On the spectrum of hypergraphs

Here we study the spectral properties of an underlying weighted graph of a non-uniform hypergraph by introducing different connectivity matrices, such as adjacency, Laplacian and normalized Laplacian matrices. We show that different structural properties of a hypergrpah, can be well studied using spectral properties of these matrices. Connectivity of a hypergraph is also investigated by the eigenvalues of these operators. Spectral radii of the same are bounded by the degrees of a hypergraph. The diameter of a hypergraph is also bounded by the eigenvalues of its connectivity matrices. We characterize different properties of a regular hypergraph characterized by the spectrum. Strong (vertex) chromatic number of a hypergraph is bounded by the eigenvalues. Cheeger constant on a hypergraph is defined and we show that it can be bounded by the smallest nontrivial eigenvalues of Laplacian matrix and normalized Laplacian matrix, respectively, of a connected hypergraph. We also show an approach to study random walk on a (non-uniform) hypergraph that can be performed by analyzing the spectrum of transition probability operator which is defined on that hypergraph. Ricci curvature on hypergraphs is introduced in two different ways. We show that if the Laplace operator, $\Delta$, on a hypergraph satisfies a curvature-dimension type inequality $CD (\mathbf{m}, \mathbf{K})$ with $\mathbf{m}>1$ and $\mathbf{K}>0$ then any non-zero eigenvalue of $- \Delta$ can be bounded below by $\frac{ \mathbf{m} \mathbf{K}}{ \mathbf{m} -1 }$. Eigenvalues of a normalized Laplacian operator defined on a connected hypergraph can be bounded by the Ollivier's Ricci curvature of the hypergraph

Structural features and near infra-red (NIR) luminescence of isomeric Yb(iii) bipyridyl-N,N'-dioxide coordination polymers

The synthesis and structural characterization of a series of lanthanide complexes formed from YbX3 salts (X = NO3(-) or CF3SO3(-)) and the isomeric 4,4'-bipyridine-N,N'-dioxide (4,4'-bpdo) or 3,3'-bipyridine-N,N'-dioxide (3,3'-bpdo) ligands has been undertaken by X-ray crystallography. Depending on the choice of anion, the complexes isolated with L = 4,4'-bpdo yield either an extended 1D linear chain {[Yb(L)(NO3)3(CH3OH)]}∞ or a coordination polymer network {[Yb(L)4](CF3SO3)3}∞ which are isostructural with previously reported compounds using other Ln(iii) metals. The isomeric 3,3'-bpdo ligand yields a similar extended 1D linear chain {[Yb(L)(NO3)3(CH3OH)]}∞ when NO3(-) is used as the anion. However, when substituted by the typically non-coordinating CF3SO3(-) anion, inner sphere coordination yields a coordination polymer {[Yb(L)3(CF3SO3)](CF3SO3)2}∞ with a (2(2)·4(8)·6(5)) network topology. In an effort to rationalize the observed difference in coordinating behavior, DFT calculations of the isomeric bipyridyl-N,N'-dioxide ligands have been undertaken, but revealed no significant differences in the charge distribution of the coordinating N-oxide groups. Lastly, sensitized Yb(iii) emission in the Near Infra-Red (NIR) region operating via the well-known antennae effect has been observed and compared for two of the coordination polymers

Linking dwarf galaxies to halo building blocks with the most metal-poor star in Sculptor

Current cosmological models indicate that the Milky Way's stellar halo was assembled from many smaller systems. Based on the apparent absence of the most metal-poor stars in present-day dwarf galaxies, recent studies claimed that the true Galactic building blocks must have been vastly different from the surviving dwarfs. The discovery of an extremely iron-poor star (S1020549) in the Sculptor dwarf galaxy based on a medium-resolution spectrum cast some doubt on this conclusion. However, verification of the iron-deficiency and measurements of additional elements, such as the alpha-element Mg, are mandatory for demonstrating that the same type of stars produced the metals found in dwarf galaxies and the Galactic halo. Only then can dwarf galaxy stars be conclusively linked to early stellar halo assembly. Here we report high-resolution spectroscopic abundances for 11 elements in S1020549, confirming the iron abundance of less than 1/4000th that of the Sun, and showing that the overall abundance pattern mirrors that seen in low-metallicity halo stars, including the alpha-elements. Such chemical similarity indicates that the systems destroyed to form the halo billions of years ago were not fundamentally different from the progenitors of present-day dwarfs, and suggests that the early chemical enrichment of all galaxies may be nearly identical.Comment: 16 pages, including 2 figures. Accepted for publication in Nature. It is embargoed for discussion in the press until formal publication in Natur

A comparison of sensitized Ln(III) emission using pyridine- and pyrazine-2,6-dicarboxylates - part II

The synthesis, X-ray structures and photophysical properties of several new Ln(iii) complexes with the dianion of pyrazine-2,6-dicarboxylic acid (H 2PYZ) that demonstrate excellent stability and solubility in non-aqueous solution are reported, and compared to structurally analogous complexes derived from pyridine-2,6-dicarboxylic acid (H2DPA). The Eu(iii) and Yb(iii) complexes demonstrate efficient metal centered luminescence in the visible and Near Infra-Red (NIR) regions, respectively. Low temperature (77 K) phosphorescence measurements using the corresponding Gd(iii) complex has allowed the photophysical properties of the sensitizer to be rationalized, together with corresponding TD-DFT studies for a model complex. Lastly, we have evaluated the sensitization efficiencies for these complexes, and have undertaken femtosecond transient absorption (TA) measurements in order to evaluate the relative importance of the intersystem crossing and energy transfer processes involved with sensitized Ln(iii) emission via the antennae effect

Towards Structure-Property-Function Relationships for Eumelanin

We discuss recent progress towards the establishment of important structure-property-function relationships in eumelanins - key functional bio-macromolecular systems responsible for photo-protection and immune response in humans, and implicated in the development of melanoma skin cancer. We focus on the link between eumelanin's secondary structure and optical properties such as broad band UV-visible absorption and strong non-radiative relaxation; both key features of the photo-protective function. We emphasise the insights gained through a holistic approach combining optical spectroscopy with first principles quantum chemical calculations, and advance the hypothesis that the robust functionality characteristic of eumelanin is related to extreme chemical and structural disorder at the secondary level. This inherent disorder is a low cost natural resource, and it is interesting to speculate as to whether it may play a role in other functional bio-macromolecular systems.Comment: 19 pages, 8 figures, Invited highlight article for Soft Matte

1,2- Hydroxypyridonates as Contrast Agents for Magnetic ResonanceImaging: TREN-1,2-HOPO

1,2-Hydroxypyridinones (1,2-HOPO) form very stable lanthanide complexes that may be useful as contrast agents for Magnetic Resonance Imaging (MRI). X-ray diffraction of single crystals established that the solid state structures of the Eu(III) and the previously reported [Inorg. Chem. 2004, 43, 5452] Gd(III) complex are identical. The recently discovered sensitizing properties of 1,2-HOPO chelates for Eu(III) luminescence allow direct measurement of the number if water molecules in the metal complex. Fluorescence measurements of the Eu(III) complex corroborate that in solution two water molecules coordinate the lanthanide (q = 2) as proposed from the analysis of NMRD profiles. In addition, fluorescence measurements have verified the anion binding interactions of lanthanide TREN-1,2-HOPO complexes in solution, studied by relaxivity, revealing only very weak oxalate binding (K{sub A} = 82.7 {+-} 6.5 M{sup -1}). Solution thermodynamic studies of the metal complex and free ligand have been carried out using potentiometry, spectrophotometry and fluorescence spectroscopy. The metal ion selectivity of TREN-1,2-HOPO supports the feasibility of using 1,2-HOPO ligands for selective lanthanide binding [pGd = 19.3 (2); pZn = 15.2 (2), pCa = 8.8 (3)]

Measuring the capability to raise revenue process and output dimensions and their application to the Zambia revenue authority

The worldwide diffusion of the good governance agenda and new public management has triggered a renewed focus on state capability and, more specifically, on the capability to raise revenue in developing countries. However, the analytical tools for a comprehensive understanding of the capability to raise revenue remain underdeveloped. This article aims at filling this gap and presents a model consisting of the three process dimensions ‘information collection and processing’, ‘merit orientation’ and ‘administrative accountability’. ‘Revenue performance’ constitutes the fourth capability dimension which assesses tax administration’s output. This model is applied to the case of the Zambia Revenue Authority. The dimensions prove to be valuable not only for assessing the how much but also the how of collecting taxes. They can be a useful tool for future comparative analyses of tax administrations’ capabilities in developing countries.Die weltweite Verbreitung der Good-Governance- und New-Public-Management-Konzepte hat zu einer zunehmenden Konzentration auf staatliche Leistungsfähigkeit und, im Besonderen, auf die Leistungsfähigkeit der Steuererhebung in Entwicklungsländern geführt. Allerdings bleiben die analytischen Werkzeuge für ein umfassendes Verständnis von Leistungsfähigkeit unterentwickelt. Dieser Artikel stellt hierfür ein Modell vor, das die drei Prozess-Dimensionen „Sammeln und Verarbeiten von Informationen“, „Leistungsorientierung der Mitarbeiter“ und „Verantwortlichkeit der Verwaltung“ beinhaltet. „Einnahmeperformanz“ ist die vierte Dimension und erfasst den Output der Steuerverwaltung. Das mehrdimensionale Modell wird für die Analyse der Leistungsfähigkeit der Steuerbehörde Zambias (Zambia Revenue Authority) genutzt. Es erweist sich nicht nur für die Untersuchung des Wieviel, sondern auch des Wie des Erhebens von Steuern als wertvoll. Die vier Dimensionen können in Zukunft zur umfassenden und vergleichenden Analyse der Leistungsfähigkeit verschiedener Steuerverwaltungen in Entwicklungsländern genutzt werden

Highly Luminescent Lanthanide Complexes of 1 Hydroxy-2-pyridinones

The synthesis, X-ray structure, stability, and photophysical properties of several trivalent lanthanide complexes formed from two differing bis-bidentate ligands incorporating either alkyl or alkyl ether linkages and featuring the 1-hydroxy-2-pyridinone (1,2-HOPO) chelate group in complex with Eu(III), Sm(III) and Gd(III) are reported. The Eu(III) complexes are among some of the best examples, pairing highly efficient emission ({Phi}{sub tot}{sup Eu} {approx} 21.5%) with high stability (pEu {approx} 18.6) in aqueous solution, and are excellent candidates for use in biological assays. A comparison of the observed behavior of the complexes with differing backbone linkages shows remarkable similarities, both in stability and photophysical properties. Low temperature photophysical measurements for a Gd(III) complex were also used to gain insight into the electronic structure, and were found to agree with corresponding TD-DFT calculations for a model complex. A comparison of the high resolution Eu(III) emission spectra in solution and from single crystals also revealed a more symmetric coordination geometry about the metal ion in solution due to dynamic rotation of the observed solid state structure

The Surgical Infection Society revised guidelines on the management of intra-abdominal infection

Background: Previous evidence-based guidelines on the management of intra-abdominal infection (IAI) were published by the Surgical Infection Society (SIS) in 1992, 2002, and 2010. At the time the most recent guideline was released, the plan was to update the guideline every five years to ensure the timeliness and appropriateness of the recommendations. Methods: Based on the previous guidelines, the task force outlined a number of topics related to the treatment of patients with IAI and then developed key questions on these various topics. All questions were approached using general and specific literature searches, focusing on articles and other information published since 2008. These publications and additional materials published before 2008 were reviewed by the task force as a whole or by individual subgroups as to relevance to individual questions. Recommendations were developed by a process of iterative consensus, with all task force members voting to accept or reject each recommendation. Grading was based on the GRADE (Grades of Recommendation Assessment, Development, and Evaluation) system; the quality of the evidence was graded as high, moderate, or weak, and the strength of the recommendation was graded as strong or weak. Review of the document was performed by members of the SIS who were not on the task force. After responses were made to all critiques, the document was approved as an official guideline of the SIS by the Executive Council. Results: This guideline summarizes the current recommendations developed by the task force on the treatment of patients who have IAI. Evidence-based recommendations have been made regarding risk assessment in individual patients; source control; the timing, selection, and duration of antimicrobial therapy; and suggested approaches to patients who fail initial therapy. Additional recommendations related to the treatment of pediatric patients with IAI have been included. Summary: The current recommendations of the SIS regarding the treatment of patients with IAI are provided in this guideline