Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

An improved strategy for evaluating the extent of chronic arterial baroreceptor denervation in conscious rats

There is no index or criterion of aortic barodenervation, nor can we differentiate among rats that have suffered chronic sham, aortic or sino-aortic denervation. The objective of this study was to develop a procedure to generate at least one quantitative, reproducible and validated index that precisely evaluates the extent of chronic arterial barodenervation performed in conscious rats. Data from 79 conscious male Wistar rats of about 65-70 days of age with diverse extents of chronic arterial barodenervation and used in previous experiments were reanalyzed. The mean arterial pressure (MAP) and the heart rate (HR) of all rats were measured systematically before (over 1 h) and after three consecutive iv bolus injections of phenylephrine (PHE) and sodium nitroprusside (SNP). Four expressions of the effectiveness of barodenervation (MAP lability, PHE ratio, SNP ratio, and SNP-PHE slope) were assessed with linear fixed models, three-level average variance, average separation among levels, outlier box plot analysis, and overlapping graphic analysis. The analysis indicated that a) neither MAP lability nor SNP-PHE slope was affected by the level of chronic sodium intake; b) even though the Box-Cox transformations of both MAP lability [transformed lability index (TLI)] and SNP-PHE slope [transformed general sensitivity index (TGSI), {((3-(ΔHRSNP-ΔHRPHE/ΔMAPSNP-ΔMAPPHE))-0.4-1)/-0.04597}] could be two promising indexes, TGSI proved to be the best index; c) TLI and TGSI were not freely interchangeable indexes for this purpose. TGSI ranges that permit differentiation between sham (10.09 to 11.46), aortic (8.40 to 9.94) and sino-aortic (7.68 to 8.24) barodenervated conscious rats were defined.

Genetic heterogeneity of within-family variance of body weight in Atlantic salmon (Salmo salar)

BACKGROUND: Canalization is defined as the stability of a genotype against minor variations in both environment and genetics. Genetic variation in degree of canalization causes heterogeneity of within-family variance. The aims of this study are twofold: (1) quantify genetic heterogeneity of (within-family) residual variance in Atlantic salmon and (2) test whether the observed heterogeneity of (within-family) residual variance can be explained by simple scaling effects. RESULTS: Analysis of body weight in Atlantic salmon using a double hierarchical generalized linear model (DHGLM) revealed substantial heterogeneity of within-family variance. The 95% prediction interval for within-family variance ranged from ~0.4 to 1.2 kg2, implying that the within-family variance of the most extreme high families is expected to be approximately three times larger than the extreme low families. For cross-sectional data, DHGLM with an animal mean sub-model resulted in severe bias, while a corresponding sire-dam model was appropriate. Heterogeneity of variance was not sensitive to Box-Cox transformations of phenotypes, which implies that heterogeneity of variance exists beyond what would be expected from simple scaling effects. CONCLUSIONS: Substantial heterogeneity of within-family variance was found for body weight in Atlantic salmon. A tendency towards higher variance with higher means (scaling effects) was observed, but heterogeneity of within-family variance existed beyond what could be explained by simple scaling effects. For cross-sectional data, using the animal mean sub-model in the DHGLM resulted in biased estimates of variance components, which differed substantially both from a standard linear mean animal model and a sire-dam DHGLM model. Although genetic differences in canalization were observed, selection for increased canalization is difficult, because there is limited individual information for the variance sub-model, especially when based on cross-sectional data. Furthermore, potential macro-environmental changes (diet, climatic region, etc.) may make genetic heterogeneity of variance a less stable trait over time and space.

Análise Bayesiana de dados composicionais na presença de covariáveis

Pós-graduação em Matematica Aplicada e Computacional - FCT

Robust automatic mapping algorithms in a network monitoring scenario

Automatically generating maps of a measured variable of interest can be problematic. In this work we focus on the monitoring network context where observations are collected and reported by a network of sensors, and are then transformed into interpolated maps for use in decision making. Using traditional geostatistical methods, estimating the covariance structure of data collected in an emergency situation can be difficult. Variogram determination, whether by method-of-moment estimators or by maximum likelihood, is very sensitive to extreme values. Even when a monitoring network is in a routine mode of operation, sensors can sporadically malfunction and report extreme values. If this extreme data destabilises the model, causing the covariance structure of the observed data to be incorrectly estimated, the generated maps will be of little value, and the uncertainty estimates in particular will be misleading. Marchant and Lark [2007] propose a REML estimator for the covariance, which is shown to work on small data sets with a manual selection of the damping parameter in the robust likelihood. We show how this can be extended to allow treatment of large data sets together with an automated approach to all parameter estimation. The projected process kriging framework of Ingram et al. [2007] is extended to allow the use of robust likelihood functions, including the two component Gaussian and the Huber function. We show how our algorithm is further refined to reduce the computational complexity while at the same time minimising any loss of information. To show the benefits of this method, we use data collected from radiation monitoring networks across Europe. We compare our results to those obtained from traditional kriging methodologies and include comparisons with Box-Cox transformations of the data. We discuss the issue of whether to treat or ignore extreme values, making the distinction between the robust methods which ignore outliers and transformation methods which treat them as part of the (transformed) process. Using a case study, based on an extreme radiological events over a large area, we show how radiation data collected from monitoring networks can be analysed automatically and then used to generate reliable maps to inform decision making. We show the limitations of the methods and discuss potential extensions to remedy these.

Power transformations in correspondence analysis

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.

Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

Tomato Flower Abnormalities Induced by Low Temperatures Are Associated with Changes of Expression of MADS-Box Genes1

Flower and fruit development in tomato (Lycopersicon esculentum Mill.) were severely affected when plants were grown at low temperatures, displaying homeotic and meristic transformations and alterations in the fusion pattern of the organs. Most of these homeotic transformations modified the identity of stamens and carpels, giving rise to intermediate organs. Complete homeotic transformations were rarely found and always affected organs of the reproductive whorls. Meristic transformations were also commonly observed in the reproductive whorls, which developed with an excessive number of organs. Scanning electron microscopy revealed that meristic transformations take place very early in the development of the flower and are related to a significant increase in the floral meristem size. However, homeotic transformations should occur later during the development of the organ primordia. Steady-state levels of transcripts corresponding to tomato MADS-box genes TM4, TM5, TM6, and TAG1 were greatly increased by low temperatures and could be related to these flower abnormalities. Moreover, in situ hybridization analyses showed that low temperatures also altered the stage-specific expression of TM4.

AFFINE INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS AND WANDERING INTERVALS

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips which have wandering intervals and are such that the support of the invariant measure is a Cantor set.

CMB in a box: Causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility gamma = e(-mu), where mu is the optical depth to Thomson scattering. We show that the contributions of order gamma(N) to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z >> 10(3), effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position (x) over right arrow = 0 and time t(0). Hence, for each multipole l there is a discrete tower of momenta k(il) (not a continuum) which can affect physical observables, with the smallest momenta being k(1l) similar to l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation-no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

Chaotic communication based on the particle-in-a-box electronic circuit

A secure communication system based on the error-feedback synchronization of the electronic model of the particle-in-a-box system is proposed. This circuit allows a robust and simple electronic emulation of the mechanical behavior of the collisions of a particle inside a box, exhibiting rich chaotic behavior. The required nonlinearity to emulate the box walls is implemented in a simple way when compared with other analog electronic chaotic circuits. A master/slave synchronization of two circuits exhibiting a rich chaotic behavior demonstrates the potentiality of this system to secure communication. In this system, binary data stream information modulates the bifurcation parameter of the particle-in-a-box electronic circuit in the transmitter. In the receiver circuit, this parameter is estimated using Pecora-Carroll synchronization and error-feedback synchronization. The performance of the demodulation process is verified through the eye pattern technique applied on the recovered bit stream. During the demodulation process, the error-feedback synchronization presented better performance compared with the Pecora-Carroll synchronization. The application of the particle-in-a-box electronic circuit in a secure communication system is demonstrated.

Universal Set-top Box: A Simple Design to Provide Accessible Services

This paper presents the design of a low cost accessible digital television set-top box. This set-top box was designed and tested to the International ISDB-T system and considered the adoption of solutions that would provide accessible services in digital television in the simplest digital television receiver. The accessible set-top box was evaluated regarding the processing and memory requirements impacts to provide the features for accessible services. The work presents also the access services bandwidth consumption analysis(1).

Nitrogen, phosphorus and potassium dose effect in the graft box of lemon tree (of the family Rutaceae) nutrition and production.

Nitrogen, phosphorus and potassium dose effect in the graft box of lemon tree (of the family Rutaceae) nutrition and production. The aim of the study was to evaluate the graft box of lemon tree (of the family Rutaceae) nutritional state and its components of growth in function of nitrogen, phosphorus and potassium dose by fertilization. The experimental outlining was entirely made casually in factorial scheme 3(3) + 1, being 3 factors (nitrogen, phosphorus and potassium - NPK), 3 doses and in evidence (without fertilization), with 3 repetitions. The experimental milt was constituted by two tubes of 2,8 cm diameter and 12,3 cm high with a graft box (Hipobioto) of lemon tree (of the family Rutaceae) in each tube. The doses used were constituted by doses of N (460; 920 e 18,10 mg dm(-3)), P (50; 100 e 200 mg dm(-3)) and K (395; 790 e 1580 mg dm(-3)). The fertilization with N and K was carried out by fertirrigations and the P added to the substract of Pinus rind and vermiculite before the seeding. when the plants were 133 days after the germination they were subdivided in radicular system and air part for the determinations of the dry matter mass, height, foliar area, stem diameter and contents of nutrients. The N, K and P doses of 920 mg dm(-3), 790 mg dm(-3), 100 mg dm(-3), respectively, were enough for the suitable development of the graft box of lemon tree (of the family Rutaceae) in tubes.