Vacuum solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory

The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial base manifold. For arbitrary values of the Gauss-Bonnet coupling, the base manifold must be Einstein with an additional scalar restriction. The geometry of the boundary can be relaxed only when the Gauss-Bonnet coupling is related with the cosmological and Newton constants, so that the theory admits a unique maximally symmetric solution. This additional freedom in the boundary metric allows the existence of three main branches of geometries in the bulk, containing new black holes and wormholes in vacuum.Comment: Prepared for the proceedings of the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, July 2008, Joao Pessoa, Brasil. 4 pages, References adde

Conformal smectics and their many metrics

We establish that equally spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal structures only found before for smectics on flat substrates

A Megacam Survey of Outer Halo Satellites. IV. Two foreground populations possibly associated with the Monoceros substructure in the direction of NGC2419 and Koposov2

The origin of the Galactic halo stellar structure known as the Monoceros ring is still under debate. In this work, we study that halo substructure using deep CFHT wide-field photometry obtained for the globular clusters NGC2419 and Koposov2, where the presence of Monoceros becomes significant because of their coincident projected position. Using Sloan Digital Sky Survey photometry and spectroscopy in the area surrounding these globulars and beyond, where the same Monoceros population is detected, we conclude that a second feature, not likely to be associated with Milky Way disk stars along the line-of-sight, is present as foreground population. Our analysis suggests that the Monoceros ring might be composed of an old stellar population of age t ~ 9Gyr and a new component ~ 4Gyr younger at the same heliocentric distance. Alternatively, this detection might be associated with a second wrap of Monoceros in that direction of the sky and also indicate a metallicity spread in the ring. The detection of such a low-density feature in other sections of this halo substructure will shed light on its nature.Comment: 10 pages, 10 figures, accepted for publication in Ap

Vitamin D: beyond bone.

In recent years, vitamin D has been received increased attention due to the resurgence of vitamin D deficiency and rickets in developed countries and the identification of extraskeletal effects of vitamin D, suggesting unexpected benefits of vitamin D in health and disease, beyond bone health. The possibility of extraskeletal effects of vitamin D was first noted with the discovery of the vitamin D receptor (VDR) in tissues and cells that are not involved in maintaining mineral homeostasis and bone health, including skin, placenta, pancreas, breast, prostate and colon cancer cells, and activated T cells. However, the biological significance of the expression of the VDR in different tissues is not fully understood, and the role of vitamin D in extraskeletal health has been a matter of debate. This report summarizes recent research on the roles for vitamin D in cancer, immunity and autoimmune diseases, cardiovascular and respiratory health, pregnancy, obesity, erythropoiesis, diabetes, muscle function, and aging

Multiple Chemodynamic Stellar Populations of the Ursa Minor Dwarf Spheroidal Galaxy

We present a Bayesian method to identify multiple (chemodynamic) stellar populations in dwarf spheroidal galaxies (dSphs) using velocity, metallicity, and positional stellar data without the assumption of spherical symmetry. We apply this method to a new Keck/DEIMOS spectroscopic survey of the Ursa Minor (UMi) dSph. We identify 892 likely members, making this the largest UMi sample with line-of-sight velocity and metallicity measurements. Our Bayesian method detects two distinct chemodynamic populations with high significance ($\ln{B}\sim33$). The metal-rich ($[{\rm Fe/H}]=-2.05\pm0.03$) population is kinematically colder (radial velocity dispersion of $\sigma_v=4.9\pm0.8 \, {\rm km \, s^{-1}}$) and more centrally concentrated than the metal-poor ($[{\rm Fe/H}]=-2.29\pm0.05$) and kinematically hotter population ($\sigma_v =11.5\pm0.9\, {\rm km \, s^{-1}}$). Furthermore, we apply the same analysis to an independent MMT/Hectochelle data set and confirm the existence of two chemodynamic populations in UMi. In both data sets, the metal-rich population is significantly flattened ($\epsilon=0.75\pm0.03$) and the metal-poor population is closer to spherical ($\epsilon=0.33_{-0.09}^{+0.12}$). Despite the presence of two populations, we are unable to robustly estimate the slope of the dynamical mass profile. We found hints for prolate rotation of order $\sim 2 \, {\rm km \, s^{-1}}$ in the MMT data set, but further observations are required to verify this. The flattened metal-rich population invalidates assumptions built into simple dynamical mass estimators, so we computed new astrophysical dark matter annihilation (J) and decay profiles based on the rounder, hotter metal-poor population and inferred $\log_{10}{(J(0.5^{\circ})/{\rm GeV^{2} \, cm^{-5}})}\approx19.1$ for the Keck data set. Our results paint a more complex picture of the evolution of Ursa Minor than previously discussed.Comment: 20 pages, 11 figures, data included. Comments welcome. Accepted to MNRA

Efficient Heralding of Photonic Qubits with Apllications to Device Independent Quantum Key Distribution

We present an efficient way of heralding photonic qubit signals using linear optics devices. First we show that one can obtain asymptotically perfect heralding and unit success probability with growing resources. Second, we show that even using finite resources, we can improve qualitatively and quantitatively over earlier heralding results. In the latte r scenario, we can obtain perfect heralded photonic qubits while maintaining a finite success probability. We demonstrate the advantage of our heralding scheme by predicting key rates for device independent quantum key distribution, taking imperfections of sources and detectors into account

Yurinskii's Coupling for Martingales

Yurinskii's coupling is a popular theoretical tool for non-asymptotic distributional analysis in mathematical statistics and applied probability, offering a Gaussian strong approximation with an explicit error bound under easily verified conditions. Originally stated in $\ell^2$-norm for sums of independent random vectors, it has recently been extended both to the $\ell^p$-norm, for $1 \leq p \leq \infty$, and to vector-valued martingales in $\ell^2$-norm, under some strong conditions. We present as our main result a Yurinskii coupling for approximate martingales in $\ell^p$-norm, under substantially weaker conditions than those previously imposed. Our formulation further allows for the coupling variable to follow a more general Gaussian mixture distribution, and we provide a novel third-order coupling method which gives tighter approximations in certain settings. We specialize our main result to mixingales, martingales, and independent data, and derive uniform Gaussian mixture strong approximations for martingale empirical processes. Applications to nonparametric partitioning-based and local polynomial regression procedures are provided.Comment: 55 pages, 1 figur

Reachability problems for products of matrices in semirings

We consider the following matrix reachability problem: given $r$ square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? We define similarly the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multiplied at left and right by prescribed row and column vectors, gives a prescribed scalar). We show that over any semiring, scalar reachability reduces to vector reachability which is equivalent to matrix reachability, and that for any of these problems, the specialization to any $r\geq 2$ is equivalent to the specialization to $r=2$. As an application of this result and of a theorem of Krob, we show that when $r=2$, the vector and matrix reachability problems are undecidable over the max-plus semiring $(Z\cup\{-\infty\},\max,+)$. We also show that the matrix, vector, and scalar reachability problems are decidable over semirings whose elements are ``positive'', like the tropical semiring $(N\cup\{+\infty\},\min,+)$.Comment: 21 page

Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence

Abstract. We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methods. 1