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

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.

A study of the centrally produced baryon-antibaryon systems in pp interactions at 450 GeV/c

A study of the centrally produced ppbar, ppbarpi, ppbarpipi and lambda lambda channels has been performed in pp collisions using an incident beam momentum of 450 GeV/c. No significant new structures are observed in the mass spectra, however, important new information on the production dynamics is obtained. A systematic study of the production properties of these systems has been performed and it is found that these systems are not produced dominantly by double Pomeron exchange.Comment: 13 pages, Latex, 4 Figure

A study of pseudoscalar states produced centrally in pp interactions at 450 GeV/c

A study has been made of pseudoscalar mesons produced centrally in pp interactions. The results show that the eta and etaprime appear to have a similar production mechanism which differs from that of the pi0. The production properties of the eta and etaprime are not consistent with what is expected from double Pomeron exchange. In addition the production mechanism for the eta and etaprime is such that the production cross section are greatest when the azimuthal angle between the pT vectors of the two protons is 90 degrees.Comment: 11 pages, Latex, 3 Figure

A measurement of the branching fractions of the f1(1285) and f1(1420) produced in central pp interactions at 450 GeV/c

A study of the f1(1285) and f1(1420) produced in central pp interactions has been performed. For the first time in a single experiment the branching fractions of both mesons in all major decay modes have been determined. Both the f1(1285) and f1(1420) are consistent with being produced by double Pomeron exchange.Comment: 15 pages, Latex, 5 Figures, submitted to Physics Letters