Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

Allocation of protective devices in distribution circuits using nonlinear programming models and genetic algorithms

The optimized allocation of protective devices in strategic points of the circuit improves the quality of the energy supply and the system reliability index. This paper presents a nonlinear integer programming (NLIP) model with binary variables, to deal with the problem of protective device allocation in the main feeder and all branches of an overhead distribution circuit, to improve the reliability index and to provide customers with service of high quality and reliability. The constraints considered in the problem take into account technical and economical limitations, such as coordination problems of serial protective devices, available equipment, the importance of the feeder and the circuit topology. The use of genetic algorithms (GAs) is proposed to solve this problem, using a binary representation that does (1) or does not (0) show allocation of protective devices (reclosers, sectionalizers and fuses) in predefined points of the circuit. Results are presented for a real circuit (134 busses), with the possibility of protective device allocation in 29 points. Also the ability of the algorithm in finding good solutions while improving significantly the indicators of reliability is shown. (C) 2003 Elsevier B.V. All rights reserved.

Robust State-Derivative Feedback LMI-Based Designs for Linear Descriptor Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comparison among three approaches for evaluation of sexual precocity in Nellore cattle

Restricted breeding seasons used in beef cattle produce censored data for reproduction traits measured in regard to these seasons. To analyze these data, adequate methods must be used. The objective of this paper was to compare three approaches aiming to evaluate sexual precocity in Nellore cattle. The final data set contained 6699 records of age at first conception (AFC14) (in days) and of heifer pregnancy (HP14) (binary) obtained from females exposed to the bulls for the first time at about 14 months of age. Records of females that did not calve in the following year after being exposed to a sire were considered censored (77.5% of total). The models used to obtain genetic parameters and expected progeny differences (EPDs) were a Weibull mixed and a censored linear model for AFC14 and threshold model for HP14. The mean heritabilities obtained were 0.76 and 0.44, respectively, for survival and censored linear models (for AFC14), and 0.58 for HP14. Ranking and Pearson correlations varied (in absolute values) from 0.54 to 0.99 (considering different percentages of sires selected), indicating moderate changes in the classification. Considering survival analysis as the best selection criterion (that would result in the best response to selection), it was observed that selection for HP14 would lead to a more significant decrease in selection response if compared with selection for AFC14 analysed by censored linear model, from which results were very similar to the survival analysis.

A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Two-component gap solitons with linear interconversion

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mixing, demixing, and structure formation in a binary dipolar Bose-Einstein condensate

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Relação entre modelos de programação não-linear com incerteza no conjunto de restrições

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Procedimento MIXED do SAS® para análise de modelos mistos

O modelo misto consiste numa importante classe de modelos que tem sido tradicionalmente analisada por meio de procedimentos da análise de variância. Nos modelos mistos, três aspectos são fundamentais: estimação e testes de hipóteses dos efeitos fixos, predição dos efeitos aleatórios e estimação dos componentes de variância. Na análise de modelos lineares mistos desbalanceados, a estimação dos componentes de variância é de fundamental importância e depende da estrutura de covariâncias e dos métodos de estimação utilizados. Nesse contexto, este artigo pretende apresentar os principais métodos de estimação e de análise utilizados no estudo de modelos lineares mistos com estruturas gerais de covariâncias nos efeitos aleatórios, disponíveis no procedimento MIXED, do SAS (Statistical Analysis System).

The symmetry group of Z(q)(n) in the Lee space and the Z(qn)-linear codes

The Z(4)-linearity is a construction technique of good binary codes. Motivated by this property, we address the problem of extending the Z(4)-linearity to Z(q)n-linearity. In this direction, we consider the n-dimensional Lee space of order q, that is, (Z(q)(n), d(L)), as one of the most interesting spaces for coding applications. We establish the symmetry group of Z(q)(n) for any n and q by determining its isometries. We also show that there is no cyclic subgroup of order q(n) in Gamma(Z(q)(n)) acting transitively in Z(q)(n). Therefore, there exists no Z(q)n-linear code with respect to the cyclic subgroup.

Mixed micelles of the anionic surfactant sodium dodecyl sulfate and the nonionic pentaethylene glycol mono-n-dodecyl ether in solution

Dynamic light scattering, surface tension, and clouding temperature have been monitored to elucidate the solution properties of mixed micelles formed between the anionic surfactant sodium dodecyl sulfate (SDS) and the nonionic surfactant pentaethylene glycol mono-n-dodecyl ether (C12E5) over a wide range of surfactant concentration and temperature. Addition of 0.1 M NaCl shifts the relaxational modes to higher frequency and lowers the clouding temperature (T-c) of the nonionic surfactant solution by about 1 degrees C compared to the salt-free system. T-c for the mixed surfactant solutions is higher than that of the binary C12E5 solutions and depends sensitively on the concentration of the two surfactants but increases only slightly when the total surfactant concentration is increased at a given molar C12E5/SDS concentration ratio. With C12E5/SDS = 5.7, for example, T-c is 46.0 and 47.5 degrees C, respectively, at 5 and 70 mM of C12E5 the mixed solutions are homogeneous and stable and contain nonspherical micelles, which are close to monodisperse over a range of surfactant concentrations and temperature. The mixed system has a lower Krafft point than binary SDS solutions and shows an approximately ideal behavior in contrast to the binary C12E5 solution. The hydrodynamic radius (RH) of the mixed micelle increases with temperature as do C12E5 micelles in the binary solutions and also with increasing C12E5/SDS ratio. At 25 degrees C, the critical micelle concentration of the mixed solution lies between those of the individual surfactants and decreases as the C12E5/SDS ratio is increased.

Synthesis and properties of branched polyethylene/high-density polyethylene blends using a homogeneous binary catalyst system composed of early and late transition metal complexes

Branched polyethylene/high-density polyethylene blends (BPE/HDPE) with a wide range of molecular weights, melt flow indexes (MFI), and intrinsic viscosity were prepared using the homogeneous binary catalyst system composed by Ni(alpha-diimine)Cl-2 (1) (alpha-diimine = 1,4-bis(2,6-diisopropylphenyl)-acenaphthenediimine) and {Tp(Ms*)} TiCl3 (2) (Tp(Ms*)=hydridobis(3-mesitylpyrazol-1-yl)(5-mesityl-pyrazol-1-yl)) activated with MAO and/or TIBA in hexane at two different polymerization temperatures (30 and 55 degreesC) and by varying the nickel loading molar fraction (x(Ni)). At all Temperatures, a non-linear correlation between the x(Ni) and the productivity was observed, suggesting the occurrence of a synergistic effect between the nickel and the titanium catalyst precursors, which is more pronounced at 55 degreesC. The molecular weight of the BPE/HDPE blends considerably decreases with increasing Al/M molar ratio. The melt flow indexes (MFI) and intrinsic viscosities (eta) are strongly affected by x(Ni), but the melting temperatures are nearly constant, 132 +/- 3 degreesC. Dynamic mechanical thermal analysis (DMTA) shows the formation of different polymeric materials where the stiffness vanes according, to the x(Ni) and temperature used in the polymerization reaction. The surface morphology of the BPE/HDPE blends studied by scanning electron microscopy (SEM) revealed a low miscibility between the PE phases resulting in the formation of a sandwich structure after etching with o-xylene.

Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Robust state-derivative feedback LMI-based designs for multivariable linear systems

In some practical problems, for instance in the control systems for the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. New necessary and sufficient linear matrix inequalities (LMI) conditions for the design of state-derivative feedback for multi-input (MI) linear systems are proposed. For multi-input/multi-output (MIMO) linear time-invariant or time-varying plants, with or without uncertainties in their parameters, the proposed methods can include in the LMI-based control designs the specifications of the decay rate, bounds on the output peak, and bounds on the state-derivative feedback matrix K. These design procedures allow new specifications and also, they consider a broader class of plants than the related results available in the literature. The LMIs, when feasible, can be efficiently solved using convex programming techniques. Practical applications illustrate the efficiency of the proposed methods.