Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed $K_C$-orbits in the Lagrangian Grassmannian as the categorical quotient. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent $K_C$-orbits, which is a "quotient" of the resolution of the null fiber.Comment: 17 pages; completely revised and add reference

Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices

This paper is mainly a review of the multi--Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include master symmetries, recursion operators, higher Poisson brackets, invariants and group symmetries for the systems. In addition to the positive hierarchy we also consider the negative hierarchy which is crucial in establishing the bi--Hamiltonian structure for each particular simple Lie group. Finally, we include some results on point and Noether symmetries and an interesting connection with the exponents of simple Lie groups. The case of exceptional simple Lie groups is still an open problem.Comment: 65 pages, 67 reference

A New Ant Species of the Genus Tetramorium Mayr, 1855 (Hymenoptera: Formicidae) from Saudi Arabia, with a Revised Key to the Arabian Species

Tetramorium amalae sp. n. is described and illustrated from Saudi Arabia based on two worker caste specimens collected in Al Bahah region. The new species belongs to the T. shilohense group and appears to be closely related to T. dysderke Bolton from Nigeria. T. amalae is distinguished by having well-developed frontal carinae, smaller eyes, greater head length and width, greater pronotal width, and the petiole node is longer than broad. Tetramorium latinode Collingwood & Agosti is recorded for the first time from Saudi Arabia and for only the second time since the original description. The worker caste of T. latinode is redescribed and illustrated using scanning electron micrographs to facilitate recognition and the gyne is described for the first time with observations given on species relationships, biology and habitat. A revised key to the nineteen Tetramorium species recorded from Arabian Peninsula based on worker castes is provided. Tetramorium bicarinatum (Nylander) is recorded for the first time from Saudi Arabia. It is suggested that T. amalae and T. latinode are endemic to the Arabian Peninsula

Non-Supersymmetric Attractor Flow in Symmetric Spaces

We derive extremal black hole solutions for a variety of four dimensional models which, after Kaluza-Klein reduction, admit a description in terms of 3D gravity coupled to a sigma model with symmetric target space. The solutions are in correspondence with certain nilpotent generators of the isometry group. In particular, we provide the exact solution for a non-BPS black hole with generic charges and asymptotic moduli in N=2 supergravity coupled to one vector multiplet. Multi-centered solutions can also be generated with this technique. It is shown that the non-supersymmetric solutions lack the intricate moduli space of bound configurations that are typical of the supersymmetric case.Comment: 50 pages, 4 figures; v2: Reference added. To appear in JHE

Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes

Four dimensional supergravity theories whose scalar manifold is a symmetric coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake universality classes. Stationary solutions of these theories, spherically symmetric or not, are identified with those of an euclidian three-dimensional sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the extremal ones are associated with H* nilpotent orbits in the K* representation emerging from the orthogonal decomposition of the algebra U[D=3] with respect to H*. It is shown that the classification of such orbits can always be reduced to the Tits-Satake projection and it is a class property of the Tits Satake universality classes. The construction procedure of Bossard et al of extremal multicenter solutions by means of a triangular hierarchy of integrable equations is completed and converted into a closed algorithm by means of a general formula that provides the transition from the symmetric to the solvable gauge. The question of the relation between H* orbits and charge orbits W of the corresponding black holes is addressed and also reduced to the corresponding question within the Tits Satake projection. It is conjectured that on the vanishing locus of the Taub-NUT current the relation between H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from multicenter solutions associated with a given H* orbit have the same W-type. For the S^3 model we provide a complete survey of its multicenter solutions associated with all of the previously classified nilpotent orbits of sl(2) x sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of this model that might provide a paradigm for the analogous classification in all the other Tits Satake universality classes.Comment: 83 pages, LaTeX; v2: few misprints corrected and references adde

Cohort profile: Scottish Health and Ethnicity Linkage Study of 4.65 million people exploring ethnic variations in disease in Scotland

Many countries require health services to show that they are meeting the needs of ethnic minority populations. This requires data on health status, healthcare uptake and outcomes and population denominators. Weaknesses in routine data collection often make such requirements difficult to meet. Routine data sources in Scotland, as in most countries, may not include a patient’s ethnicity. In Scotland, the need for such data is driven by both policy and legislation responding to rapidly increasing ethnic diversity. Fair For All (2003), Scotland’s policy, provides a strategic approach to improve the health of minority ethnic groups. The UK Race Relations (Amendment) Act (2000) placed a duty on public bodies to promote racial equality. These mandates are reflected in guidance on ethnic monitoring. Appropriate service and research is undermined by the lack of data. Ethnic variations occur in all of Scotland’s national health priority areas, including coronary heart disease/stroke, cancer, maternal and child health and mental health. In view of the mismatch between need for and availability of data by ethnic group, Bhopal proposed a demonstration project to explore retrospective approaches. The project tested proposals including name search methods, analyses by country of birth, modelling/extrapolation from other nations’ datasets, and linkage methods. The demonstration project concluded that census health records linkage methods— in the context of this project first mooted by Povey— held most promise. To our knowledge, attempting matching of a national health dataset to a complete national census using demographic identifiers rather than national identity numbers had not been reported though health data linkage is well-established in the UK and internationally, including exploring ethnicity and health