An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

Equidistributing Meshes with Constraints

Adaptive methods which “equidistribute” a given positive weight function are now used fairly widely for selecting discrete meshes. The disadvantage of such schemes is that the resulting mesh may not be smoothly varying. In this paper a technique is developed for equidistributing a function subject to constraints on the ratios of adjacent steps in the mesh. Given a weight function $f \geqq 0$ on an interval $[a,b]$ and constants $c$ and $K$, the method produces a mesh with points $x_0 = a,x_{j + 1} = x_j + h_j ,j = 0,1, \cdots ,n - 1$ and $x_n = b$ such that\[ \int_{xj}^{x_{j + 1} } {f \leqq c\quad {\text{and}}\quad \frac{1} {K}} \leqq \frac{{h_{j + 1} }} {{h_j }} \leqq K\quad {\text{for}}\, j = 0,1, \cdots ,n - 1 . \] A theoretical analysis of the procedure is presented, and numerical algorithms for implementing the method are given. Examples show that the procedure is effective in practice. Other types of constraints on equidistributing meshes are also discussed. The principal application of the procedure is to the solution of boundary value problems, where the weight function is generally some error indicator, and accuracy and convergence properties may depend on the smoothness of the mesh. Other practical applications include the regrading of statistical data.

Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to eigenvalue/stability problems. The underlying analysis consists of constructing both a dual eigenvalue problem and a dual problem for the original base solution. In this way, errors stemming from both the numerical approximation of the original nonlinear flow problem, as well as the underlying linear eigenvalue problem are correctly controlled. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

Second-order elliptic PDE with discontinuous boundary data

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Mapping glider habitat in dry eucalypt forests for Montreal Process indicator 1.1: Fragmentation of forest types

Accurate habitat mapping is critical to landscape ecological studies such as required for developing and testing Montreal Process indicator 1.1e, fragmentation of forest types. This task poses a major challenge to remote sensing, especially in mixedspecies, variable-age forests such as dry eucalypt forests of subtropical eastern Australia. In this paper, we apply an innovative approach that uses a small section of one-metre resolution airborne data to calibrate a moderate spatial resolution model (30 m resolution; scale 1:50 000) based on Landsat Thematic Mapper data to estimate canopy structural properties in St Marys State Forest, near Maryborough, south-eastern Queensland. The approach applies an image-processing model that assumes each image pixel is significantly larger than individual tree crowns and gaps to estimate crown-cover percentage, stem density and mean crown diameter. These parameters were classified into three discrete habitat classes to match the ecology of four exudivorous arboreal species (yellowbellied glider Petaurus australis, sugar glider P. breviceps, squirrel glider P. norfolcensis , and feathertail glider Acrobates pygmaeus), and one folivorous arboreal marsupial, the greater glider Petauroides volans. These species were targeted due to the known ecological preference for old trees with hollows, and differences in their home range requirements. The overall mapping accuracy, visually assessed against transects (n = 93) interpreted from a digital orthophoto and validated in the field, was 79% (KHAT statistic = 0.72). The KHAT statistic serves as an indicator of the extent that the percentage correct values of the error matrix are due to ‘true’ agreement verses ‘chance’ agreement. This means that we are able to reliably report on the effect of habitat loss on target species, especially those with a large home range size (e.g. yellow-bellied glider). However, the classified habitat map failed to accurately capture the spatial patterning (e.g. patch size and shape) of stands with a trace or sub-dominance of senescent trees. This outcome makes the reporting of the effects of habitat fragmentation more problematic, especially for species with a small home range size (e.g. feathertail glider). With further model refinement and validation, however, this moderateresolution approach offers an important, cost eff e c t i v e advancement in mapping the age of dry eucalypt forests in the region.

Earnings Management and Measurement Error

In this paper I consider the impact of a noisy indicator regarding a manager’s manipulative behavior on optimal effort incentives and the extent of earnings management. The analysis in this paper extends a twotask, single performance measure LEN model by including a binary random variable. I show that contracting on the noisy indicator variable is not always useful. More specifically, the principal uses the indicator variable to prevent earnings management only under conditions where manipulative behavior is not excessive. Thus, under conditions of excessive earnings management, accounting adjustments that yield a more congruent overall performance measure can be more effective than an appraisal of the existence of earnings management to mitigate the earnings management problem.

Detrital zircon geochronology data, petrographic point count data and paleocurrent indicator data of Triassic turbidites in the Nanpanjiang Basin, South China

Triassic turbidites of the Nanpanjiang basin of south China represent the most expansive and voluminous siliciclastic turbidite accumulation in south China. The Nanpanjiang basin occurs at a critical junction between the southern margin of the south China plate and the Indochina, Siamo and Sibumasu plates to the south and southwest. The Triassic Yangtze carbonate shelf and isolated carbonated platforms in the basin have been extensively studied, but silicilastic turbidites in the basin have received relatively little attention. Deciphering the facies, paleocurrent indicators and provenance of the Triassic turbidites is important for several reasons: it promises to help resolve the timing of plate collisions along suture zones bordering the basin to the south and southwest, it will enable evaluation of which suture zones and Precambrian massifs were source areas, and it will allow an evaluation of the impact of the siliciclastic flux on carbonate platform evolution within the basin. Turbidites in the basin include the Early Triassic Shipao Formation and the Middle-Late Triassic Baifeng, Xinyuan, Lanmu Bianyang and Laishike formations. Each ranges upward of 700 m and the thickest is nearly 3 km. The turbidites contain very-fine sand in the northern part of the basin whereas the central and southern parts of the basin also commonly contain fine and rarely medium sand size. Coarser sand sizes occur where paleocurrents are from the south, and in this area some turbidites exhibit complete bouma sequences with graded A divisions. Successions contain numerous alternations between mud-rich and sand-rich intervals with thickness trends corresponding to proximal/ distal fan components. Spectacularly preserved sedimentary structures enable robust evaluation of turbidite systems and paleocurrent analyses. Analysis of paleocurrent measurements indicates two major directions of sediment fill. The northern part of the basin was sourced primarily by the Jiangnan massif in the northeast, and the central and southern parts of the basin were sourced primarily from suture zones and the Yunkai massif to the south and southeast respectively. Sandstones of the Lower Triassic Shipao Fm. have volcaniclastic composition including embayed quartz and glass shards. Middle Triassic sandstones are moderately mature, matrix-rich, lithic wackes. The average QFL ratio from all point count samples is 54.1/18.1/27.8% and the QmFLt ratio is 37.8/ 18.1/ 44.1%. Lithic fragments are dominantly claystone and siltstone clasts and metasedimentary clasts such as quartz mica tectonite. Volcanic lithics are rare. Most samples fall in the recycled orogen field of QmFLt plots, indicating a relatively quartz and lithic rich composition consistent with derivation from Precambrian massifs such as the Jiangnan, and Yunkai. A few samples from the southwest part of the basin fall into the dissected arc field, indicating a somewhat more lithic and feldspar-rich composition consistent with derivation from a suture zone Analysis of detrial zircon populations from 17 samples collected across the basin indicate: (1) Several samples contain zircons with concordant ages greater than 3000 Ma, (2) there are widespread peaks across the basin at 1800 Ma and 2500, (3) a widespread 900 Ma population, (3) a widespread population of zircons at 440 Ma, and (5) a larger population of younger zircons about 250 Ma in the southwestern part which is replaced to the north and northwest by a somewhat older population around 260-290 Ma. The 900 Ma provenance fits derivation from the Jiangnan Massif, the 2500, 1800, and 440 Ma provenance fits the Yunkai massif, and the 250 Ma is consistent with convergence and arc development in suture zones bordering the basin on the south or southwest. Early siliciclastic turbidite flux, proximal to source areas impacted carbonate platform evolution by infilling the basin, reducing accommodation space, stabilizing carbonate platform margins and promoting margin progradation. Late arrival, in areas far from source areas caused margin aggradation over a starved basin, development of high relief aggradational escarpments and unstable scalloped margins.

An econometric analysis of international tourism demand in Hong Kong : a cointegration and error correction approach

The purpose of this study is to develop econometric models to better understand the economic factors affecting inbound tourist flows from each of six origin countries that contribute to Hong Kong’s international tourism demand. To this end, we test alternative cointegration and error correction approaches to examine the economic determinants of tourist flows to Hong Kong, and to produce accurate econometric forecasts of inbound tourism demand. Our empirical findings show that permanent income is the most significant determinant of tourism demand in all models. The variables of own price, weighted substitute prices, trade volume, the share price index (as an indicator of changes in wealth in origin countries), and a dummy variable representing the Beijing incident (1989) are also found to be important determinants for some origin countries. The average long-run income and own price elasticity was measured at 2.66 and – 1.02, respectively. It was hypothesised that permanent income is a better explanatory variable of long-haul tourism demand than current income. A novel approach (grid search process) has been used to empirically derive the weights to be attached to the lagged income variable for estimating permanent income. The results indicate that permanent income, estimated with empirically determined relatively small weighting factors, was capable of producing better results than the current income variable in explaining long-haul tourism demand. This finding suggests that the use of current income in previous empirical tourism demand studies may have produced inaccurate results. The share price index, as a measure of wealth, was also found to be significant in two models. Studies of tourism demand rarely include wealth as an explanatory forecasting long-haul tourism demand. However, finding a satisfactory proxy for wealth common to different countries is problematic. This study indicates with the ECM (Error Correction Models) based on the Engle-Granger (1987) approach produce more accurate forecasts than ECM based on Pesaran and Shin (1998) and Johansen (1988, 1991, 1995) approaches for all of the long-haul markets and Japan. Overall, ECM produce better forecasts than the OLS, ARIMA and NAÏVE models, indicating the superiority of the application of a cointegration approach for tourism demand forecasting. The results show that permanent income is the most important explanatory variable for tourism demand from all countries but there are substantial variations between countries with the long-run elasticity ranging between 1.1 for the U.S. and 5.3 for U.K. Price is the next most important variable with the long-run elasticities ranging between -0.8 for Japan and -1.3 for Germany and short-run elasticities ranging between – 0.14 for Germany and -0.7 for Taiwan. The fastest growing market is Mainland China. The findings have implications for policies and strategies on investment, marketing promotion and pricing.

Caffeine As An Indicator Of Estrogenic Activity In Source Water.

Caffeine has already been used as an indicator of anthropogenic impacts, especially the ones related to the disposal of sewage in water bodies. In this work, the presence of caffeine has been correlated with the estrogenic activity of water samples measured using the BLYES assay. After testing 96 surface water samples, it was concluded that caffeine can be used to prioritize samples to be tested for estrogenic activity in water quality programs evaluating emerging contaminants with endocrine disruptor activity.

Neck Circumference As A New Anthropometric Indicator For Prediction Of Insulin Resistance And Components Of Metabolic Syndrome In Adolescents: Brazilian Metabolic Syndrome Study.

To evaluate the correlation between neck circumference and insulin resistance and components of metabolic syndrome in adolescents with different adiposity levels and pubertal stages, as well as to determine the usefulness of neck circumference to predict insulin resistance in adolescents. Cross-sectional study with 388 adolescents of both genders from ten to 19 years old. The adolescents underwent anthropometric and body composition assessment, including neck and waist circumferences, and biochemical evaluation. The pubertal stage was obtained by self-assessment, and the blood pressure, by auscultation. Insulin resistance was evaluated by the Homeostasis Model Assessment-Insulin Resistance. The correlation between two variables was evaluated by partial correlation coefficient adjusted for the percentage of body fat and pubertal stage. The performance of neck circumference to identify insulin resistance was tested by Receiver Operating Characteristic Curve. After the adjustment for percentage body fat and pubertal stage, neck circumference correlated with waist circumference, blood pressure, triglycerides and markers of insulin resistance in both genders. The results showed that the neck circumference is a useful tool for the detection of insulin resistance and changes in the indicators of metabolic syndrome in adolescents. The easiness of application and low cost of this measure may allow its use in Public Health services.

Refractive Error In School Children In Campinas, Brazil.

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Hanseníase no município de Fortaleza, CE, Brasil: aspectos epidemiológicos e operacionais em menores de 15 anos (1995-2006)

Estudo transversal que objetiva analisar a ocorrência de casos de hanseníase em menores de 15 anos de idade residentes no Município de Fortaleza e notificados no SINAN. Os indicadores epidemiológicos nesta população mostram hiperendemicidade. Operacionalmente observa-se a manutenção da concentração de atendimento em algumas unidades de referência, apesar de alguns avanços. Diagnóstico tardio, elevado grau de incapacidade no diagnóstico e baixo grau de avaliação de contatos registrados revelam a fragilidade das ações de controle. Ressalta-se a possibilidade de erro diagnóstico frente às características da infecção nesta população. A ocorrência de casos de hanseníase nesta população representa um indicador epidemiológico de grande relevância e sua análise amplia a discussão sobre problemas operacionais na rede de serviços de saúde.

An empirical evaluation of imputation accuracy for association statistics reveals increased type-I error rates in genome-wide associations

Background: Genome wide association studies (GWAS) are becoming the approach of choice to identify genetic determinants of complex phenotypes and common diseases. The astonishing amount of generated data and the use of distinct genotyping platforms with variable genomic coverage are still analytical challenges. Imputation algorithms combine directly genotyped markers information with haplotypic structure for the population of interest for the inference of a badly genotyped or missing marker and are considered a near zero cost approach to allow the comparison and combination of data generated in different studies. Several reports stated that imputed markers have an overall acceptable accuracy but no published report has performed a pair wise comparison of imputed and empiric association statistics of a complete set of GWAS markers. Results: In this report we identified a total of 73 imputed markers that yielded a nominally statistically significant association at P < 10(-5) for type 2 Diabetes Mellitus and compared them with results obtained based on empirical allelic frequencies. Interestingly, despite their overall high correlation, association statistics based on imputed frequencies were discordant in 35 of the 73 (47%) associated markers, considerably inflating the type I error rate of imputed markers. We comprehensively tested several quality thresholds, the haplotypic structure underlying imputed markers and the use of flanking markers as predictors of inaccurate association statistics derived from imputed markers. Conclusions: Our results suggest that association statistics from imputed markers showing specific MAF (Minor Allele Frequencies) range, located in weak linkage disequilibrium blocks or strongly deviating from local patterns of association are prone to have inflated false positive association signals. The present study highlights the potential of imputation procedures and proposes simple procedures for selecting the best imputed markers for follow-up genotyping studies.