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.

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.

This volume offers profound analyses of the main theoretical and practical aspects of the concept of sustainable development: namely, current environmental problems; the building of green economies; climate policies; specifics of international cooperation in the sphere of sustainable development; specific features of business and government involvement in implementing sustainable development; the role of civil society; its social and gender aspects; and specific characteristics of national models of sustainable development. The focus on the international aspects of the implementation of sustainable development ideas makes the insights offered here fresh and unique.

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.

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 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 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.

The transmission and the circular transmission are investigated for a ring of quantum dots (in a benzene-type configuration) connected to external leads in the meta-configuration. A computational method utilizing the tight-binding approximation to the Schrödinger equation is used to solve for the transmission probabilities as a function of the electron energy and external magnetic flux. The flux dependence is incorporated into the model using a standard procedure involving the Aharonov–Bohm effect. The positions of the transmission zeros and poles in the complex energy plane, and their possible interference with or even complete cancellation of each other, are shown to correlate with the amplitude and structure of the circular transmission resonances. Large-amplitude resonances of the circular transmission are found to occur when two poles of the transmission are separated along the imaginary axis. These resonances demonstrate a high degree of flux sensitivity at specific energy values and flux ranges. A small change in flux causes the orientation of the resonance poles in the complex energy plane to rotate parallel to the real energy axis, resulting in a concurrent decrease in the circular transmission amplitude. The flux-dependent interference between the transmission poles and zeros in the complex energy plane leads to a decrease of the circular transmission resonance amplitudes. The circular transmission and its corresponding current–voltage characteristic provide more information related to the external flux than can be obtained from the normal transmission alone.

We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. The main interest in this particular equation is its close relation to the quadratic loop equation in the theory of spectral curve topological recursion, and we recall this motivation giving a new proof of the topological recursion for monotone Hurwitz numbers, obtained first by Do, Dyer, and Mathews.

Magneto-fermionic condensate under study is a Bose-Einstein condensate of cyclotron spin-flip magnetoexcitons in a quantum Hall insulator. This condensate features unique properties such as millisecond range lifetime and hundreds of micrometers of propagation length. In this study, utilizing the photo-induced resonant reflection technique, we measured the exciton escape time. Finally, we estimated the exciton condensate propagation velocity as 25 m/s, which is much higher than a single particle propagation velocity. We also proposed a mechanism of exciton condensation.

An attractive two-dimensional semiconductor with tunable direct bandgap and high carrier mobility, black phosphorus (BP) is used in batteries, solar cells, photocatalysis, plasmonics and optoelectronics. BP is sensitive to ambient conditions, with oxygen playing a critical role in structure degradation. Our simulations show that BP oxidation slows down charge recombination. This is unexpected, since typically charges are trapped and lost on defects. First, BP has no ionic character. It interacts with oxygen and water weakly, experiencing little perturbation to electronic structure. Second, phosphorus supports different oxidation states and binds extraneous atoms avoiding deep defect levels. Third, soft BP structure can accommodate foreign species without disrupting periodic geometry. Finally, BP phonon scattering on defects shortens quantum coherence and suppresses recombination. Thus, oxidation can be regarded as production of a self-protective layer that improves BP properties. These BP features should be common to other mono-elemental 2D materials, stimulating energy and electronics applications.

We propose a method of measuring low concentrations of fluorescent molecules located in a small volume of a liquid solvent (about 5 μl) based on the Ebbesen effect of the extraordinary transmission (EOT) of light through a state-of-the-art plasmonic crystal formed by a nanohole array perforated in the ultra-high-quality Ag film. In the method, the EOT effect is realized at the fluorescence wavelength of the detected molecules with a low transmission of light at the absorption wavelength. This approach enables the realization of high level sensor sensitivity approaching a sensitivity level of single molecules counting sensors, owing to the suppression of the sensor substrate’s inevitable parasitic luminescence. The proposed method was successfully demonstrated by detection an ultra-low concentration of Cy-5 fluorescent markers in a dimethyl sulfoxide solution corresponding to less than 1000 molecules in the sensor detection volume.

The issue of a recurrence of the modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation which appears from nowhere (i.e., is infinitesimal initially) and generates a rogue wave which then disappears with no trace. If so, this wave solution would be a breather solution of the primitive hydrodynamic equations. It is shown with the help of the fully nonlinear numerical simulation that when a rogue wave occurs from a uniform Stokes wave train, it excites other waves which have different lengths, what prevents the complete recurrence and, eventually, results in a quasi-periodic breathing of the wave envelope. Meanwhile the discovered effects are rather small in magnitude, and the period of the modulation breathing may be thousands of the dominant wave periods. Thus, the obtained solution may be called a quasi-breather of the Euler equations.

A Gaussian graphical model is a graphical representation of the dependence structure for

a Gaussian random vector. Gaussian graphical model selection is a statistical problem that

identifies the Gaussian graphical model from observations. There are several statistical

approaches for Gaussian graphical model identification. Their properties, such as unbiasedeness

and optimality, are not established. In this paper we study these properties.

We consider the graphical model selection problem in the framework of multiple decision

theory and suggest assessing these procedures using an additive loss function. Associated

risk function in this case is a linear combination of the expected numbers of the two types

of error (False Positive and False Negative). We combine the tests of a Neyman structure for

individual hypotheses with simultaneous inference and prove that the obtained multiple

decision procedure is optimal in the class of unbiased multiple decision procedures.

Let G be a connected semisimple algebraic group and let H⊂G be a connected reductive subgroup. Given a flag variety X of G, a result of Vinberg and Kimelfeld asserts that H acts spherically on X if and only if for every irreducible representation R of G realized in the space of sections of a homogeneous line bundle on X the restriction of R to H is multiplicity free. In this case, the information on restrictions to H of all such irreducible representations of G is encoded in a monoid, which we call the restricted branching monoid. In this paper, we review the cases of spherical actions on flag varieties of simple groups for which the restricted branching monoids are known (this includes the case where H is a Levi subgroup of G) and compute the restricted branching monoids for all spherical actions on flag varieties that correspond to triples (G,H,X) satisfying one of the following two conditions: (1) G is simple and H is a symmetric subgroup of G; (2) G=SL_n.

We investigate the effect of the proportional hazards assumption on prognostic and predictive models of the survival time of patients suffering from amyotrophic lateral sclerosis (ALS). We theoretically compare the underlying model formulations of several variants of survival forests and implementations thereof, including random forests for survival, conditional inference forests, Ranger, and survival forests with L1 splitting, with two novel variants, namely distributional and transformation survival forests. Theoretical considerations explain the low power of log-rank-based splitting in detecting patterns in non-proportional hazards situations in survival trees and corresponding forests. This limitation can potentially be overcome by the alternative split procedures suggested herein. We empirically investigated this effect using simulation experiments and a re-analysis of the PRO-ACT database of ALS survival, giving special emphasis to both prognostic and predictive models.

Tensor products of irreducible representations of a simple Lie algebra define two natural measures on the space of weights: one comes from the weight multiplicities and another is induced by the decomposition of the tensor product into irreducible components. Our first result is an explicit description of density of the limiting measure for weight multiplicities when the numbers of irreducible factors linearly tend to infinity. We use the derived density to obtain the limit of the measures coming from the decomposition into irreducibles. The density of the resulting measure in type A coincides with the density of the famous GUE joint eigenvalues density restricted to the the traceless matrices. We thus generalize Kerov's theorem and prove the Postnova-Reshetikhin formula.

We continue, generalize and expand our study of linear degenerations of flag varieties from [G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier, M. Reineke, Math. Z. 287 (2017), no. 1-2, 615-654]. We realize partial flag varieties as quiver Grassmannians for equi-oriented type A quivers and construct linear degenerations by varying the corresponding quiver representation. We prove that there exists the deepest flat degeneration and the deepest flat irreducible degeneration: the former is the partial analogue of the mf-degenerate flag variety and the latter coincides with the partial PBW-degenerate flag variety. We compute the generating function of the number of orbits in the flat irreducible locus and study the natural family of line bundles on the degenerations from the flat irreducible locus. We also describe explicitly the reduced scheme structure on these degenerations and conjecture that similar results hold for the whole flat locus. Finally, we prove an analogue of the Borel-Weil theorem for the flat irreducible locus.

Dynamics on parabolic immediate basins for rational Newton maps of entire functions have been studied. It is proved that every parabolic immediate basin contains invariant accesses to the parabolic fixed point at infinity. Moreover, among these accesses there exists a unique dynamically defined access where dynamics are attracted towards the parabolic fixed point, whereas for other accesses, if there is any, the dynamics are repelled.

It is shown that the main result of N. R. Wallach, Principal orbit type theorems for reductive algebraic group actions and the Kempf--Ness Theorem,  arXiv:1811.07195v1 (17 Nov 2018) is a special case of a more general statement, which can be deduced, using a short argument, from the classical Richardson and Luna theorems.

Under certain initial conditions, we prove the existence of set-valued selectors of univariate compact-valued multifunctions of bounded (Jordan) variation when the notion of variation is defined taking into account only the Pompeiu asymmetric excess between compact sets from the target metric space. For this, we study subtle properties of the directional variations. We show by examples that all assumptions in the main existence result are essential. As an application, we establish the existence of set-valued solutions $X(t)$ of bounded variation to the functional inclusion of the form $X(t)\subset F(t,X(t))$ satisfying the initial condition $X(t_0)=X_0$.  

This is an expanded version of the talk by the author at the conference Polynomial Rings and Affine Algebraic Geometry, February 12–16, 2018, Tokyo Metropolitan University, Tokyo, Japan. Considering a local version of the Zariski Cancellation Problem naturally leads to exploration of some classes of varieties of special kind and their equivariant versions. We discuss several topics inspired by this exploration, including the problem of classifying a class of affine algebraic groups that are naturally singled out in studying the conjugacy problem for algebraic subgroups of the Cremona groups.

We look at how evolution method deforms, when one considers Khovanov polynomials instead of Jones polynomials. We do this for the figure-eight-like knots (also known as 'double braid' knots, see arXiv:1306.3197) -- a two-parametric family of knots which "grows" from the figure-eight knot and contains both two-strand torus knots and twist knots. We prove that parameter space splits into four chambers, each with its own evolution, and two isolated points. Remarkably, the evolution in the Khovanov case features an extra eigenvalue, which drops out in the Jones (t -> -1) limit.

Estimation of the relationship between DNA sequences is one of the most important problems in genomics. Understanding these relationships is central to de- mographic inference, correction of population structure in GWAS, identifying signals of selection etc. The data structure containing the full information about sample genealogy is called the ancestral recombination graph (ARG). However, ARG inference is a very dicult problem, not least due to a very complex state space. In this work we describe a new approach for fast and scalable generation of local tree topologies relating large numbers of haplotypes. Our method is closely related to the estimation of ARG, and captures both local and global properties of an ARG. It is based on a data structure which we call tree consistent PBWT , a modi cation of PBWT data structure intro- duced by R. Durbin (2014). We also explore some methods to estimate the quality of the generated tree topologies and to make inferences based on them. At the end we discuss a probabilistic model which could potentially lead to the estimation of ARG node times.

This paper proposes a novel method, referred to as ParGenFS, for finding a most specific generalization of a query set, represented by a fuzzy set of topics assigned to leaves of the rooted tree of a taxonomy. This generalization lifts the query set to one or several head subjects in the higher ranks of the taxonomy. The head subject is supposed to tightly cover the query set, however dispersed that can be over branches of the tree, possibly bringing in some gaps, that are taxonomy nodes covered by the head subject but irrelevant to the set. To balance that, we admit some offshoots, that are nodes belonging to the query set but not covered by the head subject. The method globally minimizes the total number of head subjects and gaps and offshoots, differently weighted. Our algorithm is applied to the structural analysis and description of a collection of 17685 abstracts of research papers published in 17 Springer journals on data science for the 20-years period 1998–2017. Our taxonomy of Data Science (DST) is extracted from the international Association for Computing Machinery Computing Classification System 2012 (ACM-CCS), a six-layer hierarchical taxonomy manually developed by a team of ACM experts. The DST also involves a number of additions detailing the leaves of the ACM-CCS taxonomy and added by ourselves. We find fuzzy clusters of leaf topics over the text collection, with a specially developed machinery. Three of the clusters are thematic indeed, relating to Data Science sub-areas: (a) learning, (b) information retrieval, and (c) clustering. These three clusters are lifted with ParGenFS in the DST, which allows us to make some conclusions of the tendencies of the developments in these areas.

Thin superconducting films are usually regarded as type-II superconductors even when they are made of a type-I materials. The reason is a strong influence of the stray magnetic fields outside the superconductive sample. While very thin films indeed reach this limit, there is a sufficiently large interval of film thicknesses in which the magnetic properties cannot be classified as either of the two conventional superconductivity types. We demonstrate that in this interval superconducting condensate and magnetic field reveal exotic spatial profiles that are very sensitive to system parameters, in particular, the temperature and applied field. Magnetic properties of such systems can be attributed to a special regime of intertype superconductivity. Its physical origin lies in the removal of infinite degeneracy of the superconducting state at the critical Bogomolnyi point. Here we demonstrate that qualitative characteristics of obtained condensate-field structures and the way they change with the temperature and applied field are independent of the choice of the in-plane boundary conditions for the order parameter and magnetic field.

The article demonstrates rather general approach to problems of discrete geometry: treat them as global optimization problems to be solved by one of general purpose solver implementing branch-and-bound algorithm (B&B). This approach may be used for various types of problems, i.e. Tammes problems, Thomson problems, search of minimal potential energy of micro-clusters, etc. Here we consider a problem of densest packing of equal circles in special geometrical object, so called square flat torus ℝ2/ℤ2 with the induced metric. It is formulated as Mixed-Integer Nonlinear Problem with linear and non-convex quadratic constraints.  The open-source B&B-solver SCIP, this http URL, and its parallel implementation ParaSCIP, this http URL, had been used in computing experiments to find "very good" approximations of optimal arrangements. The main result is a confirmation of the conjecture on optimal packing for N=9 that was published in 2012 by O. Musin and A. Nikitenko. To do that, ParaSCIP took about 2000 CPU*hours (16 hours x 128 CPUs) of cluster HPC4/HPC5, National Research Centre "Kurchatov Institute", this http URL

There is a gap in the proof of the main theorem in the article [ShCh13a] on optimal bounds for the Morse lemma in Gromov-hyperbolic spaces. We correct this gap, showing that the main theorem of [ShCh13a] is correct. We also describe a computer certification of this result.

The poetic texts pose a challenge to full morphological tagging and lemmatization since the authors seek to extend the vocabulary, employ morphologically and semantically deficient forms, go beyond standard syntactic templates, use non-projective constructions and non-standard word order, among other techniques of the creative language game. In this paper we evaluate a number of probabilistic taggers based on decision trees, CRF and neural network algorithms as well as one state-of-the-art dictionary-based tagger. The taggers were trained on prosaic texts and tested on three poetic samples of different complexity. Firstly, we discuss the method to compile the gold standard datasets for the Russian poetry. Secondly, we evaluate the taggers’ performance in the identification of the part of speech tags and lemmas. Finally, we analyze different types of errors in the taggers’ output. We analyse the confusion matrix of the parts of speech and mismatches in lemma annotation.

Given two small dg categories C,D, defined over a field, we introduce their (non-symmetric) twisted tensor product C⊗∼D. We show that −⊗∼D is left adjoint to the functor Coh(D,−), where Coh(D,E) is the dg category of dg functors D→E and their coherent natural transformations. This adjunction holds in the category of small dg categories (not in the homotopy category of dg categories Hot). We show that for C,D cofibrant, the adjunction descends to the corresponding adjunction in the homotopy category. Then comparison with a result of Toën shows that, for C,D cofibtant, C⊗∼D is isomorphic to C⊗D, as an object of the homotopy category Hot.

We investigate geometry of D-affine varieties. Our main result is that a D-affine uniformly rational projective variety over an algebraically closed field of zero characteristic is a generalised flag variety of a reductive group. This is a partially converse statement for Beilinson-Bernstein Localisation Theorem.

Following the approach of Haiden-Katzarkov-Kontsevich arXiv:1409.8611, to any homologically smooth graded gentle algebra A we associate a triple (Σ_A,Λ_A;η_A), where Σ_A is an oriented smooth surface with non-empty boundary, Λ_A is a set of stops on ∂Σ_A and η_A is a line field on Σ_A, such that the derived category of perfect dg-modules of A is equivalent to the partially wrapped Fukaya category of (Σ_A,Λ_A;η_A). Modifying arguments of Johnson and Kawazumi, we classify the orbit decomposition of the action of the (symplectic) mapping class group of Σ_A on the homotopy classes of line fields. As a result we obtain a sufficient criterion for homologically smooth graded gentle algebras to be derived equivalent. Our criterion uses numerical invariants generalizing those given by Avella-Alaminos-Geiss in math/0607348, as well as some other numerical invariants. As an application, we find many new cases when the AAG-invariants determine the derived Morita class. As another application, we establish some derived equivalences between the stacky nodal curves considered in arXiv:1705.06023.

We study birational projective models of M_2,2 obtained from the moduli space of curves with nonspecial divisors. We describe geometrically which singular curves appear in these models and show that one of them is obtained by blowing down the Weierstrass divisor in the moduli stack of Z-stable curves \bar{M}_2,2(Z) defined by Smyth. As a corollary, we prove projectivity of the coarse moduli space \bar{M}_2,2(Z).