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 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.

We study the complexity of the realization of Boolean functions by circuits in infinite complete bases containing all monotone functions with zero weight (cost of use) and finitely many nonmonotone functions with unit weight. The complexity of the realization of Boolean functions in the case where the only nonmonotone element of the basis is negation was completely described by A. A. Markov: the minimum number of negations sufficient for the realization of an arbitrary Boolean function f (the inversion complexity of the function f) is equal to ]log_2(d(f) + 1)[, where d(f) is the maximum (over all increasing chains of sets of values of the variables) number of changes of the function value from 1 to 0. In the present paper, this result is generalized to the case of the computation of Boolean functions over an arbitrary basis B of prescribed form. It is shown that the minimum number of nonmonotone functions sufficient for computing an arbitrary Boolean functionf is equal to ]log_2(d(f)/D(B)+1)[, where D(B) = max d(ω); the maximum is taken over all nonmonotone functions ω of the basis B.

We investigate the realization complexity of k-valued logic functions k ≥ 2 by combinational circuits in an infinite basis that includes the negation of the Lukasiewicz function, i.e., the function k−1−x, and all monotone functions. Complexity is understood as the total number of circuit elements. For an arbitrary function f, we establish lower and upper complexity bounds that differ by at most by 2 and have the form 2 log(d(f) + 1) + o(1), where d(f) is the maximum number of times the function f switches from larger to smaller value (the maximum is taken over all increasing chains of variable tuples). For all sufficiently large n, we find the exact value of the Shannon function for the realization complexity of the most complex function of n variables.

The problem of computing the width of simplices generated by the convex hull of their integer vertices is considered. An FPT algorithm, in which the parameter is the maximum absolute value of the rank minors of the matrix consisting from the simplex vertices, is presented.

There is an ongoing evolution involving a new approach to large-scale optimisations based on co-evolutionary searches using interacting heterogeneous agent-processes via the implementation of synchronised genetic algorithms with local populations. The individualisation of heuristic operators at the level of agent-processes that implement independent evolutionary searches facilitate the improved likelihood of obtaining the best solutions in the fastest time. Based on this property, a parallel multi-agent single-objective real-coded genetic algorithm for large-scale constrained black-box single-objective optimisations (LSOPs ) is proposed. This facilitates the effective frequency exchange of the best potential decisions between interacting agent-processes with individual parameters, such as types of crossover and mutation operators with their own characteristics. We have improved the quality of both solutions and the time-efficiency of a multi-agent real-coded genetic algorithm (MA−RCGA ). A novel framework was developed that represents the aggregation of MA−RCGA with simulation models by implementing a set of objective functions for real-world large-scale optimisation problems such as the simulation model of the ecological-economics system implemented in the AnyLogic tool.

This paper studies the patterns of learning behaviour in connection with educational achievement in multi-year undergraduate data science minor specialisation for non-STEM students. In particular, this work focuses on analysing the predictors of academic achievement in blended-learning setting factors related to initial mathematics knowledge, specific traits of educational programs, online and offline learning engagement, and connections with peers. Robust linear regression and non-parametric statistical tests reveal a significant gap in the achievement of students from different educational programs and on the connection between their class attendance and achievement. The results indicate that achievement is not related to the communication on the Q&A forum while peers do affect academic success.

The issue of rogue wave lifetimes is addressed in this study, which helps to detail the general picture of this dangerous oceanic phenomenon. The direct numerical simulations of irregular wave ensembles are performed to obtain the complete accurate data on the rogue wave occurrence and evolution. Purely collinear wave systems, moderately crested, and short-crested sea states have been simulated by means of the high-order spectral method for the potential Euler equations. As rogue waves are transient and poorly reflect the physical eects, we join instant abnormally high waves in close locations and close time moments to new objects, rogue events, which helps to retrieve the abnormal occurrences more stably and more consistently from the physical point of view. The rogue event lifetime probability distributions are calculated based on the simulated wave data. They show the distinctive dierence between rough sea states with small directional bandwidth on one part, and small-amplitude sea states and short-crested states on the other part. The former support long-living rogue wave patterns (the corresponding probability distributions have heavy tails), though the latter possess exponential probability distributions of rogue event lifetimes and generally produce much shorter rogue wave events.

This work is devoted to the investigation of particle acceleration during magnetospheric dipolarizations. A numerical model is presented taking into account the four scenarios of plasma acceleration that can be realized: (A) total dipolarization with characteristic time scales of 3 min; (B) single peak value of the normal magnetic component Bz occurring on the time scale of less than 1 min; (C) a sequence of rapid jumps of Bz interpreted as the passage of a chain of multiple dipolarization fronts (DFs); and (D) the simultaneous action of mechanism (C) followed by the consequent enhancement of electric and magnetic fluctuations with the small characteristic time scale 1 s. In a frame of the model, we have obtained and analyzed the energy spectra of four plasma populations: electrons e, protons Hþ, helium Heþ, and oxygen Oþ ions, accelerated by the above-mentioned processes (A)–(D). It is shown that Oþ ions can be accelerated mainly due to the mechanism (A); Hþ and Heþ ions (and to some extent electrons) can be more effectively accelerated due to the mechanism (C) than the single dipolarization (B). It is found that high-frequency electric and magnetic fluctuations accompanying multiple DFs (D) can strongly accelerate electrons e and really weakly influence other populations of plasma. The results of modeling demonstrated clearly the distinguishable spatial and temporal resonance character of particle acceleration processes. The maximum particle energies depending on the scale of the magnetic acceleration region and the value of the magnetic field are estimated. The shapes of energy spectra are discussed.

We consider a quasi-one-dimensional model of a two-component Fermi gas at zero temperature on one, two and three-leg attractive-U Hubbard ladders. We construct the grand canonical phase diagram of a two-component spin-polarized gas. We find that the structure of the phase diagram of the attractive-U Hubbard model for two and three leg ladders significantly differs q from the structure of the phase diagram of a single chain. We argue that the single chain model is a special case, and that multichain ladders display qualitative features of the 1D-to-3D crossover, observed in experiments with trapped ultracold gases.

We consider an expansion of the strongly interacting superfluid Fermi gas in a vacuum, assuming absence of the trapping potential, in the so-called unitary regime when the chemical potential μ ~ n^2/3/m where n is the density of the Bose-Einstein condensate of Cooper pairs of fermionic atoms. In low temperatures, T → 0, such expansion can be described in the framework of the Gross-Pitaevskii equation (GPE). Because of the chemical potential dependence on the density, ∼ n^2/3, the GPE has additional symmetries, resulting in the existence of the virial theorem, connecting the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at t → ∞ to the gas cloud expansion, linearly growing in time. We study such asymptotics, and reveal the perfect match between the quasi-classical self-similar solution and the asymptotic expansion of the non-interacting gas. This match is governed by the virial theorem, derived through utilizing the Talanov transformation, which was first obtained for the stationary self-focusing of light in media with a cubic nonlinearity due to the Kerr effect. In the quasi-classical limit, the equations of motion coincide with 3D hydrodynamics for the perfect monoatomic gas with gamma = 5/3. Their self-similar solution describes, on the background of the gas expansion, the angular deformities of the gas shape in the framework of the Ermakov–Ray–Reid type system.

It is commonly believed that the visual system requires oculomotor information to perceive depth from binocular disparity. However, any effect of the oculomotor information on depth perception is too restricted to explain depth perception under natural viewing conditions. In this study, I describe a computational model that can recover depth from a stereo-pair of retinal images without using any oculomotor information. The model shows that, at least from a computational perspective, any oculomotor information is not necessary for perceiving depth from the stereo retinal images.

Bachet's game is a variant of the game of Nim. There are n objects in one pile. Two players make moves one after another. On every move, a player is allowed to take any positive number of objects not exceeding some fixed number m. The player who takes the last object loses. We consider a variant of Bachet's game in which each move is a lottery over set {1,2,…,m}. Outcome of a lottery is the number of objects that player takes from the pile. We show that under some nondegenericity assumptions on the set of available lotteries the probability that the first player wins in subgame perfect Nash equilibrium converges to 1/2 as n tends to infinity.

We study the question of realisability of iterated higher Whitehead products with a given form of nested brackets by simplicial complexes, using the notion of the moment-complex $\mathcal{Z_K}$. Namely, we say that a simplicial complex K realises an iterated higher Whitehead product w if w is a nontrivial element of the homotopy group $\pi_*(\mathcal{Z_K})$. The combinatorial approach to the question above uses the operation of substitution of simplicial complexes: for any iterated higher Whitehead product w we describe a simplicial complex $\partial\Delta_w$ that realises $w$. Furthermore, for a particular form of brackets inside w, we prove that $\partial\Delta_w$ is the smallest complex that realises $w$. We also give a combinatorial criterion for the nontriviality of the product w. In the proof of nontriviality we use the Hurewicz image of w in the cellular chains of $\mathcal{Z_K}$ and the description of the cohomology product of $\mathcal{Z_K}$. The second approach is algebraic: we use the coalgebraic versions of the Koszul complex and the Taylor resolution of the face coalgebra of $\mathcal{K}$ to describe the canonical cycles corresponding to iterated higher Whitehead products $w$. This gives another criterion for realisability of $w$.

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.

A description of rational Newton maps in terms of the partial fraction decomposition of rational functions is obtained. 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

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.