Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing

The evolution of physical and gauge degrees of freedom in the Einstein and Yang-Mills theories are separated in a gauge-invariant manner. We show that the equations of motion of these theories can always be written in flux-conservative first-order symmetric hyperbolic form. This dynamical form is ideal for global analysis, analytic approximation methods such as gauge-invariant perturbation theory, and numerical solution.Comment: 12 pages, revtex3.0, no figure

Fields in Nonaffine Bundles. I. The general bitensorially covariant differentiation procedure

The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the usual requirement that the base space should be flat or endowed with its own linear connection, and that there should be an ordinary gauge connection on the bundle, it is necessary to require also that there should be an intrinsic, bundle-group invariant connection on the fibre space. The procedure is based on the use of an appropriate primary-field (i.e. section) independent connector that is constructed in terms of the natural fibre-tangent-vector realisation of the gauge connection. The application to gauged harmonic mappings will be described in a following article.Comment: 17 page Latex file with some minor misprint corrections and added color for article originally published in black and whit

Functional interaction between the ZO-1-interacting transcription factor ZONAB/DbpA and the RNA processing factor symplekin

Epithelial tight junctions participate in the regulation of gene expression by controlling the activity of transcription factors that can interact with junctional components. One such protein is the Y-box transcription factor ZONAB/DbpA that binds to ZO-1, a component of the junctional plaque. Symplekin, another nuclear protein that can associate with tight junctions, functions in the regulation of polyadenylation and thereby promotes gene expression. Here, we addressed the question of whether these two proteins interact and whether this is of functional relevance. We demonstrate that ZONAB/DbpA and symplekin form a complex in kidney and intestinal epithelial cells that can be immunoprecipitated and that exists in the nucleus. The interaction between ZONAB/DbpA and symplekin can be reconstituted with recombinant proteins. In reporter gene assays in which ZONAB/DbpA functions as a repressor, symplekin functionally interacts with ZONAB/DbpA, indicating that symplekin can also promote transcriptional repression. RNAi experiments indicate that symplekin depletion reduces the nuclear accumulation and the transcriptional activity of ZONAB/DbpA in colon adenocarcinoma cells, resulting in inhibition of proliferation and reduced expression of the ZONAB/DbpA-target gene cyclin D1. Our data thus indicate that symplekin and ZONAB/DbpA cooperate in the regulation of transcription, and that they promote epithelial proliferation and cyclin D1 expression

Multiply Warped Products with Non-Smooth Metrics

In this article we study manifolds with $C^{0}$-metrics and properties of Lorentzian multiply warped products. We represent the interior Schwarzschild space-time as a multiply warped product space-time with warping functions and we also investigate the curvature of a multiply warped product with $C^0$-warping functions. We given the {\it{Ricci curvature}} in terms of $f_1$, $f_2$ for the multiply warped products of the form $M=(0,\ 2m)\times_{f_1}R^1\times_{f_2} S^2$.Comment: LaTeX, 7 page

Global Foliations of Vacuum Spacetimes with T2T^2 Isometry

We prove a global existence theorem (with respect to a geometrically- defined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a $T^2$ isometry group with two-dimensional spacelike orbits, acting on $T^3$ spacelike surfaces.Comment: 38 pages, 0 figures, LaTe

A large multi-ethnic genome-wide association study identifies novel genetic loci for intraocular pressure.

Elevated intraocular pressure (IOP) is a major risk factor for glaucoma, a leading cause of blindness. IOP heritability has been estimated to up to 67%, and to date only 11 IOP loci have been reported, accounting for 1.5% of IOP variability. Here, we conduct a genome-wide association study of IOP in 69,756 untreated individuals of European, Latino, Asian, and African ancestry. Multiple longitudinal IOP measurements were collected through electronic health records and, in total, 356,987 measurements were included. We identify 47 genome-wide significant IOP-associated loci (P < 5 × 10-8); of the 40 novel loci, 14 replicate at Bonferroni significance in an external genome-wide association study analysis of 37,930 individuals of European and Asian descent. We further examine their effect on the risk of glaucoma within our discovery sample. Using longitudinal IOP measurements from electronic health records improves our power to identify new variants, which together explain 3.7% of IOP variation

On completeness of orbits of Killing vector fields

A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space--times to some properties of the orbits near the Cauchy surface. In particular it is shown that all Killing orbits are complete in maximal developements of asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact manifold. This result gives a significant strengthening of the uniqueness theorems for black holes.Comment: 16 pages, Latex, preprint NSF-ITP-93-4

Isotropic cosmological singularities: other matter models

Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied (gr-qc/9903008, gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models with data at the singularity has been established. These were cosmologies with, as source, either perfect fluids with linear equations of state or massless, collisionless particles. In this article we consider how to extend these results to a variety of other matter models. These are scalar fields, massive collisionless matter, the Yang-Mills plasma of Choquet-Bruhat, or matter satisfying the Einstein-Boltzmann equation.Comment: LaTeX, 19 pages, no figure

On the relation between mathematical and numerical relativity

The large scale binary black hole effort in numerical relativity has led to an increasing distinction between numerical and mathematical relativity. This note discusses this situation and gives some examples of succesful interactions between numerical and mathematical methods is general relativity.Comment: 12 page

Discrete Dynamical Systems Embedded in Cantor Sets

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $N$ variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit $N\to\infty$. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological entropy and Lyapunov exponents through the concept of error-profile. We made explicit calculations both numerical and analytic for well known discrete dynamical models.Comment: 36 pages, 13 figures: minor text amendments in places, time running top to bottom in figures, to appear in J. Math. Phy