Generalized Bergman kernels on symplectic manifolds

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As consequence, we calculate the density of states function of the Bochner-Laplacian and establish a symplectic version of the convergence of the induced Fubini-Study metric. We also discuss generalizations of the asymptotic expansion for non-compact or singular manifolds as well as their applications. Our approach is inspired by the analytic localization techniques of Bismut-Lebeau.Comment: 48 pages. Add two references on the Hermitian scalar curvatur

Equidistribution of zeros of holomorphic sections in the non compact setting

We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed with respect to the natural measure coming from the curvature of L, as N tends to infinity. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL2(Z) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.Comment: 25 pages; v.2 is a final update to agree with the published pape

Political strategies of external support for democratization

Political strategies of external support to democratization are contrasted and critically examined in respect of the United States and European Union. The analysis begins by defining its terms of reference and addresses the question of what it means to have a strategy. The account briefly notes the goals lying behind democratization support and their relationship with the wider foreign policy process, before considering what a successful strategy would look like and how that relates to the selection of candidates. The literature's attempts to identify strategy and its recommendations for better strategies are compared and assessed. Overall, the article argues that the question of political strategies of external support for democratization raises several distinct but related issues including the who?, what?, why?, and how? On one level, strategic choices can be expected to echo the comparative advantage of the "supporter." On a different level, the strategies cannot be divorced from the larger foreign policy framework. While it is correct to say that any sound strategy for support should be grounded in a theoretical understanding of democratization, the literature on strategies reveals something even more fundamental: divergent views about the nature of politics itself. The recommendations there certainly pinpoint weaknesses in the actual strategies of the United States and Europe but they have their own limitations too. In particular, in a world of increasing multi-level governance strategies for supporting democratization should go beyond preoccupation with just an "outside-in" approach

Genome Sequencing Reveals Widespread Virulence Gene Exchange among Human Neisseria Species

Commensal bacteria comprise a large part of the microbial world, playing important roles in human development, health and disease. However, little is known about the genomic content of commensals or how related they are to their pathogenic counterparts. The genus Neisseria, containing both commensal and pathogenic species, provides an excellent opportunity to study these issues. We undertook a comprehensive sequencing and analysis of human commensal and pathogenic Neisseria genomes. Commensals have an extensive repertoire of virulence alleles, a large fraction of which has been exchanged among Neisseria species. Commensals also have the genetic capacity to donate DNA to, and take up DNA from, other Neisseria. Our findings strongly suggest that commensal Neisseria serve as reservoirs of virulence alleles, and that they engage extensively in genetic exchange