New Loop Representations for 2+1 Gravity

Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, ``old-fashioned'' loop representations - based on ordinary loops - do exist. In the case when the spatial topology is that of a two-torus, these can be constructed explicitly; {\it all} quantum states can be represented as functions of (homotopy classes of) loops and the scalar product and the action of the basic observables can be given directly in terms of loops.Comment: 28pp, 1 figure (postscript, compressed and uuencoded), TeX, Pennsylvania State University, CGPG-94/5-

Independent Loop Invariants for 2+1 Gravity

We identify an explicit set of complete and independent Wilson loop invariants for 2+1 gravity on a three-manifold $M=\R\times\Sigma^g$, with $\Sigma^g$ a compact oriented Riemann surface of arbitrary genus $g$. In the derivation we make use of a global cross section of the $PSU(1,1)$-principal bundle over Teichm\"uller space given in terms of Fenchel-Nielsen coordinates.Comment: 11pp, 2 figures (postscript, compressed and uu-encoded), TeX, Pennsylvania State University, CGPG-94/7-

Loop Quantum Cosmology I: Kinematics

The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features - e.g. the discrete volume spectrum - in certain cosmological regimes. Contrary to previous studies of quantum cosmology (minisuperspace quantizations) the symmetry reduction is carried out not at the classical level but on an auxiliary Hilbert space of the quantum theory before solving the constraints. Therefore, kinematical properties like volume quantization survive the symmetry reduction. In this first part the kinematical framework, i.e. implementation of the quantum symmetry reduction and quantization of Gauss and diffeomorphism constraints, is presented for Bianchi class A models as well as locally rotationally symmetric and spatially isotropic closed and flat models.Comment: 24 page

Loop Quantum Cosmology II: Volume Operators

Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is necessary, a complete solution of which is given for isotropic models; in this case the volume spectrum can be calculated explicitly. It is observed that the stronger the symmetry conditions are the smaller is the volume spectrum, which can be interpreted as level splitting due to broken symmetries. Some implications for quantum cosmology are presented.Comment: 21 page

Iterative Methods for Visualization of Implicit Surfaces on GPU

The original publication is available at www.springerlink.comInternational audienceThe ray-casting of implicit surfaces on GPU has been explored in the last few years. However, until recently, they were restricted to second degree (quadrics). We present an iterative solution to ray cast cubics and quartics on GPU. Our solution targets efficient implementation, obtaining interactive rendering for thousands of surfaces per frame. We have given special attention to torus rendering since it is a useful shape for multiple CAD models. We have tested four different iterative methods, including a novel one, comparing them with classical tessellation solution

The complete spectrum of the area from recoupling theory in loop quantum gravity

We compute the complete spectrum of the area operator in the loop representation of quantum gravity, using recoupling theory. This result extends previous derivations, which did not include the ``degenerate'' sector, and agrees with the recently computed spectrum of the connection-representation area operator.Comment: typos corrected in eqn.(21). Latex with IOP and epsf styles, 1 figure (eps postscript file), 12 pages. To appear in Class. Quantum Gra

Autologous microsurgical breast reconstruction and coronary artery bypass grafting: an anatomical study and clinical implications

OBJECTIVE: To identify possible avenues of sparing the internal mammary artery (IMA) for coronary artery bypass grafting (CABG) in women undergoing autologous breast reconstruction with deep inferior epigastric artery perforator (DIEP) flaps. BACKGROUND: Optimal autologous reconstruction of the breast and coronary artery bypass grafting (CABG) are often mutually exclusive as they both require utilisation of the IMA as the preferred arterial conduit. Given the prevalence of both breast cancer and coronary artery disease, this is an important issue for women's health as women with DIEP flap reconstructions and women at increased risk of developing coronary artery disease are potentially restricted from receiving this reconstructive option should the other condition arise. METHODS: The largest clinical and cadaveric anatomical study (n=315) to date was performed, investigating four solutions to this predicament by correlating the precise requirements of breast reconstruction and CABG against the anatomical features of the in situ IMAs. This information was supplemented by a thorough literature review. RESULTS: Minimum lengths of the left and right IMA needed for grafting to the left-anterior descending artery are 160.08 and 177.80 mm, respectively. Based on anatomical findings, the suitable options for anastomosis to each intercostals space are offered. In addition, 87-91% of patients have IMA perforator vessels to which DIEP flaps can be anastomosed in the first- and second-intercostal spaces. CONCLUSION: We outline five methods of preserving the IMA for future CABG: (1) lowering the level of DIEP flaps to the fourth- and fifth-intercostals spaces, (2) using the DIEP pedicle as an intermediary for CABG, (3) using IMA perforators to spare the IMA proper, (4) using and end-to-side anastomosis between the DIEP pedicle and IMA and (5) anastomosis of DIEP flaps using retrograde flow from the distal IMA. With careful patient selection, we hypothesize using the IMA for autologous breast reconstruction need not be an absolute contraindication for future CABG

Class dynamics of development: a methodological note

This article argues that class relations are constitutive of developmental processes and central to understanding inequality within and between countries. In doing so it illustrates and explains the diversity of the actually existing forms of class relations, and the ways in which they interplay with other social relations such as gender and ethnicity. This is part of a wider project to re- vitalise class analysis in the study of development problems and experiences

Rapid report on estimating incidence from cross-sectional data

PURPOSE: In prospective cohort studies, incidence is typically estimated by the ratio of the observed number of events to person-time at risk. This crude estimator is consistent for the true population incidence rate (IR) under mild assumptions. Here we consider a different setting where only cross-sectional data are available, that is, at a single time point, participants are evaluated to identify whether they have previously had the event of interest. METHODS: Unlike the prospective cohort data setting, for cross-sectional data, the crude IR estimator is biased. Instead, the maximum likelihood estimator (MLE) may be used. Although the MLE does not have a simple closed form, it is consistent and easy to compute using statistical software. To compare the bias of the MLE and the crude estimator, a simulation was conducted. RESULTS: The crude estimator underestimated the true incidence, whereas the MLE was approximately unbiased. In general, bias of the crude estimator tended to be roughly one to two orders of magnitude larger (in absolute value) than the MLE. CONCLUSIONS: Under cross-sectional data with exact event times unknown, the MLE of the IR is straightforward to calculate, more accurate than the crude IR estimator, and consistent provided the hazard is constant

Neuropsychological Correlates of Adherence in Youth with Behaviorally Acquired HIV

Youth living with behaviorally acquired HIV (YLWH) are at-risk for both neuropsychological disorders and antiretroviral therapy (ART) non-adherence; little is known about their interrelationship over time in YLWH. Neuropsychological and psychiatric functioning, substance use, and self-report of 7-day/week and weekend ART adherence were assessed at baseline and Weeks 24, 48, 96 and 144 of a longitudinal study evaluating the impact of early (CD4>350) versus standard of care (CD4≤350) treatment initiation on neuropsychological functioning in 111 treatment-naive YLWH age 18-24 years at entry. Bayesian multi-level models for adherence (≥90% vs. <90%) were fit using random intercepts for repeated measures. Adjusted odds ratios (OR [95% credible interval]) for higher versus lower baseline Motor function for visit adherence were 0.58 (0.25, 1.16), 0.5 (0.15, 1.38), 0.52 (0.16, 1.52), and 0.94 (0.3, 2.8) at Weeks 24, 48, 96, and 144, respectively. Week 24 adherence was associated with higher adjusted odds of Motor function at Week 48 (week: 0.27, -0.05-0.59; weekend: 0.28, -0.07-0.62). Week 96 Complex Executive functioning was associated with higher adjusted odds of adherence at Week 144, OR=4.26 (1.50, 14.33). Higher Motor functioning emerged most consistently associated with lower odds of adherence in YLWH. Complex Executive functioning was associated with adherence only at end of study, suggesting potential contribution in adherence over the long-term