On the asymptotic enumeration of accessible automata

We simplify the known formula for the asymptotic estimate of the number of deterministic and accessible automata with n states over a k-letter alphabet. The proof relies on the theory of Lagrange inversion applied in the context of generalized binomial series.

Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations

We consider the two-dimensional Navier-Stokes equations with a time-delayed convective term and a forcing term which contains some hereditary features. Some results on existence and uniqueness of solutions are established. We discuss the asymptotic behaviour of solutions and we also show the exponential stability of stationary solutions.

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Missing data mechanisms and their implications on the analysis of categorical data

We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

A semi-Markov multistate model for estimation of the mean quality-adjusted survival for non-progressive processes

We discuss the estimation of the expected value of the quality-adjusted survival, based on multistate models. We generalize an earlier work, considering the sojourn times in health states are not identically distributed, for a given vector of covariates. Approaches based on semiparametric and parametric (exponential and Weibull distributions) methodologies are considered. A simulation study is conducted to evaluate the performance of the proposed estimator and the jackknife resampling method is used to estimate the variance of such estimator. An application to a real data set is also included.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Asymptotic Skewness in Exponential Family Nonlinear Models

In this article, we give an asymptotic formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in exponencial family nonlinear models. We generalize the result by Cordeiro and Cordeiro ( 2001). The formula is given in matrix notation and is very suitable for computer implementation and to obtain closed form expressions for a great variety of models. Some special cases and two applications are discussed.

Medidas de associação em estudo transversal com delineamento complexo: razão de chances e razão de prevalência

O objetivo deste estudo foi apresentar e discutir a utilização das medidas de associação: razão de chances e razão de prevalências, em dados obtidos de estudo transversal realizado em 2001-2002, utilizando-se amostra estratificada por conglomerados em dois estágios (n=1.958). As razões de chances e razões de prevalências foram estimadas por meio de regressão logística não condicional e regressão de Poisson, respectivamente, utilizando-se o pacote estatístico Stata 7.0. Intervalos de confiança e efeitos do desenho foram considerados na avaliação da precisão das estimativas. Dois desfechos do estudo transversal com diferentes níveis de prevalência foram avaliados: vacinação contra influenza (66,1%) e doença pulmonar referida (6,9%). Na situação em que a prevalência foi alta, as estimativas das razões de prevalência foram mais conservadoras com intervalos de confiança menores. Na avaliação do desfecho de baixa prevalência, não se observaram grandes diferenças numéricas entre as estimações das razões de chances e razões de prevalência e erros-padrão obtidos por uma ou outra técnica. O efeito do desenho maior que a unidade indicou que a amostragem complexa, em ambos os casos, aumentou da variância das estimativas. Cabe ao pesquisador a escolha da técnica e do estimador mais adequado ao seu objeto de estudo, permanecendo a escolha no âmbito epidemiológico.

Parâmetros genéticos para idade ao primeiro parto estimados por diferentes modelos para rebanhos da raça Nelore

Com objetivo de estimar parâmetros genéticos e estudar a utilização de diferentes efeitos em avaliações genéticas para idade ao primeiro parto (IPP) por diferentes modelos, foram utilizados registros de IPP de animais da raça Nelore, nascidos entre os anos de 1990 e 2005. Foram considerados os seguintes modelos (M): M1, incluindo o efeito fixo de GC1 (constituído pelos animais nascidos na mesma fazenda e ano), além da covariável, peso aos 365 dias de idade (efeito linear e quadrático), totalizando 24.263 registros de IPP; M2, considerando os efeitos fixos de GC1, ano e estação de parição, totalizando 59.792 registros de IPP e M3, incluindo os efeitos fixos de GC2 (agrupando os animais nascidos na mesma fazenda, ano e que conceberam no mesmo manejo reprodutivo), ano e estação de parição, totalizando 59.792 registros de IPP. As estimativas dos componentes de variância e herdabilidade e os valores genéticos (VG) foram obtidos pelo método da máxima verossimilhança restrita, com a inclusão da matriz de parentesco disponível. As diferenças esperadas na progênie (DEPs) foram obtidas dividindo os VG por dois. Após a obtenção desses resultados, foram realizadas correlações entre os VG e o ranqueamento das DEPs dos reprodutores para IPP, utilizando-se o procedimento PROC CORR (SAS, 2003). Ao se considerar o ano e a estação de parto nos modelos de análise (M2 e M3), esses produziram um maior R², indicando que tais modelos conseguiram explicar, em maior grau, as diferenças existentes entre os animais para IPP. As herdabilidades estimadas foram de baixa magnitude (0,14 e 0,15). As correlações entre os VG obtidas por diferentes modelos foram 0,73 (M1 x M2); 0,91 (M2 x M3) e 0,66 (M1 x M3).

Performance of young male swimmers in the 100-meters front crawl

Youth swimming performance may be influenced by anthropometric, physiology and technical factors. The present paper examined the role of these factors in performance of 100m freestyle in swimmers 12-14 years of age (n = 24). Multiple regression analysis (forward method) was used to examine the variance of the 100 meters front crawl. Anaerobic power, swimming index and critical speed explained 88% (p < .05) of the variance in the average speed of 100 meters front crawl among young male pubertal swimmers. To conclude, performance of young swimmers in the 100 meters front crawl is determined predominantly by physiological factors and swimming technique.

Viability of fibroblasts cultured under nutritional stress irradiated with red laser, infrared laser, and red light-emitting diode

Phototherapy is noninvasive, painless and has no known side effect. However, for its incorporation into clinical practice, more well-designed studies are necessary to define optimal parameters for its application. The viability of fibroblasts cultured under nutritional stress irradiated with either a red laser, an infrared laser, or a red light-emitting diode (LED) was analyzed. Irradiation parameters were: red laser (660 nm, 40 mW, 1 W/cm(2)), infrared laser (780 nm, 40 mW, 1 W/cm(2)), and red LED (637 +/- 15 nm, 40 mW, 1 W/cm(2)). All applications were punctual and performed with a spot with 0.4 mm(2) of diameter for 4 or 8 s. The Kruskal-Wallis test and analysis of variance of the general linear model (p <= 0.05) were used for statistical analysis. After 72 h, phototherapy with low-intensity laser and LED showed no toxicity at the cellular level. It even stimulated methylthiazol tetrazolium assay (MTT) conversion and neutral red uptake of fibroblasts cultured under nutritional stress, especially in the group irradiated with infrared laser (p = 0.004 for MTT conversion and p < 0.001 for neutral red uptake). Considering the parameters and protocol of phototherapy used, it can be concluded that phototherapy stimulated the viability of fibroblasts cultured under nutritional deficit resembling those found in traumatized tissue in which cell viability is reduced. (C) 2011 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.3602850]

The number of reproductive workers in highly eusocial Hymenoptera: monogyny and monandry

Haplodiploidy results in relatedness asymmetries between colony members of highly eusocial Hymenoptera. As a consequence, queen and reproductive workers are more related to their own sons than to each other's male offspring. Kin selection theory predicts multiple optima in male parentage: either the queen or the workers should produce all the males. Nevertheless, shared male parentage is common in highly eusocial hymenopterans. An inclusive fitness model was used to analyze the effect of the number of reproductive workers on male parentage shared by the queen and laying workers by isolating the male component from an inclusive fitness equation using the equal fitness through male condition for each pairwise combination of the three female classes comprised of the queen, laying workers and non-laying workers. The main result of the theoretical analyses showed that the fraction of males produced by workers increases asymptotically with the number of laying workers at an increasingly diminishing rate, tending to an asymptotic value of 0.67. In addition, as the number of laying workers increases, the share of male parentage converges to that of non-laying workers. The diminishing return effect on male parentage share depending on the number of reproductive workers leads us to expect the number of reproductive workers to be relatively small in a stingless bee colony, even in the absence of productivity costs. The available data confirms this hypothesis, as there is an unusually small number of reproductive workers in stingless bee colonies.

Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.