Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Differential changes in transforming growth factor β isoform expression during postnatal cardiac growth

Transforming growth factor-β (TGF-β) is synthesised as an inactive precursor protein; this is cleaved to produce the mature peptide and a latency associated protein (LAP), which remains associated with the mature peptide until activation by LAP degradation. Isoform specific antibodies raised against the LAPs for TGF-β2and -β3were used to determine the myocardial levels of LAP (activatable TGF-β) and full length precursor (inactive TGF-β) forms during post-natal development in the rat. TGF-β2was present predominantly as the precursor in 2 day old myocardium. There was an age-dependent shift from precursor protein to LAP between 2 and 28 days. A corresponding increase in the level of mature (activatable) TGF-β2was found. TGF-β3was detected in significant quantities only as LAP. However, a four-fold increase in the expression of TGF-β3LAP was observed between 2 and 28 days. The substantial increases in activatable forms of TGF-β2and -β3that occur in myocardium during the first 28 days of life in the rat support a role for these proteins in post-natal cardiac development.

New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Exploration vs exploitation in differential evolution

Differential Evolution (DE) is a tool for efficient optimisation, and it belongs to the class of evolutionary algorithms, which include Evolution Strategies and Genetic Algorithms. DE algorithms work well when the population covers the entire search space, and they have shown to be effective on a large range of classical optimisation problems. However, an undesirable behaviour was detected when all the members of the population are in a basin of attraction of a local optimum (local minimum or local maximum), because in this situation the population cannot escape from it. This paper proposes a modification of the standard mechanisms in DE algorithm in order to change the exploration vs. exploitation balance to improve its behaviour.

Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.

The metaphysics of self in Praśastapāda's differential naturalism

In A Compendium of the Characteristics of Categories (Padārthadharmasaṃgraha) the classical Vaiśeṣika philosopher Praśastapāda (6th c. CE) presents an innovative metaphysics of the self. This article examines the defining metaphysical and axiological features of this conception of self and the dualist categorial schema in which it is located. It shows how this idea of the self, as a reflexive and ethical being, grounds a multinaturalist view of natural order and offers a conception of agency that claims to account for all the reflexive features of human mental and bodily life. Finally, it discusses the ends of self’s reflexivity and of human life as a return to the true self. It argues that at the heart of Praśastapāda’s metaphysics of self is the idea that ethics is metaphysics, and that epistemic practice is ethical practice.

Selection-mutation balance models with epistatic selection

We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potentials

Transport and distribution of lindane and simazine in a riverine environment: measurements in bed sediments and modelling

Aquatic sediments often remove hydrophobic contaminants from fresh waters. The subsequent distribution and concentration of contaminants in bed sediments determines their effect on benthic organisms and the risk of re-entry into the water and/or leaching to groundwater. This study examines the transport of simazine and lindane in aquatic bed sediments with the aim of understanding the processes that determine their depth distribution. Experiments in flume channels (water flow of 10 cm s(-1)) determined the persistence of the compounds in the absence of sediment with (a) de-ionised water and (b) a solution that had been in contact with river sediment. In further experiments with river bed sediments in light and dark conditions, measurements were made of the concentration of the compounds in the overlying water and the development of bacterial/algal biofilms and bioturbation activity. At the end of the experiments, concentrations in sediments and associated pore waters were determined in sections of the sediment at 1 mm resolution down to 5 mm and then at 10 mm resolution to 50 mm depth and these distributions analysed using a sorption-diffusion-degradation model. The fine resolution in the depth profile permitted the detection of a maximum in the concentration of the compounds in the pore water near the surface, whereas concentrations in the sediment increased to a maximum at the surface itself. Experimental distribution coefficients determined from the pore water and sediment concentrations indicated a gradient with depth that was partly explained by an increase in organic matter content and specific surface area of the solids near the interface. The modelling showed that degradation of lindane within the sediment was necessary to explain the concentration profiles, with the optimum agreement between the measured and theoretical profiles obtained with differential degradation in the oxic and anoxic zones. The compounds penetrated to a depth of 40-50 rum over a period of 42 days. (C) 2004 Society of Chemical Industry.

Production of tense marking in successive bilingual children: when do they converge with their monolingual peers?

Children with English as a second language (L2) with exposure of 18 months or less exhibit similar difficulties to children with Specific Language Impairment in tense marking, a marker of language impairment for English. This paper examines whether L2 children with longer exposure converge with their monolingual peers in the production of tense marking. 38 Turkish-English L2 children with a mean age of 7;8 and 33 monolingual age-matched controls completed the screening test of the Test of Early Grammatical Impairment (TEGI). The L2 children as a group were as accurate as the controls in the production of -ed, but performed significantly lower than the controls in the production of third person –s. Age and YoE affected the children’s performance. The highest age-expected performance on the TEGI was attested in eight and nine year-old children who had 4-6 YoE. L1 and L2 children performed better in regular compared to irregular verbs, but L2 children overregularized more than L1 children and were less sensitive to the phonological properties of verbs. The results show that tense marking and the screening test of the TEGI may be promising for differential diagnosis in eight and nine year-old L2 children with at least four YoE.

Transcriptome analysis of grain development in hexaploid wheat

Background: Hexaploid wheat is one of the most important cereal crops for human nutrition. Molecular understanding of the biology of the developing grain will assist the improvement of yield and quality traits for different environments. High quality transcriptomics is a powerful method to increase this understanding. Results: The transcriptome of developing caryopses from hexaploid wheat ( Triticum aestivum, cv. Hereward) was determined using Affymetrix wheat GeneChip (R) oligonucleotide arrays which have probes for 55,052 transcripts. Of these, 14,550 showed significant differential regulation in the period between 6 and 42 days after anthesis ( daa). Large changes in transcript abundance were observed which were categorised into distinct phases of differentiation ( 6 - 10 daa), grain fill ( 12 - 21 daa) and desiccation/maturation ( 28 - 42 daa) and were associated with specific tissues and processes. A similar experiment on developing caryopses grown with dry and/or hot environmental treatments was also analysed, using the profiles established in the first experiment to show that most environmental treatment effects on transcription were due to acceleration of development, but that a few transcripts were specifically affected. Transcript abundance profiles in both experiments for nine selected known and putative wheat transcription factors were independently confirmed by real time RT-PCR. These expression profiles confirm or extend our knowledge of the roles of the known transcription factors and suggest roles for the unknown ones. Conclusion: This transcriptome data will provide a valuable resource for molecular studies on wheat grain. It has been demonstrated how it can be used to distinguish general developmental shifts from specific effects of treatments on gene expression and to diagnose the probable tissue specificity and role of transcription factors.