Adaptive Multidimensional Integration Based on Rank-1 Lattices

Quasi-Monte Carlo methods are used for numerically integrating multivariate functions. However, the error bounds for these methods typically rely on a priori knowledge of some semi-norm of the integrand, not on the sampled function values. In this article, we propose an error bound based on the discrete Fourier coefficients of the integrand. If these Fourier coefficients decay more quickly, the integrand has less fine scale structure, and the accuracy is higher. We focus on rank-1 lattices because they are a commonly used quasi-Monte Carlo design and because their algebraic structure facilitates an error analysis based on a Fourier decomposition of the integrand. This leads to a guaranteed adaptive cubature algorithm with computational cost $O(mb^m)$, where $b$ is some fixed prime number and $b^m$ is the number of data points

Charging axisymmetric space-times with cosmological constant

Ernst's solution generating technique for adding electromagnetic charge to axisymmetric space-times in general relativity is generalised in presence of the cosmological constant. Ernst equations for complex potentials are found and they are traced back to an affective dual complex dynamical system, whose symmetries are studied. In particular this method is able to generate charged, asymptotically (A)dS black holes from their uncharged version: as an example, it is shown explicitly how to pass from the Kerr-(A)dS to the Kerr-Newman-(A)dS metric. A new solution describing a magnetic universe in presence of the cosmological constant is also generated.Comment: 15 pages, v2: typos correcte

Primary singularities of vector fields on surfaces

Unless another thing is stated one works in the C∞ category and manifolds have empty boundary. Let X and Y be vector fields on a manifold M. We say that Y tracks X if [Y, X] = fX for some continuous function f: M→ R. A subset K of the zero set Z(X) is an essential block for X if it is non-empty, compact, open in Z(X) and its Poincaré-Hopf index does not vanishes. One says that X is non-flat at p if its ∞-jet at p is non-trivial. A point p of Z(X) is called a primary singularity of X if any vector field defined about p and tracking X vanishes at p. This is our main result: consider an essential block K of a vector field X defined on a surface M. Assume that X is non-flat at every point of K. Then K contains a primary singularity of X. As a consequence, if M is a compact surface with non-zero characteristic and X is nowhere flat, then there exists a primary singularity of X

Election results and opportunistic policies: A new test of the rational political business cycle model

The literature on the rational political business cycle suggests that politicians systematically manipulate economic and fiscal conditions before elections to increase their chance of gaining reelection. Most tests of this theory look for evidence of pre- election distortions in fiscal policy. We propose a new test that, instead, explores the implied two-way interaction between the magnitude of the opportunistic distortion and the margin of victory. The test is implemented using a panel of 278 Portuguese municipalities (from 1979 to 2005). The results show that (1) opportunism pays off, leading to a larger win-margin for the incumbent; (2) incumbents behave more opportunistically when their win-margin is small. These results are consistent with the theoretical model

Age-dependent seismic thickness and mechanical strength of the Australian lithosphere

We present constraints on the regional variations of the seismic and mechanical thickness of the Australian lithosphere. We infer the seismic thickness from a waveform tomographic model of S-wave speed, and as a proxy for the elastic thickness we use the wavelength at which the coherence of surface topography and Bouguer gravity drops below half of its long-wavelength maximum. Our results show that on scales <1000 km the relationship between the age of the crust and the thickness of the lithosphere is more complicated than longer-wavelength or global averages suggest. Recent geochemical and geodynamical evidence for small-scale secular variations of the composition and stability of continental cratons further illustrates the complexity of the age dependence of seismo-mechanical lithospheric properties on regional scales

Human neuronal stargazin-like proteins, gamma(2), gamma(3) and gamma(4); an investigation of their specific localization in human brain and their influence on Ca(V)2.1 voltage-dependent calcium channels expressed in Xenopus oocytes

Background: Stargazin (gamma(2)) and the closely related gamma(3), and gamma(4) transmembrane proteins are part of a family of proteins that may act as both neuronal voltage-dependent calcium channel (VDCC) gamma subunits and transmembrane alpha-amino-3-hydroxy-5-methyl-4-isoxazoleproponinc (AMPA) receptor regulatory proteins (TARPs). In this investigation, we examined the distribution patterns of the stargazin-like proteins gamma(2), gamma(3), and gamma(4) in the human central nervous system (CNS). In addition, we investigated whether human gamma(2) or gamma(4) could modulate the electrophysiological properties of a neuronal VDCC complex transiently expressed in Xenopus oocytes.Results: The mRNA encoding human gamma(2) is highly expressed in cerebellum, cerebral cortex, hippocampus and thalamus, whereas gamma(3) is abundant in cerebral cortex and amygdala and gamma(4) in the basal ganglia. Immunohistochemical analysis of the cerebellum determined that both gamma(2) and gamma(4) are present in the molecular layer, particularly in Purkinje cell bodies and dendrites, but have an inverse expression pattern to one another in the dentate cerebellar nucleus. They are also detected in the interneurons of the granule cell layer though only gamma(2) is clearly detected in granule cells. The hippocampus stains for gamma(2) and gamma(4) throughout the layers of the every CA region and the dentate gyrus, whilst gamma(3) appears to be localized particularly to the pyramidal and granule cell bodies. When co-expressed in Xenopus oocytes with a Ca(V)2.1/beta(4) VDCC complex, either in the absence or presence of an alpha(2)delta(2) subunit, neither gamma(2) nor gamma(4) significantly modulated the VDCC peak current amplitude, voltage-dependence of activation or voltage-dependence of steady-state inactivation.Conclusion: The human gamma(2), gamma(3) and gamma(4) stargazin-like proteins are detected only in the CNS and display differential distributions among brain regions and several cell types in found in the cerebellum and hippocampus. These distribution patterns closely resemble those reported by other laboratories for the rodent orthologues of each protein. Whilst the fact that neither gamma(2) nor gamma(4) modulated the properties of a VDCC complex with which they could associate in vivo in Purkinje cells adds weight to the hypothesis that the principal role of these proteins is not as auxiliary subunits of VDCCs, it does not exclude the possibility that they play another role in VDCC function

A survey of hard spectrum ROSAT sources - II. Optical identification of hard sources

We have surveyed 188 ROSAT Position Sensitive Proportional Counter (PSPC) fields for X-ray sources with hard spectra (alpha 1) identified hard sources have broad lines

Structure of Quantum Wires in Au/Si(557)

The structure of the Au/Si(557) surface is determined from three-dimensional x-ray diffraction measurements, which directly mandate a single Au atom per unit cell. We use a “heavy atom” method in which the Au atom images the rest of the structure. Au is found to substitute for a row of first-layer Si atoms in the middle of the terrace, which then reconstructs by step rebonding and adatoms. The structure is consistent with the 1D metallic behavior seen by photoemission