Correlations for pairs of periodic trajectories for open billiards

In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiards similar to those established by Pollicott and Sharp for closed geodesics on negatively curved compact surfaces. The first of these estimates holds for general open billiards in any dimension. The more intricate second estimate is established for open billiards satisfying the so called Dolgopyat type estimates. This class of billiards includes all open billiards in the plane and open billiards in $\R^N, N \geq 3$ satisfying some additional conditions

Role of Landau-Rabi quantization of electron motion on the crust of magnetars within the nuclear energy density functional theory

Magnetic fields of order $10^{15}$ G have been measured at the surface of some neutron stars, and much stronger magnetic fields are expected to be present in the solid region beneath the surface. The effects of the magnetic field on the equation of state and on the composition of the crust due to Landau-Rabi quantization of electron motion are studied. Both the outer and inner crustal regions are described in a unified and consistent way within the nuclear-energy density functional theory.Comment: 23 pages, 11 figure

FREE SKIN PLASTY IN TRAUMATIC LESIONS OF THE LIMBS

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Conundrums in noun phrase coreference resolution: making sense of the state-of-the-art

Journal ArticleWe aim to shed light on the state-of-the-art in NP coreference resolution by teasing apart the differences in the MUC and ACE task definitions, the assumptions made in evaluation methodologies, and inherent differences in text corpora. First, we examine three subproblems that play a role in coreference resolution: named entity recognition, anaphoricity determination, and coreference element detection. We measure the impact of each subproblem on coreference resolution and confirm that certain assumptions regarding these subproblems in the evaluation methodology can dramatically simplify the overall task. Second, we measure the performance of a state-of-the-art coreference resolver on several classes of anaphora and use these results to develop a quantitative measure for estimating coreference resolution performance on new data sets

Step Bunching with Alternation of Structural Parameters

By taking account of the alternation of structural parameters, we study bunching of impermeable steps induced by drift of adatoms on a vicinal face of Si(001). With the alternation of diffusion coefficient, the step bunching occurs irrespective of the direction of the drift if the step distance is large. Like the bunching of permeable steps, the type of large terraces is determined by the drift direction. With step-down drift, step bunches grows faster than those with step-up drift. The ratio of the growth rates is larger than the ratio of the diffusion coefficients. Evaporation of adatoms, which does not cause the step bunching, decreases the difference. If only the alternation of kinetic coefficient is taken into account, the step bunching occurs with step-down drift. In an early stage, the initial fluctuation of the step distance determines the type of large terraces, but in a late stage, the type of large terraces is opposite to the case of alternating diffusion coefficient.Comment: 8pages, 16 figure

Landau quantization and neutron emissions by nuclei in the crust of a magnetar

Magnetars are neutron stars endowed with surface magnetic fields of the order of $10^{14}-10^{15}$~G, and with presumably much stronger fields in their interior. As a result of Landau quantization of electron motion, the neutron-drip transition in the crust of a magnetar is shifted to either higher or lower densities depending on the magnetic field strength. The impact of nuclear uncertainties is explored considering the recent series of Brussels-Montreal microscopic nuclear mass models. All these models are based on the Hartree-Fock-Bogoliubov method with generalized Skyrme functionals. They differ in their predictions for the symmetry energy coefficient at saturation, and for the stiffness of the neutron-matter equation of state. For comparison, we have also considered the very accurate but more phenomenological model of Duflo and Zuker. Although the equilibrium composition of the crust of a magnetar and the onset of neutron emission are found to be model dependent, the quantum oscillations of the threshold density are essentially universal.Comment: 7 pages, 2 figure

VASCULARIZATION OF THE UPPER LIMB ARTERIES

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The Challenge of Augmented Reality in Surgery

Imaging has revolutionized surgery over the last 50 years. Diagnostic imaging is a key tool for deciding to perform surgery during disease management; intraoperative imaging is one of the primary drivers for minimally invasive surgery (MIS), and postoperative imaging enables effective follow-up and patient monitoring. However, notably, there is still relatively little interchange of information or imaging modality fusion between these different clinical pathway stages. This book chapter provides a critique of existing augmented reality (AR) methods or application studies described in the literature using relevant examples. The aim is not to provide a comprehensive review, but rather to give an indication of the clinical areas in which AR has been proposed, to begin to explain the lack of clinical systems and to provide some clear guidelines to those intending pursue research in this area