Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

Changes in music tempo entrain movement related brain activity

The neural mechanisms of music listening and appreciation are not yet completely understood. Based on the apparent relationship between the beats per minute (tempo) of music and the desire to move (for example feet tapping) induced while listening to that music it is hypothesised that musical tempo may evoke movement related activity in the brain. Participants are instructed to listen, without moving, to a large range of musical pieces spanning a range of styles and tempos during an electroencephalogram (EEG) experiment. Event-related desynchronisation (ERD) in the EEG is observed to correlate significantly with the variance of the tempo of the musical stimuli. This suggests that the dynamics of the beat of the music may induce movement related brain activity in the motor cortex. Furthermore, significant correlations are observed between EEG activity in the alpha band over the motor cortex and the bandpower of the music in the same frequency band over time. This relationship is observed to correlate with the strength of the ERD, suggesting entrainment of motor cortical activity relates to increased ERD strength

Resonant Wave Interactions in the Equatorial Waveguide

Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial beta-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface-gravity waves in deep water and capillary-gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby-gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(epsilon) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

Autolytic Mycobacterium leprae Hsp65 fragments may act as biological markers for autoimmune diseases

Investigating the proteolytic activity of the recombinant Mycobacterium leprae Heat Shock Protein of 65 kDa (rHsp65), chaperonin 2 (cpn2), we observed that it displays high instability. The fragmentation process starts at the C-terminus followed by progressive degradation of the N-terminus, which leads to a stable fragment comprising the middle region of the molecule. Urea was able to prevent autolysis, probably due to its denaturing action, while EDTA increased degradation levels indicating the need for metal ions. Peptides originated from autolysis were purified and analyzed by mass spectrometry, generating a continuous map. Since the bacteria and mammalian Hsp60 are known to be targets of the immune response and have been implicated in autoimmune diseases and chronic inflammation, the in vivo effect of rHsp65 peptides was evaluated in the spontaneous Systemic Lupus Erythematosus (SLE) model developed by the (NZB/NZW)F(1) mouse hybrids, and their individual anti-rHsp65 IgG2a/IgG1 antibody titer ratio was determined. The results showed orientation toward a T(H)1 responsiveness, and the treatment with the rHsp65 peptides diminished the environmental variance of the survival time of treated animals. These results outline the fact that environmental factors may also act through the modified stability expression of Heat Shock Proteins intervening during autoimmune processes. (C) 2011 Elsevier Ltd. All rights reserved.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved.

Inference From Aging Information

For many learning tasks the duration of the data collection can be greater than the time scale for changes of the underlying data distribution. The question we ask is how to include the information that data are aging. Ad hoc methods to achieve this include the use of validity windows that prevent the learning machine from making inferences based on old data. This introduces the problem of how to define the size of validity windows. In this brief, a new adaptive Bayesian inspired algorithm is presented for learning drifting concepts. It uses the analogy of validity windows in an adaptive Bayesian way to incorporate changes in the data distribution over time. We apply a theoretical approach based on information geometry to the classification problem and measure its performance in simulations. The uncertainty about the appropriate size of the memory windows is dealt with in a Bayesian manner by integrating over the distribution of the adaptive window size. Thus, the posterior distribution of the weights may develop algebraic tails. The learning algorithm results from tracking the mean and variance of the posterior distribution of the weights. It was found that the algebraic tails of this posterior distribution give the learning algorithm the ability to cope with an evolving environment by permitting the escape from local traps.

Residual-based test for Nonlinear Cointegration with application in PPPs

Nested by linear cointegration first provided in Granger (1981), the definition of nonlinear cointegration is presented in this paper. Sequentially, a nonlinear cointegrated economic system is introduced. What we mainly study is testing no nonlinear cointegration against nonlinear cointegration by residual-based test, which is ready for detecting stochastic trend in nonlinear autoregression models. We construct cointegrating regression along with smooth transition components from smooth transition autoregression model. Some properties are analyzed and discussed during the estimation procedure for cointegrating regression, including description of transition variable. Autoregression of order one is considered as the model of estimated residuals for residual-based test, from which the teststatistic is obtained. Critical values and asymptotic distribution of the test statistic that we request for different cointegrating regressions with different sample sizes are derived based on Monte Carlo simulation. The proposed theoretical methods and models are illustrated by an empirical example, comparing the results with linear cointegration application in Hamilton (1994). It is concluded that there exists nonlinear cointegration in our system in the final results.

Testing linear cointegration against smooth-transition cointegration

This paper studies a smooth-transition (ST) type cointegration. The proposed ST cointegration allows for regime switching structure in a cointegrated system. It nests the linear cointegration developed by Engle and Granger (1987) and the threshold cointegration studied by Balke and Fomby (1997). We develop F-type tests to examine linear cointegration against ST cointegration in ST-type cointegrating regression models with or without time trends. The null asymptotic distributions of the tests are derived with stationary transition variables in ST cointegrating regression models. And it is shown that our tests have nonstandard limiting distributions expressed in terms of standard Brownian motion when regressors are pure random walks, while have standard asymptotic distributions when regressors contain random walks with nonzero drift. Finite-sample distributions of those tests are studied by Monto Carlo simulations. The small-sample performance of the tests states that our F-type tests have a better power when the system contains ST cointegration than when the system is linearly cointegrated. An empirical example for the purchasing power parity (PPP) data (monthly US dollar, Italy lira and dollar-lira exchange rate from 1973:01 to 1989:10) is illustrated by applying the testing procedures in this paper. It is found that there is no linear cointegration in the system, but there exits the ST-type cointegration in the PPP data.

Testing Seasonal Unit Roots in Data at Any Frequency, an HEGY approach

This paper generalizes the HEGY-type test to detect seasonal unit roots in data at any frequency, based on the seasonal unit root tests in univariate time series by Hylleberg, Engle, Granger and Yoo (1990). We introduce the seasonal unit roots at first, and then derive the mechanism of the HEGY-type test for data with any frequency. Thereafter we provide the asymptotic distributions of our test statistics when different test regressions are employed. We find that the F-statistics for testing conjugation unit roots have the same asymptotic distributions. Then we compute the finite-sample and asymptotic critical values for daily and hourly data by a Monte Carlo method. The power and size properties of our test for hourly data is investigated, and we find that including lag augmentations in auxiliary regression without lag elimination have the smallest size distortion and tests with seasonal dummies included in auxiliary regression have more power than the tests without seasonal dummies. At last we apply the our test to hourly wind power production data in Sweden and shows there are no seasonal unit roots in the series.

The relationship between muscle size and bone geometry during growth and in response to exercise

As muscles become larger and stronger during growth and in response to increased loading, bones should adapt by adding mass, size, and strength. In this unilateral model, we tested the hypothesis that (1) the relationship between muscle size and bone mass and geometry (nonplaying arm) would not change during different stages of puberty and (2) exercise would not alter the relationship between muscle and bone, that is, additional loading would result in a similar unit increment in both muscle and bone mass, bone size, and bending strength during growth. We studied 47 competitive female tennis players aged 8–17 years. Total, cortical, and medullary cross-sectional areas, muscle area, and the polar second moment of area (Ip) were calculated in the playing and nonplaying arms using magnetic resonance imaging (MRI); BMC was assessed by DXA. Growth effects: In the nonplaying arm in pre-, peri- and post-pubertal players, muscle area was linearly associated BMC, total and cortical area, and Ip (r = 0.56–0.81, P < 0.09 to < 0.001), independent of age. No detectable differences were found between pubertal groups for the slope of the relationship between muscle and bone traits. Post-pubertal players, however, had a higher BMC and cortical area relative to muscle area (i.e., higher intercept) than pre- and peri-pubertal players (P < 0.05 to < 0.01), independent of age; pre- and peri-pubertal players had a greater medullary area relative to muscle area than post-pubertal players (P < 0.05 to < 0.01). Exercise effects: Comparison of the side-to-side differences revealed that muscle and bone traits were 6–13% greater in the playing arm in pre-pubertal players, and did not increase with advancing maturation. In all players, the percent (and absolute) side-to-side differences in muscle area were positively correlated with the percent (and absolute) differences in BMC, total and cortical area, and Ip (r = 0.36–0.40, P < 0.05 to < 0.001). However, the side-to-side differences in muscle area only accounted for 11.8–15.9% of the variance of the differences in bone mass, bone size, and bending strength. This suggests that other factors associated with loading distinct from muscle size itself contributed to the bones adaptive response during growth. Therefore, the unifying hypothesis that larger muscles induced by exercise led to a proportional increase in bone mass, bone size, and bending strength appears to be simplistic and denies the influence of other factors in the development of bone mass and bone shape.

Explaining gay men's unrealistic optimism about becoming infected with HIV

Among the self-justifications that gay men use when deciding to have unprotected intercourse is the thought that they are at less risk than most gay men. Two explanatory models of such 'unrealistic optimism' (UO) have been proposed: while the motivational account holds that UO serves the function of bringing comfort, the cognitive account holds that UO serves no particular function, being simply a by-product of normal cognitive strategies. This study tested the prediction, derived from the motivational account, that highlighting the salience of the self-other comparison should increase UO. Gay men uninfected with HIV (n = 122) estimated both their own risk of contracting various health problems - among them, becoming infected with HIV - and that of the average gay man. The purported aim of collecting the data was varied, so as to either make the self-other comparison central to the aim or render one of the two types of estimate irrelevant to the aim. No effect on UO was found. It seems that the cognitive account provides a better explanation than does the motivational account of at least that form of UO measured in this study. Implications for AIDS education are discussed.

Proportional k-interval discretization for naive-Bayes classifiers

This paper argues that two commonly-used discretization approaches, fixed k-interval discretization and entropy-based discretization have sub-optimal characteristics for naive-Bayes classification. This analysis leads to a new discretization method, Proportional k-Interval Discretization (PKID), which adjusts the number and size of discretized intervals to the number of training instances, thus seeks an appropriate trade-off between the bias and variance of the probability estimation for naive-Bayes classifiers. We justify PKID in theory, as well as test it on a wide cross-section of datasets. Our experimental results suggest that in comparison to its alternatives, PKID provides naive-Bayes classifiers competitive classification performance for smaller datasets and better classification performance for larger datasets.

Relationship between body image and social and sexual functioning: gender and development trends

The purpose of this study was to examine the relationship between body image and social and sexual functioning. The respondents were 426 men and women from metropolitan and rural Victoria, who ranged in age from 18 to 86 years (mean age = 42.26). Respondents completed measures of attractiveness, body satisfaction, body image importance, body image behaviours, appearance comparison, social physique anxiety, self-esteem, depression, anxiety, and social and sexual functioning. Regression analyses were used to detelmine the prediction of social and sexual functioning by body image variables for men and women of different age groups, beyond the effects of psychological adjustment. The results demonstrated that while there were moderate correlations between body image and sociallsexual functioning variables, many of these relationships were best explained by the shared variance of self-esteem. There were some exceptions, particularly among middle-aged men, which are discussed.

Cortical and trabecular bone at the forearm show different adaptation patterns in response to tennis playing

Bone responds to impact-loading activity by increasing its size and/or density. The aim of this study was to compare the magnitude and modality of the bone response between cortical and trabecular bone in the forearms of tennis players. Bone area, bone mineral content (BMC), and bone mineral density (BMD) of the ulna and radius were measured by dual-energy X-ray absorptiometry (DXA) in 57 players (24.5 ± 5.7 yr old), at three sites: the ultradistal region (50% trabecular bone), the mid-distal regions, and third-distal (mainly cortical bone). At the ultradistal radius, the side-to-side difference in BMD was larger than in bone area (8.4 ± 5.2% and 4.9 ± 4.0%, respectively, p < 0.01). In the cortical sites, the asymmetry was lower (p < 0.01) in BMD than in bone area (mid-distal radius: 4.0 ± 4.3% vs 11.7 ± 6.8%; third-distal radius: 5.0 ± 4.8% vs 8.4 ± 6.2%). The asymmetry in bone area explained 33% of the variance of the asymmetry in BMC at the ultradistal radius, 66% at the mid-distal radius, and 53% at the third-distal radius. The ulna displayed similar results. Cortical and trabecular bone seem to respond differently to mechanical loading. The first one mainly increases its size, whereas the second one preferentially increases its density.