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.

This book constitutes extended, revised and selected papers from the 7th International Conference on Optimization Problems and Their Applications, OPTA 2018, held in Omsk, Russia in July 2018. The 27 papers presented in this volume were carefully reviewed and selected from a total of 73 submissions. The papers are listed in thematic sections, namely location problems, scheduling and routing problems, optimization problems in data analysis, mathematical programming, game theory and economical applications, applied optimization problems and metaheuristics.

Information systems in different domains, such as healthcare, tourism, banking, government and others, record operational behavior in the form of event logs. The process mining discipline offers dozens of techniques to discover, analyze, and visualize processes running in information systems, based on their event logs. The representational bias (the language for processes representation) plays an important role in the process discovery. In this work BPMN (Business Process Model and Notation) language was chosen as a representational bias and as a starting point for the process discovery, analysis and enhancement. BPMN is a common process modeling language, widely used by consultants, managers, analysts, and software engineers in various application domains. This work aims to bridge the gap between process mining techniques and BPMN. Existing techniques are often limited to a single perspective, e.g., just the control flow, subprocesses, or just resources. The goal of this work is to fully support the BPMN specification in the context of process mining and suggest a unified and integrated approach allowing for the discovery, analysis and enhancement of hierarchical high-level BPMN models. The approach proposed in this thesis is supported by tools that enable users to analyze discovered processes in BPMN-compliant tools and even automate their executions, using existing BPMN engines.

Control of Discrete-Time Descriptor Systems takes an anisotropy-based approach to the explanation of random input disturbance with an information-theoretic representation. It describes the random input signal more precisely, and the anisotropic norm minimization included in the book enables readers to tune their controllers better through the mathematical methods provided. The book contains numerous examples of practical applications of descriptor systems in various fields, from robotics to economics, and presents an information-theoretic approach to the mathematical description of coloured noise. Anisotropy-based analysis and design for descriptor systems is supplied along with proofs of basic statements, which help readers to understand the algorithms proposed, and to undertake their own numerical simulations.   This book serves as a source of ideas for academic researchers and postgraduate students working in the control of discrete-time systems. The control design procedures outlined are numerically effective and easily implementable in MATLAB®

This volume contains proceedings of the first Workshop on Data Analysis in Medicine held in May 2017 at the National Research University Higher School of Economics, Moscow. The volume contains one invited paper by Dr. Svetla Boytcheva, 6 regular contributions and 2 project proposals, carefully selected and reviewed by at least two reviewers from the international program commit- tee. The papers accepted for publication report on different aspects of analysis of medical data, among them treatment of data on particular diseases (Consoli- dated mathematical growth model of Breast Cancer CoMBreC, Artificial neural networks for prediction of final height in children with growth hormone deficiency), methods of data analysis (analysis of rare diseases, methods of machine learning and Big Data, subgroup discovery for treatment optimization), and instrumental tools (explanation-oriented methods of data analysis in medicine, information support features of the medical research process, modeling frame- work for medical data semantic transformations, radiology quality management and peer-review system). Organizers of the workshop would like to thank the reviewers for their careful work and all contributors and participants of the workshop.

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 is an advanced guide to optimal stopping and control, focusing on advanced Monte Carlo simulation and its application to finance. Written for quantitative finance practitioners and researchers in academia, the book looks at the classical simulation based algorithms before introducing some of the new, cutting edge approaches under development.

This book discusses smart, agile software development methods and their applications for enterprise crisis management, presenting a systematic approach that promotes agility and crisis management in software engineering. The key finding is that these crises are caused by both technology-based and human-related factors. Being mission-critical, human-related issues are often neglected. To manage the crises, the book suggests an efficient agile methodology including a set of models, methods, patterns, practices and tools. Together, these make a survival toolkit for large-scale software development in crises. Further, the book analyses lifecycles and methodologies focusing on their impact on the project timeline and budget, and incorporates a set of industry-based patterns, practices and case studies, combining academic concepts and practices of software engineering.

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.

Intended to bridge the gap between the latest methodological developments and cross-cultural research, this interdisciplinary resource presents the latest strategies for analyzing cross-cultural data. Techniques are demonstrated through the use of applications that employ cross-national data sets such as the latest European Social Survey. With an emphasis on the generalized latent variable approach, internationally prominent researchers from a variety of fields explain how the methods work, how to apply them, and how they relate to other methods presented in the book. Syntax and graphical and verbal explanations of the techniques are included. Online resources, available at www.routledge.com/9781138690271, include some of the data sets and syntax commands used in the book.

This book examines how Russia, the world’s most complicated country, is governed. As it resumes its place at the centre of global affairs, the book explores Russia’s overarching strategies, and how it organizes itself (or not) in policy areas ranging from foreign policy and national security to health care, education, immigration, science, sport, agriculture, the environment and criminal justice. The book also discusses the structures and institutions on which Russia relies in order to deliver its goals in these areas of national life, as well as what’s to be done, in policy terms, to improve the country’s performance in its first post-Soviet century. Edited by Irvin Studin, the book includes contributions from a tremendous list of Russia’s leading thinkers and specialists, including Alexei Kudrin, Vladimir Mau, Alexander Auzan, Simon Kordonsky, Fyodor Lukyanov, Natalia Zubarevich and Andrey Melville.

This edited collection presents a range of methods that can be used to analyse linguistic data quantitatively. A series of case studies of Russian data spanning different aspects of modern linguistics serve as the basis for a discussion of methodological and theoretical issues in linguistic data analysis. The book presents current trends in quantitative linguistics, evaluates methods and presents the advantages and disadvantages of each. The chapters contain introductions to the methods and relevant references for further reading.

The Russian language, despite being one of the most studied in the world, until recently has been little explored quantitatively. After a burst of research activity in the years 1960-1980, quantitative studies of Russian vanished. They are now reappearing in an entirely different context. Today we have large and deeply annotated corpora available for extended quantitative research, such as the Russian National Corpus, ruWac, RuTenTen, to name just a few (websites for these and other resources will be found in a special section in the References). The present volume is intended to fill the lacuna between the available data and the methods that can be applied to studying them.

Our goal is to present current trends in researching Russian quantitative linguistics, to evaluate the research methods vis-à-vis Russian data, and to show both the advantages and the disadvantages of the methods. We especially encouraged our authors to focus on evaluating statistical methods and new models of analysis. New findings concern applicability, evaluation, and the challenges that arise from using quantitative approaches to Russian data.

This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart.

These notes have appeared as a result of a one-term course in superfluidity and superconductivity given by the author to fourth-year undergraduate students and first-year graduate students of the Department of Physics, Moscow State University of Education. The goal was not to give a detailed picture of these two macroscopic quantum phenomena with an extensive coverage of the experimental background and all the modern developments, but rather to show how the knowledge of undergraduate quantum mechanics and statistical physics could be used to discuss the basic concepts and simple problems, and draw parallels between superconductivity and superfluidity.

Superconductivity and superfluidity are two phenomena where quantum mechanics, typically constrained to the microscopic realm, shows itself on the macroscopic level. Conceptually and mathematically, these phenomena are related very closely, and some results obtained for one can, with a few modifications, be immediately carried over to the other. However, the student of these notes should be aware of important differences between superconductivity and superfluidity that stem mainly from two facts: (1) electrons in a superconductor carry a charge, therefore one has to take into account interaction with electromagnetic radiation; (2) electrons move in a lattice, therefore phonons play a role not only a mediators of attractive interaction between pairs of electrons, but also as scatterers of charge carriers.

Although these are notes on superfluidity and superconductivity, and there are a few cross-references, the two subjects can be studied independently with, perhaps, a little extra work by the student to fill in the gaps resulting from such study. The material of Chapter 1 introduces the method of second quantisation that is commonly used to discuss systems with many interacting particles. It is then applied in Chaper 2 to treat the uniform weakly interacting Bose gas within the approach by N. Bogoliubov, and in Chapter 4 to formulate the theory of the uniform superconducting state put forth by J. Bardeen, L. Cooper and R. Schrieffer. Chapter 3 presents the theory proposed independently by E. Gross and L. Pitaevskii of a non-uniform weakly interacting Bose gas, with a discussion of vortices, rotation of the condensate, and the Bogoliubov equations. In Chapter 5 we discuss the Ginzburd-Landau theory of a non-uniform superconductor near the critical temperature and apply it to a few simple problems such as the surface energy of the boundary between a normal metal and a superconductor, critical current and critical magnetic field, and vortices.

The development and use of Genetically modified organisms (GMOs) has been a contentios subject for the last three decades. while there has been a number of social science analysis of the issues, this is the first book to assess the role of non-governmental organizations (NGOs) in the debate at such wide geographic scale. The various posiotions, for and against GMOs, particularly with regards to trangenic crops, articulated by NGOs in the debate are dissected, classified and juxtaposed to corresponding campaigns. these are discussed in the context of paradigms, including nature fundamentalism and the organic movement, post-colonialism, food sovereignty, anti-globalism, sustainability and feminism. This book also analyses how NGOs interprete the debate and the persuasive communication tactics. 

 

The relationship between crystal structures of three isomeric aminopyridinium iodobismuthates containing one-dimensional [(BiI4)n]n− anions, acidity of aminopyridinium cations and optical properties was revealed

The interaction of iodobismuthate anions and methyl viologen [MV]2+ cations in aqueous solutions led to the formation of three compounds, two of which were identified as [MV][BiI5] and [MV]3[Bi2I11]I. Hybrid iodobismuthates [MV]3[Bi2I11]I and [MV]3[Bi2I9]2(DMF)3(H2O) were isolated from dimethylformamide (DMF). The heating of the latter material (up to 200 o C) resulted in a mixture of products, one of which was identified as [MV][BiI5]. A simple antisolvent precipitation method was proposed to create the [MV] [BiI5]/SiO2 composite material.

Three hybrid 1,1'-(1,n-alkanediyl)bis(4-methylpyridinium) iodobismuthates 1 - 3  were prepared by a facile solution route and showed thermal stability in air up to 230°C. The structures of solid 1 and 3 contain zero-dimensional anions, and the structure of 2 contains one-dimensional linear anionic chains [BiI5]n2n-. Photoluminescence (PL) in the spectral range between 600 and 750 nm was observed for 1 and 2. DFT calculations and optical studies confirmed that compounds 1−3 are semiconductors with band gaps of 1.73−2.10 eV, which corresponds with their intense black (for 2) or red (for 1 and 3) colors. The optical absorption of 2 in the red spectral range is primarily due to charge transfer from the I5p orbitals at the top of the valence band to the Bi6p orbitals at the bottom of the conduction band.

t is known (from Counting curves and their projections by Joachim von zur Gathen, Marek Karpinski, Igor Shparlinski [1, part 4]) that counting the number of points on a curve where is a sparse polynomial over

is #P-complete under randomized reductions.

We give a simple proof of a stronger result: counting roots of a sparse univariate polynomial over

is #P-complete under deterministic reductions.

Algorithmic statistics looks for models of observed data that are good in the following sense: a model is simple (i.e., has small Kolmogorov complexity) and captures all the algorithmically discoverable regularities in the data. However, this idea can not be used in practice as is because Kolmogorov complexity is not computable. In this paper we develop an algorithmic version of algorithmic statistics that uses space-bounded Kolmogorov complexity. We prove a space-bounded version of a basic result from “classical” algorithmic statistics, the connection between optimality and randomness deficiences. The main tool is the Nisan–Wigderson pseudo-random generator. An extended abstract of this paper was presented at the 12th International Computer Science Symposium in Russia (Milovanov 10).

Perverse schobers are conjectural categorical analogs of perverse sheaves. We show that such structures appear naturally in Homological Minimal Model Program which studies the effect of birational transformations such as flops, on the coherent derived categories. More precisely, the flop data are analogous to hyperbolic stalks of a perverse sheaf. In the first part of the paper we study schober-type diagrams of categories corresponding to flops of relative dimension 1, in particular we determine the categorical analogs of the (compactly supported) cohomology with coefficients in such schobers. In the second part we consider the example of a “web of flops” provided by the Grothendieck resolution associated to a reductive Lie algebra g and study the corresponding schober-type diagram. For g = sl3 we relate this diagram to the classical space of complete triangles studied by Schubert, Semple and others.

Consider the space M = O(p, q)/O(p) × O(q) of positive p-dimensional subspaces in a pseudo-Euclidean space V of signature (p, q), where p > 0, q > 1 and (p,q)≠(1,2), with integral structure: V=Vℤ⊗ℤ. Let Γ be an arithmetic subgroup in G=O(Vℤ), and R⊂Vℤ a Γ-invariant set of vectors with negative square. Denote by R⊥ the set of all positive p-planes W ⊂ V such that the orthogonal complement W⊥ contains some r ∈ R. We prove that either R⊥ is dense in M or Γ acts on R with finitely many orbits. This is used to prove that the squares of primitive classes giving the rational boundary of the Kähler cone (i.e., the classes of “negative” minimal rational curves) on a hyperkähler manifold X are bounded by a number which depends only on the deformation class of X. We also state and prove the density of orbits in a more general situation when M is the space of maximal compact subgroups in a simple real Lie group.

We prove derived equivalence of Calabi–Yau threefolds con- structed by Ito–Miura–Okawa–Ueda as an example of non-birational Calabi– Yau varieties whose difference in the Grothendieck ring of varieties is annihi- lated by the affine line.

Purpose – The purpose of this paper is to demonstrate that process mining techniques can help to discover process models from event logs, using conventional high-level process modeling languages, such as Business Process Model and Notation (BPMN), leveraging their representational bias. Design/methodology/approach – The integrated discovery approach presented in this work is aimed to mine: control, data and resource perspectives within one process diagram, and, if possible, construct a hierarchy of subprocesses improving the model readability. The proposed approach is defined as a sequence of steps, performed to discover a model, containing various perspectives and presenting a holistic view of a process. This approach was implemented within an open-source process mining framework called ProM and proved its applicability for the analysis of real-life event logs. Findings – This paper shows that the proposed integrated approach can be applied to real-life event logs of information systems from different domains. The multi-perspective process diagrams obtained within the approach are of good quality and better than models discovered using a technique that does not consider hierarchy. Moreover, due to the decomposition methods applied, the proposed approach can deal with large event logs, which cannot be handled by methods that do not use decomposition. Originality/value – The paper consolidates various process mining techniques, which were never integrated before and presents a novel approach for the discovery of multi-perspective hierarchical BPMN models. This approach bridges the gap between well-known process mining techniques and a wide range of BPMN-complaint tools.

We consider a class of sequential interdiction settings where the interdictor has incomplete initial information about the network while the evader has complete knowledge of the network, including its structure and arc costs. In each time period, the interdictor can block at most k arcs known to him for the duration of the period. By observing the evader's actions, the interdictor learns about the network structure and costs and thus, can adjust his actions in subsequent time periods. It is known from the literature that if the evader is greedy (i.e., she uses the shortest available path in every time period), then under some assumptions on the the feedback generated from the evader's actions, the greedy interdiction policies that block k-most vital arcs in each time period are efficient and have a finite regret. In this paper, we consider the evader's perspective and explore strategic evasion policies under the assumption that the interdictor is greedy. In particular, we show that the evader's problem is NP-hard even for two time periods. Then we derive constructive properties of optimal evasion policies for two time periods when the interdictor has no initial information about the network structure. Based on these theoretical observations, we design a heuristic algorithm for a strategic evader in a general setting with an arbitrary time horizon and any initial information available to the interdictor initially. Finally, our computational experiments demonstrate that the proposed heuristic consistently outperforms the greedy evasion policy on several classes of synthetic network instances.

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.

A periodic tridiagonal matrix is a tridiagonal matrix with additional two entries at the corners. We study the space of Hermitian periodic tridiagonal n×n-matrices with a fixed simple spectrum. Using discrete Shroedinger operator we give a condition on the spectrum which guarantees that this space is a manifold. The space carries a natural effective action of a compact (n−1)-torus. We describe the topology of its orbit space and, in particular, show that whenever the isospectral space is a manifold, its orbit space is homeomorphic to S4×Tn−3. The degenerate locus of the periodic Toda flow has combinatorial structure which can be described using the regular tiling of euclidean space by permutohedra. We study the topology of the isospectral space in vicinity of degenerate locus by methods of toric topology and algebraic combinatorics. Additive structure of homology and equivariant cohomology modules in vicinity of degenerate locus are computed in terms of the face ring of the special cell structure on a torus. We call this cell structure a wonderful cell subdivision due to its unique combinatorial properties.

An arrow matrix is a matrix with zeroes outside the main diagonal, first row, and first column. We consider the space MStn,λ of Hermitian arrow (n+1)×(n+1)-matrices with fixed simple spectrum λ. We prove that this space is a smooth 2n-manifold, and its smooth structure is independent on the spectrum. Next, this manifold carries the locally standard torus action: we describe the topology and combinatorics of its orbit space. If n⩾3, the orbit space MStn,λ/Tn is not a polytope, hence this manifold is not quasitoric. However, there is a natural permutation action on MStn,λ which induces the combined action of a semidirect product Tn⋊Σn. The orbit space of this large action is a simple polytope. The structure of this polytope is described in the paper.  In case n=3, the space MSt3,λ/T3 is a solid torus with boundary subdivided into hexagons in a regular way. This description allows to compute the cohomology ring and equivariant cohomology ring of the 6-dimensional manifold MSt3,λ using the general theory developed by the first author. This theory is also applied to a certain 6-dimensional manifold called the twin of MSt3,λ. The twin carries a half-dimensional torus action and has nontrivial tangent and normal bundles.

We consider the space Xh of Hermitian matrices having staircase form and the given simple spectrum. There is a natural action of a compact torus on this space. Using generalized Toda flow, we show that Xh is a smooth manifold and its smooth type is independent of the spectrum. Morse theory is then used to show the vanishing of odd degree cohomology, so that Xh is an equivariantly formal manifold. The equivariant and ordinary cohomology of Xh are described using GKM-theory. The main goal of this paper is to show the connection between the manifolds Xh and the semisimple Hessenberg varieties well-known in algebraic geometry. Both the spaces Xh and Hessenberg varieties form wonderful families of submanifolds in the complete flag variety. There is a certain symmetry between these families which can be generalized to other submanifolds of the flag variety.

An extremal curve germ is the analytic germ of a threefold with terminal singularities along a reduced complete curve admitting a contraction whose fibers have dimension at most one. The aim of the present paper is to review the results concerning those contractions whose central fiber is irreducible and contains only one non-Gorenstein point.

We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: 𝔄5, PSL2(F7), 𝔄6, SL2(F8), 𝔄7, PSp4(F3), SL2(F7), 2.𝔄5, 2.𝔄6, 3.𝔄6 or 6.𝔄6. All of these groups with a possible exception of 2.𝔄6 and 6.𝔄6 indeed act on some rationally connected threefolds.

J.~Palis found necessary  conditions for  a Morse-Smale diffeomorphism on a closed $n$-dimensional manifold $M^n$  to  embed into a topological  flow and proved that these conditions are also sufficient for $n=2$.  For the case $n=3$ a possibility of  wild embedding of closures of separatrices of saddles is an additional obstacle  for Morse-Smale cascades to embed into topological flows.  In this paper we show that there are no such obstructions   for  Morse-Smale diffeomorphisms without heteroclinic intersection given  on  the sphere $S^n, \,n\geq 4$,  and Palis's conditions again are  sufficient for such  diffeomorphisms.

We construct an explicit solution for the multimarginal transportation problem on the unit cube [0,1]3 with the cost function xyz and one-dimensional uniform projections. We show that the primal problem is concentrated on a set with non-constant local dimension and admits many solutions, whereas the solution to the corresponding dual problem is unique (up to addition of constants).

We shall consider the product of complex random matrices from the independent complex Ginibre ensembles. The product includes complex matrices Zi,Z†i,i=1,…,n and 2n sources (complex matrices Ci and C∗i). Any such product can be represented by a chord diagram that encodes the order of the matrices in the product. We introduce the Euler characteristic E∗ of the chord diagram and show that the spectral correlation functions of the product generate Hurwitz numbers that enumerate nonequivalent branched coverings of Riemann surfaces of genus g∗. The role of sources is the generation of branching profiles in critical points which are assigned to the vertices of the graph drawn on the base surface obtained as a result of gluing of the 2n-gon related to the chord diagram in a standard way. Hurwitz numbers for Klein surfaces may also be obtained by a slight modification of the model. Namely, we consider 2n+1 polygon and consider pairing of the extra matrix Z2n+1 with a "Mobius" tau function. Thus, the presented matrix models labelled by chord diagrams generate Hurwitz numbers for any given Euler characteristic of the base surface and for any given set of ramification profiles.  

The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in other groups. The third concerns the connectedness of the Cremona groups.

We prove a partial converse to the main theorem of the author's previous paper "Proper affine actions: a sufficient criterion" (submitted; available at arXiv:1612.08942). More precisely, let G be a semisimple real Lie group with a representation rho on a finite-dimensional real vector space V, that does not satisfy the criterion from the previous paper. Assuming that rho is irreducible and under some additional assumptions on G and rho, we then prove that there does not exist a group of affine transformations acting properly discontinuously on V whose linear part is Zariski-dense in rho(G).

Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations helps with computing Gromov--Witten invariants, and the role of this story in Fanosearch programme. The challenge is to formulate enumerative symplectic geometry of complex 3-folds in a way suitable for extracting invariants under blowups, contractions, and transitions.

We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.

We show that G-Fano threefolds are mirror-modular. 1. Mirror maps are inversed reversed Hauptmoduln for moonshine subgroups of SL2(ℝ). 2. Quantum periods, shifted by an integer constant (eigenvalue of quantum operator on primitive cohomology) are expansions of weight 2 modular forms (theta-functions) in terms of inversed Hauptmoduln. 3. Products of inversed Hauptmoduln with some fractional powers of shifted quantum periods are very nice cuspforms (eta-quotients). The latter cuspforms also appear in work of Mason and others: they are eta-products, related to conjugacy classes of sporadic simple groups, such as Mathieu group M24 and Conway's group of isometries of Leech lattice. This gives a strange correspondence between deformation classes of G-Fano threefolds and conjugacy classes of Mathieu group M24.

Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving a reversible Markov chain to which methods previously introduced by the first author for the case of free groups may be applied.

The intransitive cycle of superiority is characterized by such binary relations between A, B, and C that A is superior to B, B is superior to C, and C is superior to A (i.e., A>B>C>A—in contrast with transitive relations A>B>C). The first part of the article presents a brief review of studies of intransitive cycles in various disciplines (mathematics, biology, sociology, logical games, decision theory, etc.), and their reflections in educational materials. The second part of the article introduces the issue of intransitivity in elementary physics. We present principles of building mechanical intransitive devices in correspondence with the structure of the Condorcet paradox, and describe five intransitive devices: intransitive gears; levers; pulleys, wheels, and axles; wedges; inclined planes. Each of the mechanisms are constructed as compositions of simple machines and show paradoxical intransitivity of relations such as “to rotate faster than”, “to lift”, “to be stronger than” in some geometrical constructions. The article is an invitation to develop teaching materials and problems advancing the understanding of transitivity and intransitivity in various areas, including physics education.

In dynamic malware analysis, programs are classified as malware or benign based on their execution logs. We propose a concept of applying monotonic classification models to the analysis process, to make the trained model's predictions consistent over execution time and provably stable to the injection of any noise or `benign-looking' activity into the program's behavior. The predictions of such models change monotonically through the log in the sense that the addition of new lines into the log may only increase the probability of the file being found malicious, which make them suitable for real-time classification on a user's machine. We evaluate monotonic neural network models based on the work by Chistyakovet al. (2017) and demonstrate that they provide stable and interpretable results.