The materials of The International Scientific – Practical Conference is presented below. The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies. It is interesting for a wide range of researchers, teachers, graduate students and professionals in the field of innovation and information technologies.

This book brings together reviews by internationally renowed experts on quantum optics and photonics. It describes novel experiments at the limit of single photons, and presents advances in this emerging research area. It also includes reprints and historical descriptions of some of the first pioneering experiments at a single-photon level and nonlinear optics, performed before the inception of lasers and modern light detectors, often with the human eye serving as a single-photon detector. The book comprises 19 chapters, 10 of which describe modern quantum photonics results, including single-photon sources,  direct measurement of the photon's spatial wave function, nonlinear interactions and non-classical light, nanophotonics for room-temperature single-photon sources, time-multiplexed methods for optical quantum information processing, the role of photon statistics in visual perception, light-by-light coherent control using metamaterials, nonlinear nanoplasmonics, nonlinear polarization optics, and ultrafast nonlinear optics in the mid-infrared.

This volume collects the referred papers based on plenary, invited, and oral talks, as well on the posters presented at the Third International Conference on Computer Simulations in Physics and beyond (CSP2018), which took place September 24-27, 2018 in Moscow. The Conference continues the tradition started by an inaugural conference in 2015. It took place on the campus of A.N. Tikhonov Moscow Institute of Electronics and Mathematics in Strogino, was jointly organized by the National Research University Higher School of Economics, the Landau Institute for Theoretical Physics and Science Center in Chernogolovka.

The Conference is a multidisciplinary meeting, with a focus on computational physics and related subjects. Indeed, methods of computational physics prove useful in a broad spectrum of research in multiple branches of natural sciences, and this volume provides a sample.

We hope that this volume will interest readers, and we are already looking forward to the next conference in the series.

Moscow, Russia

November, 2018

CSP2018 Conference Chair and Volume Editor

Lev Shchur

This book constitutes the refereed proceedings of the 9th International Conference on Optimization and Applications, OPTIMA 2018, held in Petrovac, Montenegro, in October 2018.The 35 revised full papers and the one short paper presented were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections on mathematical programming; combinatorial and discrete optimization; optimal control; optimization in economy, finance and social sciences; applications.

The series “Advances in Intelligent Systems and Computing” contains publications on theory, applications, and design methods of Intelligent Systems and Intelligent Computing. Virtually all disciplines such as engineering, natural sciences, computer and information science, ICT, economics, business, e-commerce, environment, healthcare, life science are covered. The list of topics spans all the areas of modern intelligent systems and computing such as: computational intelligence, soft computing including neural networks, fuzzy systems, evolutionary computing and the fusion of these paradigms, social intelligence, ambient intelligence, computational neuroscience, artificial life, virtual worlds and society, cognitive science and systems, Perception and Vision, DNA and immune based systems, self-organizing and adaptive systems, e-Learning and teaching, human-centered and human-centric computing, recommender systems, intelligent control, robotics and mechatronics including human-machine teaming, knowledge-based paradigms, learning paradigms, machine ethics, intelligent data analysis, knowledge management, intelligent agents, intelligent decision making and support, intelligent network security, trust management, interactive entertainment, Web intelligence and multimedia. The publications within “Advances in Intelligent Systems and Computing” are primarily proceedings of important conferences, symposia and congresses. They cover significant recent developments in the field, both of a foundational and applicable character. An important characteristic feature of the series is the short publication time and world-wide distribution. This permits a rapid and broad dissemination of research results.

This book contains a selection of papers accepted for the presentation and discussion at the 2018 International Conference on Digital Science (DSIC’18). This Conference had the support of the Institute of Certified Specialists, Russia, AISTI (Iberian Association for Information Systems and Technologies), and Springer. It will take place at Convention Centre, Budva, Montenegro, October 19–21, 2018. DSIC’18 is an international forum for researchers and practitioners to present and discuss the most recent innovations, trends, results, experiences, and concerns in the several perspectives of Digital Science. The main idea of this Conference is that the world of science is unified and united allowing all scientists/practitioners to be able to think, analyze, and generalize their thoughts. DSIC aims efficiently to disseminate original research results in natural, social, art, and humanities sciences. An important characteristic feature of the Conference should be the short publication time and worldwide distribution. This Conference enables fast dissemination, so conference participants can publish their papers in print and electronic format, which is then made available worldwide and accessible by numerous researchers. The Scientific Committee of DSIC’18 was composed of a multidisciplinary group of 26 experts. One hundred and seven invited reviewers who are intimately concerned with Digital Science have had the responsibility for evaluating, in a “double-blind review” process, the papers received for each of the main themes proposed for the Conference: Digital Art and Humanities; Digital Economics; Digital Education; Digital Engineering; Digital Environmental Sciences; Digital Finance, Business and Banking; Digital Media; Digital Medicine, Pharma and Public Health; Digital Public Administration; Digital Technology and Applied Sciences. DSIC’18 received 88 contributions from 16 countries around the world. The papers accepted for the presentation and discussion at the Conference are published by Springer (this book) and will be submitted for indexing by ISI, SCOPUS, among others.

This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature.

Proceedings of Third Workshop "Computational linguistics and language science"

I show that Hurwitz numbers may be generated by certain correlation functions which appear in quantum chaos.

Sustaining a competitive edge in today’s business world requires innovative approaches to product, service, and management systems design and performance. Advances in computing technologies have presented managers with additional challenges as well as further opportunities to enhance their business models.

Software Engineering for Enterprise System Agility: Emerging Research and Opportunities is a collection of innovative research that identifies the critical technological and management factors in ensuring the agility of business systems and investigates process improvement and optimization through software development. Featuring coverage on a broad range of topics such as business architecture, cloud computing, and agility patterns, this publication is ideally designed for business managers, business professionals, software developers, academicians, researchers, and upper-level students interested in current research on strategies for improving the flexibility and agility of businesses and their systems.

Computer simulations are nowadays a rmly established third pillar of modern natural sciences, complementing experimentation and paper-and-pencil theoret- ical studies. Simulations, experiments in silico, prove indispensable in diverse areas of research in physics and other natural sciences. This volume collects papers based on presentations delivered at the Sec- ond International Conference on Computer Simulations in Physics and beyond (CSP2017), which took place October 9-12, 2017 in Moscow. The Conference, which continues a biannual tradition started by an innaugural conference in 2015, took place on campus of A.N. Tikhonov Moscow Institute of Electronics and Mathematics, was jointly organized by the National Research University Higher School of Economics, the Landau Insitute for Theoretical Physics and Science Center in Chernogolovka. As the name implies, the Conference is a multidisciplinary meeting, with a focus on computational physics and related subjects. Indeed, methods of computational physics prove useful in a broad spectrum of research in multiple branches of natural sciences, and this volume provides a sample. We hope that this volume will interest a wide range of readers, and we are already looking forward for the next conference in this biannual series.

The 29th DAAAM International Symposium on Intelligent Manufacturing and Automation took place in Zadar, Croatia between the 24th and 27th October 2018, during the DAAAM International Week. The Symposium was organized by DAAAM International Vienna in cooperation with ÖIAV 1848, Vienna University of Technology, International Academy of Engineering and University of Applied Sciences – Technikum Wien and Under the Auspices of the Danube Rectors’ Conference & Rectors’ and Presidents’ Honor Committee of DAAAM International for 2018. The Symposium took place in Zadar, Croatia. This year’s symposium aimed at continuing the success of the previous years, focusing on the five-fold traditional objectives of the symposium: the presentation of the most recent high-quality results, support of development of young scientists and researchers, organization of international (summer) doctoral school, inauguration of new members of Central European Branch of International Academy of Engineering and the provision of the necessary setting for stimulating discussions, brainstorming and networking among European and international researchers coming both from the academia government agencies and industry.

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well.

The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces.

The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion.

Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework.

The IEEE Russia North West Section, Saint Petersburg Electrotechnical University “LETI”, and the European Centre for Quality (Moscow) are pleased to present the Proceedings of the 2018 IEEE International Conference "Quality Management, Transport and Information Security, Information Technologies" (IT&QM&IS). The Conference was held in St. Petersburg, Russia on September 24–29, 2018, and it was proudly hosted by Saint Petersburg Electrotechnical University “LETI”. The Organizing Committee believes and trusts that we have been true to the spirit of collegiality that members of IEEE value whilst also maintaining a high standard as we reviewed papers, provided feedback and now present a strong body of published work in this collection of proceedings. The themes for this year's conference were chosen as a means of bringing together academics and industrialists, engineering and management research, manufacturing and teaching, and providing a basis for discussion of issues arising across the engineering and business community in relation to Quality Management, Information Technologies, Transport and Information Security aimed at developing engineers and managers for the future. The goal of these proceedings has been to present high quality work in an accessible medium, for use in a wide community of academics, engineers, managers, and industrialists, the community united by the key words Science, Education, Quality, Innovations in engineering. To achieve this aim, all abstracts were blind reviewed, and full papers submitted for publication in this journal of proceedings were subjected to a rigorous reviewing process.

The assembly process is extremely complex for aircraft and its management requires to address numerous optimization problems related to the assignment of tasks to workstations, staffing problem for each workstation and finally the assignment of tasks to operators at each workstation. This paper treats the latter problem dealing with the assignment of tasks to operators under ergonomic constraints. The problem of optimal tasks scheduling in aircraft assembly line is modelled as Resource-Constrained Project Scheduling Problem (RCPSP). The objective of this research is to assign tasks to operators and to find an optimal schedule of task processing under economic and ergonomic constraints. Two different models to solve this problem are presented and evaluated on an industrial case study.

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil- Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.- P. Serre).

This book highlights selected topics of standard and modern theory of accretion onto black holes and magnetized neutron stars. The structure of stationary standard discs and non-stationary viscous processes in accretion discs are discussed to the highest degree of accuracy analytic theory can provide, including relativistic effects in flat and warped discs around black holes. A special chapter is dedicated to a new theory of subsonic settling accretion onto a rotating magnetized neutron star. The book also describes supercritical accretion in quasars and its manifestation in lensing events. Several chapters cover the underlying physics of viscosity in astrophysical discs with some important aspects of turbulent viscosity generation. The book is aimed at specialists as well as graduate students interested in the field of theoretical astrophysics.

Workshop on Program Semantics, Specification and Verification: Theory and Applications is the leading event in Russia in the field of applying of the formal methods to software analysis. Proceedings of the ninth workshop dedicated to formalisms for program semantics, formal models and verification, programming and specification languages, algebraic and logical aspects of programming.

The paper addresses the questions of data science education of current importance. It aims to introduce and justify the framework that allows flexibly evaluate the processes of a data expedition and a digital media created during it. For these purposes, the authors explore features of digital media artefacts which are specific to data expeditions and are essential to accurate evaluation. The rubrics as a power but hardly formalizable evaluation method in application to digital media artefacts are also discussed. Moreover, the paper documents the experience of rubrics creation according to the suggested framework. The rubrics were successfully adopted to two data-driven journalism courses. The authors also formulate recommendations on data expedition evaluation which should take into consideration structural features of a data expedition, distinctive features of digital media, etc.

New hybrid bromobismuthates of 1,1'-(1,4-phenylenebis(methylene))bis(n-methylpyridin-1-ium) 1 (n=4) and 2 (n=3) dications and halobismuthates of 1-{[4-(Hal-methyl)phenyl]methyl}-2-methylpyridin-1-ium) 3 (Hal=Br) and 4 (Hal=I) monocations have been synthesized and characterized. The [BiBr5]2- anion with structure unusual for halobismuthates and two [BiBr6]3- anions form a linear 0-D fragment in compound 2. The Bi-Br(ax) distance in [BiBr5]2- anion (2.587 Å) is rather short for usual bromobismuthates. The formation of the linear fragment in compound 2 and the presence of short Bi-Br(ax) bonds in its structure do not affect a value of optical band gap.

Direct numerical simulations of irregular unidirectional nonlinear wave evolution are performed within the framework of the Korteweg–de Vries equation for bimodal wave spectra model cases. The additional wave system co-existence effect on the evolution of the wave statistical characteristics and spectral shapes, and also on the attained equilibrium state is studied. The concerned problem describes, for example, the interaction between wind waves and swell in shallow seas. It is next demonstrated that a low-frequency spectral component yields more asymmetric waves with more extreme statistical properties.

We consider the Hegselmann-Krause bounded confidence model of opinion dynamics. We assume that the opinion of an agent is influenced not only by other agents, but also by external random noises. The case of independent normally distributed external noises is considered. We perform computer modeling of deterministic and stochastic models. The properties of the models were analyzed and the difference in their behavior was revealed. We study the dependence of the number of a confidence clusters on the parameters of the problem such as the initial profile of opinions, the level of confidence, the variance of noise.

We study an optimal control problem for a nonlinear spherical inverted pendulum on a movable base. As the cost functional, the mean-squared deviation of the pendulum from the upper equilibrium is considered, so optimal controls stabilize the pendulum at the unstable upper position. We show that the problem under consideration posses a singular point of the second order and there are spiral-similar solution which attains the singular point in finite time.

Intelligent computer systems aim to help humans in making decisions. Many practical decision-making problems are classification problems in their nature, but standard classification algorithms often not applicable since they assume balanced distribution of classes and constant misclassification costs. From this point of view, algorithms that consider the cost of decisions are essential since they are more consistent with the requirements of real life. These algorithms generate decisions that directly optimize parameters valuable for business, for example, the costs savings. But despite on practical value of cost-sensitive algorithms, the little number of works study this problem concentrating mainly on the case when the cost of a classifier error is constant and does not depend on a specific example. However, many real-world classification tasks are example-dependent cost-sensitive (ECS), where the costs of misclassification vary between examples and not only within classes. Existing methods of ECS learning include just modifications of the simplest models of machine learning (naive Bayes, logistic regression, decision tree). These models produce promising results, but there is a need for further improvement in performance that can be achieved by using gradient-based ensemble methods. To break this gap, we present the ECS generalization of AdaBoost. We study three models which differ by the ways to introduce cost into the loss function: inside the exponent, outside the exponent, and both inside and outside the exponent. The results of the experiments on three synthetic and two real datasets (bank marketing and insurance fraud) show that example-dependent cost-sensitive modifications of AdaBoost outperform other known models. Empirical results also show that critical factors influencing the choice of the model are not only the distribution of features, which is typical for cost-insensitive and class-dependent cost-sensitive problems but also the distribution of costs. Next, since the outputs of AdaBoost are not well calibrated posterior probabilities, we check three approaches to calibration of classifier scores: Platt scaling, isotonic regression, and ROC modification. The results show that calibration not only significantly improves the performance of specific ECS models but allows making better capabilities of original AdaBoost. Obtained results provide new insight regarding the behavior of the cost-sensitive model from a theoretical point of view and prove that the presented approach can significantly improve the practical design of intelligent systems.

Multiple Perron eigenvectors of non-negative matrices occur in applications, where

they often become a source of trouble. A usual way to avoid it and to make the

Perron eigenvector simple is a regularization of matrix: an initial non-negative matrix

A is replaced by A + "M, where M is a strictly positive matrix and " > 0 is small.

However, this operation is numerically unstable and may lead to a signicant increase

of the Perron eigenvalue, especially in high dimensions. We dene a selected Perron

eigenvector of A as the limit of normalized Perron eigenvectors of the regularizations

A + "M as " ! 0. It is shown that if the matrix M is rank-one, then the limit

eigenvector can be found by an explicit formula and, moreover, is eciently computed

by the power method. The role of the rank-one condition is explained.

Recurrent neural networks have proved to be an effective method for statistical language modeling. However, in practice their memory and run-time complexity are usually too large to be implemented in real-time offline mobile applications. In this paper we consider several compression techniques for recurrent neural networks including Long–Short Term Memory models. We make particular attention to the high-dimensional output problem caused by the very large vocabulary size. We focus on effective compression methods in the context of their exploitation on devices: pruning, quantization, and matrix decomposition approaches (low-rank factorization and tensor train decomposition, in particular). For each model we investigate the trade-off between its size, suitability for fast inference and perplexity. We propose a general pipeline for applying the most suitable methods to compress recurrent neural networks for language modeling. It has been shown in the experimental study with the Penn Treebank (PTB) dataset that the most efficient results in terms of speed and compression–perplexity balance are obtained by matrix decomposition techniques.

 

This paper is focused on the automatic extraction of persons and their attributes (gender, year of born) from album of photos and videos. A two-stage approach is proposed in which, firstly, the convolutional neural network simultaneously predicts age/gender from all photos and additionally extracts facial representations suitable for face identification. Here the MobileNet is modified and is preliminarily trained to perform face recognition in order to additionally recognize age and gender. The age is estimated as the expected value of top predictions in the neural network. In the second stage of the proposed approach, extracted faces are grouped using hierarchical agglomerative clustering techniques. The birth year and gender of a person in each cluster are estimated using aggregation of predictions for individual photos. The proposed approach is implemented in an Android mobile application. It is experimentally demonstrated that the quality of facial clustering for the developed network is competitive with the state-of-the-art results achieved by deep neural networks, though implementation of the proposed approach is much computationally cheaper. Moreover, this approach is characterized by more accurate age/gender recognition when compared to the publicly available models.

The convolution ring K^{GL_n(\OOO)⋊ℂ×}(Gr_{GL_n}) was identified with a quantum unipotent cell of the loop group LSL_2 in [Cautis-Williams, arXiv:1801.08111]. We identify the basis formed by the classes of irreducible equivariant perverse coherent sheaves with the dual canonical basis of the quantum unipotent cell.

We compute the Coulomb branch of a multiloop quiver gauge theory for the quiver with a single vertex, r loops, one-dimensional framing, and dim V = 2. We identify it with a Slodowy slice in the nilpotent cone of the symplectic Lie algebra of rank r. Hence it possesses a symplectic resolution with 2r fixed points with respect to a Hamiltonian torus action. We also idenfity its flavor deformation with a base change of the full Slodowy slice.

The Littlewood-Richardson coefficients describe the decomposition of tensor products of irreducible representations of a simple Lie algebra into irreducibles. Assuming the number of factors is large, one gets a measure on the space of weights. This limiting measure was extensively studied by many authors. In particular, Kerov computed the corresponding density in a special case in type A and Kuperberg gave a formula for the general case. The goal of this paper is to give a short, self-contained and pure Lie theoretic proof of the formula for the density of the limiting measure. Our approach is based on the link between the limiting measure induced by the Littlewood-Richardson coefficients and the measure defined by the weight multiplicities of the tensor products.

Let M be a holomorphic symplectic Kähler manifold equipped with a Lagrangian fibration π with compact fibers. The base of this manifold is equipped with a special Kähler structure, that is, a Kähler structure (I,g,ω) and a symplectic flat connection ∇ such that the metric g is locally the Hessian of a function. We prove that any Lagrangian subvariety Z⊂M which intersects smooth fibers of π and smoothly projects toπ(Z) is a toric fibration over its image π(Z) in B, and this image is also special Kähler. This answers a question of N. Hitchin related to Kapustin-Witten BBB/BAA duality.

We study the exceptional loci of birational (bimeromorphic) contractions of a hyperkähler manifold M. Such a contraction locus is the union of all minimal rational curves in a collection of cohomology classes which are orthogonal to a wall of the Kähler cone. Homology classes which can possibly be orthogonal to a wall of the Kähler cone of some deformation of M are called MBM classes. We prove that all MBM classes of type (1,1) can be represented by rational curves, called MBM curves. All MBM curves can be contracted on an appropriate birational model of M, unless b_2(M)≤5. When b_2(M)>5, this property can be used as an alternative definition of an MBM class and an MBM curve. Using the results of Bakker and Lehn, we prove that the diffeomorphism type of a contraction locus remains stable under all deformations for which these classes remains of type (1,1), unless the contracted variety has b2≤4. Moreover, these diffeomorphisms preserve the MBM curves, and induce biholomorphic maps on the contraction fibers, if they are normal.

It is well known that cohomology of any non-trivial 1-dimensional local system on a nilmanifold vanishes (this result is due to L. Alaniya). A complex nilmanifold is a quotient of a nilpotent Lie group equipped with a left-invariant complex structure by an action of a discrete, co-compact subgroup. We prove a Dolbeault version of Alaniya's theorem, showing that the Dolbeault cohomology of a nilpotent Lie algebra with coefficients in any non-trivial 1-dimensional local system vanishes. Note that the Dolbeault cohomology of the corresponding local system on the manifold is not necessarily zero. This implies that the twisted version of Console-Fino theorem is false (Console-Fino proved that the Dolbeault cohomology of a complex nilmanifold is equal to the Dolbeault cohomology of its Lie algebra). As an application, we give a new proof of a theorem due to H. Sawai, who obtained an explicit description of LCK nilmanifolds. An LCK structure on a manifold M is a Kähler structure on its cover M̃ such that the deck transform map acts on M̃ by homotheties. We show that any complex nilmanifold admitting an LCK structure is Vaisman, and is obtained as a compact quotient of the product of a Heisenberg group and the real line.

We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction provides well-behaved categorical resolutions of singular quadrics, which we use to obtain an explicit quadratic version of the main theorem of homological projective duality. As applications, we prove the duality conjecture for Gushel-Mukai varieties, and produce interesting examples of conifold transitions between noncommutative and honest Calabi-Yau threefolds.

We prove that Q-Fano threefolds of Fano index ≥8 are rational.

We study the complexity of birational self-maps of a projective threefold X by looking at the birational type of surfaces contracted. These surfaces are birational to the product of the projective line with a smooth projective curve. We prove that the genus of the curves occuring is unbounded if and only if X is birational to a conic bundle or a fibration into cubic surfaces. Similarly, we prove that the gonality of the curves is unbounded if and only if X is birational to a conic bundle.

We show that automorphism groups of Moishezon threefolds are always Jordan.

We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain one-parameter degenerations of the Lie algebras corresponding to such subgroups. As an application, we exhibit an explicit algorithm for computing the set of spherical roots of such a spherical subgroup.

Positive-Unlabeled Learning is an analog of supervised binary classification for the case when the Negative (N) sample in the training set is contaminated with latent instances of the Positive (P) class and hence is Unlabeled (U). We develop DEDPUL1 , a method able to solve two problems: first, to estimate the proportions of the mixing components (P and N) in U, and then, to classify U. The main steps are to reduce dimensionality of the data using Non-Traditional Classifier [11], to estimate densities of the reduced data in both P and U samples, and to apply the Bayes rule to density ratio. We experimentally show that DEDPUL outperforms current state-of-the-art methods for both problems. Additionally, we improve current state-of-the-art method for PU Classification [16].

We show that smooth well formed Fano weighted complete intersections of dimension at least 3 have finite automorphism groups, with two obvious exceptions.

Let G be a connected reductive complex algebraic group with a maximal torus T. We denote by Λ the cocharacter lattice of (T,G). Let Λ^+⊂Λ be the submonoid of dominant coweights. For λ∈Λ+,μ∈Λ,μ⩽λ, in arXiv:1604.03625, authors defined a generalized transversal slice W^λ_μ. This is an algebraic variety of the dimension ⟨2ρ^∨,λ−μ⟩, where 2ρ^∨ is the sum of positive roots of G. We prove that for a minuscule λ and μ appearing as a weight of V^λ (irreducible representation of the Langlands dual group G^∨ with the highest weight λ) the variety W^λ_μ is isomorphic to the affine space 𝔸⟨2ρ^∨,λ−μ⟩ and that in certain coordinates the Poisson structure on it is standard.

We develop the theory of semisimplifications of tensor categories defined by Barrett and Westbury. In particular, we compute the semisimplification of the category of representations of a finite group in characteristic p in terms of representations of the normnalizer of its Sylow p-subgroup. This allows us to compute the semisimplification of the representation category of the symmetric group S_n+p in characteristic p, where 0 ≤ n ≤ p−1, and of the Deligne category Rep^ab S_t, where t∈ℕ. We also compute the semisimplification of the category of representations of the Kac-De Concini quantum group of the Borel subalgebra of 𝔰𝔩_2. We also study tensor functors between Verlinde categories of semisimple algebraic groups arising from the semisimplification construction, and objects of finite type in categories of modular representations of finite groups (i.e., objects generating a fusion category in the semisimplification). Finally, we determine the semisimplifications of the tilting categories of GL(n), SL(n) and PGL(n) in characteristic 2. In the appendix, we classify categorifications of the Grothendieck ring of representations of SO(3) and its truncations.

For an even qudit dimension d≥2, we introduce a class of two-qudit states exhibiting perfect correlations/anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value 3/2 -- the upper bound attained on some two-qubit states. We show that the two-qudit Greenberger--Horne-- Zeilinger (GHZ) state with an arbitrary even d≥2 exhibits perfect correlations/anticorrelations and belongs to the introduced two-qudit state class. These new results are important steps towards proving in general the 3/2 upper bound on quantum violation of the original Bell inequality. The latter would imply that similarly as the Tsirelson upper bound 2√2 specifies the quantum analog of the CHSH inequality for all bipartite quantum states, the upper bound (3/2) specifies the quantum analog of the original Bell inequality for all bipartite quantum states with perfect correlations/ anticorrelations. Possible consequences for the experimental tests on violation of the original Bell inequality are briefly discussed.

We have investigated the critical temperature behavior in periodic superconductor/ ferromagnet (S/F) multilayers as a function of the ferromagnetic layer thickness $d_f$ and the interface transparency. The critical temperature $T_c(d_f)$ exhibits a damped oscillatory behavior in these systems due to an exchange field in the ferromagnetic material. In this work we have performed $T_c$ calculations using the self-consistent \textit{multimode approach}, which is considered to be exact solving method. Using this approach we have derived the conditions of 0 or $\pi$ state realization in periodic S/F multilayers. Moreover, we have presented the comparison between the single-mode and multimode approaches and established the limits of applicability of the single-mode approximation, frequently used by experimentalists.

We formulate and prove the main properties of the generalized Gell-Mann representation for traceless qudit observables and analyze via this representation violation of the CHSH inequality by a general two-qudit state. For the maximal CHSH violation by a two-qudit state with an arbitrary qudit dimension d≥2, this allows us to derive two new bounds, lower and upper, which are expressed via the spectral properties of the correlation matrix for a two-qudit state. We have not yet been able to specify a class of two-qudit states for which the new upper bound improves the general upper bound of Tsirelson. However, this is the case for each two-qubit state, where the new lower bound and the new upper bound coincide and reduce to the precise two-qubit CHSH result of Horodecki, and also, for the Greenberger--Horne--Zeilinger (GHZ) state with an arbitrary odd qudit dimension d≥2, where the new upper bound is less than the upper bound of Tsirelson. Moreover, we explicitly find the correlation matrix for the GHZ state and prove that, for this state, the new upper bound is attained for each d≥2 and this specifies the following new result: the maximal violation of the CHSH inequality by the two-qudit GHZ state is equal to √2  if a qudit dimension d≥2 is even and to ((d-1)/d)√2  if a qudit dimension d≥2 is odd.