a robust alternative to modeling data sets involving errors with longer than Normal tails. We derive the appropriate matrices for assessing the local influence for different perturbation schemes and use a real data as an illustration of the usefulness of the application.


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9/2003 Equação diferencial com parâmetro fuzzy
Yurilev Chalco-Cano, Marina T. Mizukoshi, Laécio C. Barros, Rodney C. Bassanezi
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