Dispersive Shock Wave, Generalized Laguerre Polynomials and Asymptotic Solitons of the Focusing Nonlinear Schr\"odinger Equation

We consider dispersive shock wave to the focusing nonlinear Schr\"odinger equation generated by a discontinuous initial condition which is periodic or quasi-periodic on the left semi-axis and zero on the right semi-axis. As an initial function we use a finite-gap potential of the Dirac operator given in an explicit form through hyper-elliptic theta-functions. The paper aim is to study the long-time asymptotics of the solution of this problem in a vicinity of the leading edge, where a train of asymptotic solitons are generated. Such a problem was studied in \cite{KK86} and \cite{K91} using Marchenko's inverse scattering technics. We investigate this problem exceptionally using the Riemann-Hilbert problems technics that allow us to obtain explicit formulas for the asymptotic solitons themselves that in contrast with the cited papers where asymptotic formulas are obtained only for the square of absolute value of solution. Using transformations of the main RH problems we arrive to a model problem corresponding to the parametrix at the end points of continuous spectrum of the Zakharov-Shabat spectral problem. The parametrix problem is effectively solved in terms of the generalized Laguerre polynomials which are naturally appeared after appropriate scaling of the Riemann-Hilbert problem in a small neighborhoods of the end points of continuous spectrum. Further asymptotic analysis give an explicit formula for solitons at the edge of dispersive wave. Thus, we give the complete description of the train of asymptotic solitons: not only bearing envelope of each asymptotic soliton, but its oscillating structure are found explicitly. Besides the second term of asymptotics describing an interaction between these solitons and oscillating background is also found. This gives the fine structure of the edge of dispersive shock wave.Comment: 36 pages, 5 figure

Towards the automatic evaluation of stylistic quality of natural texts: constructing a special-­purpose corpus of stylistic edits from the Wikipedia revision history

This thesis proposes an approach to automatic evaluation of the stylistic quality of natural texts through data-driven methods of Natural Language Processing. Advantages of data driven methods and their dependency on the size of training data are discussed. Also the advantages of using Wikipedia as a source for textual data mining are presented. The method in this project crucially involves a program for quick automatic extraction of sentences edited by users from the Wikipedia Revision History. The resulting edits have been compiled in a large-scale corpus of examples of stylistic editing. The complete modular structure of the extraction program is described and its performance is analyzed. Furthermore, the need to separate stylistic edits stylistic edits from factual ones is discussed and a number of Machine Learning classification algorithms for this task are proposed and tested. The program developed in this project was able to process approximately 10% of the whole Russian Wikipedia Revision history (200 gigabytes of textual data) in one month, resulting in the extraction of more than two millions of user edits. The best algorithm for the classification of edits into factual and stylistic ones achieved 86.2% cross-validation accuracy, which is comparable with state-of-the-art performance of similar models described in published papers.Master i Datalingvistikk og språkteknologiMAHF-DASPDASP35

Virtual Bronchoscopy for Tumors and Traumatic Lesions of the Airways

The given MSCT of 26 patients with tumoral damage of a trachea is analyzed. Data of MSCT of 61 patients with tumoral damage of bronchial tubes of primary and secondary genesis and hyperplastic lymph nodes are analyzed. In the analysis, a comprehensive analysis of the native, post-processing data and volumetric reconstructions allows more fully appreciating the nature of the changes, the topography, the extent and prevalence of neoplastic lesions tracheobronchial system. Differential diagnostics of benign and malignant lesions are conducted especially in the stenotic lesions when execution of bronchofibroscopy was impossible. Virtual bronchoscopy (VB) MSCT allowed determining the presence of a complete or partial rupture of the main bronchus, its distance to the bifurcation of the trachea, the state of the collapsed lung, the presence of fluid in the hemithorax, and secondary changes in the bone structures of the chest. The VB played an important role in monitoring the adequacy of reconstructive measures on the damaged bronchus, excluding the occurrence of postoperative stenosis. Virtual bronchoscopy of multispiral computed tomography with the capabilities of multiplanar and volumetric reconstructions and post-processing image processing is an optimal noninvasive method for determining the traumatic lesion of the main bronchi and monitoring the success of the reconstructive surgical manua