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.

Understanding distributions of chess performances

This paper presents evidence for several features of the population of chess players, and the distribution of their performances measured in terms of Elo ratings and by computer analysis of moves. Evidence that ratings have remained stable since the inception of the Elo system in the 1970’s is given in several forms: by showing that the population of strong players fits a simple logistic-curve model without inflation, by plotting players’ average error against the FIDE category of tournaments over time, and by skill parameters from a model that employs computer analysis keeping a nearly constant relation to Elo rating across that time. The distribution of the model’s Intrinsic Performance Ratings can hence be used to compare populations that have limited interaction, such as between players in a national chess federation and FIDE, and ascertain relative drift in their respective rating systems.

Root distributions of Australian herbaceous perennial legumes in response to phosphorus placement

Many Australian plant species have specific root adaptations for growth in phosphorus-impoverished soils, and are often sensitive to high external P concentrations. The growth responses of native Australian legumes in agricultural soils with elevated P availability in the surface horizons are unknown. The aim of these experiments was to test the hypothesis that increased P concentration in surface soil would reduce root proliferation at depth in native legumes. The effect of P placement on root distribution was assessed for two Australian legumes, Kennedia prorepens F. Muell. and Lotus australis Andrews, and the exotic Medicago sativa L. Three treatments were established in a low-P loam soil: amendment of 0.15 g mono-calcium phosphate in either (i) the top 50 mm (120 µg P g–1) or (ii) the top 500 mm (12 µg P g–1) of soil, and an unamended control. In the unamended soil M. sativa was shallow rooted, with 58% of the root length of in the top 50 mm. K. prorepens and L. australis had a more even distribution down the pot length, with only 4 and 22% of their roots in the 0–50 mm pot section, respectively. When exposed to amendment of P in the top 50 mm, root length in the top 50 mm increased 4-fold for K. prorepens and 10-fold for M. sativa, although the pattern of root distribution did not change for M. sativa. L. australis was relatively unresponsive to P additions and had an even distribution of roots down the pot. Shoot P concentrations differed according to species but not treatment (K. prorepens 2.1 mg g–1, L. australis 2.4 mg g–1, M. sativa 3.2 mg g–1). Total shoot P content was higher for K. prorepens than for the other species in all treatments. In a second experiment, mono-ester phosphatases were analysed from 1-mm slices of soil collected directly adjacent to the rhizosphere. All species exuded phosphatases into the rhizosphere, but addition of P to soil reduced phosphatase activity only for K. prorepens. Overall, high P concentration in the surface soil altered root distribution, but did not reduce root proliferation at depth. Furthermore, the Australian herbaceous perennial legumes had root distributions that enhanced P acquisition from low-P soils.

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.

Modeling distributions of immediate memory effects: No strategies needed?

Many models of immediate memory predict the presence or absence of various effects, but none have been tested to see whether they predict an appropriate distribution of effect sizes. The authors show that the feature model (J. S. Nairne, 1990) produces appropriate distributions of effect sizes for both the phonological confusion effect and the word-length effect. The model produces the appropriate number of reversals, when participants are more accurate with similar items or long items, and also correctly predicts that participants performing less well overall demonstrate smaller and less reliable phonological similarity and word-length effects and are more likely to show reversals. These patterns appear within the model without the need to assume a change in encoding or rehearsal strategy or the deployment of a different storage buffer. The implications of these results and the wider applicability of the distributionmodeling approach are discussed.

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.

Influence of environmental stress on distributions of times to first division in Escherichia coli populations, as determined by digital-image analysis of individual cells

The distributions of times to first cell division were determined for populations of Escherichia coli stationary-phase cells inoculated onto agar media. This was accomplished by using automated analysis of digital images of individual cells growing on agar and calculation of the "box area ratio." Using approximately 300 cells per experiment, the mean time to first division and standard deviation for cells grown in liquid medium at 37 degrees C and inoculated on agar and incubated at 20 degrees C were determined as 3.0 h and 0.7 h, respectively. Distributions were observed to tail toward the higher values, but no definitive model distribution was identified. Both preinoculation stress by heating cultures at 50 degrees C and postinoculation stress by growth in the presence of higher concentrations of NaCl increased mean times to first division. Both stresses also resulted in an increase in the spread of the distributions that was proportional to the mean division time, the coefficient of variation being constant at approximately 0.2 in all cases. The "relative division time," which is the time to first division for individual cells expressed in terms of the cell size doubling time, was used as measure of the "work to be done" to prepare for cell division. Relative division times were greater for heat-stressed cells than for those growing under osmotic stress.

Diversification when it hurts? The joint distributions of real estate and equity markets

Much of the literature on the construction of mixed asset portfolios and the case for property as a risk diversifier rests on correlations measured over the whole of a given time series. Recent developments in finance, however, focuses on dependence in the tails of the distribution. Does property offer diversification from equity markets when it is most needed - when equity returns are poor. The paper uses an empirical copula approach to test tail dependence between property and equity for the UK and for a global portfolio. Results show strong tail dependence: in the UK, the dependence in the lower tail is stronger than in the upper tail, casting doubt on the defensive properties of real estate stocks.

Evaluating the Survey of Professional Forecasters probability distributions of expected inflation based on derived event probability forecasts

Techniques are proposed for evaluating forecast probabilities of events. The tools are especially useful when, as in the case of the Survey of Professional Forecasters (SPF) expected probability distributions of inflation, recourse cannot be made to the method of construction in the evaluation of the forecasts. The tests of efficiency and conditional efficiency are applied to the forecast probabilities of events of interest derived from the SPF distributions, and supplement a whole-density evaluation of the SPF distributions based on the probability integral transform approach.

Profiling of composition and metabolic activities of the colonic microflora of growing pigs fed diets supplemented with prebiotic oligosaccharides

It is evident that quantitative information on different microbial groups and their contribution in terms of activity in the gastrointestinal (GI) tract of humans and animals is required in order to formulate functional diets targeting improved gut function and host health. In this work, quantitative information on levels and spatial distributions of Bacteroides spp, Eubacterium spp, Clostridium spp, Escherichia coli, Bifidobacterium spp and Lactobacillus/Enterococcus spp. along the porcine large intestine was investigated using 16S rRNA targeted probes and fluorescent in situ hybridisation (FISH). Caecum, ascending colon (AC) and rectum luminal digesta from three groups of individually housed growing pigs fed either a corn-soybean basal diet (CON diet) or a prebiotic diet containing 10 g/kg oligofructose (FOS diet) or trans-galactooligosaccharides (TOS diet) at the expense of cornstarch were analysed. DAPI staining was used to enumerate total number of cells in the samples. Populations of total cells, Bacteroides, Eubacterium, Clostridium and Bifidobacterium, declined significantly (P < 0.05) from caecum to rectum, and were not affected by dietary treatments. Populations of Lactobacillus/ Enterococcus and E coli did not differ throughout the large intestine. The relative percent (%) contribution of each bacterial group to the total cell count did not differ between caecum and rectum, with the exception of Eubacterium that was higher in the AC digesta. FISH analysis showed that the sum of all bacterial groups made up a small percentage of the total cells, which was 12.4%, 21.8% and 10.3% in caecum, AC and rectum, respectively. This supports the view that in swine, the diversity of GI microflora might be higher compared to other species. In terms of microflora metabolic activity, the substantially higher numerical trends seen in FOS and TOS treatments regarding total volatile fatty acid, acetate concentrations and glycolytic activities, it could be postulated that FOS and TOS promoted saccharolytic activities in the porcine colon. (c) 2006 Elsevier Ltd. All rights reserved.