Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data

We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment.Comment: 23 page

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

From Coulomb excitation cross sections to non-resonant astrophysical rates in three-body systems: 17^{17}Ne case

Coulomb and nuclear dissociation of $^{17}$Ne on light and heavy targets are studied theoretically. The dipole E1 strength function is determined in a broad energy range including energies of astrophysical interest. Dependence of the strength function on different parameters of the $^{17}$Ne ground state structure and continuum dynamics is analyzed in a three-body model. The discovered dependence plays an important role for studies of the strength functions for the three-body E1 dissociation and radiative capture. The constraints on the $[s^2]/[d^2]$ configuration mixing in $^{17}$Ne and on $p$-wave interaction in the $^{15}$O+$p$ channel are imposed based on experimental data for $^{17}$Ne Coulomb dissociation on heavy target.Comment: 12 pages, 13 figure

Emerg. Infect. Dis

The multidrug-resistant (MDR) Salmonella enterica serotype Newport strain that produces CMY-2 β-lactamase(Newport MDR-AmpC) was the source of sporadic cases and outbreaks in humans in France during 2000–2005. Because this strain was not detected in food animals, it was most likely introduced into France through imported food products

On UHECR energy estimation algorithms based on the measurement of electromagnetic component parameters in EAS

Model calculations are performed of extensive air shower (EAS) component energies using a variety of hadronic interaction parameters. A conversion factor from electromagnetic component energy to the energy of ultra-high energy cosmic rays (UHECRs) and its model and primary mass dependence is studied. It is shown that model dependence of the factor minimizes under the necessary condition of the same maximum position and muon content of simulated showers.Comment: contracted version is accepted for publication in Doklady Physic

Long-Time Asymptotics of Perturbed Finite-Gap Korteweg-de Vries Solutions

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of solutions of the Korteweg--de Vries equation which are decaying perturbations of a quasi-periodic finite-gap background solution. We compute a nonlinear dispersion relation and show that the $x/t$ plane splits into $g+1$ soliton regions which are interlaced by $g+1$ oscillatory regions, where $g+1$ is the number of spectral gaps. In the soliton regions the solution is asymptotically given by a number of solitons travelling on top of finite-gap solutions which are in the same isospectral class as the background solution. In the oscillatory region the solution can be described by a modulated finite-gap solution plus a decaying dispersive tail. The modulation is given by phase transition on the isospectral torus and is, together with the dispersive tail, explicitly characterized in terms of Abelian integrals on the underlying hyperelliptic curve.Comment: 45 pages. arXiv admin note: substantial text overlap with arXiv:0705.034

Large deep neural networks for MS lesion segmentation

Multiple sclerosis (MS) is a multi-factorial autoimmune disorder, characterized by spatial and temporal dissemination of brain lesions that are visible in T2-weighted and Proton Density (PD) MRI. Assessment of lesion burden and is useful for monitoring the course of the disease, and assessing correlates of clinical outcomes. Although there are established semi-automated methods to measure lesion volume, most of them require human interaction and editing, which are time consuming and limits the ability to analyze large sets of data with high accuracy. The primary objective of this work is to improve existing segmentation algorithms and accelerate the time consuming operation of identifying and validating MS lesions. In this paper, a Deep Neural Network for MS Lesion Segmentation is implemented. The MS lesion samples are extracted from the Partners Comprehensive Longitudinal Investigation of Multiple Sclerosis (CLIMB) study. A set of 900 subjects with T2, PD and a manually corrected label map images were used to train a Deep Neural Network and identify MS lesions. Initial tests using this network achieved a 90% accuracy rate. A secondary goal was to enable this data repository for big data analysis by using this algorithm to segment the remaining cases available in the CLIMB repository

In memoriam of Alexander Golovin (1939–2013)

No abstract available