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.

Forest ecosystems, their products and services play an important role in achieving ambitious climate change mitigation objectives at the same time requiring profound adaptation to climate change. Forest management schemes to support climate action have to be developed within their regional context but also have to be aligned with national or EU-level climate, forest and sustainability policies. The conference on “Managing forests in the 21st century” is the final conference of the FORMASAM, REFORCE and FOREXCLIM research projects. The conference bringstogether scientific experts on forest management from all over Europe facing very specific management challenges. The aim isto discuss and improve the understanding the role of forests and forest management in the context of climate change. The conference addresses climate change impacts, as well as needs for mitigation and adaptation especially with regard to the following scientific questions: 1. What are the impacts of climate extremes and disturbances? 2. What are the management challenges (and options) for resilient forests? 3. What can we do to increase the contribution of forest management to climate change mitigation?

This concise book provides a survival toolkit for efficient, large-scale software development. Discussing a multi-contextual research framework that aims to harness human-related factors in order to improve flexibility, it includes a carefully selected blend of models, methods, practices, and case studies. To investigate mission-critical communication aspects in system engineering, it also examines diverse, i.e. cross-cultural and multinational, environments.

This book helps students better organize their knowledge bases, and presents conceptual frameworks, handy practices and case-based examples of agile development in diverse environments. Together with the authors’ previous books, "Crisis Management for Software Development and Knowledge Transfer" (2016) and "Managing Software Crisis: A Smart Way to Enterprise Agility" (2018), it constitutes a comprehensive reference resource that adds value to this book.

This is the third book in a series on Medieval Novgorod and its surroundings and deals with a substantial body of animal bones that have been recovered over the last decade. The zooarchaeological evidence is discussed by the editor and a number of English and Russian specialists who dug the site, looking at domestic exploitation of animals, diet, animal husbandry, and butchery practices. Detailed data sets are provided to enable the reader to make comparisons with their own research, but the book is also suitable for those with a more general interest in Medieval Russian archaeology.

This book constitutes the proceedings of the 8th International Conference on Analysis of Images, Social Networks and Texts, AIST 2019, held in Kazan, Russia, in July 2019.

The 24 full papers and 10 short papers were carefully reviewed and selected from 134 submissions (of which 21 papers were rejected without being reviewed). The papers are organized in topical sections on general topics of data analysis; natural language processing; social network analysis; analysis of images and video; optimization problems on graphs and network structures; analysis of dynamic behaviour through event data.

This book introduces a 'Big History' perspective to understand the acceleration of social, technological and economic trends towards a near-term singularity, marking a radical turning point in the evolution of our planet. It traces the emergence of accelerating innovation rates through global history and highlights major historical transformations throughout the evolution of life, humans, and civilization. The authors pursue an interdisciplinary approach, also drawing on concepts from physics and evolutionary biology, to offer potential models of the underlying mechanisms driving this acceleration, along with potential clues on how it might progress.  The contributions gathered here are divided into five parts, the first of which studies historical mega-trends in relation to a variety of aspects including technology, population, energy, and information. The second part is dedicated to a variety of models that can help understand the potential mechanisms, and support extrapolation. In turn, the third part explores various potential future scenarios, along with the paths and decisions that are required. The fourth part presents philosophical perspectives on the potential deeper meaning and implications of the trend towards singularity, while the fifth and last part discusses the implications of the Search for Extraterrestrial Intelligence (SETI). Given its scope, the book will appeal to scholars from various disciplines interested in historical trends, technological change and evolutionary processes. 

This volume contains the refereed proceedings of the 8th International Conference on Analysis of Images, Social Networks, and Texts (AIST 2019). The previous conferences during 2012–2018 attracted a significant number of data scientists – students, researchers, academics, and engineers working on interdisciplinary data analysis of images, texts, and social networks.

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.

Offers a clear and insightful look at the state of the art in network clustering and blockmodeling Provides an excellent mix of mathematical rigor and practical application in a comprehensive manner Presents a suite of new methods, procedures, algorithms for partitioning networks, as well as new techniques for visualizing matrix arrays Features numerous examples throughout, enabling readers to gain a better understanding of research methods and to conduct their own research effectively Written by leading contributors in the field of spatial networks analysis

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.

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.​

Cancer cells require exogenous methionine for survival and therefore methionine restriction is a promising avenue for treatment. The basis for methionine dependence in cancer cells is still not entirely clear. While the lack of the methionine salvage enzyme methylthioadenosine phosphorylase (MTAP) is associated with methionine auxotrophy in cancer cells, there are other causes for tumors to require exogenous methionine. Restricting methionine by diet or by enzyme depletion, alone or in combination with certain chemotherapeutics, is a promising antitumor strategy.

Proceedings of the international conference "Neural Information Processing Systems 2019." (NeurIPS 2019)

This book constitutes the refereed proceedings of the 11th International Conference on Intelligent Data Processing, IDP 2016, held in Barcelona, Spain, in October 2016.  

 

The 11 revised full papers were carefully reviewed and selected from 52 submissions. The papers of this volume are organized in topical sections on machine learning theory with applications; intelligent data processing in life and social sciences; morphological and technological approaches to image analysis.

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided.

We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contractible space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications.

After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc.

The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

In the last 30 years a new pattern of interaction between mathematics and physics emerged, in which the latter catalyzed the creation of new mathematical theories. Most notable examples of this kind of interaction can be found in the theory of moduli spaces. In algebraic geometry the theory of moduli spaces goes back at least to Riemann, but they were first rigorously constructed by Mumford only in the 1960s. The theory has experienced an extraordinary development in recent decades, finding an increasing number of connections with other fields of mathematics and physics. In particular, moduli spaces of different objects (sheaves, instantons, curves, stable maps, etc.) have been used to construct invariants (such as Donaldson, Seiberg-Witten, Gromov-Witten, Donaldson-Thomas invariants) that solve longstanding, difficult enumerative problems. These invariants are related to the partition functions and expectation values of quantum field and string theories. In recent years, developments in both fields have led to an unprecedented cross-fertilization between geometry and physics. These striking interactions between geometry and physics were the theme of the CIME School Geometric Representation Theory and Gauge Theory. The School took place at the Grand Hotel San Michele, Cetraro, Italy, in June, Monday 25 to Friday 29, 2018. The present volume is a collection of notes of the lectures delivered at the school. It consists of three articles from Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively.

The paper provides findings of the research work and scientific discussions under the “Global Sustainability Strategy Forum” (GSSF) that aims to develop evidence-informed judgments on challenges and solutions. It views attaining sustainability as a set of closely-coupled societal and environmental challenges and opportunities that require integration of multiple disciplines, new research methods, and new knowledge sources with sensitivity to regional and cultural diversities. The project is designed to produce innovative insights and strategies to support effective governance of transitions to sustainability of our complex global social-ecological system within its inherent resource limitations, and to develop sustainable lifestyles that are practical and appealing in the different regions and cultures of the world. 

The global climate change is one of the most dangerous threats to human society in the 21st Century. The dramatic losses have already been observed, and the risks are rising over time. CEECCA region experiences many negative impacts of global warming, which is faster and stronger than the world average. Numerous adaptation and resilience measures are required to protect people, but regional governments often underestimate and ignore the social implications of climate policies.This paper explores what are the priority challenges for CEECCA countries and how to address them effectively.

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.

The crystal structures of 204 polybromides and bromine solvates were extracted from the Cambridge Structural Database and the Inorganic Crystal Structures Database. The electron density distribution was theoretically obtained for 18 selected compounds and topological analysis of the electron density by means of the R. Bader atoms in molecules (AIM) theory was performed. For the 18 compounds, the topology of networks formed by Br–Br and Br⋯Br interactions was revealed only within the AIM approach and compared with that found by means of the Voronoi tessellation. Satisfactory correlation between the description of Br⋯Br bonding within the AIM and the Voronoi approaches was found. The effect of cation size, presence of C–Br bonds and bromine content on the dimensionality of the network was studied for 204 solids using the Voronoi tessellation. The Voronoi approach demonstrated good potential to reveal extended architectures based on Br⋯Br interactions that are typical for electroconductive polybromide-based materials.

The Great Acceleration of the anthropogenic impact on the Earth system is marked by the ubiquitous distribution of anthropogenic materials throughout the global environment, including technofossils, radionuclides and the exponential increases of methane and carbon dioxide concentrations. However, personal care products as direct tracers of human domestic habits are often overlooked. Here, we present the first research combining fragrances, as novel personal care products, and polycyclic aromatic hydrocarbons (PAHs) as combustion and industrial markers, across the onset of the Great Acceleration in the Elbrus, Caucasus, ice core. This archive extends from the 1930s to 2005, spanning the profound changes in the relationship between humans and the environment during the twentieth century. Concentrations of both fragrances and PAHs rose throughout the considered period, reflecting the development of the Anthropocene. However, within this rising trend, remarkable decreases of the tracers track the major socioeconomic crises that occurred in Eastern Europe during the second half of the twentieth century.

Detection of positive selection signatures in populations around the world is helping to uncover recent human evolutionary history as well as the genetic basis of diseases. Most human evolutionary genomic studies have been performed in European, African and Asian populations. However, populations with Native American ancestry have been largely underrepresented. Here, we used a genome-wide local ancestry enrichment approach complemented with neutral simulations to identify post-admixture adaptations underwent by admixed Chileans through gene flow from Europeans into local Native Americans. The top significant hits (P = 2.4 x 10−7) are variants in a region on chromosome 12 comprising multiple regulatory elements. This region includes rs12821256, which regulates the expression of KITLG, a well-known gene involved in lighter hair and skin pigmentation in Europeans. Another variant from that region is associated with the long noncoding RNA RP11-13A1.1, which has been specifically involved in the innate immune response against infectious pathogens (Riege, et al. 2017). Our results suggest that these genes were relevant for adaption in Chileans following the Columbian exchange.

We study the propagation and stability of kink waves in a twisted magnetic tube with the flow. The flow velocity is assumed to be parallel to the magnetic field, and the magnetic field lines are straight outside the tube. The density is constant inside and outside of the tube, and it monotonically decreases from its value inside the tube to that outside in the transitional or boundary layer. The flow speed and magnetic twist monotonically decrease in the transitional layer from their values inside the tube to zero outside. Using the thin tube and thin boundary layer (TTTB) approximation, we derived the dispersion equation determining the dependence of the wave frequency and decrement/increment on the wavenumber. When the kink wave frequency coincides with the local Alfvén frequency at a resonant surface inside the transitional layer, the kink wave is subjected to either resonant damping or resonant instability. We study the properties of kink waves in a particular unperturbed state where there is no flow and magnetic twist in the transitional layer. It is shown that in a tube with flow, the kink waves can propagate without damping for particular values of the flow speed. Kink waves propagating in the flow direction either damp or propagate without damping. Waves propagating in the opposite direction can either propagate without damping, or damp, or become unstable. The theoretical results are applied to the problem of excitation of kink waves in spicules and filaments in the solar atmosphere.

A self-consistent model for the formation and evolution of dusty plasmas in the Martian ionosphere is developed. The effects of the initial distributions of dust particles, as well as condensation and absorption of carbon dioxide and water molecules by dust particles, are studied. Theory values of characteristic sizes of dust grains and their charges are obtained. The theoretical values of the sizes are in agreement with the data of observations. The possibility of the formation of dusty plasma structures in the Martian ionosphere which are analogous to noctilucent clouds in the atmosphere of the Earth is discussed.

We study dust vortices called dust devils and dynamics of dust in this structures. Dust devils are well formed relatively short-lived vortices that can appear over well heated surfaces like deserts and are clearly visible due to large amount of dust raised. Dust particles rotating in a flow bump and scrape each other and as a result particles obtain electric charges. Space separation of particles with opposite charges leads to generation of macroscopic electric field. We simulate dust dynamics with taking into account the electric field of the vortex.

This paper is a review of results on multiple flag varieties, i.e., varieties of the form G/P1×· · ·×G/Pr. We provide a classification of multiple flag varieties of complexity 0 and 1 and results on the combinatorics and geometry of B-orbits and their closures in double cominuscule flag varieties. We also discuss questions of finiteness for the number of G-orbits and existence of an open G-orbits on a multiple flag variety.

There are only 10 Euclidean forms, that is  flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of $n$-fold coverings over the orientable Euclidean manifolds $\mathcal{G}_{3}$ and $\mathcal{G}_{5}$, and calculate the numbers of non-equivalent coverings of each type. The manifolds $\mathcal{G}_{3}$ and $\mathcal{G}_{5}$ are uniquely determined among other forms by their homology groups $H_1(\mathcal{G}_{3})=\ZZ_3\times \ZZ$ and $H_1(\mathcal{G}_{5})= \ZZ$.

We classify subgroups in the fundamental groups $\pi_1(\mathcal{G}_{3})$ and $\pi_1(\mathcal{G}_{5})$ up to isomorphism.  Given index $n$,  we calculate the numbers of subgroups and the numbers of conjugacy classes of subgroups for each isomorphism type and provide the Dirichlet generating functions for the above sequences.

There are only 10 Euclidean forms, that is  flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of $n$-fold coverings over orientable Euclidean manifolds $\mathcal{G}_{2}$ and $\mathcal{G}_{4}$, and calculate the numbers of non-equivalent coverings of each type. We classify subgroups in the fundamental groups $\pi_1(\mathcal{G}_{2})$ and $\pi_1(\mathcal{G}_{4})$ up to isomorphism and calculate the numbers of conjugated classes of each type of subgroups for index $n$. The manifolds $\mathcal{G}_{2}$ and $\mathcal{G}_{4}$ are uniquely determined among the others orientable forms by their homology groups $H_1(\mathcal{G}_{2})=\ZZ_2\times \ZZ_2 \times \ZZ$ and $H_1(\mathcal{G}_{4})=\ZZ_2 \times \ZZ$.  

Subword complexes were defined by A.Knutson and E.Miller in 2004 for describing Gröbner degenerations of matrix Schubert varieties. The facets of such a complex are indexed by pipe dreams, or, equivalently, by the monomials in the corresponding Schubert polynomial. In 2017 S.Assaf and D.Searles defined a basis of slide polynomials, generalizing Stanley symmetric functions, and described a combinatorial rule for expanding Schubert polynomials in this basis. We describe a decomposition of subword complexes into strata called slide complexes, that correspond to slide polynomials. The slide complexes are shown to be homeomorphic to balls or spheres.

The properties of a two-dimensional low density (n<<1) electron system with strong onsite Hubbard attraction U>W (W is the bandwidth) in the presence of a strong random potential V uniformly distributed in the range from -V to +V are considered. Electronic hoppings only at neighboring sites on the square lattice are taken into account, thus W = 8t. The calculations were carried out for a lattice of 24x24 sites with periodic boundary conditions. In the framework of the Bogoliubov - de Gennes approach we observed an appearance of inhomogeneous states of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the matrix of the unpaired normal states.  

We study smooth Fano weighted complete intersections with respect to the new invariant -- the variance var(X) = coindex(X) - codim(X).

Given a connected reductive complex algebraic group G and a spherical subgroup H⊂G, the extended weight monoid Λˆ+G(G/H) encodes the G-module structures on spaces of regular sections of all G-linearized line bundles on G/H. Assuming that G is semisimple and simply connected and H is specified by a regular embedding in a parabolic subgroup P⊂G, in this paper we obtain a description of Λˆ+G(G/H) via the set of simple spherical roots of~G/H together with certain combinatorial data explicitly computed from the pair (P,H). As an application, we deduce a new proof of a result of Avdeev and Gorfinkel describing Λˆ+G(G/H) in the case where H is strongly solvable.

The parallel annealing method is one of the promising approaches for large scale simulations as potentially scalable on any parallel architecture. We present an implementation of the algorithm on the hybrid program architecture combining CUDA and MPI. The problem is to keep all general-purpose graphics processing unit devices as busy as possible redistributing replicas and to do that efficiently. We provide details of the testing on Intel Skylake/Nvidia V100 based hardware running in parallel more than two million replicas of the Ising model sample. The results are quite optimistic because the acceleration grows toward the perfect line with the growing complexity of the simulated system.

We introduce a class of new centrality indices in networks which take into account a para meter of a node, direct and indirect (with fixed length of the path) connections of nodes, and a group influence of nodes to a node. Total influence is evaluated as a linear combination of its components, however, other rules can be used as well.

Let P=A_1...A_n be a generic polygon in three-dimensional space and let v_1,v_2,...,v_n be vectors A_1A_2,A_2A_3,...,A_nA_1, respectively. P will be called regular, if there exist vectors u_1,...,u_n such that cross products  [u_1,u_2],[u_2,u_3],...,[u_n,u_1] are equal to vectors v_2,v_3,...,v_1, respectively. In this case the polygon P', defined be vectors u_2-u_1,u_3-u_2,...,u_1-u_n will be called the derived polygon or the derivative of the polygon P. In this work we formulate conditions for regularity and discuss geometric properties of derived polygons for n=4,5,6.

We propose a system of fermionic screening fields depending on a continuous parameter b, which defines eta-deformed OSp(n|2m) sigma-model in the limit b to infinity and a super-renormalizable QFT in b to 0. In the sigma-model regime  we show that leading UV asymptotic of the one-loop RG group flow equations coincides with perturbation around Gaussian theory. In perturbative regime b to 0 we show that the tree level two-particle scattering matrix matches the expansion of the trigonometric OSp(n|2m) R-matrix.

We review the applications of the Quantum Spectral Curve (QSC) method to the Regge (BFKL) limit in N=4 supersymmetric Yang-Mills theory.  QSC, based on quantum integrability of the AdS_5/CFT_4 duality, was initially developed as a tool for the study of the spectrum of anomalous dimensions of local operators in the N=4 SYM in the planar, N_c to infinity limit.  We explain how to apply the QSC for the BFKL limit, which requires non-trivial analytic continuation in spin S and extends the initial construction to non-local light-ray operators. We give a brief review of high precision non-perturbative numerical solutions and analytic perturbative data resulting from this approach. We also describe as a simple example of the QSC construction at the leading order in the BFKL limit. We show that the QSC substantially simplifies in this limit and reduces to the Faddeev-Korchemsky Baxter equation for Q-functions.   Finally, we review recent results for the  Fishnet CFT, which carries a number of similarities with the Lipatov's integrable spin chain for interacting reggeized gluons.

We explore whether a root lattice may be similar to the lattice $\mathscr O$ of integers  of a number field $K$ endowed with the inner product $(x, y):={\rm Trace}_{K/\mathbb Q}(x\cdot\theta(y))$, where $\theta$ is an involution of $K$. We classify all  pairs $K$, $\theta$ such that $\mathscr O$ is similar to either an even root lattice or the root lattice $\mathbb Z^{[K:\mathbb Q]}$. We also classify all  pairs $K$, $\theta$ such that $\mathscr O$ is a root lattice. In addition to this, we show that $\mathscr O$ is never similar to a positive-definite even unimodular lattice of rank $\leqslant 48$, in particular, $\mathscr O$ is not similar to the Leech lattice. In appendix, we give a general cyclicity criterion for the primary components of the discriminant group of $\mathscr O$.

Multilevel modeling (MLM, also known as hierarchical linear modeling, HLM) is a methodological frameworkwidely usedin the social sciences to analyze data with a hierarchical structure,where lower units of aggregation are ‘nested’ in higher units, including longitudinal data.In economics, however, MLM is usedvery rarely.Instead, economists use separate econometric techniques including cluster-robust standard errors and fixedeffects models. In this paper, we reviewthe methodological literature and contrast the econometrictechniques typically used in economics with the analysis ofhierarchical data using MLM. Ourreview suggests that economic techniques are generally lessconvenient, flexible, and efficientcompared to MLM. Theimportant limitation of MLM, however, isits inability to deal with the omitted variable problem at the lowest level of data, while standard economic techniques may be complemented by quasi-experimental methods mitigatingthis problem.It is unlikely, though, that this limitation can explain and justify the rare use of MLM in economics.Overall, we conclude that MLM has been unreasonably ignored in economics,and we encourage economists to apply this frameworkbyproviding ‘when and how’ guidelines.

We consider NP-hard multi{machine scheduling problems with the criterion of minimizing the maximum penalty, e.g. maximum lateness. For such problems, we introduce a metric which delivers an upper bound on the absolute error of the objective function value. Taking the given in- stance of some problem and using the introduced metric, we determine the nearest instance for which a polynomial or pseudo-polynomial algorithm is known. For this determined instance, we construct a schedule which is then applied to the original instance. It is shown how this approach is applied to di_erent scheduling problems.

Main subject of the paper is a (strong) Morse function on a compact manifold with boundary. We construct a cellular structure and discuss its algebraic properties in this paper.

Construction of new integrable systems and methods of their investigation is one of the main directions of development of the modern mathematical physics. Here we present an approach based on the study of behavior of roots of functions of canonical variables with respect to a parameter of simultaneous shift of space variables. Dynamics of singularities of the KdV and Sinh--Gordon equations, as well as rational cases of the Calogero--Moser and Ruijsenaars--Schneider models are shown to provide examples of such induced dynamics. Some other examples are given to demonstrates highly nontrivial collisions of particles and Liouville integrability of induced dynamical systems.

Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradients. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. Our proof-of-concept experiment recasts optimization over permutations as a variational optimization w.r.t. the Plackett-Luce distribution and solves it using stochastic gradient descent.

We consider quadrangles of perimeter 2 in the plane with marked directed edge. To such quadrangle  Q two-dimensional plane  P with orthonormal base is corresponded. Orthoganal plane defines  a plane quadrangle R of perimeter 2 and with marked directed edge. This quadrangle is definded uniquely ( up to rotation and symmetry ). Quadrangles Q and R will be called dual to each ather. The following properties of duality are prooved: a)duality preserves qonvexity, non convexity and self-intersection;b) duality preserves the length of diagonals; c) the sum of length of corresponding edges in Q and R is 1.l