Topology Change in (2+1)-Dimensional Gravity

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial topology change are nonvanishing---in fact, they can be infrared divergent---but that they are infinitely suppressed relative to similar topology-preserving amplitudes.Comment: 19 pages of text plus 4 pages of figures, LaTeX (using epsf), UCD-11-9

Mean curvature flow in a Ricci flow background

Following work of Ecker, we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-with-boundary. We compute its variational properties and its time derivative under Perelman's modified Ricci flow. The answer has a boundary term which involves an extension of Hamilton's Harnack expression for the mean curvature flow in Euclidean space. We also derive the evolution equations for the second fundamental form and the mean curvature, under a mean curvature flow in a Ricci flow background. In the case of a gradient Ricci soliton background, we discuss mean curvature solitons and Huisken monotonicity.Comment: final versio

Confidence Level Of Primary Care Providers In Authorizing Athletic Return-To-Play

The purpose of this study was to identify the level of confidence for primary care providers in authorizing athletic retum-to-play following sports-related injury. The Centers for Disease Control and Prevention (CDC) (as cited in Patel, Yamasaki, & Brown, 2017) reported that 2.6 million children and teens ages 0-19 years are treated annually for sports-related injuries, and 7.2 million high school students participate in sports and suffer an estimated 2 million injuries that require 500,000 doctor visits and 30,000 hospitalizations annually. Although primary care providers are providing care for musculoskeletal and concussive injuries, Benham and Geier (2016) reported that they may not have the confidence, knowledge, or skill to manage common musculoskeletal conditions in their primary care practice. Excellent provisions of such care will require providers who are safe and confident in the management and treatment of sports-related injuries to ensure high-quality patient care (Benham & Geier, 2016). Researchers distributed written surveys, and links to a survey were distributed via social media postings, email, and SurveyMonkey to qualifying participants including Doctors of Medicine (MD), Doctors of Osteopathic Medicine (DO), nurse practitioners (NP), and physician assistants (PA). Data collected indicated that only 47.6% primary care providers were confident with returning youth athletes back-to-play following a sports injury, 34.7% were confident in treating sports-related concussive injuries, and 50% were confident in treating sports-related musculoskeletal injuries. Primary care providers can use this information to expose areas for confidence improvement that can be met with continued education, in-services, and workshops. Schools of medicine and nursing can use these findings to improve musculoskeletal curricula in primary care education. Determining primary care provider confidence level in authorizing athletic retum-to-play is imperative in ensuring patient safety and access to thorough and competent care from initial injury to full resolution

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

A new automated method for measuring noble gases and their isotopic ratios in water samples

Author Posting. © American Geophysical Union, 2009. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 10 (2009): Q05008, doi:10.1029/2009GC002429.A method is presented for precisely measuring all five noble gases and their isotopic ratios in water samples using multiple programmed multistage cryogenic traps in conjunction with quadrupole mass spectrometry and magnetic sector mass spectrometry. Multiple automated cryogenic traps, including a two-stage cryotrap used for removal of water vapor, an activated charcoal cryotrap used for helium separation, and a stainless steel cryotrap used for neon, argon, krypton, and xenon separation, allow reproducible gas purification and separation. The precision of this method for gas standards is ±0.10% for He, ±0.14% for Ne, ±0.10% for Ar, ±0.14% for Kr, and ±0.17% for Xe. The precision of the isotopic ratios of the noble gases in gas standards are ±1.9‰ for 20Ne/22Ne, ±2.0‰ for 84Kr/86Kr, ±2.5‰ for 84Kr/82Kr, ±0.9‰ for 132Xe/129Xe, and ±1.3‰ for 132Xe/136Xe. The precision of this method for water samples, determined by measurement of duplicate pairs, is ±1% for He, ±0.9% for Ne, ±0.3% for Ar, ±0.3% for Kr, and ±0.2% for Xe. An attached magnetic sector mass spectrometer measures 3He/4He with precisions of ±0.1% for air standards and ±0.14% for water samples.We are grateful for support by the National Science Foundation Chemical Oceanography program (OCE-0221247), by the Department of Defense (graduate fellowship to RHRS), and by the Woods Hole Oceanographic Institution (postdoctoral fellowship for B.B.)

L^2 torsion without the determinant class condition and extended L^2 cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L^2 cohomology. Under the determinant class assumption the L^2 torsions of this paper specialize to the invariants studied in our previous work. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions.Comment: 39 page

Apparent oxygen utilization rates calculated from tritium and helium-3 profiles at the Bermuda Atlantic Time-series Study site

© The Author(s), 2012. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 9 (2012): 1969-1983, doi:10.5194/bg-9-1969-2012.We present three years of Apparent Oxygen Utilization Rates (AOUR) estimated from oxygen and tracer data collected over the ocean thermocline at monthly resolution between 2003 and 2006 at the Bermuda Atlantic Time-series Study (BATS) site. We estimate water ages by calculating a transit time distribution from tritium and helium-3 data. The vertically integrated AOUR over the upper 500 m, which is a regional estimate of export, during the three years is 3.1 ± 0.5 mol O2 m−2 yr−1. This is comparable to previous AOUR-based estimates of export production at the BATS site but is several times larger than export estimates derived from sediment traps or 234Th fluxes. We compare AOUR determined in this study to AOUR measured in the 1980s and show AOUR is significantly greater today than decades earlier because of changes in AOU, rather than changes in ventilation rates. The changes in AOU are likely a methodological artefact associated with problems with early oxygen measurements.Support from this work came from the National Science Foundation (OCE-0221247, OCE-0623034, and OCE-1029676) and from the WHOI Penzance Endowed Fund in Support of Assistant Scientists

Transcriptomic and proteomic insights into innate immunity and adaptations to a symbiotic lifestyle in the gutless marine worm Olavius algarvensis

Background: The gutless marine worm Olavius algarvensis has a completely reduced digestive and excretory system, and lives in an obligate nutritional symbiosis with bacterial symbionts. While considerable knowledge has been gained of the symbionts, the host has remained largely unstudied. Here, we generated transcriptomes and proteomes of O. algarvensis to better understand how this annelid worm gains nutrition from its symbionts, how it adapted physiologically to a symbiotic lifestyle, and how its innate immune system recognizes and responds to its symbiotic microbiota. Results: Key adaptations to the symbiosis include (i) the expression of gut-specific digestive enzymes despite the absence of a gut, most likely for the digestion of symbionts in the host's epidermal cells; (ii) a modified hemoglobin that may bind hydrogen sulfide produced by two of the worm's symbionts; and (iii) the expression of a very abundant protein for oxygen storage, hemerythrin, that could provide oxygen to the symbionts and the host under anoxic conditions. Additionally, we identified a large repertoire of proteins involved in interactions between the worm's innate immune system and its symbiotic microbiota, such as peptidoglycan recognition proteins, lectins, fibrinogen-related proteins, Toll and scavenger receptors, and antimicrobial proteins. Conclusions: We show how this worm, over the course of evolutionary time, has modified widely-used proteins and changed their expression patterns in adaptation to its symbiotic lifestyle and describe expressed components of the innate immune system in a marine oligochaete. Our results provide further support for the recent realization that animals have evolved within the context of their associations with microbes and that their adaptive responses to symbiotic microbiota have led to biological innovations