Supersolutions for a class of semilinear heat equations

A semilinear heat equation $u_{t}=\Delta u+f(u)$ with nonnegative initial data in a subset of $L^{1}(\Omega)$ is considered under the assumption that $f$ is nonnegative and nondecreasing and $\Omega\subseteq \R^{n}$. A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is applied to the model case $f(s)=s^{p}$, $\phi\in L^{q}(\Omega)$: new sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.Comment: Expanded version of the previous submission arXiv:1111.0258v1. 14 page

Identification and Characterisation of the RalA-ERp57 Interaction: Evidence for GDI Activity of ERp57

RalA is a membrane-associated small GTPase that regulates vesicle trafficking. Here we identify a specific interaction between RalA and ERp57, an oxidoreductase and signalling protein. ERp57 bound specifically to the GDP-bound form of RalA, but not the GTP-bound form, and inhibited the dissociation of GDP from RalA in vitro. These activities were inhibited by reducing agents, but no disulphide bonds were detected between RalA and ERp57. Mutation of all four of ERp57's active site cysteine residues blocked sensitivity to reducing agents, suggesting that redox-dependent conformational changes in ERp57 affect binding to RalA. Mutations in the switch II region of the GTPase domain of RalA specifically reduced or abolished binding to ERp57, but did not block GTP-specific binding to known RalA effectors, the exocyst and RalBP1. Oxidative treatment of A431 cells with H2O2 inhibited cellular RalA activity, and the effect was exacerbated by expression of recombinant ERp57. The oxidative treatment significantly increased the amount of RalA localised to the cytosol. These findings suggest that ERp57 regulates RalA signalling by acting as a redox-sensitive guanine-nucleotide dissociation inhibitor (RalGDI). © 2012 Brymora et al

Winter wheat roots grow twice as deep as spring wheat roots, is this important for N uptake and N leaching losses?

Cropping systems comprising winter catch crops followed by spring wheat could reduce N leaching risks compared to traditional winter wheat systems in humid climates. We studied the soil mineral N (Ninorg) and root growth of winter- and spring wheat to 2.5 m depth during three years. Root depth of winter wheat (2.2 m) was twice that of spring wheat, and this was related to much lower amounts of Ninorg in the 1 to 2.5 m layer after winter wheat (81 kg Ninorg ha-1 less). When growing winter catch crops before spring wheat, N content in the 1 to 2.5 m layer after spring wheat was not different from that after winter wheat. The results suggest that by virtue of its deep rooting, winter wheat may not lead to high levels of leaching as it is often assumed in humid climates. Deep soil and root measurements (below 1 m) in this experiment were essential to answer the questions we posed

Vigorous star formation hidden by dust in a galaxy at z=1.4z=1.4

Near-infrared surveys have revealed a substantial population of enigmatic faint galaxies with extremely red optical-to-near-infrared colours and with a sky surface density comparable to that of faint quasars. There are two scenarios for these extreme colours: (i) these distant galaxies have formed virtually all their stars at very high redshifts and, due to the absence of recently formed stars, the colours are extremely red and (ii) these distant galaxies contain large amounts of dust, severely reddening the rest-frame UV--optical spectrum. HR10 ($z = 1.44$) is considered the archetype of the extremely red galaxies. Here we report the detection of the continuum emission from HR10 at 850$\mu$m and at 1250$\mu$m, demonstrating that HR10 is a very dusty galaxy undergoing a major episode of star formation. Our result provides a clear example of a high-redshift galaxy where the star formation rate inferred from the ultraviolet luminosity would be underestimated by a factor up to 1000, and shows that great caution should be used to infer the global star formation history of the Universe from optical observations only.Comment: 12 pages, 1 figure, Nature, in press (30 April 1998

DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

We present the latest major release version 6.0 of the quantified Boolean formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of the conflict-driven clause learning (CDCL) paradigm implemented in state of the art propositional satisfiability (SAT) solvers. The Q-resolution calculus (QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0 implements a variant of QCDCL which is based on a generalization of QRES. This generalization is due to a set of additional axioms and leaves the original Q-resolution rules unchanged. The generalization of QRES enables QCDCL to potentially produce exponentially shorter proofs than the traditional variant. We present an overview of the features implemented in DepQBF and report on experimental results which demonstrate the effectiveness of generalized QRES in QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS, Springer, 201

Alterations in vascular function in primary aldosteronism - a cardiovascular magnetic resonance imaging study

Introduction: Excess aldosterone is associated with increased cardiovascular risk. Aldosterone has a permissive effect on vascular fibrosis. Cardiovascular magnetic resonance imaging (CMR) allows study of vascular function by measuring aortic distensibility. We compared aortic distensibility in primary aldosteronism (PA), essential hypertension (EH) and normal controls and explored the relationship between aortic distensibility and pulse wave velocity (PWV).<p></p> Methods: We studied PA (n=14) and EH (n=33) subjects and age-matched healthy controls (n=17) with CMR, including measurement of aortic distensibility, and measured PWV using applanation tonometry. At recruitment, PA and EH patients had similar blood pressure and left ventricular mass.<p></p> Results: Subjects with PA had significantly lower aortic distensibilty and higher PWV compared to EH and healthy controls. These changes were independent of other factors associated with reduced aortic distensibility, including aging. There was a significant relationship between increasing aortic stiffness and age in keeping with physical and vascular aging. As expected, aortic distensibility and PWV were closely correlated.<p></p> Conclusion: These results demonstrate that PA patients display increased arterial stiffness compared to EH, independent of vascular aging. The implication is that aldosterone invokes functional impairment of arterial function. The long-term implications of arterial stiffening in aldosterone excess require further study.<p></p&gt

Demography and disorders of German Shepherd Dogs under primary veterinarycare in the UK

The German Shepherd Dog (GSD) has been widely used for a variety of working roles. However, concerns for the health and welfare of the GSD have been widely aired and there is evidence that breed numbers are now in decline in the UK. Accurate demographic and disorder data could assist with breeding and clinical prioritisation. The VetCompassTM Programme collects clinical data on dogs under primary veterinary care in the UK. This study included all VetCompassTM dogs under veterinary care during 2013. Demographic, mortality and clinical diagnosis data on GSDs were extracted and reported

Engaging with community researchers for exposure science: lessons learned from a pesticide biomonitoring study

A major challenge in biomonitoring studies with members of the general public is ensuring their continued involvement throughout the necessary length of the research. The paper presents evidence on the use of community researchers, recruited from local study areas, as a mechanism for ensuring effective recruitment and retention of farmer and resident participants for a pesticides biomonitoring study. The evidence presented suggests that community researchers' abilities to build and sustain trusting relationships with participants enhanced the rigour of the study as a result of their on-the-ground responsiveness and flexibility resulting in data collection beyond targets expected

On-the-fly decoding luminescence lifetimes in the microsecond region for lanthanide-encoded suspension arrays

Significant multiplexing capacity of optical time-domain coding has been recently demonstrated by tuning luminescence lifetimes of the upconversion nanoparticles called 'τ-Dots'. It provides a large dynamic range of lifetimes from microseconds to milliseconds, which allows creating large libraries of nanotags/microcarriers. However, a robust approach is required to rapidly and accurately measure the luminescence lifetimes from the relatively slow-decaying signals. Here we show a fast algorithm suitable for the microsecond region with precision closely approaching the theoretical limit and compatible with the rapid scanning cytometry technique.We exploit this approach to further extend optical time-domain multiplexing to the downconversion luminescence, using luminescence microspheres wherein lifetimes are tuned through luminescence resonance energy transfer.We demonstrate real-time discrimination of these microspheres in the rapid scanning cytometry, and apply them to the multiplexed probing of pathogen DNA strands. Our results indicate that tunable luminescence lifetimes have considerable potential in high-throughput analytical sciences. © 2014 Macmillan Publishers Limited. All rights reserved

Process evaluation for complex interventions in primary care: understanding trials using the normalization process model

Background: the Normalization Process Model is a conceptual tool intended to assist in understanding the factors that affect implementation processes in clinical trials and other evaluations of complex interventions. It focuses on the ways that the implementation of complex interventions is shaped by problems of workability and integration.Method: in this paper the model is applied to two different complex trials: (i) the delivery of problem solving therapies for psychosocial distress, and (ii) the delivery of nurse-led clinics for heart failure treatment in primary care.Results: application of the model shows how process evaluations need to focus on more than the immediate contexts in which trial outcomes are generated. Problems relating to intervention workability and integration also need to be understood. The model may be used effectively to explain the implementation process in trials of complex interventions.Conclusion: the model invites evaluators to attend equally to considering how a complex intervention interacts with existing patterns of service organization, professional practice, and professional-patient interaction. The justification for this may be found in the abundance of reports of clinical effectiveness for interventions that have little hope of being implemented in real healthcare setting