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 International Workshop on Enterprise and Organizational Modeling and Simulation (EOMAS) represents a forum where researchers and practitioners exchange and mutually enrich their views, approaches, and obtain results in the field of enterprise engineering and enterprise architecture. The most valuable asset of every conference and workshop is its community. The community of EOMAS is small, but it consists of founding members, long-term contributors, and every year it attracts new innovative participants. This year, EOMAS reached its 15th edition and took place in Rome, Italy, during June 3–4, 2019. Traditionally, we can offer a balanced assortment of papers addressing formal foundations of enterprise modeling and simulation, conceptual modeling approaches, higher-level insights and applications bringing novel ideas to traditional approaches, as well as new emerging trends. Out of 24 submitted papers, 12 were accepted for publication as full papers and for oral presentation, and each paper was carefully selected, reviewed, and revised. In additional to this we reflected on the interest of last year’s invited workshop on usability and invited the experts to make a sequel. You can find a short report in this issue. This year, we included a novel outlet of Master and Doctoral Consortium, which attracted young talent to present their work. The presented work was then discussed, and feedback, advice, and encouragement was given. We were really surprised by the relevance, methodological quality, and results of their work – you may find their contributions on our website https://eomas-workshop.org. We would like to express our sincere thanks to the entire EOMAS community: the authors, the Program Committee and the CAiSE organizers, the chairs for their enthusiasm and devotion, as well as all participants for their contributions. We look forward to the 16th edition of EOMAS!

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.

Hybrid membranes were prepared by incorporating silica with propyl-imidazoline groups in polybenzimidazoles (phthalide-containing PBI or PBI based on 2,6- or 2,5-pyridinedicarboxylic acids). The influence effects of the silica precursor hydrolysis conditions on the conductivity of the hybrid membranes are studied. Ionic conductivity, water uptake, phosphoric acid doping, and gas permeability of the obtained materials were found to depend on the preparation method and the silica loading. The materials with 10 wt% of functionalized silica present the highest conductivity. A decrease of hydrogen permeability is observed for low silica loadings.

Using the integral transformation, the field-theoretical Hamiltonian of the statistical field theory of fluids is obtained, along with the microscopic expressions for the coefficients of the Hamiltonian. Applying this approach to the liquid-vapor interface, we derive an explicit analytical expression for the surface tension in terms of temperature, density and parameters of inter-molecular potential. We also demonstrate that a clear physical interpretation may be given to the formal statistical field arising in the integral transformation – it may be associated with the one-body local microscopic potential. The results of the theory, lacking any ad-hoc or fitting parameters are in a good agreement with available simulation data.

Topic modeling is a popular technique for clustering large collections of text documents. A variety of different types of regularization is implemented in topic modeling. In this paper, we propose a novel approach for analyzing the influence of different regularization types on results of topic modeling. Based on Renyi entropy, this approach is inspired by the concepts from statistical physics, where an inferred topical structure of a collection can be considered an information statistical system residing in a non-equilibrium state. By testing our approach on four models—Probabilistic Latent Semantic Analysis (pLSA), Additive Regularization of Topic Models (BigARTM), Latent Dirichlet Allocation (LDA) with Gibbs sampling, LDA with variational inference (VLDA)—we, first of all, show that the minimum of Renyi entropy coincides with the “true” number of topics, as determined in two labelled collections. Simultaneously, we find that Hierarchical Dirichlet Process (HDP) model as a well-known approach for topic number optimization fails to detect such optimum. Next, we demonstrate that large values of the regularization coefficient in BigARTM significantly shift the minimum of entropy from the topic number optimum, which effect is not observed for hyper-parameters in LDA with Gibbs sampling. We conclude that regularization may introduce unpredictable distortions into topic models that need further research.

t is known that the turbulence in a fast-rotating volume becomes effectively two- dimensional. The latter is characterized by an inverse energy cascade leading to the formation of coherent flow in finite systems. In a rotating three-dimensional vessel this flow has the form of columnar vortices. Here we develop an analytical theory describing interaction of the vortex with turbulent pulsations. This interaction results in energy transfer from small-scale eddies to the large-scale vortex. We derive the equation for the radial velocity profile of the vortex and solve it for the simplest boundary conditions. We indicate the domain of physical parameters where our theory works.

Existence, weak uniqueness, and Markov - Dobrushin's conditions are established for Markov solutions of highly degenerate stochastic differential equations.

Aim of the work was to study the influence of different brain rhythms (i.e. theta, beta, gamma ranges with frequencies from 5 to 80 Hz) on the ultraslow oscillations with frequency of 0.5 Hz and below, where high and low activity states alternate. Ultraslow oscillations are usually observed within neural activity in the human brain and in the prefrontal cortex in particular during rest. Ultraslow oscillations are considered to be generated by local cortical circuitry together with pulse-like inputs and neuronal noise. Structure of ultraslow oscillations shows specific statistics and their characteristics has been connected with cognitive abilities, such as working memory performance and capacity. Methods. In the study we used previously constructed computational model describing activity of a cortical circuit consisting of the populations of pyramidal cells and interneurons. This model was developed to mimic global input impinging on the local prefrontal cortex circuit from other cortical areas or subcortical structures. The model dynamics was studied numerically. Results. We found that frequency increase deferentially lengthens the up states and therefore increases stability of self-sustained activity with oscillations in the gamma band. Discussion. We argue that such effects would be beneficial to information processing and transfer in cortical networks with hierarchical inhibition.

We consider two-dimensional turbulence in the presence of a condensate. The nondiagonal correlation functions of the Lagrangian accelerations are calculated, and it is shown that they have the same universality properties as the nondiagonal correlation functions of the velocity fluctuations.

The term Big Data refers to an extensive collections of digital data generating every second. Produced datasets come in structured, semi-structured, and unstructured formats throughout the world, which is difficult for the traditional database management systems to analyze. Recently, big data analytics emerges as an essential research area due to the popularity of the Internet and the advent of new Web technologies. This growing area of research represents a multi-disciplinary that attracts researchers from various research fields. Interested researchers are invited to design, develop, and implement several tools, technologies, architecture, and platforms for analyzing these large volumes of data. This paper begins with a brief introduction to big data and related concepts, including the main characteristics of big data, followed by discussions of the most significant open research challenges and emerging trends. Next, we review a study of big data analytics, the advantages of using big data solutions, and the preliminary assessments required before migrating from traditional solutions. Finally, we present a review of the recent main applications to obtain a broad perspective of big data analytics.  

We present the European Russia Drought Atlas (ERDA) that covers the East European Plain to the Ural Mountains from 1400–2016 CE. Like the Old World Drought Atlas (OWDA) for the Euro-Mediterranean region, the ERDA is a one-half degree gridded reconstruction of summer Palmer Drought Severity Indices estimated from a network of annual tree-ring chronologies. Ensemble point-by-point regression is used to generate the ERDA with the identical protocols used for developing the OWDA. Split calibration/validation tests of the ERDA indicate that it has significant skill over most of its domain and is much more skillful than the OWDA where they overlap in the western part of ERDA domain. Comparisons to historical droughts over European Russia additionally support the ERDA’s overall validity. The ERDA has been spatially smoothed and infilled using a local regression method to yield a spatially complete drought atlas back to 1400 CE. EOF analysis indicates that there are three principal modes of hydroclimatic variability in the ERDA. After Varimax rotation, these modes correlate significantly with independent climate data sets extending back to the late nineteenth century in a physically interpretable way and relate to atmospheric circulation dynamics of droughts and heatwaves over European Russia based on more recent instrumental data.

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 $\mathscr O$.

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

Presburger Arithmetic PrA is the true theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and establish various necessary and sucient conditions for interpretability depending on dimension n of interpretation. We note this problem is relevant to the interpretations of Presburger Arithmetic in itself, as well as the characterization of automatic orderings. For n = 2 we obtain the complete criterion of interpretability.

We consider quadrangles of perimeter 2 in the plane with marked directed edge. To such quadrangle $Q$ a two-dimensional plane $\Pi\in\mathbb{R}^4$ with orthonormal base is corresponded. Orthogonal plane $\Pi^bot$ defines a plane quadrangle $Q^\circ$ of perimeter 2 and with marked directed edge. This quadrangle is defined uniquely (up to rotation and symmetry). Quadrangles $Q$ and $Q^\circ$ will be called dual to each other. The following properties of duality are proved: a) duality preserves convexity, non convexity and self-intersection; b) duality preserves the length of diagonals; c) the sum of lengths of corresponding edges in $Q$ and $Q^\circ$ is 1.

Interactions between vortices in thin superconducting films are investigated in the crossover (intertype) regime between superconductivity types I and II. We consider two main factors responsible for this crossover: a) changes in the material characteristics of the film and b) variations of the film thickness controlling the effect of the stray magnetic fields outside superconducting sample. The analysis is done within the formalism that combines the perturbation expansion of the microscopic equations to one order beyond the Ginzburg-Landau theory with the leading contribution of the stray fields. It is shown that the latter gives rise to qualitatively different spatial profile and temperature dependence of the vortex interaction potential, as compared to bulk vortex interactions. The resulting interaction is long-range repulsive while exhibiting complex competition of attraction and repulsion at small and intermediate separations of vortices. This explains the appearance of vortex chains reported earlier for superconducting films.

Buchstaber and Terzic introduced a notion of universal space of parameters F for a manifold M^2n, which has an effective action of compact torus T^k , k≤n with some additional properties. with special properties. This space is needed to construction of factor M^2n/T^k. Buchstaber and Terzic constructed the universal space of parameters for G_5,2. In this work we construct universal space of parameters for complex Grassmann manifold G_q+1,2. Our construction is based on the construction of moduli space of stable curves of genus zero with q+1 marked points due to Salamon, McDuff and Hofer.

Let G be a complex Lie group acting on a compact complex Hermitian manifold M by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result to compute the Dolbeault cohomology of Vaisman manifolds.

Motivated by the Chern-Weil theory, we prove that for a given vector bundle E on a smooth scheme X over a field k of any characteristic, the Chern classes of E in the Hodge cohomology can be recovered from the Atiyah class. Although this problem was solved by Illusie in \cite{i}, we present another proof by means of derived algebraic geometry.  Also, for a scheme X over a field k of characteristic p with a vector bundle E we construct elements c^cris_n(E,α(E))∈H^2n_dR(X) using an obstruction α(E) to a lifting of F∗E to a crystal modulo p2 and prove that c^cris_n(E,α(E))=n!⋅c^dR_n(E), where cdRn(E)are the Chern classes of E in the de Rham cohomology and F is the Frobenius map.

Sasakian manifolds are odd-dimensional counterpart to Kahler manifolds. They can be defined as contact manifolds equipped with an invariant Kahler structure on their symplectic cone. The quotient of this cone by the homothety action is a complex manifold called Vaisman. We study harmonic forms and Hodge decomposition on Vaisman and Sasakian manifolds. We construct a Lie superalgebra associated to a Sasakian manifold in the same way as the Kahler supersymmetry algebra is associated to a Kahler manifold. We use this construction to produce a self-contained, coordinate-free proof of the results by Tachibana, Kashiwada and Sato on the decomposition of harmonic forms and cohomology of Sasakian and Vaisman manifolds. In the last section, we compute the supersymmetry algebra of Sasakian manifolds explicitly.

We construct a mirabolic analogue of the geometric Satake equivalence. We also prove an equivalence that relates representations of a supergroup with the category of GL(N−1,ℂ[[t]])-equivariant perverse sheaves on the affine Grassmannian of GL_N. We explain how our equivalences fit into a more general conjectural framework proposed by D. Gaiotto.