Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

In this work a p-adaptation (modification of the polynomial order) strategy based on the minimization of the truncation error is developed for high order discontinuous Galerkin methods. The truncation error is approximated by means of a truncation error estimation procedure and enables the identification of mesh regions that require adaptation. Three truncation error estimation approaches are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. Fine solutions, which are obtained by enriching the polynomial order, are required to solve the numerical problem with adequate accuracy. For the three truncation error estimation methods the former needs time converged solutions, while the last two rely on non-converged solutions, which lead to faster computations. Based on these truncation error estimation methods, algorithms for mesh adaptation were designed and tested. Firstly, an isotropic adaptation approach is presented, which leads to equally distributed polynomial orders in different coordinate directions. This first implementation is improved by incorporating a method to extrapolate the truncation error. This results in a significant reduction of computational cost. Secondly, the employed high order method permits the spatial decoupling of the estimated errors and enables anisotropic p-adaptation. The incorporation of anisotropic features leads to meshes with different polynomial orders in the different coordinate directions such that flow-features related to the geometry are resolved in a better manner. These adaptations result in a significant reduction of degrees of freedom and computational cost, while the amount of improvement depends on the test-case. Finally, this anisotropic approach is extended by using error extrapolation which leads to an even higher reduction in computational cost. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. The main result is that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of a factor of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively. RESUMEN En este trabajo se ha desarrollado una estrategia de adaptación-p (modificación del orden polinómico) para métodos Galerkin discontinuo de alto orden basada en la minimización del error de truncación. El error de truncación se estima utilizando el método tau-estimation. El estimador permite la identificación de zonas de la malla que requieren adaptación. Se distinguen tres técnicas de estimación: a posteriori, quasi a priori y quasi a priori con correción. Todas las estrategias requieren una solución obtenida en una malla fina, la cual es obtenida aumentando de manera uniforme el orden polinómico. Sin embargo, mientras que el primero requiere que esta solución esté convergida temporalmente, el resto utiliza soluciones no convergidas, lo que se traduce en un menor coste computacional. En este trabajo se han diseñado y probado algoritmos de adaptación de malla basados en métodos tau-estimation. En primer lugar, se presenta un algoritmo de adaptacin isótropo, que conduce a discretizaciones con el mismo orden polinómico en todas las direcciones espaciales. Esta primera implementación se mejora incluyendo un método para extrapolar el error de truncación. Esto resulta en una reducción significativa del coste computacional. En segundo lugar, el método de alto orden permite el desacoplamiento espacial de los errores estimados, permitiendo la adaptación anisotropica. Las mallas obtenidas mediante esta técnica tienen distintos órdenes polinómicos en cada una de las direcciones espaciales. La malla final tiene una distribución óptima de órdenes polinómicos, los cuales guardan relación con las características del flujo que, a su vez, depenen de la geometría. Estas técnicas de adaptación reducen de manera significativa los grados de libertad y el coste computacional. Por último, esta aproximación anisotropica se extiende usando extrapolación del error de truncación, lo que conlleva un coste computational aún menor. Las estrategias se verifican y se comparan en téminors de precisión y coste computacional utilizando las ecuaciones de Euler y Navier Stokes. Los dos métodos quasi a priori consiguen una reducción significativa del coste computacional en comparación con aumento uniforme del orden polinómico. En concreto, para una capa límite viscosa, obtenemos una mejora en tiempo de computación de 6.6 y 7.6 respectivamente, para las aproximaciones quasi-a priori y quasi-a priori con corrección.

The Arabidopsis thaliana AGRAVITROPIC 1 gene encodes a component of the polar-auxin-transport efflux carrier

Auxins are plant hormones that mediate many aspects of plant growth and development. In higher plants, auxins are polarly transported from sites of synthesis in the shoot apex to their sites of action in the basal regions of shoots and in roots. Polar auxin transport is an important aspect of auxin functions and is mediated by cellular influx and efflux carriers. Little is known about the molecular identity of its regulatory component, the efflux carrier [Estelle, M. (1996) Current Biol. 6, 1589–1591]. Here we show that mutations in the Arabidopsis thaliana AGRAVITROPIC 1 (AGR1) gene involved in root gravitropism confer increased root-growth sensitivity to auxin and decreased sensitivity to ethylene and an auxin transport inhibitor, and cause retention of exogenously added auxin in root tip cells. We used positional cloning to show that AGR1 encodes a putative transmembrane protein whose amino acid sequence shares homologies with bacterial transporters. When expressed in Saccharomyces cerevisiae, AGR1 promotes an increased efflux of radiolabeled IAA from the cells and confers increased resistance to fluoro-IAA, a toxic IAA-derived compound. AGR1 transcripts were localized to the root distal elongation zone, a region undergoing a curvature response upon gravistimulation. We have identified several AGR1-related genes in Arabidopsis, suggesting a global role of this gene family in the control of auxin-regulated growth and developmental processes.

Multiple pathways for ultrafast transduction of light energy in the photosynthetic reaction center of Rhodobacter sphaeroides

A pathway of electron transfer is described that operates in the wild-type reaction center (RC) of the photosynthetic bacterium Rhodobacter sphaeroides. The pathway does not involve the excited state of the special pair dimer of bacteriochlorophylls (P*), but instead is driven by the excited state of the monomeric bacteriochlorophyll (BA*) present in the active branch of pigments along which electron transfer occurs. Pump-probe experiments were performed at 77 K on membrane-bound RCs by using different excitation wavelengths, to investigate the formation of the charge separated state P+HA−. In experiments in which P or BA was selectively excited at 880 nm or 796 nm, respectively, the formation of P+HA− was associated with similar time constants of 1.5 ps and 1.7 ps. However, the spectral changes associated with the two time constants are very different. Global analysis of the transient spectra shows that a mixture of P+BA− and P* is formed in parallel from BA* on a subpicosecond time scale. In contrast, excitation of the inactive branch monomeric bacteriochlorophyll (BB) and the high exciton component of P (P+) resulted in electron transfer only after relaxation to P*. The multiple pathways for primary electron transfer in the bacterial RC are discussed with regard to the mechanism of charge separation in the RC of photosystem II from higher plants.

Borate-Rhamnogalacturonan II Bonding Reinforced by Ca2+ Retains Pectic Polysaccharides in Higher-Plant Cell Walls1

The extent of in vitro formation of the borate-dimeric-rhamnogalacturonan II (RG-II) complex was stimulated by Ca2+. The complex formed in the presence of Ca2+ was more stable than that without Ca2+. A naturally occurring boron (B)-RG-II complex isolated from radish (Raphanus sativus L. cv Aokubi-daikon) root contained equimolar amounts of Ca2+ and B. Removal of the Ca2+ by trans-1,2-diaminocyclohexane-N,N,N′,N′-tetraacetic acid induced cleavage of the complex into monomeric RG-II. These data suggest that Ca2+ is a normal component of the B-RG-II complex. Washing the crude cell walls of radish roots with a 1.5% (w/v) sodium dodecyl sulfate solution, pH 6.5, released 98% of the tissue Ca2+ but only 13% of the B and 22% of the pectic polysaccharides. The remaining Ca2+ was associated with RG-II. Extraction of the sodium dodecyl sulfate-washed cell walls with 50 mm trans-1,2-diaminocyclohexane-N,N,N′,N′-tetraacetic acid, pH 6.5, removed the remaining Ca2+, 78% of B, and 49% of pectic polysaccharides. These results suggest that not only Ca2+ but also borate and Ca2+ cross-linking in the RG-II region retain so-called chelator-soluble pectic polysaccharides in cell walls.

Microsomal Electron Transfer in Higher Plants: Cloning and Heterologous Expression of NADH-Cytochrome b5 Reductase from Arabidopsis

AtCBR, a cDNA encoding NADH-cytochrome (Cyt) b5 reductase, and AtB5-A and AtB5-B, two cDNAs encoding Cyt b5, were isolated from Arabidopsis. The primary structure deduced from the AtCBR cDNA was 40% identical to those of the NADH-Cyt b5 reductases of yeast and mammals. A recombinant AtCBR protein prepared using a baculovirus system exhibited typical spectral properties of NADH-Cyt b5 reductase and was used to study its electron-transfer activity. The recombinant NADH-Cyt b5 reductase was functionally active and displayed strict specificity to NADH for the reduction of a recombinant Cyt b5 (AtB5-A), whereas no Cyt b5 reduction was observed when NADPH was used as the electron donor. Conversely, a recombinant NADPH-Cyt P450 reductase of Arabidopsis was able to reduce Cyt b5 with NADPH but not with NADH. To our knowledge, this is the first evidence in higher plants that both NADH-Cyt b5 reductase and NADPH-Cyt P450 reductase can reduce Cyt b5 and have clear specificities in terms of the electron donor, NADH or NADPH, respectively. This substrate specificity of the two reductases is discussed in relation to the NADH- and NADPH-dependent activities of microsomal fatty acid desaturases.

Linear and nonlinear pathways of spectral information transmission in the cochlear nucleus

At the level of the cochlear nucleus (CN), the auditory pathway divides into several parallel circuits, each of which provides a different representation of the acoustic signal. Here, the representation of the power spectrum of an acoustic signal is analyzed for two CN principal cells—chopper neurons of the ventral CN and type IV neurons of the dorsal CN. The analysis is based on a weighting function model that relates the discharge rate of a neuron to first- and second-order transformations of the power spectrum. In chopper neurons, the transformation of spectral level into rate is a linear (i.e., first-order) or nearly linear function. This transformation is a predominantly excitatory process involving multiple frequency components, centered in a narrow frequency range about best frequency, that usually are processed independently of each other. In contrast, type IV neurons encode spectral information linearly only near threshold. At higher stimulus levels, these neurons are strongly inhibited by spectral notches, a behavior that cannot be explained by level transformations of first- or second-order. Type IV weighting functions reveal complex excitatory and inhibitory interactions that involve frequency components spanning a wider range than that seen in choppers. These findings suggest that chopper and type IV neurons form parallel pathways of spectral information transmission that are governed by two different mechanisms. Although choppers use a predominantly linear mechanism to transmit tonotopic representations of spectra, type IV neurons use highly nonlinear processes to signal the presence of wide-band spectral features.

The ethylene hormone response in Arabidopsis: a eukaryotic two-component signaling system.

The simple gas ethylene affects numerous physiological processes in the growth and development of higher plants. With the use of molecular genetic approaches, we are beginning to learn how plants perceive ethylene and how this signal is transduced. Components of ethylene signal transduction are defined by ethylene response mutants in Arabidopsis thaliana. The genes corresponding to two of these mutants, etr1 and etr1, have been cloned. The ETR1 gene encodes a homolog of two-component regulators that are known almost exclusively in prokaryotes. The two-component regulators in prokaryotes are involved in the perception and transduction of a wide range of environmental signals leading to adaptive responses. The CTR1 gene encodes a homolog of the Raf family of serine/threonine protein kinases. Raf is part of a mitogen-activated protein kinase cascade known to regulate cell growth and development in mammals, worms, and flies. The ethylene response pathway may, therefore, exemplify a conserved protein kinase cascade regulated by a two-component system. The dominance of all known mutant alleles of ETR1 may be due to either constitutive activation of the ETR1 protein or dominant interference of wild-type activity. The discovery of Arabidopsis genes encoding proteins related to ETR1 suggests that the failure to recover recessive etr1 mutant alleles may be due to the presence of redundant genes.

The XMM deep survey in the CDF-S. VI. Obscured AGN selected as infrared power-law galaxies

Context. Accretion onto supermassive black holes is believed to occur mostly in obscured active galactic nuclei (AGN). Such objects are proving rather elusive in surveys of distant galaxies, including those at X-ray energies. Aims. Our main goal is to determine whether the revised IRAC criteria of Donley et al. (2012, ApJ, 748, 142; objects with an infrared (IR) power-law spectral shape), are effective at selecting X-ray type-2 AGN (i.e., absorbed N_H > 10^22 cm^-2). Methods. We present the results from the X-ray spectral analysis of 147 AGN selected by cross-correlating the highest spectral quality ultra-deep XMM-Newton and the Spitzer/IRAC catalogues in the Chandra Deep Field South. Consequently it is biased towards sources with high S/N X-ray spectra. In order to measure the amount of intrinsic absorption in these sources, we adopt a simple X-ray spectral model that includes a power-law modified by intrinsic absorption at the redshift of each source and a possible soft X-ray component. Results. We find 21/147 sources to be heavily absorbed but the uncertainties in their obscuring column densities do not allow us to confirm their Compton-Thick nature without resorting to additional criteria. Although IR power-law galaxies are less numerous in our sample than IR non-power-law galaxies (60 versus 87 respectively), we find that the fraction of absorbed (N_H^intr > 10^22 cm^-2) AGN is significantly higher (at about 3 sigma level) for IR-power-law sources (similar to 2/3) than for those sources that do not meet this IR selection criteria (~1/2). This behaviour is particularly notable at low luminosities, but it appears to be present, although with a marginal significance, at all luminosities. Conclusions. We therefore conclude that the IR power-law method is efficient in finding X-ray-absorbed sources. We would then expect that the long-sought dominant population of absorbed AGN is abundant among IR power-law spectral shape sources not detected in X-rays.

Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings

A reduced set of measurement geometries allows the spectral reflectance of special effect coatings to be predicted for any other geometry. A physical model based on flake-related parameters has been used to determine nonredundant measurement geometries for the complete description of the spectral bidirectional reflectance distribution function (BRDF). The analysis of experimental spectral BRDF was carried out by means of principal component analysis. From this analysis, a set of nine measurement geometries was proposed to characterize special effect coatings. It was shown that, for two different special effect coatings, these geometries provide a good prediction of their complete color shift.

Circumstellar emission in Be/X-ray binaries of the Magellanic Clouds and the Milky Way

Aims. We study the optical and near-infrared colour excesses produced by circumstellar emission in a sample of Be/X-ray binaries. Our main goals are exploring whether previously published relations, valid for isolated Be stars, are applicable to Be/X-ray binaries and computing the distance to these systems after correcting for the effects of the circumstellar contamination. Methods. Simultaneous UBVRI photometry and spectra in the 3500−7000 Å spectral range were obtained for 11 optical counterparts to Be/X-ray binaries in the LMC, 5 in the SMC and 12 in the Milky Way. As a measure of the amount of circumstellar emission we used the Hα equivalent width corrected for photospheric absorption. Results. We find a linear relationship between the strength of the Hα emission line and the component of E(B − V) originating from the circumstellar disk. This relationship is valid for stars with emission lines weaker than EW ≈ −15   Å. Beyond this point, the circumstellar contribution to E(B − V) saturates at a value ≈0.17   mag. A similar relationship is found for the (V − I) near infrared colour excess, albeit with a steeper slope and saturation level. The circumstellar excess in (B − V) is found to be about five times higher for Be/X-ray binaries than for isolated Be stars with the same equivalent width EW(Hα), implying significant differences in the physical properties of their circumstellar envelopes. The distance to Be/X-ray binaries (with non-shell Be star companions) can only be correctly estimated by taking into account the excess emission in the V band produced by free-free and free-bound transitions in the circumstellar envelope. We provide a simple method to determine the distances that includes this effect.

Non-spectral interferences due to the presence of sulfuric acid in inductively coupled plasma mass spectrometry

Results of a systematic study concerning non-spectral interferences from sulfuric acid containing matrices on a large number of elements in inductively coupled plasma–mass spectrometry (ICP-MS) are presented in this work. The signals obtained with sulfuric acid solutions of different concentrations (up to 5% w w− 1) have been compared with the corresponding signals for a 1% w w− 1− nitric acid solution at different experimental conditions (i.e., sample uptake rates, nebulizer gas flows and r.f. powers). The signals observed for 128Te+, 78Se+ and 75As+ were significantly higher when using sulfuric acid matrices (up to 2.2-fold for 128Te+ and 78Se+ and 1.8-fold for 75As+ in the presence of 5 w w-1 sulfuric acid) for the whole range of experimental conditions tested. This is in agreement with previously reported observations. The signal for 31P+ is also higher (1.1-fold) in the presence of sulfuric acid. The signal enhancements for 128Te+, 78Se+, 75As+ and 31P+ are explained in relation to an increase in the analyte ion population as a result of charge transfer reactions involving S+ species in the plasma. Theoretical data suggest that Os, Sb, Pt, Ir, Zn and Hg could also be involved in sulfur-based charge transfer reactions, but no experimental evidence has been found. The presence of sulfuric acid gives rise to lower ion signals (about 10–20% lower) for the other nuclides tested, thus indicating the negative matrix effect caused by changes in the amount of analyte loading of the plasma. The elemental composition of a certified low-density polyethylene sample (ERM-EC681K) was determined by ICP-MS after two different sample digestion procedures, one of them including sulfuric acid. Element concentrations were in agreement with the certified values, irrespective of the acids used for the digestion. These results demonstrate that the use of matrix-matched standards allows the accurate determination of the tested elements in a sulfuric acid matrix.

SPECTRAL DOMAIN-OPTICAL COHERENCE TOMOGRAPHY IMAGE CONTRAST AND BACKGROUND COLOR SETTINGS INFLUENCE IDENTIFICATION OF RETINAL STRUCTURES.

PURPOSE To evaluate image contrast and color setting on assessment of retinal structures and morphology in spectral-domain optical coherence tomography. METHODS Two hundred and forty-eight Spectralis spectral-domain optical coherence tomography B-scans of 62 patients were analyzed by 4 readers. B-scans were extracted in 4 settings: W + N = white background with black image at normal contrast 9; W + H = white background with black image at maximum contrast 16; B + N = black background with white image at normal contrast 12; B + H = black background with white image at maximum contrast 16. Readers analyzed the images to identify morphologic features. Interreader correlation was calculated. Differences between Fleiss-kappa correlation coefficients were examined using bootstrap method. Any setting with significantly higher correlation coefficient was deemed superior for evaluating specific features. RESULTS Correlation coefficients differed among settings. No single setting was superior for all respective spectral-domain optical coherence tomography parameters (P = 0.3773). Some variables showed no differences among settings. Hard exudates and subretinal fluid were best seen with B + H (κ = 0.46, P = 0.0237 and κ = 0.78, P = 0.002). Microaneurysms were best seen with W + N (κ = 0.56, P = 0.025). Vitreomacular interface, enhanced transmission signal, and epiretinal membrane were best identified using all color/contrast settings together (κ = 0.44, P = 0.042, κ = 0.57, P = 0.01, and κ = 0.62, P ≤ 0.0001). CONCLUSION Contrast and background affect the evaluation of retinal structures on spectral-domain optical coherence tomography images. No single setting was superior for all features, though certain changes were best seen with specific settings.

The impact of spectral composition and light periodicity on the activity of two antioxidant enzymes (SOD and CAT) in the coral Favia favus

In oligotrophic waters the light spectrum is mostly blue, and therefore the physiological and biochemical responses to blue light occurring in the coral tissue and in the symbiotic algae are important. Examination of the wavelength dependence of two free radical scavenger enzyme activity revealed an increase in activity in the blue light range (440-480 nm) compared to the red (640680 nm) in the full visible light (400-700 nm) range. These data show for the first time the relationship between the action spectra of photosynthesis and the activity of two main antioxidant enzymes in the symbiotic coral Favia favus. It was found that in the animal (host) the enzyme response to the spectral distribution of light was higher than that of the zooxanthellae, probably due to accumulation of free radicals within the host tissue. Furthermore, we found that the activity of these enzymes is affected in nature by the length of the day and night, and in the laboratory, by the duration of the illumination. Changes in the pigment concentrations were also observed in response to growth under the blue region and the whole PAR spectrum, while fluorescence measurements with the fast repetition rate fluorometer (FRRF) showed a decrease in the sigma cross section and a decrease in the quantum yield also in the blue part of the spectrum. These changes of scavenger enzymes activity, pigment concentration and fluorescence yield at different light spectra are vital in acclimatization and survival of corals in shallow water environments with high light radiation. (c) 2005 Elsevier B.V. All rights reserved.

Drying process of microcrystalline cellulose studied by attenuated total reflection IR spectroscopy with two-dimensional correlation spectroscopy and principal component analysis

Molecular interactions between microcrystalline cellulose (MCC) and water were investigated by attenuated total reflection infrared (ATR/IR) spectroscopy. Moisture-content-dependent IR spectra during a drying process of wet MCC were measured. In order to distinguish overlapping O–H stretching bands arising from both cellulose and water, principal component analysis (PCA) and, generalized two-dimensional correlation spectroscopy (2DCOS) and second derivative analysis were applied to the obtained spectra. Four typical drying stages were clearly separated by PCA, and spectral variations in each stage were analyzed by 2DCOS. In the drying time range of 0–41 min, a decrease in the broad band around 3390 cm−1 was observed, indicating that bulk water was evaporated. In the drying time range of 49–195 min, decreases in the bands at 3412, 3344 and 3286 cm−1 assigned to the O6H6cdots, three dots, centeredO3′ interchain hydrogen bonds (H-bonds), the O3H3cdots, three dots, centeredO5 intrachain H-bonds and the H-bonds in Iβ phase in MCC, respectively, were observed. The result of the second derivative analysis suggests that water molecules mainly interact with the O6H6cdots, three dots, centeredO3′ interchain H-bonds. Thus, the H-bonding network in MCC is stabilized by H-bonds between OH groups constructing O6H6cdots, three dots, centeredO3′ interchain H-bonds and water, and the removal of the water molecules induces changes in the H-bonding network in MCC.

Grouping and the pitch of a mistuned fundamental component:effects of applying simultaneous multiple mistunings to the other harmonics

Mistuning a harmonic produces an exaggerated change in its pitch. This occurs because the component becomes inconsistent with the regular pattern that causes the other harmonics (constituting the spectral frame) to integrate perceptually. These pitch shifts were measured when the fundamental (F0) component of a complex tone (nominal F0 frequency = 200 Hz) was mistuned by +8% and -8%. The pitch-shift gradient was defined as the difference between these values and its magnitude was used as a measure of frame integration. An independent and random perturbation (spectral jitter) was applied simultaneously to most or all of the frame components. The gradient magnitude declined gradually as the degree of jitter increased from 0% to ±40% of F0. The component adjacent to the mistuned target made the largest contribution to the gradient, but more distant components also contributed. The stimuli were passed through an auditory model, and the exponential height of the F0-period peak in the averaged summary autocorrelation function correlated well with the gradient magnitude. The fit improved when the weighting on more distant channels was attenuated by a factor of three per octave. The results are consistent with a grouping mechanism that computes a weighted average of periodicity strength across several components. © 2006 Elsevier B.V. All rights reserved.