Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

On stratifiable locally convex spaces

In the present paper we prove several results on the stratifiability of locally convex spaces. In particular, we show that a free locally convex sum of an arbitrary set of stratifiable LCS is a stratifiable LCS, and that all locally convex F'-spaces whose bounded subsets are metrizable are stratifiable. Moreover, we prove that a strict inductive limit of metrizable LCS is stratifiable and establish the stratifiability of many important general and specific spaces used in functional analysis. We also construct some examples that clarify the relationship between the stratifiability and other properties.

Liquid-crystal-based reflectarray antenna with electronically switchable monopulse patterns

A printed rcflectarray antenna, which generates a beam that can be electronically switched from a sum to a difference radiation pattern, is presented. This is achieved by applying a bias voltage of 20 V to one-half of the aperture, which is constructed above a 500 mu m cavity containing liquid crystals. Simulated results are shown to be in good agreement with measurements at X-band.

Comparison of two construction algorithms for local model networks

The divide-and-conquer approach of local model (LM) networks is a common engineering approach to the identification of a complex nonlinear dynamical system. The global representation is obtained from the weighted sum of locally valid, simpler sub-models defined over small regions of the operating space. Constructing such networks requires the determination of appropriate partitioning and the parameters of the LMs. This paper focuses on the structural aspect of LM networks. It compares the computational requirements and performances of the Johansen and Foss (J&F) and LOLIMOT tree-construction algorithms. Several useful and important modifications to each algorithm are proposed. The modelling performances are evaluated using real data from a pilot plant of a pH neutralization process. Results show that while J&F achieves a more accurate nonlinear representation of the pH process, LOLIMOT requires significantly less computational effort.

Prediction of ionic liquid properties. I. Volumetric properties as a function of temperature at 0.1 MPa

The prediction of molar volumes and densities of several ionic liquids has been achieved using a group contribution model as a function of temperature between (273 and 423) K at atmospheric pressure. It was observed that the calculation of molar volumes or densities could be performed using the "ideal" behavior of the molar volumes of mixtures of ionic liquids. This model is based on the observations of Canongia Lopes et al. (J. Phys. Chem. B 2005, 109, 3519-3525) which showed that this ideal behavior is independent of the temperature and allows the molar volume of a given ionic liquid to be calculated by the sum of the effective molar volume of the component ions. Using this assumption, the effective molar volumes of ions constituting more than 220 different ionic liquids were calculated as a function of the temperature at 0.1 MPa using more than 2150 data points. These calculated results were used to build up a group contribution model for the calculation of ionic liquid molar volumes and densities with an estimated repeatability and uncertainty of 0.36% and 0.48%, respectively. The impact of impurities (water and halide content) in ionic liquids as well as the method of determination were also analyzed and quantified to estimate the overall uncertainty. © 2008 American Chemical Society.

Analysing orchestrations with risk profiles and angel-daemon games

In this paper game theory is used to analyse the effect of a number of service failures during the execution of a grid orchestration. A service failure may be catastrophic in that it causes an entire orchestration to fail. Alternatively, a grid manager may utilise alternative services in the case of failure, allowing an orchestration to recover, A risk profile provides a means of modelling situations in a way that is neither overly optimistic nor overly pessimistic. Risk profiles are analysed using angel and daemon games. A risk profile can be assigned a valuation through an analysis of the structure of its associated Nash equilibria. Some structural properties of valuation functions, that show their validity as a measure for risk, are given. Two main cases are considered, the assessment of Orc expressions and the arrangement of a meeting using reputations.

The outflow ranking method for weighted directed graphs

A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms. Besides the well-known axioms of anonymity and positive responsiveness we introduce outflow monotonicity – meaning that in pairwise comparison between two nodes, a node is not doing worse in case its own outflow does not decrease and the other node’s outflow does not increase – and order preservation – meaning that adding two weighted digraphs such that the pairwise ranking between two nodes is the same in both weighted digraphs, then this is also their pairwise ranking in the ‘sum’ weighted digraph. The outflow ranking method generalizes the ranking by outdegree for directed graphs, and therefore also generalizes the ranking by Copeland score for tournaments.

The notion of space in the artistic language of Alfredo Jaar

Conceptual art and communicator role has influenced the work of Chilean architect Alfredo Jaar, which has been proposed report, with other codes [verbal and nonverbal], global events influencing contemporary society. His early training as an architect has driven innovation in the design of artistic space , using the message to convey to the viewer the reason for his work for more than three decades, highlights the artistic composition with various material resources whose purpose lies in conceptualizing various topics relevant in considering the role of artistic communication. Jaar’s style is the sum of his own life experience in relation to the contradictions of the world today, which is exposed and from the perspective of postmodernism from the exploitation of the notion of space as an open stage for visual and expressiveness beyond national borders, societies and cultures of the world.

Translating evidence into practice: A shared priority in public health?

Translational and transdisciplinary research is needed to tackle complex public health problems. This article has three aims. Firstly, to determine how academics and non-academics (practitioners, policy makers and community workers) identified with the goals of the UKCRC Centre of Excellence for Public Health in Northern Ireland and how their attitudes varied in terms of knowledge brokerage and translation. Secondly, to map and analyse the network structure of the public health sector and the placement of the Centre within this. Thirdly, to aggregate responses from members of the network by work setting to construct the trans-sectoral network and devise the Root Mean Sum of Squares to determine the quality and potential value of connections across this network.The analysis was based on data collected from 98 individuals who attended the launch of the Centre in June 2008. Analysis of participant expectations and personal goals suggests that the academic members of the network were more likely to expect the work of the Centre to produce new knowledge than non-academics, but less likely to expect the Centre to generate health interventions and influence health policy. Academics were also less strongly oriented than non-academics to knowledge transfer as a personal goal, though more confident that research findings would be diffused beyond the immediate network. A central core of five nodes is crucial to the overall configuration of the regional public health network in Northern Ireland, with the Centre being well placed to exert influence within this. Though the overall network structure is fairly robust, the connections between some component parts of the network - such as academics and the third sector - are unidirectional.Identifying these differences and core network structure is key to translational and transdisciplinary research. Though exemplified in a regional study, these techniques are generalisable and applicable to many networks of interest: public health, interdisciplinary research or organisational involvement and stakeholder linkage.

Unite and conquer: univariate and multivariate approaches for finding differentially expressed gene sets

Motivation: Recently, many univariate and several multivariate approaches have been suggested for testing differential expression of gene sets between different phenotypes. However, despite a wealth of literature studying their performance on simulated and real biological data, still there is a need to quantify their relative performance when they are testing different null hypotheses.

Results: In this article, we compare the performance of univariate and multivariate tests on both simulated and biological data. In the simulation study we demonstrate that high correlations equally affect the power of both, univariate as well as multivariate tests. In addition, for most of them the power is similarly affected by the dimensionality of the gene set and by the percentage of genes in the set, for which expression is changing between two phenotypes. The application of different test statistics to biological data reveals that three statistics (sum of squared t-tests, Hotelling's T2, N-statistic), testing different null hypotheses, find some common but also some complementing differentially expressed gene sets under specific settings. This demonstrates that due to complementing null hypotheses each test projects on different aspects of the data and for the analysis of biological data it is beneficial to use all three tests simultaneously instead of focusing exclusively on just one.

Balanced Weights and Three-Sided Coalition Formation

We consider three-sided coalition formation problems when each agent is concerned about his local status as measured by his relative rank position within the group of his own type and about his global status as measured by the weighted sum of the average rankings of the other types of groups. We show that a core stable coalition structure always exists, provided that the corresponding weights are balanced and each agent perceives the two types of status as being substitutable.

Nebular and auroral emission lines of [Cl III] in the optical spectra of planetary nebulae

Electron impact excitation rates in Cl III, recently determined with the R-matrix code, are used to calculate electron temperature (T-e) and density (N-e) emission line ratios involving both the nebular (5517.7, 5537.9 Angstrom) and auroral (8433.9, 8480.9, 8500.0 Angstrom) transitions. A comparison of these results with observational data for a sample of planetary nebulae, obtained with the Hamilton Echelle Spectrograph on the 3-m Shane Telescope, reveals that the R-1 = /(5518 Angstrom)/I(5538 Angstrom) intensity ratio provides estimates of N-e in excellent agreement with the values derived from other line ratios in the echelle spectra. This agreement indicates that R-1 is a reliable density diagnostic for planetary nebulae, and it also provides observational support for the accuracy of the atomic data adopted in the line ratio calculations. However the [Cl III] 8433.9 Angstrom line is found to be frequently blended with a weak telluric emission feature, although in those instances when the [Cl III] intensity may be reliably measured, it provides accurate determinations of T-e when ratioed against the sum of the 5518 and 5538 Angstrom line fluxes. Similarly, the 8500.0 Angstrom line, previously believed to be free of contamination by the Earth's atmosphere, is also shown to be generally blended with a weak telluric emission feature. The [CI III] transition at 8480.9 Angstrom is found to be blended with the He I 8480.7 Angstrom line, except in planetary nebulae that show a relatively weak He I spectrum, where it also provides reliable estimates of T-e when ratioed against the nebular lines. Finally, the diagnostic potential of the near-UV [Cl III] lines at 3344 and 3354 Angstrom is briefly discussed.

Two Arginine-Glutamate Ionic Locks Near the Extracellular Surface of FFAR1 Gate Receptor Activation

Activation of a number of class A G protein-coupled receptors (GPCRs) is thought to involve two molecular switches, a rotamer toggle switch within the transmembrane domain and an ionic lock at the cytoplasmic surface of the receptor; however, the mechanism by which agonist binding changes these molecular interactions is not understood. Importantly, 80% of GPCRs including free fatty acid receptor 1 (FFAR1) lack the complement of amino acid residues implicated in either or both of these two switches; the mechanism of activation of these GPCRs is therefore less clear. By homology modeling, we identified two Glu residues (Glu-145 and Glu-172) in the second extracellular loop of FFAR1 that form putative interactions individually with two transmembrane Arg residues (Arg-183(5.39) and Arg-258(7.35)) to create two ionic locks. Molecular dynamics simulations showed that binding of agonists to FFAR1 leads to breakage of these Glu-Arg interactions. In mutagenesis experiments, breakage of these two putative interactions by substituting Ala for Glu-145 and Glu-172 caused constitutive receptor activation. Our results therefore reveal a molecular switch for receptor activation present on the extracellular surface of FFAR1 that is broken by agonist binding. Similar ionic locks between the transmembrane domains and the extracellular loops may constitute a mechanism common to other class A GPCRs also.

Discovery of novel Agonists and antagonists of the free fatty acid receptor 1 (FFAR1) using virtual screening

The G-protein-coupled receptor free fatty acid receptor 1 (FFAR1), previously named GPR40, is a possible novel target for the treatment of type 2 diabetes. In an attempt to identify new ligands for this receptor, we performed virtual screening (VS) based on two-dimensional (2D) similarity, three-dimensional (3D) pharmacophore searches, and docking studies by using the structure of known agonists and our model of the ligand binding site, which was validated by mutagenesis. VS of a database of 2.6 million compounds followed by extraction of structural neighbors of functionally confirmed hits resulted in identification of 15 compounds active at FFAR1 either as full agonists, partial agonists, or pure antagonists. Site-directed mutagenesis and docking studies revealed different patterns of ligand-receptor interactions and provided important information on the role of specific amino acids in binding and activation of FFAR1.