Finite element approximation of a sixth order nonlinear degenerate parabolic equation

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ?.( b(u)? 2u), where generically b(u) := |u|? for any given ? ? (0,?). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ? 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented.

An adaptive finite element water column model using the Mellor-Yamada level 2.5 turbulence closure scheme

A one-dimensional water column model using the Mellor and Yamada level 2.5 parameterization of vertical turbulent fluxes is presented. The model equations are discretized with a mixed finite element scheme. Details of the finite element discrete equations are given and adaptive mesh refinement strategies are presented. The refinement criterion is an "a posteriori" error estimator based on stratification, shear and distance to surface. The model performances are assessed by studying the stress driven penetration of a turbulent layer into a stratified fluid. This example illustrates the ability of the presented model to follow some internal structures of the flow and paves the way for truly generalized vertical coordinates. (c) 2005 Elsevier Ltd. All rights reserved.

Beurling zeta functions, generalised primes, and fractal membranes

We study generalised prime systems P (1 < p(1) <= p(2) <= ..., with p(j) is an element of R tending to infinity) and the associated Beurling zeta function zeta p(s) = Pi(infinity)(j=1)(1 - p(j)(-s))(-1). Under appropriate assumptions, we establish various analytic properties of zeta p(s), including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of zeta p(s). Further we study 'well-behaved' g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on N-2. Some of the above results are relevant to the second author's theory of 'fractal membranes', whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.

Early social experience and individual differences in infants' joint attention

Fifty-nine healthy infants were filmed with their mothers and with a researcher at two, four, six and nine months in face-to-face play, and in toy-play at six and nine months. During toy-play at both ages, two indices of joint attention (JA)—infant bids for attention, and percent of time in shared attention—were assessed, along with other behavioural measures. Global ratings were made at all four ages of infants’ and mothers’ interactive style. The mothers varied in psychiatric history (e.g., half had experienced postpartum depression) and socioeconomic status, so their interactive styles were diverse. Variation in nine-month infant JA — with mother and with researcher — was predicted by variation in maternal behaviour and global ratings at six months, but not at two or four months. Concurrent adult behaviour also influenced nine-month JA, independent of infant ratings. Six-month maternal behaviours that positively predicted later JA (some of which remained important at nine months) included teaching, conjoint action on a toy, and global sensitivity. Other behaviours (e.g., entertaining) negatively predicted later JA. Findings are discussed in terms of social-learning and neurobiological accounts of JA emergence.

Excision of anabaena PCC 7120 nifD element in escherichia coli: growth kinetics and RecA regulated xisA expression and DNA rearrangement

Anabaena PCC 7120 nifHDK operon is interrupted by an 11 kb DNA element which is excised during the development of heterocysts by Excisase A, encoded by the xisA gene residing on the element. The excision is a site-specific recombination event that occurs at the I I base pair direct repeats flanking the element. Earlier work showed the excision of the I I kb element in Escherichia coli at a frequency 0.3%. We report here the excision of this element at 1.1% and 1.98% in E. coli DH5 alpha, and 1.9% and 10.9% in E. coli JM 101 when grown on Luria broth and minimal media, respectively. Excision of nifD element in isogenic recA(-) (RK1) and recA(+) (RK2) E. coli JM101 P1 transductants, showed similar results to that of E. coli JM101 and DH5 alpha, respectively. A plasmid pMX32, carrying a xisA defective 11 kb element, showed no excision in E. coli RK2 strain. In contrast to Anabaena PCC 7120, excision of nifD element did not increase in E. call DH5 alpha grown in iron-deficient conditions. A PxisA::lacZ transcriptional fusion, used to detect the expression of elusive xisA gene, showed maximal beta-galactosidase activity in the stationary phase. The results suggest that the excision event in E. coli may involve additional factors, such as RecA and that the physiological status can influence the excision of nifD element. (C) 2007 Elsevier Ltd. All rights reserved.

Fitting models for the joint action of two drugs using SAS(R)

Combinations of drugs are increasingly being used for a wide variety of diseases and conditions. A pre-clinical study may allow the investigation of the response at a large number of dose combinations. In determining the response to a drug combination, interest may lie in seeking evidence of synergism, in which the joint action is greater than the actions of the individual drugs, or of antagonism, in which it is less. Two well-known response surface models representing no interaction are Loewe additivity and Bliss independence, and Loewe or Bliss synergism or antagonism is defined relative to these. We illustrate an approach to fitting these models for the case in which the marginal single drug dose-response relationships are represented by four-parameter logistic curves with common upper and lower limits, and where the response variable is normally distributed with a common variance about the dose-response curve. When the dose-response curves are not parallel, the relative potency of the two drugs varies according to the magnitude of the desired effect and the models for Loewe additivity and synergism/antagonism cannot be explicitly expressed. We present an iterative approach to fitting these models without the assumption of parallel dose-response curves. A goodness-of-fit test based on residuals is also described. Implementation using the SAS NLIN procedure is illustrated using data from a pre-clinical study. Copyright © 2007 John Wiley & Sons, Ltd.

Towards a population ecology of stressed environments: the effects of zinc on the springtail Folsomia candida

1. To understand population dynamics in stressed environments it is necessary to join together two classical lines of research. Population responses to environmental stress have been studied at low density in life table response experiments. These show how the population's growth rate (pgr) at low density varies in relation to levels of stress. Population responses to density, on the other hand, are based on examination of the relationship between pgr and population density. 2. The joint effects of stress and density on pgr can be pictured as a contour map in which pgr varies with stress and density in the same way that the height of land above sea level varies with latitude and longitude. Here a microcosm experiment is reported that compared the joint effects of zinc and population density on the pgr of the springtail Folsomia candida (Collembola). 3. Our experiments allowed the plotting of a complete map of the effects of density and a stressor on pgr. Particularly important was the position of the pgr= 0 contour, which suggested that carrying capacity varied little with zinc concentration until toxic levels were reached. 4. This prediction accords well with observations of population abundance in the field. The method also allowed us to demonstrate, simultaneously, hormesis, toxicity, an Allee effect and density dependence. 5. The mechanisms responsible for these phenomena are discussed. As zinc is an essential trace element the initial increase in pgr is probably a consequence of dietary zinc deficiency. The Allee effect may be attributed to productivity of the environment increasing with density at low density. Density dependence is a result of food limitation. 6. Synthesis and applications. We illustrate a novel solution based on mapping a population's growth rate in relation to stress and population density. Our method allows us to demonstrate, simultaneously, hormesis, toxicity, an Allee effect and density dependence in an important ecological indicator species. We hope that the approach followed here will prove to have general applicability enabling predictions of field abundance to be made from estimates of the joint effects of the stressors and density on population growth rate.