On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Effects of acute physical exercise on executive functions: a comparison between aerobic and strength exercise

The aim of this study was to compare the effects of acute aerobic and strength exercises on selected executive functions. A counterbalanced, crossover, randomized trial was performed. Forty-two healthy women were randomly submitted to three different conditions: (1) aerobic exercise, (2) strength exercise, and (3) control condition. Before and after each condition, executive functions were measured by the Stroop Test and the Trail Making Test. Following the aerobic and strength sessions, the time to complete the Stroop "non-color word" and "color word" condition was lower when compared with that of the control session. The performance in the Trail Making Test was unchanged. In conclusion, both acute aerobic and strength exercises improve the executive functions. Nevertheless, this positive effect seems to be task and executive function dependent.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Genetic analysis of kernel oil content in tropical maize with design III and QTL mapping

Oil content and grain yield in maize are negatively correlated, and so far the development of high-oil high-yielding hybrids has not been accomplished. Then a fully understand of the inheritance of the kernel oil content is necessary to implement a breeding program to improve both traits simultaneously. Conventional and molecular marker analyses of the design III were carried out from a reference population developed from two tropical inbred lines divergent for kernel oil content. The results showed that additive variance was quite larger than the dominance variance, and the heritability coefficient was very high. Sixteen QTL were mapped, they were not evenly distributed along the chromosomes, and accounted for 30.91% of the genetic variance. The average level of dominance computed from both conventional and QTL analysis was partial dominance. The overall results indicated that the additive effects were more important than the dominance effects, the latter were not unidirectional and then heterosis could not be exploited in crosses. Most of the favorable alleles of the QTL were in the high-oil parental inbred, which could be transferred to other inbreds via marker-assisted backcross selection. Our results coupled with reported information indicated that the development of high-oil hybrids with acceptable yields could be accomplished by using marker-assisted selection involving oil content, grain yield and its components. Finally, to exploit the xenia effect to increase even more the oil content, these hybrids should be used in the Top Cross((TM)) procedure.

On S-asymptotically omega-periodic functions and applications

Let (X, parallel to . parallel to) be a Banach space and omega is an element of R. A bounded function u is an element of C([0, infinity); X) is called S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. In this paper, we establish conditions under which an S-asymptotically omega-periodic function is asymptotically omega-periodic and we discuss the existence of S-asymptotically omega-periodic and asymptotically omega-periodic solutions for an abstract integral equation. Some applications to partial differential equations and partial integro-differential equations are considered. (C) 2011 Elsevier Ltd. All rights reserved.

Kurzweil integral for Riesz space-valued functions: Uniform convergence theorem

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both in finite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

Identification of novel components of NAD-utilizing metabolic pathways and prediction of their biochemical functions

Nicotinamide adenine dinucleotide (NAD) is a ubiquitous cofactor participating in numerous redox reactions. It is also a substrate for regulatory modifications of proteins and nucleic acids via the addition of ADP-ribose moieties or removal of acyl groups by transfer to ADP-ribose. In this study, we use in-depth sequence, structure and genomic context analysis to uncover new enzymes and substrate-binding proteins in NAD-utilizing metabolic and macromolecular modification systems. We predict that Escherichia coli YbiA and related families of domains from diverse bacteria, eukaryotes, large DNA viruses and single strand RNA viruses are previously unrecognized components of NAD-utilizing pathways that probably operate on ADP-ribose derivatives. Using contextual analysis we show that some of these proteins potentially act in RNA repair, where NAD is used to remove 2'-3' cyclic phosphodiester linkages. Likewise, we predict that another family of YbiA-related enzymes is likely to comprise a novel NAD-dependent ADP-ribosylation system for proteins, in conjunction with a previously unrecognized ADP-ribosyltransferase. A similar ADP-ribosyltransferase is also coupled with MACRO or ADP-ribosylglycohydrolase domain proteins in other related systems, suggesting that all these novel systems are likely to comprise pairs of ADP-ribosylation and ribosylglycohydrolase enzymes analogous to the DraG-DraT system, and a novel group of bacterial polymorphic toxins. We present evidence that some of these coupled ADP-ribosyltransferases/ribosylglycohydrolases are likely to regulate certain restriction modification enzymes in bacteria. The ADP-ribosyltransferases found in these, the bacterial polymorphic toxin and host-directed toxin systems of bacteria such as Waddlia also throw light on the evolution of this fold and the origin of eukaryotic polyADP-ribosyltransferases and NEURL4-like ARTs, which might be involved in centrosomal assembly. We also infer a novel biosynthetic pathway that might be involved in the synthesis of a nicotinate-derived compound in conjunction with an asparagine synthetase and AMPylating peptide ligase. We use the data derived from this analysis to understand the origin and early evolutionary trajectories of key NAD-utilizing enzymes and present targets for future biochemical investigations.

Alteration of distortion product otoacoustic emission input/output functions in subjects with a previous history of middle ear dysfunction

Background: The aim of this study was to investigate the effects of sub-clinical alterations on the amplitudes and slopes of the DPOAE input-output responses from subjects with previous history of middle ear dysfunction. Material/Methods: The study included 15 subjects with and 15 subjects without a history of otitis media in the last 10 years. All participants were assessed with acoustic immittance, pure-tone audiometry, and DPOAEs. For the later, I/O functions and I/O slopes were estimated at 1501, 2002, 3174, 4004 and 6384Hz. Results: No statistically significant differences were found between the 2 groups in terms of behavioral thresholds. The group with a previous history of middle ear dysfunction presented significantly lower mean DPOAE amplitudes at 2002, 3174 and 4004 Hz. In terms of DPOAE slopes, no statistically significant differences were observed at the tested frequencies, except at 3174 Hz. Conclusions: Middle ear pathologies can produce subclinical alterations that are undetectable with traditional pure-tone audiometry. The data from the present study show that reduced amplitude DPOAEs are associated with a previous history of middle ear complications. The corresponding DPOAE slopes were affected at only 1 tested frequency, suggesting that the cochlear non-linearity is preserved. Considering these results, it remains to be elucidated to what degree the DPOAE amplitude attenuation interferes with higher-order auditory tasks.

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Longitudinal familial analysis of blood pressure involving parametric (co)variance functions

Abstract Background For analyzing longitudinal familial data we adopted a log-linear form to incorporate heterogeneity in genetic variance components over the time, and additionally a serial correlation term in the genetic effects at different levels of ages. Due to the availability of multiple measures on the same individual, we permitted environmental correlations that may change across time. Results Systolic blood pressure from family members from the first and second cohort was used in the current analysis. Measures of subjects receiving hypertension treatment were set as censored values and they were corrected. An initial check of the variance and covariance functions proposed for analyzing longitudinal familial data, using empirical semi-variogram plots, indicated that the observed trait dispersion pattern follows the assumptions adopted. Conclusion The corrections for censored phenotypes based on ordinary linear models may be an appropriate simple model to correct the data, ensuring that the original variability in the data was retained. In addition, empirical semi-variogram plots are useful for diagnosis of the (co)variance model adopted.

Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order q − 2, with respect to both z and 'Z BARRA'. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z ∈ C: |z| < 1} up to the same order.

Reconstruction of spatiotemporal capture data by means of orthogonal functions: the case of skipjack tuna (Katsuwonus pelamis) in the central-east Atlantic

[EN] The information provided by the International Commission for the Conservation of Atlantic Tunas (ICCAT) on captures of skipjack tuna (Katsuwonus pelamis) in the central-east Atlantic has a number of limitations, such as gaps in the statistics for certain fleets and the level of spatiotemporal detail at which catches are reported. As a result, the quality of these data and their effectiveness for providing management advice is limited. In order to reconstruct missing spatiotemporal data of catches, the present study uses Data INterpolating Empirical Orthogonal Functions (DINEOF), a technique for missing data reconstruction, applied here for the first time to fisheries data. DINEOF is based on an Empirical Orthogonal Functions decomposition performed with a Lanczos method. DINEOF was tested with different amounts of missing data, intentionally removing values from 3.4% to 95.2% of data loss, and then compared with the same data set with no missing data. These validation analyses show that DINEOF is a reliable methodological approach of data reconstruction for the purposes of fishery management advice, even when the amount of missing data is very high.