Control and Stabilization of the Benjamin-Ono equation in L2(T)L^2(\mathbb T)

We prove the control and stabilization of the Benjamin-Ono equation in L^2(\T), the lowest regularity where the initial value problem is well-posed. This problem was already initiated in \cite{LinaresRosierBO} where a stronger stabilization term was used (that makes the equation of parabolic type in the control zone). Here we employ a more natural stabilization term related to the $L^2$ norm. Moreover, by proving a theorem of controllability in $L^2$, we manage to prove the global controllability in large time. Our analysis relies strongly on the bilinear estimates proved in \cite{MolinetPilodBO} and some new extension of these estimates established here

Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain

This paper aims at completing an earlier work of Russell and Zhang to study internal control problems for the distributed parameter system described by the Korteweg-de Vries equation on a periodic domain T^1. In their article, Russell and Zhang showed that the system is locally exactly controllable and locally exponentially stabilizable when the control acts on an arbitrary nonempty subdomain of T^1. In this paper, we show that the system is in fact globally exactly controllable and globally exponentially stabilizable. The global exponential stabilizability corresponding to a natural feedback law is first established with the aid of certain properties of propagation of compactness and propagation of regularity in Bourgain spaces for solutions of the associated linear system. Then, using a different feedback law, the resulting closed-loop system is shown to be locally exponentially stable with an arbitrarily large decay rate. A time-varying feedback law is further designed to ensure a global exponential stability with an arbitrary large decay rate

A deep neural network for 12-lead electrocardiogram interpretation outperforms a conventional algorithm, and its physician overread, in the diagnosis of atrial fibrillation

Background: Automated electrocardiogram (ECG) interpretations may be erroneous, and lead to erroneous overreads, including for atrial fibrillation (AF). We compared the accuracy of the first version of a new deep neural network 12-Lead ECG algorithm (Cardiologs®) to the conventional Veritas algorithm in interpretation of AF. Methods: 24,123 consecutive 12-lead ECGs recorded over 6 months were interpreted by 1) the Veritas® algorithm, 2) physicians who overread Veritas® (Veritas® + physician), and 3) Cardiologs® algorithm. We randomly selected 500 out of 858 ECGs with a diagnosis of AF according to either algorithm, then compared the algorithms' interpretations, and Veritas® + physician, with expert interpretation. To assess sensitivity for AF, we analyzed a separate database of 1473 randomly selected ECGs interpreted by both algorithms and by blinded experts. Results: Among the 500 ECGs selected, 399 had a final classification of AF; 101 (20.2%) had ≥1 false positive automated interpretation. Accuracy of Cardiologs® (91.2%; CI: 82.4–94.4) was higher than Veritas® (80.2%; CI: 76.5–83.5) (p < 0.0001), and equal to Veritas® + physician (90.0%, CI:87.1–92.3) (p = 0.12). When Veritas® was incorrect, accuracy of Veritas® + physician was only 62% (CI 52–71); among those ECGs, Cardiologs® accuracy was 90% (CI: 82–94; p < 0.0001). The second database had 39 AF cases; sensitivity was 92% vs. 87% (p = 0.46) and specificity was 99.5% vs. 98.7% (p = 0.03) for Cardiologs® and Veritas® respectively. Conclusion: Cardiologs® 12-lead ECG algorithm improves the interpretation of atrial fibrillation

Discovery of VHE gamma-rays from the high-frequency-peaked BL Lac object RGB J0152+017

Aims: The BL Lac object RGB J0152+017 (z=0.080) was predicted to be a very high-energy (VHE; > 100 GeV) gamma-ray source, due to its high X-ray and radio fluxes. Our aim is to understand the radiative processes by investigating the observed emission and its production mechanism using the High Energy Stereoscopic System (H.E.S.S.) experiment. Methods: We report recent observations of the BL Lac source RGB J0152+017 made in late October and November 2007 with the H.E.S.S. array consisting of four imaging atmospheric Cherenkov telescopes. Contemporaneous observations were made in X-rays by the Swift and RXTE satellites, in the optical band with the ATOM telescope, and in the radio band with the Nancay Radio Telescope. Results: A signal of 173 gamma-ray photons corresponding to a statistical significance of 6.6 sigma was found in the data. The energy spectrum of the source can be described by a powerlaw with a spectral index of 2.95+/-0.36stat+/-0.20syst. The integral flux above 300 GeV corresponds to ~2% of the flux of the Crab nebula. The source spectral energy distribution (SED) can be described using a two-component non-thermal synchrotron self-Compton (SSC) leptonic model, except in the optical band, which is dominated by a thermal host galaxy component. The parameters that are found are very close to those found in similar SSC studies in TeV blazars. Conclusions: RGB J0152+017 is discovered as a source of VHE gamma-rays by H.E.S.S. The location of its synchrotron peak, as derived from the SED in Swift data, allows clearly classification it as a high-frequency-peaked BL Lac (HBL).Comment: Accepted for publication in A&A Letters (5 pages, 4 figures

Exact Controllability of nonlinear Heat equations in spaces of analytic functions

International audienceIt is by now well known that the use of Carleman estimates allows to establish the control-lability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is indeed reachable. In this paper, we pursue the study of the reachable states of parabolic equations based on a direct approach using control inputs in Gevrey spaces by considering a nonlinear heat equation in dimension one. The nonlinear part is assumed to be an analytic function of the spatial variable x, the unknown y, and its derivative ∂ x y. By investigating carefully a nonlinear Cauchy problem in the spatial variable and the relationship between the jet of space derivatives and the jet of time derivatives, we derive an exact controllability result for small initial and final data that can be extended as analytic functions on some ball of the complex plane. 2010 Mathematics Subject Classification: 35K40, 93B0