Integrability of the Minimal Strain Equations for the Lapse and Shift in 3+1 Numerical Relativity

Brady, Creighton and Thorne have argued that, in numerical relativity simulations of the inspiral of binary black holes, if one uses lapse and shift functions satisfying the ``minimal strain equations'' (MSE), then the coordinates might be kept co-rotating, the metric components would then evolve on the very slow inspiral timescale, and the computational demands would thus be far smaller than for more conventional slicing choices. In this paper, we derive simple, testable criteria for the MSE to be strongly elliptic, thereby guaranteeing the existence and uniqueness of the solution to the Dirichlet boundary value problem. We show that these criteria are satisfied in a test-bed metric for inspiraling binaries, and we argue that they should be satisfied quite generally for inspiraling binaries. If the local existence and uniqueness that we have proved holds globally, then, for appropriate boundary values, the solution of the MSE exhibited by Brady et. al. (which tracks the inspiral and keeps the metric evolving slowly) will be the unique solution and thus should be reproduced by (sufficiently accurate and stable) numerical integrations.Comment: 6 pages; RevTeX; submitted to Phys. Rev. D15. Technical issue of the uniqueness of the solution to the Dirichlet problem clarified. New subsection on the nature of the boundary dat

A framework for P2P application development

Although Peer-to-Peer (P2P) computing has become increasingly popular over recent years, there still exist only a very small number of application domains that have exploited it on a large scale. This can be attributed to a number of reasons including the rapid evolution of P2P technologies, coupled with their often-complex nature. This paper describes an implemented abstraction framework that seeks to aid developers in building P2P applications. A selection of example P2P applications that have been developed using this framework are also presented

Rotating Fermi gases in an anharmonic trap

Motivated by recent experiments on rotating Bose-Einstein condensates, we investigate a rotating, polarized Fermi gas trapped in an anharmonic potential. We apply a semiclassical expansion of the density of states in order to determine how the thermodynamic properties depend on the rotation frequency. The accuracy of the semiclassical approximation is tested and shown to be sufficient for describing typical experiments. At zero temperature, rotating the gas above a given frequency $\Omega_{\rm DO}$ leads to a `donut'-shaped cloud which is analogous to the hole found in two-dimensional Bose-Einstein condensates. The free expansion of the gas after suddenly turning off the trap is considered and characterized by the time and rotation frequency dependence of the aspect ratio. Temperature effects are also taken into account and both low- and high-temperature expansions are presented for the relevant thermodynamical quantities. In the high-temperature regime a virial theorem approach is used to study the delicate interplay between rotation and anharmonicity

Appendiix II: List of genera and species cited in this issue

Non

Efficacy of Different Leuprolide Administration Schedules in Premenopausal Breast Cancer: A Retrospective Review

Background Leuprolide is a safe and effective treatment of estrogen receptor–positive premenopausal breast cancer. Data from the SOFT/TEXT trials solidified leuprolide in combination with an aromatase inhibitor as an effective hormonal treatment for premenopausal breast cancer. However, the efficacy of monthly leuprolide depot compared to leuprolide depot every 3 months in combination with an aromatase inhibitor in this patient population is unclear. Patients and Methods In this single center retrospective study, 201 patients were enrolled between January 1, 2015, and October 1, 2016; 100 were included in the 7.5 mg leuprolide monthly injection plus aromatase inhibitor group and 101 in the 22.5 mg leuprolide injection every 3 months plus aromatase inhibitor group. The primary end point was the proportion of patients who experienced ovarian ablation, defined as an estradiol concentration less than 40 pg/mL and a follicle-stimulating hormone concentration of 23 to 116 mU/mL after 3 months of treatment. Significance threshold was P < .05 (2 sided). Secondary end points included disease-free survival and overall survival at 1-year follow-up, as well as adverse events reported during treatment. Results All patients in the monthly leuprolide arm experienced ovarian ablation compared to 100 (99%) of 101 patients in the arm treated every 3 months ( P = 1). The disease-free survival rate at 1 year was 95% in the monthly leuprolide arm and 97% in the arm treated every 3 months ( P = .75). The overall survival rate at 1 year was 100% in the monthly leuprolide arm and 99% in the arm treated every 3 months ( P = 1). The most common treatment-related adverse events between the 2 groups were musculoskeletal pain, hot flashes, fatigue, and insomnia. Conclusion Leuprolide acetate depot administered every 3 months is as efficacious and tolerable as a monthly injection in combination with an aromatase inhibitor for premenopausal patients with hormone receptor–positive breast cancer