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.

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"

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.

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 present book gathers chapters from colleagues of A. Ezersky from Russia, especially those from Nizhny Novgorod Institute of Applied Physics of the Russian Academy of Science and from France, with whom he has been collaborating on experimental and theoretical developments. The book is subdivided into two parts. Part I contains eight chapters related to nonlinear water waves and Part II addresses in five chapters, patterns dynamics in nonequilibrium media. The contributions of Alexander B. Ezersky were valuable from both the experimental and the theoretical points of view. We thank all the authors for their contributions and the Springer Editor for having kindly accepted the edition of this book in memory of our colleague and friend, Prof. Alexander Borisovich Ezersky.

This book constitutes the refereed proceedings of the 14th International Workshop on Enterprise and Organizational Modeling and Simulation, EOMAS 2018, held in Tallinn, Estonia, in June 2018. The main focus of EOMAS is on the role, importance, and application of modeling and simulation within the extended organizational and enterprise context. The 11 full papers presented in this volume were carefully reviewed and selected from 22 submissions. They were organized in topical sections on conceptual modeling, enterprise engineering, and formal methods.

This state-of-the-art survey is dedicated to the memory of Emmanuil Markovich Braverman (1931-1977), a pioneer in developing the machine learning theory. The 12 revised full papers and 4 short papers included in this volume were presented at the conference "Braverman Readings in Machine Learning: Key Ideas from Inception to Current State" held in Boston, MA, USA, in April 2017, commemorating the 40th anniversary of Emmanuil Braverman's decease. The papers present an overview of some of Braverman's ideas and approaches. The collection is divided in three parts. The first part bridges the past and the present. Its main contents relate to the concept of kernel function and its application to signal and image analysis as well as clustering. The second part presents a set of extensions of Braverman's work to issues of current interest both in theory and applications of machine learning. The third part includes short essays by a friend, a student, and a colleague.

It is researched a wide class of parametric estimations of power spectral density based on principle of entropy maximum and autoregression observation model. At that there is distinguished the key parameter which is used model order. It is considered a problem of a priori uncertainty when true value of order is a priori unknown. It is proposed a new criterion for definition of order using finite sampling volume with purpose of overcome of the drawbacks of existing algorithms in conditions of small sampling. The principle of guaranteed significance level in a problem of complex statistic hypothesis verification is a basic principle of this criterion. In contrast to criteria of AIC, BIC, etc. this criterion is not related to determination of measurements inaccuracy, since it uses a conception of “significance level” of formed solution only. The efficiency of proposed criterion is researched theoretically and experimentally. An example of its application in a problem of spectral analysis of voice signals is considered. Recommendations about its practical application in the systems of digital signal processing are given.

We developed a new method for measuring the pitch frequency of speech signals with elevated noise immunity. The problem of protection against intense background noise is solved in this method by the frequency selection of vocalized segments of speech signals according to a scheme with comb filter of interperiodic accumulation. The efficiency of the method is analyzed both theoretically and experimentally with the help of a multichannel frequency meter intended for the acoustic speech analysis. It is shown that, for a signal-to-noise ratio of 10 dB and higher, the error of the method does not exceed 2%.

We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient D(t ) ∼ t α−1 with α > 0 (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. In the present work we discuss the situation in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. The situation when the resetting of the coordinate does not affect the diffusion coefficient’s time dependence is considered in the other work of this series [A. S. Bodrova et al., Phys. Rev. E 100, 012119 (2019)]. We show that the properties of the probability densities in such processes (erasing or retaining the memory on the diffusion coefficient) are vastly different. In addition we discuss the first-passage properties of the scaled Brownian motion with renewal resetting and consider the dependence of the efficiency of search on the parameters of the process.

We investigate an intermittent stochastic process in which diffusive motion with a time-dependent diffusion coefficient, D(t ) ∼ t α−1, α > 0 (scaled Brownian motion), is stochastically reset to its initial position and starts anew. The resetting follows a renewal process with either an exponential or a power-law distribution of the waiting times between successive renewals. The resetting events, however, do not affect the time dependence of the diffusion coefficient, so that the whole process appears to be a nonrenewal one.We discuss the mean squared displacement of a particle and the probability density function of its positions in this process.We show that scaled Brownian motion with resetting demonstrates rich behavior whose properties essentially depend on the interplay of the parameters of the resetting process and the particle’s displacement infree motion. The motion of particles can remain almost unaffected by resetting but can also get slowed down or even be completely suppressed. Especially interesting are the nonstationary situations in which the mean squared displacement stagnates but the distribution of positions does not tend to any steady state. This behavior is compared to the situation [discussed in the companion paper; A. S. Bodrova et al., Phys. Rev. E 100, 012120 (2019)] in which the memory of the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. We show that the properties of the probability densities in such processes (erasing or retaining the memory on the diffusion coefficient) are vastly different.

√√􏰈 Abstract Let f(a,b,c,d) = a2+b2 + c2+d2 − (a+c)2+(b+d)2, let

(a,b,c,d) stand for a,b,c,d ∈ Z􏰁0 such that ad − bc = 1. Define􏰉s

In other words, we consider the sum of the powers of the triangle inequality defects for the lattice parallelograms (in the first quadrant) of area one. We prove that F(s) converges when s > 1 and diverges at s = 1/2. We also prove that

􏰉1=1,(a,b,c,d) (a+c)2(b+d)2(a+b+c+d)2 3

We present an upper bound on the number of solutions of an algebraic equation P(x,y)=0 where x and y belong to the union of cosets of some subgroup of the multiplicative group κ∗ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy.

Complexes [(1,2,4-Ph3C5H2)2NdCl2K(THF)2]2 (Nd1), {[1,2-Ph2-4-(4-MeOC6H4)C5H2]2NdCl2K(THF)2}2 (Nd2), {[1,2-Ph2-4-(2-MeOC6H4)C5H2]2NdCl2[K(THF)4]}(THF)0.5 (Nd3), and [(1,2,4-Ph3C5H2)2TbCl2K]2 (Tb1) have been synthesized, studied by X-ray diffraction analysis, and used in coordinative chain transfer polymerization (CCTP) of ethylene upon activation by alkyl magnesium derivatives. The complexes Nd1 and Tb1 exhibiting similar molecular structures and the same core type have demonstrated similar catalytic activities. Two types of alkylating/chain transfer agents, namely, di-n-butyl magnesium and heteroleptic complex (BHT)Mg(THF)2nBu Mg1 (BHT = 2,6-di-tert-butyl-4-methylphenoxide), have been studied in this reaction. We have found that (BHT)Mg(PE) products (PE is an oligoethylene chain) are being formed at a relatively high rate while using Mg1 at 40 °C in the solution polymerization of ethylene; the oligomeric products comprise more than 40 ethylene fragments, unlike Mg(PE)2 derivatives, which are obtained from MgnBu2 and contain about 20 ethylene fragments. Luminescence spectroscopy study of the reaction mixtures, while initiating the complex Tb1 by MgnBu2 or Mg1, confirmed the structural proximity and high symmetry of the catalytic complexes for both types of Mg reagents. These experimental results reaffirmed the hypothesis about the CCTP mechanism, suggesting the formation of trinuclear LnMg2 catalytic species. Within this mechanism, we can explain the increase in the polymerization degree (Pn) when Mg1 is used by growing a single oligoethylene chain (PE) per a Mg atom to form (μ-BHT)2Mg2(PE)2 species, whereas application of MgnBu2 provides the growth of two PE chains to form the Mg2(PE)4 product with lower solubility.

sized and structurally characterized. Their reaction with THF leads to the formation of the solvent-separated ion pairs [(Ph3CCOO)2Ln(THF)5]+[(Al(CH3)4]−. The tendency of the La3+ cation to interact with the π-electron system of phenyl rings has been revealed by molecular structure analysis for La-Al and Nd – Al tetramethylaluminate complexes in combination with the study of butadiene and isoprene polymerization by using catalyst system based on these complexes and aluminum alkyl cocatalysts. Coordination of Ln3+ cation by the π- electron conjugated system makes it difficult to form the catalytically active intermediates and decreases the catalytic activity.

For over a decade IT-business alignment has been ranked as a top-priority management concern, but there is little research on practical ways to achieve the alignment. EA development is a continuous iterative process, which implicitly ensures the achievement of a specific IT-business alignment level. Therefore, it is necessary to formalize the requirements for architecture and be able to automatically verify them. We propose a new methodology for detecting logical contradictions in enterprise architecture models based on a model checking approach adopted in the context of business modeling. In such methodology we use ArchiMate standard for a conceptual enterprise architecture description language which is fully aligned with TOGAF. We also offer several important verification queries and demonstrate practical applicability of our approach using a software prototype of the modeling tool which exploits MIT Alloy Analyzer model checking framework integrated with AchiMate Archi workbench.

We characterize open embeddings of Stein spaces and of $C^\infty$-manifolds in terms of certain flatness-type conditions on the respective homomorphisms of function algebras.  

Let S={s1<s2<s3<…} be the sequence of all natural numbers which can be represented as a sum of two squares of integers. For X≥2 we denote by g(X) the largest gap between consecutive elements of S that do not exceed X. We prove that for X→+∞ the lower bound g(X)≥(390/449−o(1))lnX holds.  This estimate is twice the recent estimate by R. Dietmann and C. Elsholtz.

We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of the single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the 3- and 4-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat.

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.