Hierarchies from D-brane instantons in globally defined Calabi-Yau Orientifolds

We construct the first globally consistent semi-realistic Type I string vacua on an elliptically fibered manifold where the zero modes of the Euclidean D1-instanton sector allow for the generation of non-perturbative Majorana masses of an intermediate scale. In another class of global models, a D1-brane instanton can generate a Polonyi-type superpotential breaking supersymmetry at an exponentially suppressed scale.Comment: 4 pages, 4 tables, uses revtex; v2: Discussion of instanton curves improved, typos fixed, references added; v3: version published in PR

On the Evolutionary History of Stars and their Fossil Mass and Light

The total extragalactic background radiation can be an important test of the global star formation history (SFH). Using direct observational estimates of the SFH, along with standard assumptions about the initial mass function (IMF), we calculate the total extragalactic background radiation and the observed stellar density today. We show that plausible SFHs allow a significant range in each quantity, but that their ratio is very tightly constrained. Current estimates of the stellar mass and extragalactic background are difficult to reconcile, as long as the IMF is fixed to the Salpeter slope above 1 Msun. The joint confidence interval of these two quantities only agrees with that determined from the allowed range of SFH fits at the 3-sigma level, and for our best-fit values the discrepancy is about a factor of two. Alternative energy sources that contribute to the background, such as active galactic nuclei (AGN), Population III stars, or decaying particles, appear unlikely to resolve the discrepancy. However, changes to the IMF allow plausible solutions to the background problem. The simplest is an average IMF with an increased contribution from stars around 1.5--4 Msun. A ``paunchy'' IMF of this sort could emerge as a global average if low mass star formation is suppressed in galaxies experiencing rapid starbursts. Such an IMF is consistent with observations of star-forming regions, and would help to reconcile the fossil record of star formation with the directly observed SFH.Comment: 21 pages, 7 figures, 3 tables; submitted to Monthly Notice

On Nori's Fundamental Group Scheme

We determine the quotient category which is the representation category of the kernel of the homomorphism from Nori's fundamental group scheme to its \'etale and local parts. Pierre Deligne pointed out an error in the first version of this article. We profoundly thank him, in particular for sending us his enlightning example reproduced in Remark 2.4 2).Comment: 29 page

An improved sum-product estimate for general finite fields

This paper improves on a sum-product estimate obtained by Katz and Shen for subsets of a finite field whose order is not prime

Gravitational energy

Observers at rest in a stationary spacetime flat at infinity can measure small amounts of rest-mass+internal energies+kinetic energies+pressure energy in a small volume of fluid attached to a local inertial frame. The sum of these small amounts is the total "matter energy" for those observers. The total mass-energy minus the matter energy is the binding gravitational energy. Misner, Thorne and Wheeler evaluated the gravitational energy of a spherically symmetric static spacetime. Here we show how to calculate gravitational energy in any static and stationary spacetime for isolated sources with a set of observers at rest. The result of MTW is recovered and we find that electromagnetic and gravitational 3-covariant energy densities in conformastatic spacetimes are of opposite signs. Various examples suggest that gravitational energy is negative in spacetimes with special symmetries or when the energy-momentum tensor satisfies usual energy conditions.Comment: 12 pages. Accepted for publication in Class. Quantum Gra

Decreasing Medical Complications for Total Knee Arthroplasty: Effect of Critical Pathways on Outcomes

BACKGROUND: Studies on critical pathway use have demonstrated decreased length of stay and cost without compromise in quality of care. However, pathway effectiveness is difficult to determine given methodological flaws, such as small or single center cohorts. We studied the effect of critical pathways on total knee replacement outcomes in a large population-based study. METHODS: We identified hospitals in four US states that performed total knee replacements. We sent a questionnaire to surgical administrators in these hospitals including items about critical pathway use and hospital characteristics potentially related to outcomes. Patient data were obtained from Medicare claims, including demographics, comorbidities, 90-day postoperative complications and length of hospital stay. The principal outcome measure was the risk of having one or more postoperative complications. RESULTS: Two hundred ninety five hospitals (73%) responded to the questionnaire, with 201 reporting the use of critical pathways. 9,157 Medicare beneficiaries underwent TKR in these hospitals with a mean age of 74 years (± 5.8). After adjusting for both patient and hospital related variables, patients in hospitals with pathways were 32% less likely to have a postoperative complication compared to patients in hospitals without pathways (OR 0.68, 95% CI 0.50-0.92). Patients managed on a critical pathway had an average length of stay 0.5 days (95% CI 0.3-0.6) shorter than patients not managed on a pathway. CONCLUSION: Medicare patients undergoing total knee replacement surgery in hospitals that used critical pathways had fewer postoperative complications than patients in hospitals without pathways, even after adjusting for patient and hospital related factors. This study has helped to establish that critical pathway use is associated with lower rates of postoperative mortality and complications following total knee replacement after adjusting for measured variables

On the mass of a Kerr-anti-de Sitter spacetime in D dimensions

We show how to compute the mass of a Kerr-anti-de Sitter spacetime with respect to the anti-de Sitter background in any dimension, using a superpotential which has been derived from standard Noether identities. The calculation takes no account of the source of the curvature and confirms results obtained for black holes via the first law of thermodynamics.Comment: minor changes; accepted by CQ

Mass and angular momenta of Kerr anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory

We compute the mass and angular momenta of rotating anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory of gravity using a superpotential derived from standard Noether identities. The calculation relies on the fact that the Einstein and Einstein-Gauss-Bonnet vacuum equations are the same when linearized on maximally symmetric backgrounds and uses the recently discovered D-dimensional Kerr-anti-de Sitter solutions to Einstein's equations

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc