First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Wavelets and the generalization of the variogram

The experimental variogram computed in the usual way by the method of moments and the Haar wavelet transform are similar in that they filter data and yield informative summaries that may be interpreted. The variogram filters out constant values; wavelets can filter variation at several spatial scales and thereby provide a richer repertoire for analysis and demand no assumptions other than that of finite variance. This paper compares the two functions, identifying that part of the Haar wavelet transform that gives it its advantages. It goes on to show that the generalized variogram of order k=1, 2, and 3 filters linear, quadratic, and cubic polynomials from the data, respectively, which correspond with more complex wavelets in Daubechies's family. The additional filter coefficients of the latter can reveal features of the data that are not evident in its usual form. Three examples in which data recorded at regular intervals on transects are analyzed illustrate the extended form of the variogram. The apparent periodicity of gilgais in Australia seems to be accentuated as filter coefficients are added, but otherwise the analysis provides no new insight. Analysis of hyerpsectral data with a strong linear trend showed that the wavelet-based variograms filtered it out. Adding filter coefficients in the analysis of the topsoil across the Jurassic scarplands of England changed the upper bound of the variogram; it then resembled the within-class variogram computed by the method of moments. To elucidate these results, we simulated several series of data to represent a random process with values fluctuating about a mean, data with long-range linear trend, data with local trend, and data with stepped transitions. The results suggest that the wavelet variogram can filter out the effects of long-range trend, but not local trend, and of transitions from one class to another, as across boundaries.

Preparation and properties of gallaborane, GaBH6: structure of the gaseous molecule H2Ga(μ-H)2BH2 as determined by vibrational, electron diffraction, and ab initio studies, and structure of the crystalline solid at 110 K as determined by x-ray diffraction``

Gallaborane (GaBH6, 1), synthesized by the metathesis of LiBH4 with [H2GaCl]n at ca. 250 K, has been characterized by chemical analysis and by its IR and 1H and 11B NMR spectra. The IR spectrum of the vapor at low pressure implies the presence of only one species, viz. H2Ga(μ-H)2BH2, with a diborane-like structure conforming to C2v symmetry. The structure of this molecule has been determined by gas-phase electron diffraction (GED) measurements afforced by the results of ab initio molecular orbital calculations. Hence the principal distances (rα in Å) and angles ( α in deg) are as follows: r(Ga•••B), 2.197(3); r(Ga−Ht), 1.555(6); r(Ga−Hb), 1.800(6); r(B−Ht), 1.189(7); r(B−Hb), 1.286(7); Hb−Ga−Hb, 71.6(4); and Hb−B−Hb, 110.0(5) (t = terminal, b = bridging). Aggregation of the molecules occurs in the condensed phases. X-ray crystallographic studies of a single crystal at 110 K reveal a polymeric network with helical chains made up of alternating pseudotetrahedral GaH4 and BH4 units linked through single hydrogen bridges; the average Ga•••B distance is now 2.473(7) Å. The compound decomposes in the condensed phases at temperatures exceeding ca. 240 K with the formation of elemental Ga and H2 and B2H6. The reactions with NH3, Me3N, and Me3P are also described.

Epidermal growth factor-stimulated extravillous cytotrophoblast motility is mediated by the activation of PI3-K, Akt and both p38 and p42/44 mitogen-activated protein kinases

BACKGROUND: Trophoblast invasion is a temporally and spatially regulated scheme of events that can dictate pregnancy outcome. Evidence suggests that the potent mitogen epidermal growth factor (EGF) regulates cytotrophoblast (CTB) differentiation and invasion during early pregnancy. METHODS AND RESULTS: In the present study, the first trimester extravillous CTB cell line SGHPL-4 was used to investigate the signalling pathways involved in the motile component of EGF-mediated CTB migration/invasion. EGF induced the phosphorylation of the phosphatidylinositol 3-kinase (PI3-K)-dependent proteins, Akt and GSK-3β as well as both p42/44 MAPK and p38 mitogen-activated protein kinases (MAPK). EGF-stimulated motility was significantly reduced following the inhibition of PI3-K (P < 0.001), Akt (P < 0.01) and both p42/44 MAPK (P < 0.001) and p38 MAPKs (P < 0.001) but not the inhibition of GSK-3β. Further analysis indicated that the p38 MAPK inhibitor SB 203580 inhibited EGF-stimulated phosphorylation of Akt on serine 473, which may be responsible for the effect SB 203580 has on CTB motility. Although Akt activation leads to GSK-3β phosphorylation and the subsequent expression of β-catenin, activation of this pathway by 1-azakenpaullone was insufficient to stimulate the motile phenotype. CONCLUSION: We demonstrate a role for PI3-K, p42/44 MAPK and p38 MAPK in the stimulation of CTB cell motility by EGF, however activation of β-catenin alone was insufficient to stimulate cell motility.

Bryophyte diversity and community structure on thatched roofs of the Holnicote Estate, Somerset, U.K.

We investigated patterns of bryophyte species richness and community structure, and their relation to roof variables, on thatched roofs of the Holnicote Estate, South Somerset. Thirty-two bryophyte species were recorded from 28 sampled roofs, including the globally rare and endangered thatch moss, Leptodontium gemmascens. Multiple regression analyses revealed that thatch age has a highly significant positive effect on the number of species present, accounting for nearly half the observed variation in species richness after removal of outliers. Aspect has a slight and marginally significant effect on species diversity (accounting for an additional 6% of variation), with north-facing samples having slightly more species. Age also has a significant impact on total bryophyte cover after removal of outlying observations. TWINSPAN analysis of bryophyte cover data suggests the existence of at least five discrete communities. Simple Discriminant Analyses indicate that these communities occupy different ecological subspaces as defined by the measured roof variables, with pitch, aspect and thatch age emerging as especially significant attributes. Contingency Analysis indicates that some communities are disfavoured by water reed as compared to wheat straw. The findings are significant for understanding the structure of bryophyte communities, for evaluating the effect of bryophyte cover on thatch performance, and for conservation of thatch communities, especially those harbouring rare species.

An in situ time-dependent study of the photodimerisation of chloro-derivatives of trans-cinnamic acid using infrared microspectroscopy with a synchrotron radiation source

The photodimerisation of single crystals of substituted cinnamic acid has been monitored continuously by infrared microscopy using a synchrotron source. The beta-form of 2,4-dichloro-trans-cinnamic acid dimerises under ultraviolet irradiation to form the corresponding beta-truxinic acid derivative in a reaction which follows strictly first order kinetics. By contrast the corresponding reactions in single crystals of beta-2-chloro-trans-cinnamic acid and beta-4-chloro-trans-cinnamic acid deviate somewhat from first order kinetics as a result of solid-state effects. In all three cases the reactions proceed smoothly from monomer to dimer with no hint of any reaction intermediate.

PDGF regulates the actin cytoskeleton through hnRNP-K-mediated activation of the ubiquitin E-3-ligase MIR

PDGF is a potent chemotactic mitogen and a strong inductor of fibroblast motility. In Swiss 3T3 fibroblasts, exposure to PDGF but not EGF or IGF-1 causes a rapid loss of actin stress fibers (SFs) and focal adhesions (FAs), which is followed by the development of retractile dendritic protrusions and induction of motility. The PDGF-specific actin reorganization was blocked by inhibition of Src-kinase and the 26S proteasome. PDGF induced Src-dependent association between the multifunctional transcription/translation regulator hnRNP-K and the mRNA-encoding myosin regulatory light-chain (MRLC)-interacting protein (MIR), a E3-ubiquitin ligase that is MRLC specific. This in turn rapidly increased MIR expression, and led to ubiquitination and proteasome-mediated degradation of MRLC. Downregulation of MIR by RNA muting prevented the reorganization of actin structures and severely reduced the migratory and wound-healing potential of PDGF-treated cells. The results show that activation of MIR and the resulting removal of diphosphorylated MRLC are essential for PDGF to instigate and maintain control over the actin-myosin-based contractile system in Swiss 3T3 fibroblasts. The PDGF induced protein destabilization through the regulation of hnRNP-K controlled ubiquitin-ligase translation identifies a novel pathway by which external stimuli can regulate phenotypic development through rapid, organelle-specific changes in the activity and stability of cytoskeletal regulators.

Results of an aqueous source term model for a radiological risk assessment of the Drigg LLW Site, U.K.

A radionuclide source term model has been developed which simulates the biogeochemical evolution of the Drigg low level waste (LLW) disposal site. The DRINK (DRIgg Near field Kinetic) model provides data regarding radionuclide concentrations in groundwater over a period of 100,000 years, which are used as input to assessment calculations for a groundwater pathway. The DRINK model also provides input to human intrusion and gaseous assessment calculations through simulation of the solid radionuclide inventory. These calculations are being used to support the Drigg post closure safety case. The DRINK model considers the coupled interaction of the effects of fluid flow, microbiology, corrosion, chemical reaction, sorption and radioactive decay. It represents the first direct use of a mechanistic reaction-transport model in risk assessment calculations.

Laboratory measurements of the water vapor continuum in the 1200–8000 cm−1 region between 293 K and 351 K

Laboratory Fourier transform spectroscopy of pure water vapor and water vapor mixed with air has been conducted between 1200 and 8000 cm−1 and at temperatures between 293 and 351 K with the purpose of detecting and characterizing the water vapor continuum. The spectral features of the continuum within the major water absorption bands are presented and compared where possible to those from previous experimental studies and to the commonly used MT_CKD and CKD models. It was observed that in the main, both models adequately capture the general spectral form of the continuum; however, there were a number of exceptions. Overall, there is no evidence to indicate that MT_CKD is an improvement upon the older CKD model in these spectral regions. There was generally good agreement between our results and those of other experimental investigators. The general mathematical forms of the self-continuum temperature dependence, given by both Roberts et al. (1976) and CKD/MT_CKD, fit well to the experimental continuum in these spectral regions. However, the range of temperatures over which we made measurements is not sufficient to discriminate between these two forms or to exclude the possibility of other forms of temperature dependence being more appropriate. At the same time, the actual parameters currently used in CKD/MT_CKD to describe the temperature dependence in many spectral regions cannot reproduce the observed strong spectral variation in the temperature dependence. It has not been possible to make definitive conclusions about the magnitude of the continuum absorption in the far wings of the absorption bands investigated here.

Determination by MAD-DM of the structure of the DNA duplex d[ACGTACG(5-BrU)]2 at 1.46 Å and 100 K

A four-wavelength MAD experiment on a new brominated octanucleotide is reported here. d[ACGTACG(5-BrU)], C77H81BrN30O32P7, (DNA) = 2235, tetragonal, P43212 (No. 96), a = 43.597, c = 26.268 Å, V = 49927.5 Å3, Z = 8, T = 100 K, R = 10.91% for 4312 reflections between 15.0 and 1.46 Å resolution. The self-complementary brominated octanucleotide d[ACGTACG(5-BrU)]2 has been crystallized and data measured to 1.45 Å at both 293 K and a second crystal flash frozen at 100 K. The latter data collection was carried out to the same resolution at the four wavelengths 0.9344, 0.9216, 0.9208 and 0.9003 Å, around the Br K edge at 0.92 Å and the structure determined from a map derived from a MAD data analysis using pseudo-MIR methodology, as implemented in the program MLPHARE. This is one of the first successful MAD phasing experiments carried out at Sincrotrone Elettra in Trieste, Italy. The structure was refined using the data measured at 0.9003 Å, anisotropic temperature factors and the restrained least-squares refinement implemented in the program SHELX96, and the helical parameters are compared with those previously determined for the isomorphous d(ACGTACGT)2 analogue. The asymmetric unit consists of a single strand of octamer with 96 water molecules. No countercations were located. The A-DNA helix geometry obtained has been analysed using the CURVES program.