Ducks on the torus: existence and uniqueness

We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually occur in two-parametric families. Here we treat systems with a convex slow curve. In this case there is a set of parameter values accumulating to zero for which the system has exactly one attracting and one repelling canard cycle. The basin of the attracting cycle is almost the whole torus.Comment: To appear in Journal of Dynamical and Control Systems, presumably Vol. 16 (2010), No. 2; The final publication is available at www.springerlink.co

A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries

Gravitational waveforms from the inspiral and ring-down stages of the binary black hole coalescences can be modelled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the non-perturbative merger phase of the binary black-hole coalescence problem. This enables us to \emph{coherently} search for all three stages of the coalescence of non-spinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspiral, merger, and ring-down stages of the coalescence of non-spinning binary black holes that follow quasi-circular inspiral. This two-dimensional template family is explicitly parametrized by the physical parameters of the binary. We show that the template family is not only \emph{effectual} in detecting the signals from black hole coalescences, but also \emph{faithful} in estimating the parameters of the binary. We compare the sensitivity of a search (in the context of different ground-based interferometers) using all three stages of the black hole coalescence with other template-based searches which look for individual stages separately. We find that the proposed search is significantly more sensitive than other template-based searches for a substantial mass-range, potentially bringing about remarkable improvement in the event-rate of ground-based interferometers. As part of this work, we also prescribe a general procedure to construct interpolated template banks using non-spinning black hole waveforms produced by numerical relativity.Comment: A typo fixed in Eq.(B11

Aspirin and extended-release dipyridamole versus clopidogrel for recurrent stroke

Background Recurrent stroke is a frequent, disabling event after ischemic stroke. This study compared the efficacy and safety of two antiplatelet regimens — aspirin plus extendedrelease dipyridamole (ASA–ERDP) versus clopidogrel. Methods In this double-blind, 2-by-2 factorial trial, we randomly assigned patients to receive 25 mg of aspirin plus 200 mg of extended-release dipyridamole twice daily or to receive 75 mg of clopidogrel daily. The primary outcome was first recurrence of stroke. The secondary outcome was a composite of stroke, myocardial infarction, or death from vascular causes. Sequential statistical testing of noninferiority (margin of 1.075), followed by superiority testing, was planned. Results A total of 20,332 patients were followed for a mean of 2.5 years. Recurrent stroke occurred in 916 patients (9.0%) receiving ASA–ERDP and in 898 patients (8.8%) receiving clopidogrel (hazard ratio, 1.01; 95% confidence interval [CI], 0.92 to 1.11). The secondary outcome occurred in 1333 patients (13.1%) in each group (hazard ratio for ASA–ERDP, 0.99; 95% CI, 0.92 to 1.07). There were more major hemorrhagic events among ASA–ERDP recipients (419 [4.1%]) than among clopidogrel recipients (365 [3.6%]) (hazard ratio, 1.15; 95% CI, 1.00 to 1.32), including intracranial hemorrhage (hazard ratio, 1.42; 95% CI, 1.11 to 1.83). The net risk of recurrent stroke or major hemorrhagic event was similar in the two groups (1194 ASA–ERDP recipients [11.7%], vs. 1156 clopidogrel recipients [11.4%]; hazard ratio, 1.03; 95% CI, 0.95 to 1.11). Conclusions The trial did not meet the predefined criteria for noninferiority but showed similar rates of recurrent stroke with ASA–ERDP and with clopidogrel. There is no evidence that either of the two treatments was superior to the other in the prevention of recurrent stroke. (ClinicalTrials.gov number, NCT00153062.

Diatomic molecules in ultracold Fermi gases - Novel composite bosons

We give a brief overview of recent studies of weakly bound homonuclear molecules in ultracold two-component Fermi gases. It is emphasized that they represent novel composite bosons, which exhibit features of Fermi statistics at short intermolecular distances. In particular, Pauli exclusion principle for identical fermionic atoms provides a strong suppression of collisional relaxation of such molecules into deep bound states. We then analyze heteronuclear molecules which are expected to be formed in mixtures of different fermionic atoms. It is found how an increase in the mass ratio for the constituent atoms changes the physics of collisional stability of such molecules compared to the case of homonuclear ones. We discuss Bose-Einstein condensation of these composite bosons and draw prospects for future studies.Comment: 10 pages, 5 figure

Transparent Anomalous Dispersion and Superluminal Light Pulse Propagation at a Negative Group Velocity

Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light pulse propagation can be observed even at a negative group velocity through a transparent medium with almost no pulse distortion. Consequently, a {\it negative transit time} is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the {\it rephasing} process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.Comment: 12 journal pages, 9 figure