Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Emergence of Chenopodium album and Stellaria media of different origins under different climatic conditions

The emergence behaviour of weed species in relation to cultural and meteorological events was studied. Dissimilarities between populations in dormancy and germination ecology, between-year maturation conditions and seed quality and burial site climate all contribute to potentially unpredictable variability. Therefore, a weed emergence data set was produced for weed seeds of Stellaria media and Chenopodium album matured and collected from three populations (Italy, Sweden and UK). The seeds were collected in two consecutive seasons (1999 and 2000) and subsequently buried in the autumn of the same year of maturation in eight contrasting climatic locations throughout Europe and the USA. The experiment sought to explore and explain differences between the three populations in their emergence behaviour. Evidence was demonstrated of synchrony in the timing of the emergence of different populations of a species at a given burial site. The relative magnitudes of emergence from the three populations at a given burial site in a given year were generally similar across all the burial sites in the study. The resulting data set was also used to construct a simple weed emergence model, which was tested for its application to the range of different burial environments and populations. The study demonstrated the possibility of using a simple thermal time-based model to describe part of the emergence behaviour across different burial sites, seed populations and seasons, and a simple winter chilling relationship to adjust for the magnitude of the flush of emergence at a given burial site. This study demonstrates the possibility of developing robust generic models for simple predictions of emergence timing across populations.

The postfusion structure of baculovirus gp64 supports a unified view of viral fusion machines

Viral fusion proteins mediate the merger of host and viral membranes during cell entry for all enveloped viruses. Baculovirus glycoprotein gp64 (gp64) is unusual in promoting entry into both insect and mammalian cells and is distinct from established class I and class II fusion proteins. We report the crystal structure of its postfusion form, which explains a number of gp64's biological properties including its cellular promiscuity, identifies the fusion peptides and shows it to be the third representative of a new class (III) of fusion proteins with unexpected structural homology with vesicular stomatitis virus G and herpes simplex virus type 1 gB proteins. We show that domains of class III proteins have counterparts in both class I and II proteins, suggesting that all these viral fusion machines are structurally more related than previously thought.

Dual-specificity phosphatases in the hypo-osmotic stress response of keratin-defective epithelial cell lines

Although mutations in intermediate filament proteins cause many human disorders, the detailed pathogenic mechanisms and the way these mutations affect cell metabolism are unclear. In this study, selected keratin mutations were analysed for their effect on the epidermal stress response. Expression profiles of two keratin-mutant cell lines from epidermolysis bullosa simplex patients (one severe and one mild) were compared to a control keratinocyte line before and after challenge with hypo-osmotic shock, a common physiological stress that transiently distorts cell shape. Fewer changes in gene expression were found in cells with the severely disruptive mutation (55 genes altered) than with the mild mutation (174 genes) or the wild type cells (261 genes) possibly due to stress response pre-activation in these cells. We identified 16 immediate-early genes contributing to a general cell response to hypo-osmotic shock, and 20 genes with an altered expression pattern in the mutant keratin lines only. A number of dual-specificity phosphatases (MKP-1, MKP-2, MKP-3, MKP-5 and hVH3) are differentially regulated in these cells, and their downstream targets p-ERK and p-p38 are significantly up-regulated in the mutant keratin lines. Our findings strengthen the case for the expression of mutant keratin proteins inducing physiological stress, and this intrinsic stress may affect the cell responses to secondary stresses in patients' skin.

Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467-475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters' prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters' prior beliefs. (c) 2006 Elsevier B.V. All rights reserved.

Statistical isomorphism of three-level factional factorial designs

From a statistician's standpoint, the interesting kind of isomorphism for fractional factorial designs depends on the statistical application. Combinatorially isomorphic fractional factorial designs may have different statistical properties when factors are quantitative. This idea is illustrated by using Latin squares of order 3 to obtain fractions of the 3(3) factorial. design in 18 runs.

Large supersaturated designs

A supersaturated design (SSD) is an experimental plan, useful for evaluating the main effects of m factors with n experimental units when m > n - 1, each factor has two levels and when the first-order effects of only a few factors are expected to have dominant effects on the response. Use of these plans can be extremely cost-effective when it is necessary to screen hundreds or thousands of factors with a limited amount of resources. In this article we describe how to use cyclic balanced incomplete block designs and regular graph designs to construct E (s(2)) optimal and near optimal SSDs when m is a multiple of n - 1. We also provide a table that can be used to construct these designs for screening thousands of factors. We also explain how to obtain SSDs when m is not a multiple of n - 1. Using the table and the approaches given in this paper, SSDs can be developed for designs with up to 24 runs and up to 12,190 factors.

Some new three-level orthogonal main effects plans robust to model uncertainty

In this paper, we list some new orthogonal main effects plans for three-level designs for 4, 5 and 6 factors in IS runs and compare them with designs obtained from the existing L-18 orthogonal array. We show that these new designs have better projection properties and can provide better parameter estimates for a range of possible models. Additionally, we study designs in other smaller run-sizes when there are insufficient resources to perform an 18-run experiment. Plans for three-level designs for 4, 5 and 6 factors in 13 to 17 runs axe given. We show that the best designs here are efficient and deserve strong consideration in many practical situations.

A Bayesian design criterion for locating the optimum point on a response surface

Most factorial experiments in industrial research form one stage in a sequence of experiments and so considerable prior knowledge is often available from earlier stages. A Bayesian A-optimality criterion is proposed for choosing designs, when each stage in experimentation consists of a small number of runs and the objective is to optimise a response. Simple formulae for the weights are developed, some examples of the use of the design criterion are given and general recommendations are made. (C) 2003 Elsevier B.V. All rights reserved.

Chemical and aerosol characterisation of the troposphere over West Africa during the monsoon period as part of AMMA

During June, July and August 2006 five aircraft took part in a campaign over West Africa to observe the aerosol content and chemical composition of the troposphere and lower stratosphere as part of the African Monsoon Multidisciplinary Analysis (AMMA) project. These are the first such measurements in this region during the monsoon period. In addition to providing an overview of the tropospheric composition, this paper provides a description of the measurement strategy (flights performed, instrumental payloads, wing-tip to wing-tip comparisons) and points to some of the important findings discussed in more detail in other papers in this special issue. The ozone data exhibits an "S" shaped vertical profile which appears to result from significant losses in the lower troposphere due to rapid deposition to forested areas and photochemical destruction in the moist monsoon air, and convective uplift of ozone-poor air to the upper troposphere. This profile is disturbed, particularly in the south of the region, by the intrusions in the lower and middle troposphere of air from the southern hemisphere impacted by biomass burning. Comparisons with longer term data sets suggest the impact of these intrusions on West Africa in 2006 was greater than in other recent wet seasons. There is evidence for net photochemical production of ozone in these biomass burning plumes as well as in urban plumes, in particular that from Lagos, convective outflow in the upper troposphere and in boundary layer air affected by nitrogen oxide emissions from recently wetted soils. This latter effect, along with enhanced deposition to the forested areas, contributes to a latitudinal gradient of ozone in the lower troposphere. Biogenic volatile organic compounds are also important in defining the composition both for the boundary layer and upper tropospheric convective outflow. Mineral dust was found to be the most abundant and ubiquitous aerosol type in the atmosphere over Western Africa. Data collected within AMMA indicate that injection of dust to altitudes favourable for long-range transport (i.e. in the upper Sahelian planetary boundary layer) can occur behind the leading edge of mesoscale convective system (MCS) cold-pools. Research within AMMA also provides the first estimates of secondary organic aerosols across the West African Sahel and have shown that organic mass loadings vary between 0 and 2 μg m−3 with a median concentration of 1.07 μg m−3. The vertical distribution of nucleation mode particle concentrations reveals that significant and fairly strong particle formation events did occur for a considerable fraction of measurement time above 8 km (and only there). Very low concentrations were observed in general in the fresh outflow of active MCSs, likely as the result of efficient wet removal of aerosol particles due to heavy precipitation inside the convective cells of the MCSs. This wet removal initially affects all particle size ranges as clearly shown by all measurements in the vicinity of MCSs.

Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Anticancer activity of organotin compounds. 2. Interaction of diorganotin dihalides with nucleic acid bases and nucleosides; the synthesis of adenine, adenosine and 9-methyladenine adducts

The syntheses of the complexes formulated as SnMe2Cl2(Ad)2 (I), SnMe2Cl2(Ado)2 (II), SnMe2Cl2- (9-MeAd)2 (III) [Ad = adenine, Ado = adenosine, 9-MeAd = 9-methyladenine] as well as the more unexpected SnPhCl2(OH)(Ad)2·3H2O (IV) and SnPhCl3(Ado)2 (V) by reaction of SnMe2Cl2 or SnPh2Cl2 with the appropriate bases in methanol is described. 1H NMR studies suggest that coordination is through the N-7 position of the adenine base.