N=4 mechanics, WDVV equations and roots

N=4 superconformal multi-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial differential equations linear in U and generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F. Putting U=0 yields a class of models (with zero central charge) which are encoded by the finite Coxeter root systems. We extend these WDVV solutions F in two ways: the A_n system is deformed n-parametrically to the edge set of a general orthocentric n-simplex, and the BCF-type systems form one-parameter families. A classification strategy is proposed. A nonzero central charge requires turning on U in a given F background, which we show is outside of reach of the standard root-system ansatz for indecomposable systems of more than three particles. In the three-body case, however, this ansatz can be generalized to establish a series of nontrivial models based on the dihedral groups I_2(p), which are permutation symmetric if 3 divides p. We explicitly present their full prepotentials.Comment: 1+25 pages; v2: major revision (more general analysis, new solutions, additional references); v3: improvements in sects.5,8,9, refs. adde

Non-backtracking walks reveal compartments in sparse chromatin interaction networks

Chromatin communities stabilized by protein machinery play essential role in gene regulation and refine global polymeric folding of the chromatin fiber. However, treatment of these communities in the framework of the classical network theory (stochastic block model, SBM) does not take into account intrinsic linear connectivity of the chromatin loci. Here we propose the "polymer" block model, paving the way for community detection in polymer networks. On the basis of this new model we modify the non-backtracking flow operator and suggest the first protocol for annotation of compartmental domains in sparse single cell Hi-C matrices. In particular, we prove that our approach corresponds to the maximum entropy principle. The benchmark analyses demonstrates that the spectrum of the polymer non-backtracking operator resolves the true compartmental structure up to the theoretical detectability threshold, while all commonly used operators fail above it. We test various operators on real data and conclude that the sizes of the non-backtracking single cell domains are most close to the sizes of compartments from the population data. Moreover, the found domains clearly segregate in the gene density and correlate with the population compartmental mask, corroborating biological significance of our annotation of the chromatin compartmental domains in single cells Hi-C matrices

АНАЛИЗ ФУНКЦИОНАЛЬНЫХ СХЕМ ЭЛЕКТРИЧЕСКОЙ ЧАСТИ ВЕТРОЭЛЕКТРИЧЕСКИХ УСТАНОВОК

The paper considers basic concepts in the design of modern wind energy conversion systems (WECS). The analysis of control methods and systems which are capable to realize operational mode  with maximum  output  power  has been presented in the paper.  Functional diagrams of systems for different electric generators, mechanical gears and various combinations of electric power supply and control systems have been have been given in the paper. WECS structures that meet the operational requirements in Belarus have been determined in the paper. Рассмотрены  основные  концепции  в  проектировании  современных  ветроэлектрических установок. Проведен анализ способов управления и систем, способных реализовывать режим работы с максимальной выходной мощностью. Приведены функциональные схемы систем для различных электрических генераторов, механических передач и комбинаций  силовых преобразовательных устройств. Определены структуры ветроэлектрических установок, наиболее отвечающие условиям эксплуатации в Беларуси

ЭКСПОРТ ВЫСШЕГО ОБРАЗОВАНИЯ: СОСТОЯНИЕ И ПЕРСПЕКТИВЫ В МИРЕ И РОССИИ

Статья посвящена экспорту высшего образования, приобретающему все более важное значение в стратегиях социально-экономического развития в различных странах мира. Эксперты оценивают мировой рынок высшего образования в 150 млрд. долл. США. Россия в настоящее время занимает менее 1% этого рынка. Впервые предпринимается попытка оценить вклад иностранных студентов, обучающихся в РФ, в экономику страны. Для проведения расчетов были использованы данные по численности иностранных студентов в 2013/2014 учебном году, обучавшихся в российских вузах. Показано, что за рассматриваемый период иностранные студенты потратили в России примерно 25,4 млрд. руб. Даны рекомендации по первоочередным мерам по расширению российского экспорта высшего образования.

Field-induced hybridization of moir\'e excitons in MoSe2_2/WS2_2 heterobilayers

We study experimentally and theoretically the hybridization among intralayer and interlayer moir\'e excitons in a MoSe$_2$/WS$_2$ heterostructure with antiparallel alignment. Using a dual-gate device and cryogenic white light reflectance and narrow-band laser modulation spectroscopy, we subject the moir\'e excitons in the MoSe$_2$/WS$_2$ heterostack to a perpendicular electric field, monitor the field-induced dispersion and hybridization of intralayer and interlayer moir\'e exciton states, and induce a cross-over from type I to type II band alignment. Moreover, we employ perpendicular magnetic fields to map out the dependence of the corresponding exciton Land\'e $g$-factors on the electric field. Finally, we develop an effective theoretical model combining resonant and non-resonant contributions to moir\'e potentials to explain the observed phenomenology, and highlight the relevance of interlayer coupling for structures with close energetic band alignment as in MoSe$_2$/WS$_2$.Comment: Replacement by the accepted manuscript versio