The representation of conditional expectations of non-Gaussian noise

For Wiener spaces conditional expectations and $L^{2}$-martingales w.r.t. the natural filtration have a natural representation in terms of chaos expansion. In this note an extension to larger classes of processes is discussed. In particular, it is pointed out that orthogonality of the chaos expansion is not required.

On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

The Representative Soil Sampling Scheme of England and Wales: a statistical analysis of topsoil nutrient status and pH between 1971 and 2001

The Representative Soil Sampling Scheme of England and Wales has recorded information on the soil of agricultural land in England and Wales since 1969. It is a valuable source of information about the soil in the context of monitoring for sustainable agricultural development. Changes in soil nutrient status and pH were examined over the period 1971-2001. Several methods of statistical analysis were applied to data from the surveys during this period. The main focus here is on the data for 1971, 1981, 1991 and 2001. The results of examining change over time in general show that levels of potassium in the soil have increased, those of magnesium have remained fairly constant, those of phosphorus have declined and pH has changed little. Future sampling needs have been assessed in the context of monitoring, to determine the mean at a given level of confidence and tolerable error and to detect change in the mean over time at these same levels over periods of 5 and 10 years. The results of a non-hierarchical multivariate classification suggest that England and Wales could be stratified to optimize future sampling and analysis. To monitor soil quality and health more generally than for agriculture, more of the country should be sampled and a wider range of properties recorded.

Estimating uncertainty in terrestrial critical loads and their exceedances at four sites in the UK

Critical loads are the basis for policies controlling emissions of acidic substances in Europe and elsewhere. They are assessed by several elaborate and ingenious models, each of which requires many parameters, and have to be applied on a spatially-distributed basis. Often the values of the input parameters are poorly known, calling into question the validity of the calculated critical loads. This paper attempts to quantify the uncertainty in the critical loads due to this "parameter uncertainty", using examples from the UK. Models used for calculating critical loads for deposition of acidity and nitrogen in forest and heathland ecosystems were tested at four contrasting sites. Uncertainty was assessed by Monte Carlo methods. Each input parameter or variable was assigned a value, range and distribution in an objective a fashion as possible. Each model was run 5000 times at each site using parameters sampled from these input distributions. Output distributions of various critical load parameters were calculated. The results were surprising. Confidence limits of the calculated critical loads were typically considerably narrower than those of most of the input parameters. This may be due to a "compensation of errors" mechanism. The range of possible critical load values at a given site is however rather wide, and the tails of the distributions are typically long. The deposition reductions required for a high level of confidence that the critical load is not exceeded are thus likely to be large. The implication for pollutant regulation is that requiring a high probability of non-exceedance is likely to carry high costs. The relative contribution of the input variables to critical load uncertainty varied from site to site: any input variable could be important, and thus it was not possible to identify variables as likely targets for research into narrowing uncertainties. Sites where a number of good measurements of input parameters were available had lower uncertainties, so use of in situ measurement could be a valuable way of reducing critical load uncertainty at particularly valuable or disputed sites. From a restricted number of samples, uncertainties in heathland critical loads appear comparable to those of coniferous forest, and nutrient nitrogen critical loads to those of acidity. It was important to include correlations between input variables in the Monte Carlo analysis, but choice of statistical distribution type was of lesser importance. Overall, the analysis provided objective support for the continued use of critical loads in policy development. (c) 2007 Elsevier B.V. All rights reserved.

The Structure and implications of children's attitudes to school

The paper reports a study of children's attitudes to school based on a questionnaire survey of 845 pupils in their first year of secondary school in England, together with interviews with a sample of the children. A clearly structured set of attitudes emerged from a factor analysis which showed a distinction between instrumental and affective aspects of attitudes but also dimensions within these, including a sense of teacher commitment and school as a difficult environment. Virtually all children had a strong sense of the importance of doing well at school. However, a substantial minority were not sure that they would stay on after 16. There were few differences between boys and girls or between children from different socio-economic backgrounds but children planning to leave at 16 enjoyed school less and were less sure that it had anything to offer them. There was an almost universal commitment to the value of education but, for a minority, an ambivalence about the experience and relevance of schooling for them.

Transformation of maize using silicon carbide whiskers

As the most commercially valuable cereal grown worldwide and the best-characterized in genetic terms, maize was predictably the first target for transformation among the important crops. Indeed, the first attempt at transformation of any plant was conducted on maize (1). These early efforts, however, were inevitably unsuccessful, since at that time, there were no reliable methods to permit the introduction of DNA into a cell, the expression of that DNA, and the identification of progeny derived from such a “transgenic” cell (2). Almost 20 years later, these technologies were finally combined, and the first transgenic cereals were produced. In the last few years, methods have become increasingly efficient, and transgenic maize has now been produced from protoplasts as well as from Agrobacterium-medieited or “Biolistic” delivery to embryogenic tissue (for a general comparison of methods used for maize, the reader is referred to a recent review—ref. 3). The present chapter will describe probably the simplest of the available procedures, namely the delivery of DNA to the recipient cells by vortexing them in the presence of silicon carbide (SiC) whiskers (this name will be used in preference to the term “fiber,” since it more correctly describes the single crystal nature of the material).

Hay strewing, brush harvesting of seed and soil disturbance as tools for the enhancement of botanical diversity in grasslands

Since the middle of the last century agricultural intensification within Europe has led to a drastic decline in the extent of botanically diverse grasslands. Whilst measures to enhance the diversity of agriculturally-improved grasslands are in place, success has often been limited. One of the primary factors limiting success is the paucity of sources of propagules of desirable species in the surrounding landscape. The restoration of two contrasting grassland types lowland hay meadow and chalk grassland) was examined using a replicated block experiment to assess the effectiveness of two methods of seed application (hay strewing and brush harvesting) and two methods of pre-treatment disturbance (power harrowing and turf stripping). The resulting changes in botanical composition were monitored for 4 years. Seed addition by both methods resulted in significant temporal trends in plant species composition and increases in plant species richness, which were further enhanced by disturbance. Power harrowing increased the effectiveness of the seed addition treatments at the lowland hay meadow site. At the chalk grassland site a more severe disturbance created by turf stripping was used and shown to be preferable. Whilst both hay strewing and brush harvesting increased plant species richness, hay strewing was more effective at creating a sward similar to that of the donor site. Soil disturbance and seed application rate at the recipient site and timing of the hay cut at the donor site are all factors to be considered prior to the commencement of restoration management. (c) 2006 Elsevier Ltd. All rights reserved.

Consumer welfare effects of introducing and labeling genetically modified food

Non-hypothetical valuations obtained from experimental auctions in three United States and two European locations were used to calculate welfare effects of introducing and labeling of genetically modified food. Under certain assumptions, we find that introduction of genetically modified food has been welfare enhancing, on average, for United States consumers but not so for Europeans and while mandatory labeling has been beneficial for European consumers, such a policy would be detrimental in the United States. (c) 2005 Elsevier B.V. All rights reserved.

Forced expression of the cyclin B1-CDC2 complex induces proliferation in adult rat cardiomyocytes

Repair of the mature mammalian myocardium following injury is impaired by the inability of the majority of cardiomyocytes to undergo cell division. We show that overexpression of the cyclin B1-CDC2 (cell division cycle 2 kinase) complex re-initiates cell division in adult cardiomyocytes. Thus strategies targeting the cyclin B1-CDC2 complex might re-initiate cell division in mature cardiomyocytes in vivo and facilitate myocardial regeneration following injury.