Огляд підходів до розв’язання задач ідентифікації парафраз

The article is devoted to a review of approaches to solving the problem of identifying paraphrases. This problem's relevance and use in tasks such as plagiarism detection, text simplification, and information search are described. Several classes of solutions were considered. The first approach is based on manual rules - it uses manually selected features based on the fundamental properties of paraphrases. The second approach is based on lexical similarity and various databases and ontologies. Machine learning-based approaches are also presented in this paper and describe different architectures that can be used to identify paraphrases. The last approach considered is based on deep learning and modern models of transformers. Pages of the article in the issue: 71 - 78 Language of the article: UkrainianСтаття присвячена огляду підходів до розв’язання задачі ідентифікації парафраз. Описується актуальність та використання даної задачі у таких задачах як виявлення плагіату, спрощення тексту та пошук інформації. Було розглянуто декілька класів вирішення даної задачі. Перший підхід заснований на ручних правилах - використовує вручну підібрані особливості базуючись на базових властивостях парафраз. Другий підхід заснований на лексичній подібності та різноманітних базах даних і онтології. Підходи, засновані на машинному навчанні також представлені у даній статті та описує архітектури, які можуть бути використані для ідентифікації парафраз. Останній підхід який розглянуто базується на глибокому навчанні та сучасних моделях трансформерів

Random Vibrations of Elastic-plastic Structures

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A 10-hour period revealed in optical spectra of the highly variable WN8 Wolf-Rayet star WR 123

Aims. What is the origin of the large-amplitude variability in Wolf-Rayet WN8 stars in general and WR123 in particular? A dedicated spectroscopic campaign targets the ten-hour period previously found in the high-precision photometric data obtained by the MOST satellite. Methods. In June-August 2003 we obtained a series of high signal-to-noise, mid-resolution spectra from several sites in the {\lambda}{\lambda} 4000 - 6940 A^{\circ} domain. We also followed the star with occasional broadband (Johnson V) photometry. The acquired spectroscopy allowed a detailed study of spectral variability on timescales from \sim 5 minutes to months. Results. We find that all observed spectral lines of a given chemical element tend to show similar variations and that there is a good correlation between the lines of different elements, without any significant time delays, save the strong absorption components of the Hei lines, which tend to vary differently from the emission parts. We find a single sustained periodicity, P \sim 9.8 h, which is likely related to the relatively stable pulsations found in MOST photometry obtained one year later. In addition, seemingly stochastic, large-amplitude variations are also seen in all spectral lines on timescales of several hours to several days.Comment: 6 pages, 4 figures, 2 tables, data available on-line, accepted in A&A Research Note

Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials

We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and suggest an algorithm reconstructing the potential from the spectral data that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO

Random matrices, non-backtracking walks, and orthogonal polynomials

Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the limiting spectral measure play a role in this approach.Comment: (more) minor change

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru

Clinical case of chemoresistant tuberculosis in the patient with tuberous sclerosis: difficulties of diagnosis, features of the course and treatment.

In the practical activities of a modern doctor, significant difficulties are noted in the diagnostics and proper management of patients with hereditary diseases due to the limited coverage of the population by genetic researches. For a long time, the patients with a variety of complaints are observed by doctors of various specialties, and the therapy often has little effect due to a lack of understanding of the true causes of pathological changes. The situation is complicated by case of a combined course of a hereditarily caused disease and some other disease of an infectious, non-infectious or tumor nature. The aim of the research was to study the characteristics of clinical manifestations, course of tuberculosis with resistance to anti-TB drugs in a patient with a rare hereditary disease from the group of phacomotoses - Bourneville-Pringle disease or tuberous sclerosis. This disease has a wide range of clinical manifestations, accompanied with the development of benign neoplasms in various organs and systems, damages to the skin, brain, organs of vision, lungs, kidneys, heart, as well as the musculoskeletal and endocrine system. It leads to development of various infectious and non-infectious pathologies in these organs. The article covers a 4-year period of observation of a young patient with late diagnosed tuberous sclerosis, suffering from pulmonary tuberculosis and tuberculosis of urinary system, includes the initial diagnosis of a specific disease, the course, the dynamics against received treatment and the development of relapse with the formation of resistance to anti-TB drugs. The difficulties in the management of tuberculosis in this patient were in the detection of numerous neoplasms and changes in the internal organs, in particular in the kidneys and lungs, which characterized tuberous sclerosis, on the one hand this contributed to untimely diagnosis of tuberculosis, and on the other hand – worsening the course and the progression of a specific process, as well as an unfavourable prognosis for recovery

Explicit solutions to the Korteweg-de Vries equation on the half line

Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schr\"odinger equation. In the reflectionless case such solutions reduce to pure $N$-soliton solutions. An illustrative example is provided.Comment: 17 pages, no figure

On a systematic approach to defects in classical integrable field theories

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Backlund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical $r$-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.Comment: 27 pages, no figures. Final version accepted for publication. References added and section 5 amende