Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic gamma : [0, 1] -> M joining p and U whose endpoints are conjugate along gamma. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

A matrix formula for the skewness of maximum likelihood estimators

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model. (c) 2010 Elsevier B.V. All rights reserved.

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

INSECT CHYMOTRYPSINS: CHLOROMETHYL KETONE INACTIVATION AND SUBSTRATE SPECIFICITY RELATIVE TO POSSIBLE COEVOLUTIONAL ADAPTATION OF INSECTS AND PLANTS

Insect digestive chymotrypsins are present in a large variety of insect orders but their substrate specificity still remains unclear. Ewer insect chymotrypsins from 3 different insect orders (Dictyoptera, Coleoptera and two Lepidoptera) were isolated using affinity chromatography. Enzymes presented molecular masses in the range of 20 to 31 kDa and pH optima in the range of 7.5 to 10.0. Kinetic characterization. using different, colorimetric and fluorescent substrates indicated that insect chymotrypsins differ from, bovine chymotrypsin in their primary specificity toward small substrates (like N-benzoyl-L-Tyr p-nitroanilide) rather than on their preference for large substrates (exemplified by Succynil-Ala-Ala-Pro-Phe P-nitroanilide). Chloromethyl ketones (TPCK, N-alpha-tosyl-L-Phe chloromethyl ketone and Z-GGF-CK, N-carbobenzoxy-Gly-Gly-phe-CK) inactivated all chymotrypsins legated. Inactivation rates follow apparent first-order kinetics with variable second order rates (TPCK, 42 to 130 M(-1)s(-1); Z-GGF-CK, 150 to 450 M(-1)s(-1) that may be remarkably low for S. frugiperda chymotrypsin (TPCK, 6 M(-1)s(-1); Z-GGF-CK, 6.1 M(-1) s(-1)). Homology modelling and sequence alignment showed that. in lepidopteran chymotrypsins, differences in the amino acid residues in the neighborhood of the catalytic His 57 may affect its pKa, value. This is Proposed as the cause of the decrease in His 57 reactivity toward chloromethyl ketones. Such amino acid replacement in the active site is proposed. to be an adaptation to the presence of dietary ketones. (C) 2009 Wiley Periodicals, Inc.

Inhibition of myeloperoxidase-mediated protein nitration by tempol: Kinetics, mechanism, and implications

Despite the therapeutic potential of tempol (4-hydroxy-2,2,6,6-tetra-methyl-1-piperidinyloxy) and related nitroxides as antioxidants, their effects on peroxidase-mediated protein tyrosine nitration remain unexplored. This posttranslational protein modification is a biomarker of nitric oxide-derived oxidants, and, relevantly, it parallels tissue injury in animal models of inflammation and is attenuated by tempol treatment. Here, we examine tempol effects on ribonuclease (RNase) nitration mediated by myeloperoxidase (MPO), a mammalian enzyme that plays a central role in various inflammatory processes.. Some experiments were also performed with horseradish peroxidase (HRP). We show that tempol efficiently inhibits peroxidase-mediated RNase nitration. For instance, 10 mu M tempol was able to inhibit by 90% the yield of 290 mu M 3-nitrotyrosine produced from 370 mu M RNase. The effect of tempol was not completely catalytic because part of it was consumed by recombination with RNase-tyrosyl radicals. The second-order rate constant of the reaction of tempol with MPO compound I and 11 were determined by stopped-flow kinetics as 3.3 x 10(6) and 2.6 x 10(4) M-1 s(-1), respectively (pH 7.4, 25 degrees C); the corresponding HRP constants were orders of magnitude smaller. Time-dependent hydrogen peroxide and nitrite consumption and oxygen production in the incubations were quantified experimentally and modeled by kinetic simulations. The results indicate that tempol inhibits peroxidase-mediated RNase nitration mainly because of its reaction with nitrogen dioxide to produce the oxammonium cation, which, in turn, recycles back to tempol by reacting with hydrogen peroxide and superoxide radical to produce oxygen and regenerate nitrite. The implications for nitroxide antioxidant mechanisms are discussed.

Horseradish peroxidase compound I as a tool to investigate reactive protein-cysteine residues: from quantification to kinetics

Proteins containing reactive cysteine residues (protein-Cys) are receiving increased attention as mediators of hydrogen peroxide signaling. These proteins are mainly identified by mining the thiol proteomes of oxidized protein-Cys in cells and tissues. However, it is difficult to determine if oxidation occurs through a direct reaction with hydrogen peroxide or by thiol-disulfide exchange reactions. Kinetic studies with purified proteins provide invaluable information about the reactivity of protein-Cys residues with hydrogen peroxide. Previously, we showed that the characteristic UV-Vis spectrum of horseradish peroxidase compound I, produced from the oxidation of horseradish peroxidase by hydrogen peroxide, is a simple, reliable, and useful tool to determine the second-order rate constant of the reaction of reactive protein-Cys with hydrogen peroxide and peroxynitrite. Here, the method is fully described and extended to quantify reactive protein-Cys residues and micromolar concentrations of hydrogen peroxide. Members of the peroxiredoxin family were selected for the demonstration and validation of this methodology. In particular, we determined the pK(a) of the peroxidatic thiol of rPrx6 (5.2) and the second-order rate constant of its reactions with hydrogen peroxide ((3.4 +/- 0.2) x 10(7) M(-1) s(-1)) and peroxynitrite ((3.7 +/- 0.4) x 10(5) M(-1) s(-1)) at pH 7.4 and 25 degrees C. (C) 2011 Elsevier Inc. All rights reserved.

Polymethine cyanine dyes in beta-cyclodextrin solution: multiple equilibria and chemical oxidation

Absorption and fluorescence spectroscopy, electrochemical techniques, and semiempirical calculations were employed to characterize the multiple complexation equilibria between two polymethine cyanine dyes (IR-786 and Indocyanine green-ICG, 5) and beta-cyclodextrin (beta-CD, L), as well as the chemical reactivity of the complexed and uncomplexed species against the oxidizing agents hypochlorite (HC) and hydrogen peroxide (HP). IR-786 dimerization is favored with the increase in beta-CD concentration in the form of (SL)(2) complexes. In the case of ICG, free dimers (D) and SL complexes are favored. Both IR-786 and ICG react and discolor in the presence of HC and HP. For IR-786, the reaction with HP and HC proceeds with observed rate constants of 10(-3) and 0.28 s(-1) and second-order rate constants (k(2)) of similar to 10(-3) and 10(4) M(-1) s(-1), respectively. The intermediate species observed in the bleaching reactions of IR-786 and ICG were shown, by cyclic voltammetry and VIS absorption, to result from one electron oxidation. IR-786 complexed with beta-CD is protected against bleaching in the presence of HP and HC by factors of 20 and 4, respectively. This protection was not observed in ICG complexes. Superdelocalizability profile of both dyes and frontier orbital analysis indicates that beta-CD does not protect ICG from oxidation by HP or HC, whereas the 2:2 IR-786/beta-Cd complex is able to avoid the oxidation of IR-786. We concluded that the decrease in the chemical reactivity of the dyes against oxidant agents in the presence of beta-CD is due to the formation of (SL)(2) complexes. Copyright (C) 2010 John Wiley & Sons, Ltd.

Electronic Structure of the Ground and Low-Lying Electronic States of MoB and MoB(+)

Multiconfigurational second-order perturbation theory (CASSCF//CASPT2) and quadruple-zeta ANO-RCC basis sets were employed to investigate the ground and low-lying electronic states of MoB and MoB(+). Spectroscopic constants, potential energy curves, wavefunctions, Mulliken population analyses, and ionization energies are given. The ground state of MoB is of X(6)Pi symmetry (R(e) = 1.968 angstrom, omega(e) = 664 cm(-1), and mu = 2.7 D), giving rise to a Omega = 7/2 ground state after including spin-orbit coupling. For MoB(+), the ground state is computed to be of X(7)Sigma(+) symmetry (R(e) = 2.224 angstrom, omega(e) = 141 cm(-1), and mu = 1.2 D), with an adiabatic ionization energy of 7.19 eV and a vertical one of 7.53 eV. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 3362-3370, 2011

Degradation and adsorption of AZO RR239 dye in aqueous solution by nanoscale zerovalent iron particles immobilized on sawdust

Carra sawdust pretrated with formaldehyde was used to adsorb RR239 (reactive azo dye) at varying pH and zerovalent iron (ZVI) dosage. Modeling of kinetic results shows that sorption process is best described by the pseudo-second-order model. Batch experiments suggest that the decolorization efficiency was strongly enhanced with the presence of ZVI and low solution pH. The kinetics of dye sorption by mixed sorbent (5 g of sawdust and 180 mg of ZVI) at pH 2.0 was rapid, reaching more than 90% of the total discoloration in three minutes.

Electronic Structure and Chemical Bonding in the Lowest Electronic States of TcN

Multiconfiguration second-order perturbation theory, with the inclusion of relativistic effects and spin-orbit Coupling, was employed to investigate the nature of the ground and low-lying Lambda-S and Omega states of the TcN molecule. Spectroscopic constants, effective bond order, and potential energy curves for 13 low-lying Lambda-S states and 5 Omega states are given, The computed ground state of TcN is of Omega = 3 symmetry (R(e) = 1.605 angstrom and omega(e) = 1085 cm(-1)), originating mainly from the (3)Delta Lambda-S ground state. This result is contrasted with the nature of the ground state for other VIIB transtion-metal mononitrides, including X(3)Sigma(-) symmetry for MnN and Omega = 0(+) symmetry for ReN, derived also from a X(3)Sigma(-) state.