Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

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.

Tori embedded in S³ with dense asymptotic lines

In this paper are given examples of tori T² embedded in S³ with all their asymptotic lines dense.

Notificação imprecisa da ingestão energética na dieta de adolescentes

Objetivos: Examinar a prevalência da sub e supernotificação da ingestão energética em adolescentes e seus fatores associados. Métodos: Estudo transversal com 96 adolescentes na pós-puberdade (47 com peso normal e 49 obesos), com idade média de 16,6±1,3 anos. Peso e altura foram medidos e o índice de massa corporal foi calculado. A composição corporal foi avaliada através de absorciometria por raios X de dupla energia. A ingestão de alimentos foi avaliada por meio de um registro alimentar de 3 dias. Realizou-se uma avaliação bioquímica (níveis séricos de colesterol total, LDL, HDL, glicose plasmática e insulina). Os subnotificadores relataram uma ingestão energética < 1,35 x taxa metabólica basal (TMB), enquanto os supernotificadores relataram uma ingestão energética > 2,4 x TMB. Resultados: Notificação imprecisa (sub ou supernotificação) da ingestão energética foi identificada em 65,6 por cento dos adolescentes (64,6 e 1 por cento de sub e supernotificação, respectivamente). Os adolescentes obesos apresentaram 5.0 vezes mais chances de subnotificar a ingestão energética (IC95 por cento 2,0-12,7) do que os participantes com peso normal. Os subnotificadores apresentaram taxas mais altas de ingestão insuficiente de carboidratos (19,3 versus 12,1 por cento, p = 0,046) e de lipídios (11,3 versus 0 por cento, p < 0,001) do que os notificadores plausíveis. A ingestão de colesterol também foi mais baixa entre os subnotificadores (p = 0,017). Não houve diferenças significativas na composição corporal e nos parâmetros bioquímicos em relação à notificação imprecisa. Conclusões: Os resultados obtidos demonstraram alta porcentagem de notificação imprecisa da ingestão energética entre adolescentes, principalmente entre os obesos, o que sugere que os valores de consumo de nutrientes ajustado para o consumo de energia deveriam ser empregados na análise de risco da relação dieta-doença a fim de contribuir para a redução de erros associados à notificação imprecisa

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Influence of a light meal on routine haematological tests

Introduction Patient-related variables such as physical exercise stress and fasting status are Important sources of variability in laboratory testing However no clear indications about tasting requirements exist for routine haematological tests nor has the influence of meals been assessed Methods We studied 17 healthy volunteers who consumed a light meal containing a standardized amount of carbohydrates, protein and lipids Blood was taken for routine haematological tests before the meal and 1 2 and 4 hours thereafter Results One hour after the meal neutrophil count and mean corpuscular haemoglobin (MHC) increased significantly whereas lymphocyte and monocyte counts red blood cell distribution width, haematocrit, and mean corpuscular volume decreased significantly A clinically significant variation was only observed for lymphocytes Two hours after the meal a significant increase was observed for neutrophils and MCH whereas lymphocytes eosinophils, haemoglobin and haematocrit decreased significantly Clinically significant variations were recorded for lymphocytes red blood cells (RBC), haemoglobin haematocrit and MCH Four hours after the meal MCH was significantly increased while lymphocytes eosinophils, RBC, haemoglobin and haematocrit were significantly decreased Clinically significant variations were recorded for neutrophils eosinophils RBC hematocrit and MCH Conclusion The significant variation of several haematological parameters after a light meal demonstrates that the fasting time needs to be carefully considered in order to interpret the results of haematological tests correctly

A frequency approach to identifying asteroid families II. Families interacting with nonlinear secular resonances and low-order mean-motion resonances

Aims. In an earlier paper we introduced a new method for determining asteroid families where families were identified in the proper frequency domain (n, g, g + s) ( where n is the mean-motion, and g and s are the secular frequencies of the longitude of pericenter and nodes, respectively), rather than in the proper element domain (a, e, sin(i)) (semi-major axis, eccentricity, and inclination). Here we improve our techniques for reliably identifying members of families that interact with nonlinear secular resonances of argument other than g or g + s and for asteroids near or in mean-motion resonant configurations. Methods. We introduce several new distance metrics in the frequency space optimal for determining the diffusion in secular resonances of argument 2g - s, 3g - s, g - s, s, and 2s. We also regularize the dependence of the g frequency as a function of the n frequency (Vesta family) or of the eccentricity e (Hansa family). Results. Our new approaches allow us to recognize as family members objects that were lost with previous methods, while keeping the advantages of the Carruba & Michtchenko (2007, A& A, 475, 1145) approach. More important, an analysis in the frequency domain permits a deeper understanding of the dynamical evolution of asteroid families not always obtainable with an analysis in the proper element domain.

Recovery of the star formation history of the LMC from the VISTA survey of the Magellanic system

The VISTA near infrared survey of the Magellanic System (VMC) will provide deep YJK(s) photometry reaching stars in the oldest turn-off point throughout the Magellanic Clouds (MCs). As part of the preparation for the survey, we aim to access the accuracy in the star formation history (SFH) that can be expected from VMC data, in particular for the Large Magellanic Cloud (LMC). To this aim, we first simulate VMC images containing not only the LMC stellar populations but also the foreground Milky Way (MW) stars and background galaxies. The simulations cover the whole range of density of LMC field stars. We then perform aperture photometry over these simulated images, access the expected levels of photometric errors and incompleteness, and apply the classical technique of SFH-recovery based on the reconstruction of colour-magnitude diagrams (CMD) via the minimisation of a chi-squared-like statistics. We verify that the foreground MW stars are accurately recovered by the minimisation algorithms, whereas the background galaxies can be largely eliminated from the CMD analysis due to their particular colours and morphologies. We then evaluate the expected errors in the recovered star formation rate as a function of stellar age, SFR(t), starting from models with a known age-metallicity relation (AMR). It turns out that, for a given sky area, the random errors for ages older than similar to 0.4 Gyr seem to be independent of the crowding. This can be explained by a counterbalancing effect between the loss of stars from a decrease in the completeness and the gain of stars from an increase in the stellar density. For a spatial resolution of similar to 0.1 deg(2), the random errors in SFR(t) will be below 20% for this wide range of ages. On the other hand, due to the lower stellar statistics for stars younger than similar to 0.4 Gyr, the outer LMC regions will require larger areas to achieve the same level of accuracy in the SFR( t). If we consider the AMR as unknown, the SFH-recovery algorithm is able to accurately recover the input AMR, at the price of an increase of random errors in the SFR(t) by a factor of about 2.5. Experiments of SFH-recovery performed for varying distance modulus and reddening indicate that these parameters can be determined with (relative) accuracies of Delta(m-M)(0) similar to 0.02 mag and Delta E(B-V) similar to 0.01 mag, for each individual field over the LMC. The propagation of these errors in the SFR(t) implies systematic errors below 30%. This level of accuracy in the SFR(t) can reveal significant imprints in the dynamical evolution of this unique and nearby stellar system, as well as possible signatures of the past interaction between the MCs and the MW.

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.

Energy gain induced by boundary crisis

We consider a nonlinear system and show the unexpected and surprising result that, even for high dissipation, the mean energy of a particle can attain higher values than when there is no dissipation in the system. We reconsider the time-dependent annular billiard in the presence of inelastic collisions with the boundaries. For some magnitudes of dissipation, we observe the phenomenon of boundary crisis, which drives the particles to an asymptotic attractive fixed point located at a value of energy that is higher than the mean energy of the nondissipative case and so much higher than the mean energy just before the crisis. We should emphasize that the unexpected results presented here reveal the importance of a nonlinear dynamics analysis to explain the paradoxical strategy of introducing dissipation in the system in order to gain energy.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Knowledge acquisition by networks of interacting agents in the presence of observation errors

In this work we investigate knowledge acquisition as performed by multiple agents interacting as they infer, under the presence of observation errors, respective models of a complex system. We focus the specific case in which, at each time step, each agent takes into account its current observation as well as the average of the models of its neighbors. The agents are connected by a network of interaction of Erdos-Renyi or Barabasi-Albert type. First, we investigate situations in which one of the agents has a different probability of observation error (higher or lower). It is shown that the influence of this special agent over the quality of the models inferred by the rest of the network can be substantial, varying linearly with the respective degree of the agent with different estimation error. In case the degree of this agent is taken as a respective fitness parameter, the effect of the different estimation error is even more pronounced, becoming superlinear. To complement our analysis, we provide the analytical solution of the overall performance of the system. We also investigate the knowledge acquisition dynamic when the agents are grouped into communities. We verify that the inclusion of edges between agents (within a community) having higher probability of observation error promotes the loss of quality in the estimation of the agents in the other communities.

The impact of measurement errors in the identification of regulatory networks

Background: There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise. Results: This article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data. Conclusions: Measurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.

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.

Antimicrobial drug administration errors identified in Brazilian multicentric study

Medication administration errors (MAE) are the most frequent kind of medication errors. Errors with antimicrobial drugs (AD) are relevant because they may interfere inpatient safety and in the development of microbial resistance. The aim of this study is to analyze the AD errors detected in a Brazilian multicentric study of MAE. It was a devcriptive and explorotory study carried out in clinical units in five Brazilian teaching hospitals. The hospitals were investigated during 30 days. MAE were detected by observation technique. MAE were classified in categories: wrong route(WR), wrong patient(WP), wrong dose(WD) wrong time (WT) and unordered drug (UD). AD with MA E were classified by Anatomical-Therapeutical-Chemical Classification System. AD with narrow therapeutic index (NTI) wet-e identified A descriptive statistical analysis was performed using SPSS version 11.5 software. A total of 1500 errors were observed, 277 (18.5%) of them were error with AD. The hopes of AD error were: WT87.7%, QD 6.9%, WR 1.5%, UD 3.2% and WP 0.7%. The number of AD found was 36. The mostly ATC class were fluoroquinolones 13.9%, combinations of penicillin 13.9%, macrolides 8.3% and third-generation cephalosporines 5.6%. The parenteral drug dosage form was associated with 55.6% of AD. 16.7% of AD were NTI. 47.4% of WD and 21.8% WT were with NTI drugs. This study shows that these errors should be considered potential areas for improvement in the medication process and patient safety plus there is requirement to develop rational drug use of AD.