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.

Recategorization and subgroup identification: predicting and preventing threats from common ingroups

Much work has supported the idea that recategorization of ingroups and outgroups into a superordinate category can have beneficial effects for intergroup relations. Recently, however, increases in bias following recategorization have been observed in some contexts. It is argued that such unwanted consequences of recategorization will only be apparent for perceivers who are highly committed to their ingroup subgroups. In Experiments 1 to 3, the authors observed, on both explicit and implicit measures, that an increase in bias following recategorization occurred only for high subgroup identifiers. In Experiment 4, it was found that maintaining the salience of subgroups within a recategorized superordinate group averted this increase in bias for high identifiers and led overall to the lowest levels of bias. These findings are discussed in the context of recent work on the Common Ingroup Identity Model.

On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.

On the maximal connected component of hypercube with faulty vertices (II)

evaluating the fault tolerance of an interconnection network, it is essential to estimate the size of a maximal connected component of the network at the presence of faulty processors. Hypercube is one of the most popular interconnection networks. In this paper, we prove that for ngreater than or equal to6, an n-dimensional cube with a set F of at most (4n-10) failing processors has a component of size greater than or equal to2"-\F-3. This result demonstrates the superiority of hypercube in terms of the fault tolerance.

On the maximal connected component of a hypercube with faulty vertices III

Hypercube is one of the most popular topologies for connecting processors in multicomputer systems. In this paper we address the maximum order of a connected component in a faulty cube. The results established include several known conclusions as special cases. We conclude that the hypercube structure is resilient as it includes a large connected component in the presence of large number of faulty vertices.

Effective elements of cognitive behaviour therapy for psychosis: results of a novel type of subgroup analysis based on principal stratification

Background. Meta-analyses show that cognitive behaviour therapy for psychosis (CBT-P) improves distressing positive symptoms. However, it is a complex intervention involving a range of techniques. No previous study has assessed the delivery of the different elements of treatment and their effect on outcome. Our aim was to assess the differential effect of type of treatment delivered on the effectiveness of CBT-P, using novel statistical methodology. Method. The Psychological Prevention of Relapse in Psychosis (PRP) trial was a multi-centre randomized controlled trial (RCT) that compared CBT-P with treatment as usual (TAU). Therapy was manualized, and detailed evaluations of therapy delivery and client engagement were made. Follow-up assessments were made at 12 and 24 months. In a planned analysis, we applied principal stratification (involving structural equation modelling with finite mixtures) to estimate intention-to-treat (ITT) effects for subgroups of participants, defined by qualitative and quantitative differences in receipt of therapy, while maintaining the constraints of randomization. Results. Consistent delivery of full therapy, including specific cognitive and behavioural techniques, was associated with clinically and statistically significant increases in months in remission, and decreases in psychotic and affective symptoms. Delivery of partial therapy involving engagement and assessment was not effective. Conclusions. Our analyses suggest that CBT-P is of significant benefit on multiple outcomes to patients able to engage in the full range of therapy procedures. The novel statistical methods illustrated in this report have general application to the evaluation of heterogeneity in the effects of treatment.

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

Exposure to parabens at the concentration of maximal proliferative response increases migratory and invasive activity of human breast cancer cells in vitro

Alkyl esters of p–hydroxybenzoic acid (parabens) are widely used as preservatives in personal care products, foods and pharmaceuticals. Their oestrogenic activity, their measurement in human breast tissue and their ability to drive proliferation of oestrogen-responsive human breast cancer cells has opened a debate on their potential to influence breast cancer development. Since proliferation is not the only hallmark of cancer cells, we have investigated the effects of exposure to parabens at concentrations of maximal proliferative response on migratory and invasive properties using three oestrogen-responsive human breast cancer cell lines (MCF-7, T-47-D, ZR-75-1). Cells were maintained short-term (1 week) or long-term (20±2 weeks) in phenol-red-free medium containing 5% charcoal-stripped serum with no addition, 10-8M 17-oestradiol, 1-5x10-4M methylparaben, 10-5M n-propylparaben or 10-5M n-butylparaben. Long-term exposure (20±2 weeks) of MCF-7 cells to methylparaben, n-propylparaben or n-butylparaben increased migration as measured using a scratch assay, time-lapse microscopy and xCELLigence technology: invasive properties were found to increase in matrix degradation assays and migration through matrigel on xCELLigence. Western immunoblotting showed an associated downregulation of E-cadherin and -catenin in the long-term paraben-exposed cells which could be consistent with a mechanism involving epithelial to mesenchymal transition. Increased migratory activity was demonstrated also in long-term paraben-exposed T-47-D and ZR-75-1 cells using a scratch assay and time-lapse microscopy. This is the first report that in vitro, parabens can influence not only proliferation but also migratory and invasive properties of human breast cancer cells.

A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Regulation of the ERK subgroup of MAP kinase cascades through G protein-coupled receptors.

The extracellularly-responsive kinase (ERK) subfamily of mitogen-activated protein kinases (MAPKs) has been implicated in the regulation of cell growth and differentiation. Activation of ERKs involves a two-step protein kinase cascade lying upstream from ERK, in which the Raf family are the MAPK kinase kinases and the MEK1/MEK2 isoforms are the MAPK kinases. The linear sequence of Raf --> MEK --> ERK constitutes the ERK cascade. Although the ERK cascade is activated through growth factor-regulated receptor protein tyrosine kinases, they are also modulated through G protein-coupled receptors (GPCRs). All four G protein subfamilies (Gq/11 Gi/o, Gs and G12/13) influence the activation state of ERKs. In this review, we describe the ERK cascade and characteristics of its activation through GPCRs. We also discuss the identity of the intervening steps that may couple agonist binding at GPCRs to activation of the ERK cascade.