Black hole boundaries

Classical black holes and event horizons are highly non-local objects, defined in relation to the causal past of future null infinity. Alternative, quasilocal characterizations of black holes are often used in mathematical, quantum, and numerical relativity. These include apparent, killing, trapping, isolated, dynamical, and slowly evolving horizons. All of these are closely associated with two-surfaces of zero outward null expansion. This paper reviews the traditional definition of black holes and provides an overview of some of the more recent work on alternative horizons.Comment: 27 pages, 8 figures, invited Einstein Centennial Review Article for CJP, final version to appear in journal - glossary of terms added, typos correcte

Linear independence of Gamma values in positive characteristic

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.Comment: 51 page

Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012

Membrane, Four-Brane and Dual Coordinates in the M(atrix) Theory Compactified on Tori

In the M(atrix) theory by making the expansions of the matrices around the membrane and four-brane solutions we derive the three- and five-dimensional gauge theories on the dual tori. The explicit forms of solutions yield the dual coordinates and each expansion is related to a toroidal compactification of the M(atrix) theory. From the derived Lorentz and gauge invariant actions the gauge coupling constants are shown to be characterized by the volume of the dual tori.Comment: 9 pages, latex, no figure

Relativity in Introductory Physics

A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski spacetime, displays covariant symmetries, and enables calculations of boosts and spatial rotations without matrices or tensors. The approach is part of a comprehensive geometric algebra with applications in many areas of physics, but only an intuitive subset is needed at the introductory level. The approach and some of its extensions are given here and illustrated with insights into the geometry of spacetime.Comment: 29 pages, 5 figures, several typos corrected, some discussion polishe

Glucose availability and sensitivity to anoxia of isolated rat peripheral nerve

The contrast between resistance to ischemia and ischemic lesions in peripheral nerves of diabetic patients was explored by in vitro experiments. Isolated and desheathed rat peroneal nerves were incubated in the following solutions with different glucose availability: 1) 25 mM glucose, 2) 2.5 mM glucose, and 3) 2.5 mM glucose plus 10 mM 2-deoxy-D-glucose. Additionally, the buffering power of all of these solutions was modified. Compound nerve action potential (CNAP), extracellular pH, and extracellular potassium activity (aKe) were measured simultaneously before, during, and after a period of 30 min of anoxia. An increase in glucose availability led to a slower decline in CNAP and to a smaller rise in aKe during anoxia. This resistance to anoxia was accompanied by an enhanced extracellular acidosis. Postanoxic recovery of CNAP was always complete in 25 mM HCO3(-)-buffered solutions. In 5 mM HCO3- and in HCO3(-)-free solutions, however, nerves incubated in 25 mM glucose did not recover functionally after anoxia, whereas nerves bathed in solutions 2 or 3 showed a complete restitution of CNAP. We conclude that high glucose availability and low PO2 in the combination with decreased buffering power and/or inhibition of HCO3(-)-dependent pH regulation mechanisms may damage peripheral mammalian nerves due to a pronounced intracellular acidosis

Shrinking a large dataset to identify variables associated with increased risk of Plasmodium falciparum infection in Western Kenya

Large datasets are often not amenable to analysis using traditional single-step approaches. Here, our general objective was to apply imputation techniques, principal component analysis (PCA), elastic net and generalized linear models to a large dataset in a systematic approach to extract the most meaningful predictors for a health outcome. We extracted predictors for Plasmodium falciparum infection, from a large covariate dataset while facing limited numbers of observations, using data from the People, Animals, and their Zoonoses (PAZ) project to demonstrate these techniques: data collected from 415 homesteads in western Kenya, contained over 1500 variables that describe the health, environment, and social factors of the humans, livestock, and the homesteads in which they reside. The wide, sparse dataset was simplified to 42 predictors of P. falciparum malaria infection and wealth rankings were produced for all homesteads. The 42 predictors make biological sense and are supported by previous studies. This systematic data-mining approach we used would make many large datasets more manageable and informative for decision-making processes and health policy prioritization

Distributional composition using higher-order dependency vectors

This paper concerns how to apply compositional methods to vectors based on grammatical dependency relation vectors. We demonstrate the potential of a novel approach which uses higher-order grammatical dependency relations as features. We apply the approach to adjective-noun compounds with promising results in the prediction of the vectors for (held-out) observed phrases

Radiative Corrections to W^+W^- \to W^+W^- in the Electroweak Standard Model

The cross-section for W^+W^- \to W^+W^- with arbitrarily polarized W bosons is calculated within the Electroweak Standard Model including the complete virtual and soft-photonic O(alpha) corrections. We show the numerical importance of the radiative corrections for the dominating polarized cross-sections and for the unpolarized cross-section. The numerical accuracy of the equivalence theorem is investigated in O(alpha) by comparing the cross-section for purely longitudinal W bosons obtained from the equivalence theorem and from the direct calculation. We point out that the instability of the W boson, which is inherent in the one-loop corrections, prevents a consistent calculation of radiative corrections to the scattering of on-real-mass-shell longitudinal W bosons beyond O(alpha).Comment: 24 pages, LaTeX, uses axodraw, epsfig. Statement clarifie

W+W- Hadronic Decay Properties

Recent measurements of the properties of W+W- events produced in e+e- collisions at Ecm=183 GeV at LEP are reviewed. The data are used to investigate the predicted effects of final state interactions, specifically "colour reconnection".Comment: 6 pages, 7 figures. To appear in the "Proceedings of the XXIX International Conference on High Energy Physics", Vancouver, CA, 23-29 July 199