On the free field realization of the osp(1|2) current algebra

The free field representation of the osp(1|2) current algebra is analyzed. The four point conformal blocks of the theory are studied. The structure constants for the product of an arbitrary primary operator and a primary field that transforms according to the fundamental representation of osp(1|2) are explicitly calculated.Comment: 11 pages, phyzz

БИБЛИОТЕКА PYTHON ДЛЯ СИНТЕЗА ИНТЕЛЛЕКТУАЛЬНЫХ СИСТЕМ УПРАВЛЕНИЯ

This article is devoted to the desription of аpython library based on symbolic regression methods for control systems synthesis problem. Control sysnthesis is becoming more and more relevant, gaining particular importance in view of the rapid development of robotics. Usually, practicians and engineers apply template-type regulators when modeling, and then select optimal parameters for them. At a time when the computing power of PC’s has reached its peak, and programming languages have become extremely expressive due to the high level of abstraction and the vastness of libraries, it is better to implement the synthesis in the form of a library. Python was chosen as the language for synthesis implementation. According to the authors of the article, Python is a convenient language for programming matrix and vector calculations thanks to the numpy package. Moreover, the share of projects written in Python in the web service for hosting Github has been steadily increasing recently, which indicates the support of the language from the developer community. This article describes how to use the package to solve the problem of control synthesis. The authors provide the description of the symbolic regression method, the network operator and algorithms for finding the optimal solution using the principle of small variations of the basic solution. In the experimental part of the article, an example of how to use the library to solve the problem of synthesis of control of a mobile robot moving on a planewith obstacles is considered.Статья посвящена описанию библиотеки программ на языке Python для решения задач синтеза систем управления методами символьной регрессии. Задача синтеза становится все более актуальной, приобретая особое значение ввиду стремительного развития робототехники. Как правило, инженеры и просто практики используют регуляторы шаблонного типа при моделировании, а затем подбирают под них параметры. В условиях, когда вычислительная мощность персональных компьютеров достигла своего апогея, а языки программирования стали чрезвычайно выразительны за счет высокого уровня абстрактности и обширности библиотек, целесообразнее реализовать синтез в виде пакета. В качестве языка для реализации синтеза был выбран Python. По мнению авторов статьи, Python является удобным языком для программирования матричных и векторных вычислений благодаря пакету numpy. Более того, доля проектов, написанных на Python, в веб-сервисе для хостинга Github за последнее время неизменно растет, что говорит о поддержке языка со стороны сообщества разработчиков. В данной статье представлено описание применения библиотеки для решения задачи синтеза управления. Приведено описание метода символьной регрессии, метода сетевого оператора и алгоритмов поиска оптимального решения с использованием принципа малых вариаций базисного решения. Рассмотрен пример использования библиотеки для решения задачи синтеза управления мобильным роботом, движущимся на плоскости, в условиях препятствий

Effect of \gamma-irradiation on superconducting transition temperature and resistive transition in polycrystalline YBa_{2}Cu_{3}O_(7-\delta)

A bulk polycrystalline sample of YBa_(2)Cu_(3)O_(7-\delta) (\delta \approx 0.1) has been irradiated by \gamma-rays with ^{60}Co source. Non-monotonic behavior of T_{c} with increasing irradiation dose \Phi (up to 220 MR) is observed: T_{c} decreases at low doses (\Phi < 50 MR) from initial value (\approx 93 K) by about 2 K and then rises, forming a minimum. At higher doses (\Phi > 120 MR) T_{c} goes down again. The temperature width of resistive transition increases rather sharply with dose below 75 MR and drops somewhat at higher dose. The results observed are discussed, taking into account the granular structure of sample studied and the influence of \gamma-rays on intergrain Josephson coupling.Comment: 2 pages, to appear in the proceeding of M2S-HTSC-VI conference, Housto

Structure constants for the osp(1|2) current algebra

We study the free field realization of the two-dimensional osp(1|2) current algebra. We consider the case in which the level of the affine osp(1|2) symmetry is a positive integer. Using the Coulomb gas technique we obtain integral representations for the conformal blocks of the model. In particular, from the behaviour of the four-point function, we extract the structure constants for the product of two arbitrary primary operators of the theory. From this result we derive the fusion rules of the osp(1|2) conformal field theory and we explore the connections between the osp(1|2) affine symmetry and the N=1 superconformal field theories.Comment: 64 pages, phyzzx, no figure

Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory

In this paper we consider parafermionic Liouville field theory. We study integral representations of three-point correlation functions and develop a method allowing us to compute them exactly. In particular, we evaluate the generalization of Selberg integral obtained by insertion of parafermionic polynomial. Our result is justified by different approach based on dual representation of parafermionic Liouville field theory described by three-exponential model

Infrared Factorization, Wilson Lines and the Heavy Quark Limit

It is shown that, in QCD, the same universal function \Gamma_{cusp}(\vartheta, \alpha_\s) determines the infrared behaviour of the on-shell quark form factor, the velocity-dependent anomalous dimension in the heavy quark effective field theory (HQET) and the renormalization properties of the vacuum averaged Wilson lines with a cusp. It is demonstrated that a combined use of the methods developed in the relevant different branches of quantum field theory essentially facilitates the all-order study of the asymptotic and analytic properties of this function.Comment: 10 page

H(3)+ correlators from Liouville theory

We prove that arbitrary correlation functions of the H(3)+ model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations between the structure constants of Liouville theory and the H(3)+ model. In the critical level limit, these results imply a direct link between eigenvectors of the Gaudin Hamiltonians and the problem of uniformization of Riemann surfaces. We also present an expression for correlation functions of the SL(2)/U(1) coset model in terms of correlation functions in Liouville theory.Comment: 24 pages, v3: minor changes, references adde

The start of systems biology in Ukraine

The first laboratory of Systems Biology in Ukraine (IMBIG NASU) represents a track record of its scientific results. They include the pioneered development of a web-based tool for genome-wide surveys of eukaryotic promoters for the presence of transcription factors binding sites (COTRASIF); the deciphered mechanisms of the fine-tuned and balanced response of primary hepatocytes to interferon alpha levels recorded after partial hepatectomy; the elaboration of a novel method of gene regulatory network inference compatible with GRID environment and the development of a stoichiometric model of folate-related one carbon unit metabolism in human placenta and its application for the characteristics of the system’s behavior as a whole at different human pathologies.Представлено наукові здобутки першої в Україні (ІМБіГ НАН України) лабораторії системної біології. Вони включають створення веб-інструменту для всегеномного пошуку сайтів зв’язування транскрипційних факторів у промоторах евкаріотних генів; розкриття тонко збалансованого механізму відповіді первинних гепатоцитів на дію інтерферону альфа в дозі, зареєстрованій на першому етапі регенерації печінки після часткової гепатектомії; розробку нового методу інференції мережі генної регуляції для його використання в середовищі ГРІД і створення стехіометричної моделі фолатного циклу у плаценті людини для характеристики поведінки системи за різних патологічних станів.Представлены научные наработки первой в Украине (ИМБиГ НАН Украины) лаборатории системной биологии. Они включают создание веб-инструмента для всегеномного поиска сайтов связывания транскрипционных факторов в промоторах эукариотических генов; раскрытие тонко сбалансированного механизма ответа первичных гепатоцитов на действие интерферона альфа в дозе, регистрируемой в печени на раннем этапе после частичной гепатэктомии; разработку нового метода инференции сетей генной регуляции для его использования в среде ГРИД и создание модели фолатного цикла в плаценте человека для характеристики поведения системы при разных патологических состояниях

Electrons in an annealed environment: A special case of the interacting electron problem

The problem of noninteracting electrons in the presence of annealed magnetic disorder, in addition to nonmagnetic quenched disorder, is considered. It is shown that the proper physical interpretation of this model is one of electrons interacting via a potential that is long-ranged in time, and that its technical analysis by means of renormalization group techniques must also be done in analogy to the interacting problem. As a result, and contrary to previous claims, the model does not simply describe a metal-insulator transition in $d=2+\epsilon$ ($\epsilon\ll 1$) dimensions. Rather, it describes a transition to a ferromagnetic state that, as a function of the disorder, precedes the metal-insulator transition close to $d=2$. In $d=3$, a transition from a paramagnetic metal to a paramagnetic insulator is possible.Comment: 13 pp., LaTeX, 2 eps figs; final version as publishe

Zero temperature phases of the frustrated J1-J2 antiferromagnetic spin-1/2 Heisenberg model on a simple cubic lattice

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges (J1 and J2) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Neel phase for small J2 (AF), and a collinear antiferromagnetic phase at large J2 (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, pc = 0.28. Our results for the value of pc are in excellent agreement with results from Monte-Carlo simulations and variational spin wave theory. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear.Comment: 19 pages, 4 figures, Fig. 1b modified, Appendix B text modifie