## Mathematics

We propose a novel machine-learning-based approach to detect bid leakage in first-price sealed-bid auctions. We extract and analyze the data on more than 1.4 million Russian procurement auctions between 2014 and 2018. As bid leakage in each particular auction is tacit, the direct classification is impossible. Instead, we reduce the problem of bid leakage detection to Positive-Unlabeled Classification. The key idea is to regard the losing participants as fair and the winners as possibly corrupted. This allows us to estimate the prior probability of bid leakage in the sample, as well as the posterior probability of bid leakage for each specific auction. We find that at least 16% of auctions are exposed to bid leakage. Bid leakage is more likely in auctions with a higher reserve price, lower number of bidders and lower price fall, and where the winning bid is received in the last hour before the deadline.

Workshop concentrates on an interdisciplinary approach to modelling human behavior incorporating data mining and expert knowledge from behavioral sciences. Data analysis results extracted from clean data of laboratory experiments will be compared with noisy industrial datasets from the web e.g. Insights from behavioral sciences will help data scientists. Behavior scientists will see new inspirations to research from industrial data science. Market leaders in Big Data, as Microsoft, Facebook, and Google, have already realized the importance of experimental economics know-how for their business.

In Experimental Economics, although financial rewards restrict subjects preferences in experiments, exclusive application of analytical game theory is not enough to explain the collected data. It calls for the development and evaluation of more sophisticated models. The more data is used for evaluation, the more statistical significance can be achieved. Since large amounts of behavioral data are required to scan for regularities, along with automated agents needed to simulate and intervene in human interactions, Machine Learning is the tool of choice for research in Experimental Economics. This workshop is aimed at bringing together researchers from both Data Analysis and Economics in order to achieve mutually beneficial results.

This is an advanced text on ordinary differential equations (ODES) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It yields the concise exposition of the fundamentals with the fast, but rigorous and systematic transition to the up-fronts of modern research in linear and nonlinear partial and pseudo-differential equations, general kinetic equations and fractional evolutions. The level of generality is chosen to be suitable for the study of the most important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii, Vlasov, Landau-Fokker-Planck, Cahn-Hilliard, Hamilton-Jacobi-Bellman, nonlinear Schroedinger, McKean-Vlasov diffusions and their nonlocal extensions, mass-action-law kinetics from chemistry. It also covers nonlinear evolutions arising in evolutionary biology and mean-field games, optimization theory, epidemics and system biology, in general models of interacting particles or agents describing splitting and merging, collisions and breakage, mutations and the preferential-attachment growth on networks. The book is meant for final year undergraduate and postgraduate students and researchers in differential equations and their applications. A significant amount of attention is paid to the interconnections between various topics revealing where and how a particular result is used in other chapters or may be used in other contexts, as well as to the clarification of the links between the languages of pseudo-differential operators, generalized functions, operator theory, abstract linear spaces, fractional calculus and path integrals.

**Provides an overview of the developments and advances in the field of network clustering and blockmodeling over the last 10 years**

This book offers an integrated treatment of network clustering and blockmodeling, covering all of the newest approaches and methods that have been developed over the last decade. Presented in a comprehensive manner, it offers the foundations for understanding network structures and processes, and features a wide variety of new techniques addressing issues that occur during the partitioning of networks across multiple disciplines such as community detection, blockmodeling of valued networks, role assignment, and stochastic blockmodeling.

Written by a team of international experts in the field, *Advances in Network Clustering and Blockmodeling *offers a plethora of diverse perspectives covering topics such as: bibliometric analyses of the network clustering literature; clustering approaches to networks; label propagation for clustering; and treating missing network data before partitioning. It also examines the partitioning of signed networks, multimode networks, and linked networks. A chapter on structured networks and coarsegrained descriptions is presented, along with another on scientific coauthorship networks. The book finishes with a section covering conclusions and directions for future work. In addition, the editors provide numerous tables, figures, case studies, examples, datasets, and more.

*Advances in Network Clustering and Blockmodeling *is an ideal book for graduate and undergraduate students taking courses on network analysis or working with networks using real data. It will also benefit researchers and practitioners interested in network analysis.

Modal logics, both propositional and predicate, have been used in computer science since the late 1970s. One of the most important properties of modal logics of relevance to their applications in computer science is the complexity of their satisﬁability problem. The complexity of satisﬁability for modal logics is rather high: it ranges from NP-complete to undecidable for propositional logics and is undecidable for predicate logics. This has, for a long time, motivated research in drawing the borderline between tractable and intractable fragments of propositional modal logics as well as between decidable and undecidable fragments of predicate modal logics. In the present thesis, we investigate some very natural restrictions on the languages of propositional and predicate modal logics and show that placing those restrictions does not decrease complexity of satisﬁability. For propositional languages, we consider restricting the number of propositional variables allowed in the construction of formulas, while for predicate languages, we consider restricting the number of individual variables as well as the number and arity of predicate letters allowed in the construction of formulas. We develop original techniques, which build on and develop the techniques known from the literature, for proving that satisﬁability for a ﬁnite-variable fragment of a propositional modal logic is as computationally hard as satisﬁability for the logic in the full language and adapt those techniques to predicate modal logics and prove undecidability of fragments of such logics in the language with a ﬁnite number of unary predicate letters as well as restrictions on the number of individual variables. The thesis is based on four articles published or accepted for publication. They concern propositional dynamic logics, propositional branchingand alternating-time temporal logics, propositional logics of symmetric rela tions, and ﬁrst-order predicate modal and intuitionistic logics. In all cases, we identify the “minimal,” with regard to the criteria mentioned above, fragments whose satisﬁability is as computationally hard as satisﬁability for the entire logic.

This book deals with mathematical modeling, namely, it describes the mathematical model of heat transfer in a silicon cathode of small (nano) dimensions with the possibility of partial melting taken into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type free boundary problems. The approach used is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the mathematical model including its parallel implementation. The results of numerical simulation concludes the book. The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.

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 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.

In this work we construct and discuss special solutions of a homogeneous problem for the Laplace equation in a domain with the cone-shaped boundaries. The problem at hand is interpreted as that describing oscillatory linear wave movement of a uid under gravity in such a domain. These so- lutions are found in terms of the Mellin transform and by means of the reduction to some new functional-difference equations solved in an explicit form (in quadratures). The behavior of the so- lutions at far distances is studied by use of the saddle point technique. The corresponding eigenoscil- lations of a uid are then interpreted as eigenfunctions of the continuous spectrum.

The monograph provides a detailed presentation of the theory of weak convergence of measures.

The Third Workshop on Computer Modelling in Decision Making (CMDM 2018) was held in Saratov State University (Saratov, Russia) within the VII International Youth Research and Practice Conference ‘Mathematical and Computer Modelling in Economics, Insurance and Risk Management’. The workshop 's main topic is computer and mathematical modeling in decision making in finance, insurance, banking, economic forecasting, investment and financial analysis. Researchers, postgraduate students, academics as well as financial, bank, insurance and government workers participated in the Workshop.

This work discusses a possibility to assess the probability of company default using system dynamic model. This approach is based on Monte Carlo Simulation with various inputs for a system dynamic model. The results are compared with the estimations of rating agencies.

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.

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 constitutes the proceedings of the 7th International Conference on Analysis of Images, Social Networks and Texts, AIST 2018, held in Moscow, Russia, in July 2018.

The 29 full papers were carefully reviewed and selected from 107 submissions (of which 26 papers were rejected without being reviewed). The papers are organized in topical sections on natural language processing; analysis of images and video; general topics of data analysis; analysis of dynamic behavior through event data; optimization problems on graphs and network structures; and innovative systems.

We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration.

Given a holomorphic conic bundle without sections, we show that the orders of finite groups acting by its fiberwise bimeromorphic transformations are bounded. This provides an analog of a similar result obtained by Bandman and Zarhin for quasi-projective conic bundles.

We propose an accelerated gradient-free method with a non-Euclidean proximal operator associated with the *p*-norm (1 ⩽ *p* ⩽ 2). We obtain estimates for the rate of convergence of the method under low noise arising in the calculation of the function value. We present the results of computational experiments.

We discuss the quantization of the ̂ sl 2 coset vertex operator algebra W D(2,1;α) using the bosonization technique. We show that after quantization, there exist three families of commuting integrals of motion coming from three copies of the quantum toroidal algebra associated with gl 2 .

On a Fock space constructed from mn free bosons and lattice Z mn , we give a level n action of the quantum toroidal algebra E m associated to gl m , together with a level m action of the quantum toroidal algebra E n associated to gl n . We prove that the E m transfer matrices commute with the E n transfer matrices after an appropriate identification of parameters.

We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G=(V,E), with local rewards r:E→Z, and three types of positions: black VB, white VW, and random VR forming a partition of *V*. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, or not, even when |VR|=0. In fact, a pseudo-polynomial algorithm for BWR-games would already imply their polynomial solvability. In this paper,1 we show that BWR-games with a constant number of random positions can be solved in pseudo-polynomial time. More precisely, in any BWR-game with |VR|=O(1), a saddle point in uniformly optimal pure stationary strategies can be found in time polynomial in |VW|+|VB|, the maximum absolute local reward, and the common denominator of the transition probabilities.

A hypergraph is Sperner if no hyperedge contains another one. A Sperner hypergraph is equilizable (resp., threshold) if the characteristic vectors of its hyperedges are the (minimal) binary solutions to a linear equation (resp., inequality) with positive coefficients. These combinatorial notions have many applications and are motivated by the theory of Boolean functions and integer programming. We introduce in this paper the class of 1-Sperner hypergraphs, defined by the property that for every two hyperedges the smallest of their two set differences is of size one. We characterize this class of Sperner hypergraphs by a decomposition theorem and derive several consequences from it. In particular, we obtain bounds on the size of 1-Sperner hypergraphs and their transversal hypergraphs, show that the characteristic vectors of the hyperedges are linearly independent over the reals, and prove that 1-Sperner hypergraphs are both threshold and equilizable. The study of 1-Sperner hypergraphs is motivated also by their applications in graph theory, which we present in a companion paper.

The work is devoted to the problem of enumerating maps on an orientable or non-orientable surface of a given genus g up to all symmetries (so called unsensed maps). We obtain general formulas which reduce the problem of counting such maps to the problem of enumerating rooted quotient maps on orbifolds. In addition, we solve the problem of describing all cyclic orbifolds for a given orientable or non-orientable surface of fixed genus g. We also derive recurrence relations for quotient rooted maps on orbifolds that can be orientable or non-orientable surfaces with r branch points, h boundary components and g handles or cross-caps. These results allowed us to calculate the numbers of unsensed maps on orientable or non-orientable surfaces of arbitrary genus g by the number of edges.

Any compact body with regular boundary in *R^N* defines a two-valued function on the

space of affine hyperplanes: the volumes of the two parts into which these hyperplanes cut the body.

This function is never algebraic if N is even and is very rarely algebraic if N is odd: all known bodies

defining algebraic volume functions are ellipsoids (and have been essentially found by Archimedes

for *N = 3*). We demonstrate a new series of *locally* algebraically integrable bodies with algebraic

boundaries in spaces of arbitrary dimensions, that is, of bodies such that the corresponding volume

functions coincide with algebraic ones in some open domains of the space of hyperplanes intersecting

the body.