Simulating hot Abelian gauge dynamics

The time evolution of soft modes in a quantum gauge field theory is to first approximation classical, but the equations of motion are non-local. We show how they can be written in a local and Hamiltonian way in an Abelian theory, and that this formulation is particularly suitable for numerical simulations. This makes it possible to simulate numerically non-equilibrium processes such as the phase transition in the Abelian Higgs model and and to study, for instance, bubble nucleation and defect formation. Such simulations would also help to understand phase transitions in more complicated gauge theories. Moreover, we show that the existing analytical results for the time-evolution in a pure-gauge theory correspond to a special class of initial conditions and that different initial conditions can lead to qualitatively different behavior. We compare the results of the simulations to analytical calculations and find an excellent agreement.Comment: 18 pages, 5 figures, REVTe

Apixaban for Extended Treatment of Venous Thromboembolism

BACKGROUND: Apixaban, an oral factor Xa inhibitor that can be administered in a simple, fixed-dose regimen, may be an option for the extended treatment of venous thromboembolism. METHODS: In this randomized, double-blind study, we compared two doses of apixaban (2.5 mg and 5 mg, twice daily) with placebo in patients with venous thromboembolism who had completed 6 to 12 months of anticoagulation therapy and for whom there was clinical equipoise regarding the continuation or cessation of anticoagulation therapy. The study drugs were administered for 12 months. RESULTS: A total of 2486 patients underwent randomization, of whom 2482 were included in the intention-to-treat analyses. Symptomatic recurrent venous thromboembolism or death from venous thromboembolism occurred in 73 of the 829 patients (8.8%) who were receiving placebo, as compared with 14 of the 840 patients (1.7%) who were receiving 2.5 mg of apixaban (a difference of 7.2 percentage points; 95% confidence interval [CI], 5.0 to 9.3) and 14 of the 813 patients (1.7%) who were receiving 5 mg of apixaban (a difference of 7.0 percentage points; 95% CI, 4.9 to 9.1) (P<0.001 for both comparisons). The rates of major bleeding were 0.5% in the placebo group, 0.2% in the 2.5-mg apixaban group, and 0.1% in the 5-mg apixaban group. The rates of clinically relevant nonmajor bleeding were 2.3% in the placebo group, 3.0% in the 2.5-mg apixaban group, and 4.2% in the 5-mg apixaban group. The rate of death from any cause was 1.7% in the placebo group, as compared with 0.8% in the 2.5-mg apixaban group and 0.5% in the 5-mg apixaban group. CONCLUSIONS: Extended anticoagulation with apixaban at either a treatment dose (5 mg) or a thromboprophylactic dose (2.5 mg) reduced the risk of recurrent venous thromboembolism without increasing the rate of major bleeding. (Funded by Bristol-Myers Squibb and Pfizer; AMPLIFY-EXT ClinicalTrials.gov number, NCT00633893.)