3,155 research outputs found
The Generalized Ricci Flow for 3D Manifolds with One Killing Vector
We consider 3D flow equations inspired by the renormalization group (RG)
equations of string theory with a three dimensional target space. By modifying
the flow equations to include a U(1) gauge field, and adding carefully chosen
De Turck terms, we are able to extend recent 2D results of Bakas to the case of
a 3D Riemannian metric with one Killing vector. In particular, we show that the
RG flow with De Turck terms can be reduced to two equations: the continual Toda
flow solved by Bakas, plus its linearizaton. We find exact solutions which flow
to homogeneous but not always isotropic geometries
Circles in the Sky: Finding Topology with the Microwave Background Radiation
If the universe is finite and smaller than the distance to the surface of
last scatter, then the signature of the topology of the universe is writ large
on the microwave background sky. We show that the microwave background will be
identified at the intersections of the surface of last scattering as seen by
different ``copies'' of the observer. Since the surface of last scattering is a
two-sphere, these intersections will be circles, regardless of the background
geometry or topology. We therefore propose a statistic that is sensitive to all
small, locally homogeneous topologies. Here, small means that the distance to
the surface of last scatter is smaller than the ``topology scale'' of the
universe.Comment: 14 pages, 10 figures, IOP format. This paper is a direct descendant
of gr-qc/9602039. To appear in a special proceedings issue of Class. Quant.
Grav. covering the Cleveland Topology & Cosmology Worksho
Spherical structures on torus knots and links
The present paper considers two infinite families of cone-manifolds endowed
with spherical metric. The singular strata is either the torus knot or the torus link . Domains of existence for a
spherical metric are found in terms of cone angles and volume formul{\ae} are
presented.Comment: 17 pages, 5 figures; typo
Holography for the Lorentz Group Racah Coefficients
A known realization of the Lorentz group Racah coefficients is given by an
integral of a product of 6 ``propagators'' over 4 copies of the hyperbolic
space. These are ``bulk-to-bulk'' propagators in that they are functions of two
points in the hyperbolic space. It is known that the bulk-to-bulk propagator
can be constructed out of two bulk-to-boundary ones. We point out that there is
another way to obtain the same object. Namely, one can use two bulk-to-boundary
and one boundary-to-boundary propagator. Starting from this construction and
carrying out the bulk integrals we obtain a realization of the Racah
coefficients that is ``holographic'' in the sense that it only involves
boundary objects. This holographic realization admits a geometric
interpretation in terms of an ``extended'' tetrahedron.Comment: 12 pages, 2 figures; v2: minor changes; v3: "extended" tetrahedron
interpretation adde
Comments on Closed Bianchi Models
We show several kinematical properties that are intrinsic to the Bianchi
models with compact spatial sections. Especially, with spacelike hypersurfaces
being closed, (A) no anisotropic expansion is allowed for Bianchi type V and
VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to
show them, we put into geometric terms what is meant by spatial homogeneity and
employ a mathematical result on 3-manifolds. We make clear the relation between
the Bianchi type symmetry of space-time and spatial compactness, some part of
which seem to be unnoticed in the literature. Especially, it is shown under
what conditions class B Bianchi models do not possess compact spatial sections.
Finally we briefly describe how this study is useful in investigating global
dynamics in (3+1)-dimensional gravity.Comment: 14 pages with one table, KUCP-5
Current End-of-Life Care Needs and Care Practices in Acute Care Hospitals
A descriptive-comparative study was undertaken to examine current end-of-life care needs and practices in hospital. A chart review for all 1,018 persons who died from August 1, 2008 through July 31, 2009 in two full-service Canadian hospitals was conducted. Most decedents were elderly (73.8%) and urbanite (79.5%), and cancer was the most common diagnosis (36.2%). Only 13.8% had CPR performed at some point during this hospitalization and 8.8% had CPR immediately preceding death, with 87.5% having a DNR order and 30.8% providing an advance directive. Most (97.3%) had one or more life-sustaining technologies in use at the time of death. These figures indicate, when compared to those in a similar mid-1990s Canadian study, that impending death is more often openly recognized and addressed. Technologies continue to be routinely but controversially used. The increased rate of end-stage CPR from 2.9% to 8.8% could reflect a 1994+ shift of expected deaths out of hospital
Soft phonons and structural phase transitions in LaBaCuO
Soft phonon behavior associated with a structural phase transition from the
low-temperature-orthorhombic (LTO) phase ( symmetry) to the
low-temperature-tetragonal (LTT) phase ( symmetry) was investigated
in LaBaCuO using neutron scattering. As temperature
decreases, the TO-mode at -point softens and approaches to zero energy
around K, where the LTO -- LTT transition occurs. Below , the phonon hardens quite rapidly and it's energy almost saturates below
50 K. At , the energy dispersion of the soft phonon along in-plane
direction significantly changes while the dispersion along out-of-plane
direction is almost temperature independent. Coexistence between the LTO phase
and the LTT phase, seen in both the soft phonon spectra and the peak profiles
of Bragg reflection, is discussed in context of the order of structural phase
transitions.Comment: 6 pages, 8 figure
Invariant Peano curves of expanding Thurston maps
We consider Thurston maps, i.e., branched covering maps
that are postcritically finite. In addition, we assume that is expanding in
a suitable sense. It is shown that each sufficiently high iterate of
is semi-conjugate to , where is equal to the
degree of . More precisely, for such an we construct a Peano curve
(onto), such that
(for all ).Comment: 63 pages, 12 figure
A Bayesian partial membership model for multiple exposures with uncertain group memberships
We present a Bayesian partial membership model that estimates the associations between an outcome, a small number of latent variables, and multiple observed exposures where the number of latent variables is specified a priori. We assign one observed exposure as the sentinel marker for each latent variable. The model allows non-sentinel exposures to have complete membership in one latent group, or partial membership across two or more latent groups. MCMC sampling is used to determine latent group partial memberships for the non-sentinel exposures, and estimate all model parameters. We compare the performance of our model to competing approaches in a simulation study and apply our model to inflammatory marker data measured in a large mother-child cohort of the Seychelles Child Development Study (SCDS). In simulations, our model estimated model parameters with little bias, adequate coverage, and tighter credible intervals compared to competing approaches. Under our partial membership model with two latent groups, SCDS inflammatory marker classifications generally aligned with the scientific literature. Incorporating additional SCDS inflammatory markers and more latent groups produced similar groupings of markers that also aligned with the literature. Associations between covariates and birth weight were similar across latent variable models and were consistent with earlier work in this SCDS cohort. Supplementary materials accompanying this paper appear online.</p
Future asymptotic expansions of Bianchi VIII vacuum metrics
Bianchi VIII vacuum solutions to Einstein's equations are causally
geodesically complete to the future, given an appropriate time orientation, and
the objective of this article is to analyze the asymptotic behaviour of
solutions in this time direction. For the Bianchi class A spacetimes, there is
a formulation of the field equations that was presented in an article by
Wainwright and Hsu, and in a previous article we analyzed the asymptotic
behaviour of solutions in these variables. One objective of this paper is to
give an asymptotic expansion for the metric. Furthermore, we relate this
expansion to the topology of the compactified spatial hypersurfaces of
homogeneity. The compactified spatial hypersurfaces have the topology of
Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII
spacetimes, the length of a circle fibre converges to a positive constant but
that in the case of general Bianchi VIII solutions, the length tends to
infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces
correcte
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