Geometrization of metric boundary data for Einstein's equations

The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new formulation of constraint-preserving boundary conditions of the Sommerfeld type has recently been established for such systems. In this paper these boundary conditions are recast in a geometric form. This serves as a first step toward their application to other metric formulations of Einstein's equations.Comment: Article to appear in Gen. Rel. Grav. volume in memory of Juergen Ehler

Initial data for fluid bodies in general relativity

We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary. PACS: 04.20.Ex, 04.40.Nr, 02.30.JrComment: 38 pages, LaTeX 2e, no figures. Accepted for publication in Phys. Rev.

The Cauchy Problem for the Einstein Equations

Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in this context. The question of producing reduced systems of equations which are hyperbolic is examined in detail and some new results on that subject are presented. Relevant background from the theory of partial differential equations is also explained at some lengthComment: 98 page

Collective modes in the electronic polarization of double-layer systems in the superconducting state

Standard weak coupling methods are used to study collective modes in the superconducting state of a double-layer system with intralayer and interlayer interaction, as well as a Josephson-type coupling and single particle hopping between the layers by calculating the electronic polarization function perpendicular to the layers. New analytical results are derived for the mode frequencies corresponding to fluctuations of the relative phase and amplitude of the layer order parameters in the case of interlayer pairing and finite hopping $t$. A new effect is found for finite $k$-dependent hopping: then the amplitude and phase fluctuations are coupled. Therefore two collective modes may appear in the dynamical c-axis conductivity below the threshold energy for breaking Cooper pairs. With help of numerical calculations we investigate the temperature dependence of the collective modes and show how a plasmon corresponding to charge fluctuations between the layers evolves in the normal state.Comment: 17 pages, latex, 8 ps figure

The Chromosomal High-Affinity Binding Sites for the Drosophila Dosage Compensation Complex

Dosage compensation in male Drosophila relies on the X chromosome–specific recruitment of a chromatin-modifying machinery, the dosage compensation complex (DCC). The principles that assure selective targeting of the DCC are unknown. According to a prevalent model, X chromosome targeting is initiated by recruitment of the DCC core components, MSL1 and MSL2, to a limited number of so-called “high-affinity sites” (HAS). Only very few such sites are known at the DNA sequence level, which has precluded the definition of DCC targeting principles. Combining RNA interference against DCC subunits, limited crosslinking, and chromatin immunoprecipitation coupled to probing high-resolution DNA microarrays, we identified a set of 131 HAS for MSL1 and MSL2 and confirmed their properties by various means. The HAS sites are distributed all over the X chromosome and are functionally important, since the extent of dosage compensation of a given gene and its proximity to a HAS are positively correlated. The sites are mainly located on non-coding parts of genes and predominantly map to regions that are devoid of nucleosomes. In contrast, the bulk of DCC binding is in coding regions and is marked by histone H3K36 methylation. Within the HAS, repetitive DNA sequences mainly based on GA and CA dinucleotides are enriched. Interestingly, DCC subcomplexes bind a small number of autosomal locations with similar features

Generation and quality control of lipidomics data for the alzheimers disease neuroimaging initiative cohort.

Alzheimers disease (AD) is a major public health priority with a large socioeconomic burden and complex etiology. The Alzheimer Disease Metabolomics Consortium (ADMC) and the Alzheimer Disease Neuroimaging Initiative (ADNI) aim to gain new biological insights in the disease etiology. We report here an untargeted lipidomics of serum specimens of 806 subjects within the ADNI1 cohort (188 AD, 392 mild cognitive impairment and 226 cognitively normal subjects) along with 83 quality control samples. Lipids were detected and measured using an ultra-high-performance liquid chromatography quadruple/time-of-flight mass spectrometry (UHPLC-QTOF MS) instrument operated in both negative and positive electrospray ionization modes. The dataset includes a total 513 unique lipid species out of which 341 are known lipids. For over 95% of the detected lipids, a relative standard deviation of better than 20% was achieved in the quality control samples, indicating high technical reproducibility. Association modeling of this dataset and available clinical, metabolomics and drug-use data will provide novel insights into the AD etiology. These datasets are available at the ADNI repository at http://adni.loni.usc.edu/

Assessment of Metabolome Annotation Quality: A Method for Evaluating the False Discovery Rate of Elemental Composition Searches

BACKGROUND: In metabolomics researches using mass spectrometry (MS), systematic searching of high-resolution mass data against compound databases is often the first step of metabolite annotation to determine elemental compositions possessing similar theoretical mass numbers. However, incorrect hits derived from errors in mass analyses will be included in the results of elemental composition searches. To assess the quality of peak annotation information, a novel methodology for false discovery rates (FDR) evaluation is presented in this study. Based on the FDR analyses, several aspects of an elemental composition search, including setting a threshold, estimating FDR, and the types of elemental composition databases most reliable for searching are discussed. METHODOLOGY/PRINCIPAL FINDINGS: The FDR can be determined from one measured value (i.e., the hit rate for search queries) and four parameters determined by Monte Carlo simulation. The results indicate that relatively high FDR values (30-50%) were obtained when searching time-of-flight (TOF)/MS data using the KNApSAcK and KEGG databases. In addition, searches against large all-in-one databases (e.g., PubChem) always produced unacceptable results (FDR >70%). The estimated FDRs suggest that the quality of search results can be improved not only by performing more accurate mass analysis but also by modifying the properties of the compound database. A theoretical analysis indicates that FDR could be improved by using compound database with smaller but higher completeness entries. CONCLUSIONS/SIGNIFICANCE: High accuracy mass analysis, such as Fourier transform (FT)-MS, is needed for reliable annotation (FDR <10%). In addition, a small, customized compound database is preferable for high-quality annotation of metabolome data

Measurement of event shapes in deep inelastic scattering at HERA

Inclusive event-shape variables have been measured in the current region of the Breit frame for neutral current deep inelastic ep scattering using an integrated luminosity of 45.0 pb^-1 collected with the ZEUS detector at HERA. The variables studied included thrust, jet broadening and invariant jet mass. The kinematic range covered was 10 < Q^2 < 20,480 GeV^2 and 6.10^-4 < x < 0.6, where Q^2 is the virtuality of the exchanged boson and x is the Bjorken variable. The Q dependence of the shape variables has been used in conjunction with NLO perturbative calculations and the Dokshitzer-Webber non-perturbative corrections (`power corrections') to investigate the validity of this approach.Comment: 7+25 pages, 6 figure

Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity