7th International School and Conference "Saint-Petersburg OPEN 2020" on Optoelectronics, Photonics, Engineering and Nanostructures was held on April 27 - 30, 2020. The Organizer of the conference is the Alferov Federal State Budgetary Institution of Higher Education and Science Saint Petersburg National Research Academic University of the Russian Academy of Sciences. Initially, the School and Conference was supposed to be held in full-time format at the Alferov Academic University (Saint-Petersburg, Russia), as it happened in the past. However, due to the restrictions imposed by the city authorities on holding mass events due to the threat of the spread of the COVID-19 infection, the conference committees decided to move the conference to the online format. The conference consisted of poster reports presented by the participants and online oral presentations by invited speakers. Posters and video reports of the participants were posted on the conference website. Invited speakers made their presentations online. During their speeches, participants could discuss and ask questions in the chat. The School and Conference included a series of invited talks given by leading professors with the aim to introduce young scientists with actual problems and major advances in physics and technology.

This textbook on political geography is devoted to a discipline concerned with the spatial dimensions of politics. This course is an introduction to the study of political science, international relations and area studies, providing a systemic approach to the spatial dimension of political processes at all levels. It covers their basic elements, including states, supranational unions, geopolitical systems, regions, borders, capitals, dependent, and internationally administered territories. Political geography develops fundamental theoretical approaches that give insight into the peculiarities of foreign and domestic policies. The ability to use spatial analysis techniques allows determining patterns and regularities of political phenomena both at the global and the regional and local levels.

The article suggests the integration of a neural network as a parallel element base in a telecommunication system. In this case, the ability to learn or adapt to external conditions is applied as the main advantage. For telecommunication systems in conditions when it is possible, this ability will improve noise immunity, reliability, operability, etc. The article considers an example of the integration of a neural network into a discrete matched signal filter. It is noted that the use of parallel mathematical methods in signal processing leads to the maximum effect of increasing the quality parameters of such telecommunication elements

Artificial intelligence and machine learning helps to improve the quality of customer service and change the methods of companies’ activities. For this reason, enterprises should consider integrating these technologies into digital transformation plans to remain competitive. Low-code machine learning platforms allow companies and business professionals with minimal coding experience to create applications and fill in the gaps of the personnel in their organization. Automated machine leaning (AutoML) technology represents the next step in the evolution of machine learning, providing non-technical companies with the ability to create machine learning applications quickly and cheaply

The article discusses the possibilities of studying the state of the social sphere according to the repository of the Moscow Government open data portal by administrative districts and city districts using Business Intelligence Platforms and Data Science and Machine Learning Platforms intellectual technologies. Opportunities are presented for using machine learning technologies for business analytics platforms to identify hidden patterns in order to make informed management decisions

Contents Authors................................................................................................................................ 7 Acknowledgements............................................................................................................9 Executive summary ........................................................................................................... 11 1. Introduction....................................................................................................................13 Riccardo Valentini, Pekka Leskinen, Pieter Johannes Verkerk, Gert-Jan Nabuurs, George Safonov and Elena Kulikova 2. State of Russian forests and forestry............................................................................17 Dmitry Zamolodchikov, Anatoly Shvidenko, Sergey Bartalev, Elena Kulikova, Alexander Held, Riccardo Valentini and Marcus Lindner 2.1 Major characteristics of Russian forests..........................................................17 2.2 Natural forest disturbances.............................................................................. 21 2.3 Forest governance and use..............................................................................26 2.4 Ecosystem functions and services of Russia’s forests....................................28 2.5 Key challenges in forest resource management..............................................35 2.6 Key messages.................................................................................................... 38 3. Climate change in Russia – past, present and future................................................. 45 Riccardo Valentini, Dmitry Zamolodchikov, Christopher Reyer, Sergio Noce, Monia Santini and Marcus Lindner 3.1 Observed changes of Russian climate in recent decades.............................. 45 3.2 Climate change scenarios................................................................................48 3.3 Key messages.....................................................................................................51 4. Climate change and Russian forests: impacts, vulnerability and adaptation needs... 53 Christopher Reyer, Marcus Lindner, Dmitry Zamolodchikov, Anatoly Shvidenko, Martin Gutsch and Sergey Bartalev 4.1 Observed impacts of climate change...............................................................53 4.2 Projected impacts.............................................................................................56 4.3 Vulnerability assessment................................................................................. 61 4.4 Adaptation needs............................................................................................. 64 4.5 Key messages....................................................................................................67

5. Climate-Smart Forestry in Russia and potential climate change mitigation benefits.............................................................................................................................. 73 Bas Lerink, Mariana Hassegawa, Alexander Kryshen, Anton Kovalev, Eldar Kurbanov, Gert-Jan Nabuurs, Sergei Moshnikov and Pieter Johannes Verkerk 5.1 Introduction...................................................................................................... 73 5.2 Approach and general scenario assumptions.................................................74 5.3 Case study: Republic of Karelia.......................................................................78 5.4 Case study: Republic of Mari El.......................................................................84 5.5 Case study: Angara macro-district (Krasnoyarsk kray).................................. 91 5.6 Concluding remarks, discussion and implications....................................... 98 5.7 Key messages...................................................................................................101 6. The role of the bioeconomy in climate change mitigation in Russia..................... 105 Pekka Leskinen, Jo Van Brusselen, Mariana Hassegawa, Alexander Alekseev, Natalia Lukina, Olga Rakitova, George Safonov, Elena Kulikova and Mikhail Safonov 6.1 Introduction.................................................................................................... 105 6.2 The bioeconomy concept in Russia...............................................................106 6.3 The link between bioeconomy and climate change mitigation.................. 107 6.4 State of Russian forest industry and potential for bioeconomy................... 111 6.5 Sectoral development and outlook................................................................. 113 6.6 Summary and conclusions: Opportunities and challenges for a bioeconomy in Russia.....................................................................................123 6.7 Key messages...................................................................................................125 7. Conclusions.................................................................................................................. 131 Pekka Leskinen, Jo Van Brusselen, Marcus Lindner, Gert-Jan Nabuurs, Pieter Johannes Verkerk, Natalia Lukina, Sergey Bartalev and Elena Kulikova 7.1 Forest resources............................................................................................... 131 7.2 Climate change impacts, adaptation and mitigation....................................132 7.3 Forest management........................................................................................ 133 7.4 Enabling environment for a bioeconomy......................................................134 7.5 Holistic view.................................................................................................... 135 7.6 Key messages and next steps ........................................................................ 136

Logic has found application in virtually all aspects of Information Technology, from software engineering and hardware to programming and artificial intelligence. Indeed, logic, artificial intelligence and theoretical computing are influencing each other to the extent that a new interdisciplinary area of Logic and Computation is emerging.

The Journal of Logic and Computation aims to promote the growth of logic and computing, including, among others, the following areas of interest: Logical Systems, such as classical and non-classical logic, constructive logic, categorical logic, modal logic, type theory, feasible maths.... Logical issues in logic programming, knowledge-based systems and automated reasoning; logical issues in knowledge representation, such as non-monotonic reasoning and systems of knowledge and belief; logics and semantics of programming; specification and verification of programs and systems; applications of logic in hardware and VLSI, natural language, concurrent computation, planning, and databases.

This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves.

This book focuses on crisis management in software development which includes forecasting, responding and adaptive engineering models, methods, patterns and practices. It helps the stakeholders in understanding and identifying the key technology, business and human factors that may result in a software production crisis. These factors are particularly important for the enterprise-scale applications, typically considered very complex in managerial and technological aspects and therefore, specifically addressed by the discipline of software engineering. Therefore, this book throws light on the crisis responsive, resilient methodologies and practices; therewith, it also focuses on their evolutionary changes and the resulting benefits.

Proceedings of Machine Learning Research: Volume 119: International Conference on Machine Learning, 12-18 July 2020

The 24th European Conference on Advances in Databases and Information Systems (ADBIS 2020) was set to be held in Lyon, France, during August 25–28, 2020, in conjunction with the 24th International Conference on Theory and Practice of Digital Libraries (TPDL 2020) and the 16th EDA days on Business Intelligence & Big Data (EDA 2020). However, because of the worldwide COVID-19 crisis, ADBIS, TPDL, and EDA had to take place online during August 25–27, 2020. Yet, the three con- ferences joined their forces to propose common keynotes, workshops, and a Doctoral Consortium.  

The 24th European Conference on Advances in Databases and Information Systems (ADBIS 2020) was set to be held in Lyon, France, during August 25–28, 2020, in conjunction with the 24th International Conference on Theory and Practice of Digital Libraries (TPDL 2020) and the 16th EDA days on Business Intelligence & Big Data (EDA 2020). However, because of the worldwide COVID-19 crisis, ADBIS, TPDL, and EDA had to take place online during August 25–27, 2020. Yet, the three con- ferences joined their forces to propose common keynotes, workshops, and a Doctoral Consortium.

This CCIS volume published by Springer contains the post-proceedings of the XXI International Conference on Data Analytics and Management in Data Intensive Domains (DAMDID/RCDL 2019) that took place during October 15–18 at the Kazan Federal University, Russia.

DAMDID is held as a multidisciplinary forum of researchers and practitioners from various domains of science and research, promoting cooperation and exchange of ideas in the area of data analysis and management in domains driven by data-intensive research. Approaches to data analysis and management being developed in specific data-intensive domains (DID) of X-informatics (such as X = astro, bio, chemo, geo, med, neuro, physics, chemistry, material science, etc.), social sciences, as well as in various branches of informatics, industry, new technologies, finance, and business are expected to contribute to the conference content.

Proceedings of the SPIE PHOTONICS EUROPE Conference on Biophotonics in Point-of-Care, 6-10 April 2020, Online Only, France. Proc. SPIE volume 11361

This book studies complex systems with elements represented by random variables. Its main goal is to study and compare uncertainty of algorithms of network structure identification with applications to market network analysis. For this, a mathematical model of random variable network is introduced, uncertainty of identification procedure is defined through a risk function, random variables networks with different measures of similarity (dependence) are discussed, and general statistical properties of identification algorithms are studied. The volume also introduces a new class of identification algorithms based on a new measure of similarity and prove its robustness in a large class of distributions, and presents applications to social networks, power transmission grids, telecommunication networks, stock market networks, and brain networks through a theoretical analysis that identifies network structures. Both researchers and graduate students in computer science, mathematics, and optimization will find the applications and techniques presented useful.

 

For many peripheral membrane-binding proteins (MBPs), especially β-structural ones, the precise molecular mechanisms of membrane insertion remain unclear. In most cases, only the terminal water-soluble and membrane-bound states have been elucidated, whereas potential functionally important intermediate stages are still not understood in sufficient detail. In this study we present one of the first successful attempts to describe step-by-step embedding of the MBP cardiotoxin 2 (CT2) from cobra N. oxiana venom into a lipid bilayer at the atomistic level. CT2 possesses a highly conservative and rigid b-structured three-finger fold shared by many other exogenous and endogenous proteins performing a wide variety of functions. Incorporation of CT2 into the lipid bilayer was analyzed via a 2-μs all-atom molecular dynamics (MD) simulation without restraints. This process was shown to occur over a number of distinct steps, while the geometry of initial membrane attachment drastically differs from the final equilibrated state. In the latter one, the hydrophobic platform (“bottom”) formed by the tips of the three loops is deeply buried into the lipid bilayer. This agrees well with the NMR data obtained earlier for CT2 in detergent micelles. However, the bottom is too bulky to insert itself into the membrane at once. Instead, gradual immersion of CT2 initiated by the loop-1 was observed. This initial binding stage was also demonstrated in a series of MD runs with varying starting orientations of the toxin with respect to the bilayer surface. Apart from non-specific long-range electrostatic attraction and hydrophobic match/mismatch factor, several specific lipid binding sites were identified in CT2. They were shown to promote membrane insertion by engaging in strong interactions with lipid head groups, fine-tuning the toxin-membrane accommodation. We therefore propose that the toxin insertion relies on an interplay of nonspecific and specific interactions, which are determined by the “dynamic molecular portraits” of the two players, the protein and the membrane. The proposed model does not require protein oligomerization for membrane insertion and can be further employed to design MBPs with predetermined properties with regard to particular membrane targets.

Artists can represent a 3D object by using only contours in a 2D drawing. Prior studies have shown that people can use such drawings to perceive 3D shapes reliably, but it is not clear how useful this kind of contour information actually is in a real dynamical scene in which people interact with objects. To address this issue, we developed an Augmented Reality (AR) device that can show a participant a contour-drawing or a grayscale-image of a real dynamical scene in an immersive manner. We compared the performance of people in a variety of run-of-the-mill tasks with both contour-drawings and grayscale-images under natural viewing conditions in three behavioral experiments. The results of these experiments showed that the people could perform almost equally well with both types of images. This contour information may be sufficient to provide the basis for our visual system to obtain much of the 3D information needed for successful visuomotor interactions in our everyday life.

We consider a spatially distributed evolutionary game based on the Prisoner’s Dilemma with agents arranged on a three-dimensional simple cubic lattice. Comparing to two- dimensional arrangements, we find that the larger number of neighbors favors the formation of spatial chaos: the steady state of the game is chaotic unless the payoff parameter is small.

We consider a dynamic version of the HP model of a linear polymer: a self-avoiding walk on the square lattice, with monomers being either hydrophobic (H) or polar (P). We simulate the model in two dimensions in the grand canonical assemble via the Berretti-Sokal algorithm across the globule-coil transition and map out the phase diagram. Our results are consistent with the universality class of the transition being the same as the universality class of the theta-transition of an interacting self-avoiding walk.

Modern large-scale data-farms consist of hundreds of thousands of storage devices that span distributed infrastructure. Devices used in modern data centers (such as controllers, links, SSD- and HDD-disks) can fail due to hardware as well as software problems. Such failures or anomalies can be detected by monitoring the activity of components using machine learning techniques. In order to use these techniques, researchers need plenty of historical data of devices in normal and failure mode for training algorithms. In this work, we challenge two problems: 1) lack of storage data in the methods above by creating a simulator and 2) applying existing online algorithms that can faster detect a failure occurred in one of the components.

We created a Go-based (golang) package for simulating the behavior of modern storage infrastructure. The software is based on the discrete-event modeling paradigm and captures the structure and dynamics of high-level storage system building blocks. The package's exible structure allows us to create a model of a real-world storage system with a configurable number of components. The primary area of interest is exploring the storage machine's behavior under stress testing or exploitation in the medium-or long-term for observing failures of its components.

To discover failures in the time series distribution generated by the simulator, we modified a change point detection algorithm that works in online mode. The goal of the change-point detection is to discover differences in time series distribution. This work describes an approach for failure detection in time series data based on direct density ratio estimation via binary classifiers.

Today art museum is facing the challenge of adapting it’s mechanisms of keeping and presenting the works of art to spectators belonging to the communication society. Therefore, a museum gets more and more engaged in the process of digitalization using such newer technologies as internet of things, virtual reality, artificial intelligence, bid data design etc. The aims of a museum are currently shifting from traditional keeping the art pieces and studying them to—developing a scientific networks, announcing the highlights in social media and creating platforms which present digitalized pieces online allowing a viewer to collect the information through the web, moreover, an offline visit could be guided by a specified application customized to fit the necessitates of each user. An art institution today is supposed to be flexible and democratic enough to create an engaging, immersive area for a visitor to interact with, in other words, we argue that a museum armed with newer technologies is supposed not only a to secure and present the works of art but also to incorporate these pieces into the bigger flux of information, make them visible and important to viewers, to create the conditions for a lasting dialogue. We argue that this process involves not only the technical development of a museum, but also a new approach no narration of art history.

Anomalous behavior of spin stiffness is revealed in ZnO-based two-dimensional electron systems (2DESs) with strong Coulomb interaction and Wigner-Seitz parameter r_s > 6. The spin stiffness is extracted directly from the quadratic k-dispersion of spin excitons at ν = 1 probed by inelastic light scattering. The resulting values are found to be dramatically rescaled compared to the case of weakly interacting 2DESs—spin stiffness turned out to be of the order of the cyclotron energy with the effective mass of Fermi-liquid quasiparticles. This result is also confirmed by the exact diagonalization simulations.

We propose a novel algorithm for the construction of the sparse, nonetheless, the massive and rigid structure. The generated structures possess two significant properties reminiscent of the metallic foams. Firstly, the weight of the structures can be as low as the percent of the bulk one. Secondly, the structures are mechanically rigid. The structures are necessary for the simulation of the physical models of the foam properties.

Although the high-pressure phase diagram of carbon at extreme temperatures and pressures is in focus of theoretical and experimental dynamic compression studies, there still exist outstanding problems including disagreement between theoretical predictions and experiments. Using first-principles molecular dynamics simulations at high temperatures and pressures and employing large unit cells, we construct an accurate phase diagram of carbon using two-phase and Z-methods. In accord with previous simulations, a large positive slope of the melting line is observed for pressures from 0 to 200 GPa, whereas at pressures above 500 GPa a very small negative slope exists, which is in contrast to most of previous simulations and experiment. Our accurate results demonstrate the necessity for future dynamic compression experiments to clarify behavior of carbon at extreme conditions including its melting line.

Let M be the space of triangles, defined up to shifts, rotations and dilations. We define two maps f:M->M and g:M->M.  The map f corresponds to a triangle of perimeter pi the triangle with angles numerically equal to edges of the initial triangle. The map g corresponds to a triangle of perimeter 2pi the triangle with exterior angles numerically equal to edges of the initial triangle. For p in M the sequence {p,f(p),f(f(p)),...} converges to the equilateral triangle and the sequence {p,g(p),g(g(p)),...} converges to the "degenerate triangle" with angles (0,0,pi). In Supplement an analogous problem about inscribed-circumscribed quadrangles is discussed.

In the following paper we investigate the critical temperature Tc behavior in the two-dimensional S/TI (S denotes superconductor and TI - topological insulator) junction with a proximity induced in-plane helical magnetization in the TI surface. The calculations of Tc are performed using the general self-consistent approach based on the Usadel equations in Matsubara Green's functions technique. We show that the presence of the helical magnetization leads to the nonmonotonic behavior of the critical temperature as a function of the topological insulator layer thickness.

  An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same level of a Hamiltonian and two non-symmetric heteroclinic orbits permuted by the involution. This is a co- dimension one structure and therefore it can be met generally in one-parameter families of reversible Hamiltonian systems. There exist two possible types of such connections in dependence on how the involution acts near the equilibrium. We prove a series of theorems which show a chaotic behavior of the system and those in its unfoldings, in particular, the existence of countable sets of transverse homoclinic orbits to the saddle periodic orbit in the critical level, transverse heteroclinic connections involving a pair of saddle periodic orbits, families of elliptic periodic orbits, homoclinic tangencies, families of homoclinic orbits to saddle-centers in the unfolding, etc. As a byproduct, we get a criterion of the existence of homoclinic orbits to a saddle-center.  

We introduce a notion of a topologically flat locally convex module, which extends the notion of a flat Banach module and which is well adapted to the nonmetrizable setting (and especially to the setting of DF-modules). By using this notion, we introduce topologically amenable locally convex algebras and we show that a complete barrelled DF-algebra is topologically amenable if and only if it is Johnson amenable, extending thereby Helemskii-Sheinberg's criterion for Banach algebras. As an application, we completely characterize topologically amenable Köthe co-echelon algebras.

Paul Chernoff in 1968 proposed his approach to approximations of one-parameter operator semigroups while trying to give a rigorous mathematical meaning to Feynman's path integral formulation of quantum mechanics. In early 2000's Oleg Smolyanov noticed that Chernoff's theorem may be used to obtain approximations to solutions of initial-value problems for linear partial differential equations (LPDEs) of evolution type with variable coefficients, including parabolic equations, Schr\"odinger equation, and some other. Chernoff expressions are explicit formulas containing variable coefficients of LPDE and the initial condition, hence they can be used as a numerical method for solving LPDEs. However, the speed of convergence of such approximations at the present time is understudied which makes it risky to employ this class of numerical methods. In the present paper we take two equations with known solutions (heat equation and transport equation) and study both analytically and numerically the speed of decay of the norm of the difference between Chernoff approximations and exact solutions. We also provide graphical illustrations of convergence and its rate. These model examples, being relatively simple, allow to demonstrate general properties of Chernoff approximations. The observations obtained build a base for the future employment of the approach based on Chernoff's theorem to the problem of construction of new numerical methods for solving initial-value problem for parabolic LPDEs with variable coefficients.

Abstract. The method of Chernoff approximation was discovered by Paul Chernoff in 1968 and now is a powerful and flexible tool of contemporary  functional analysis. This method is different from grid-based approach and helps to solve numerically the Cauchy problem for evolution equations, e.g., for heat equation and for more general parabolic second-order partial differential equations with variable coefficients. The case of heat equation is well-studied and does not require any approximations because Green's function is known in that case; but for more general equations exact formulas for solutions are unknown, so numerical approximations of solutions are often requested by engineers and other researchers dealing with PDEs. Chernoff approximations are functions defined by explicit expressions that contain variable  coefficients of the equation and initial condition as parameters. Traditionally researchers construct Chernoff approximations with the use of integral operators which lead to Feynman formulas that are connected with representation of solution in terms of Feynman path integral and Feynman-Kac formulas. This traditional approach has two features that restrict its practical use. First, one needs to integrate over the Cartesian product of $n$ copies of the real line hence $n$-tuple integrals are improper (for better quality of approximation one needs to take larger values of $n$, and this leads to improper integrals of high multiplicity which are difficult to handle in practice). Second, the speed of convergence usually is not very high (not better than $1/n$).  In the present paper we construct Chernoff approximations of a new kind which are free from these disadvantages: all integrals in our formulas are over the segment $[-1,1]$, and the speed of convergence is higher than $1/n$ for  initial conditions that are smooth enough. Our approximations provide solution in a form of quasi-Feynman formula which is not clearly connected with Feynman integral but is much better for practical purposes.

This short communication (preprint) is devoted to mathematical study of evolution equations that are important for mathematical physics and quantum theory; we present new explicit formulas for solutions of these equations and discuss their properties. The results are given without proofs but the proofs will appear in the longer text which is now under preparation. In this paper, infinite-dimensional generalizations of the Euclidean analogue of the Schrödinger equation for anharmonic oscillator are considered in the class of measures. The Cauchy problem for these equations is solved. In particular cases, explicit formulas for fundamental solutions are obtained, which are a generalization of the Mehler formula, and the uniqueness of the solution with certain properties is proved. An analogue of the Ornstein-Uhlenbeck measure is constructed. The definition of Gaussian semigroups is given and their connection with the considered parabolic equations is described.

We present 1.5D Vlasov code simulations of the dynamics of electron holes in non-uniform magnetic and electric fields typical of current sheets and, particularly, of the Earth's magnetotail current sheet. The simulations show that spatial width and amplitude of electron holes do not substantially vary in the course of propagation, but there arises a double layer localized around the electron hole and manifested as a drop of the electrostatic potential along the electron hole. We demonstrate that electron holes produced around the neutral plane of a current sheet slow down in the course of propagation toward the current sheet boundaries. The leading contribution to electron hole braking is provided by the non-uniform magnetic field, though electrostatic fields typical of the current sheets do provide a noticeable contribution. The simulations also show that electron holes with larger amplitudes are slowed faster. The simulation results suggest that some of slow electron holes recently reported in the Earth's plasma sheet boundary layer may appear due to braking of initially fast electron holes in the course of propagation in the current sheet.

The basic automorphism group   of a Cartan foliation (M, F) is the quotient group of the automorphism group of (M, F) by the normal subgroup, which preserves every leaf invariant. For Cartan foliations covered by fibrations, we find sufficient conditions for the existence of a structure of a finite-dimensional Lie group in their basic automorphism groups. Estimates of the dimension of these groups are obtained. For some class of Cartan foliations with integrable an Ehresmann connection, a method for finding of basic automorphism groups is specified.

We prove that maximal log Fano manifolds are generalized Bott towers. As an application, we prove that in each dimension, there is a unique maximal snc Fano variety satisfying Friedman's d-semistability condition.

We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the $n$-dimensional non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by both the classical Numerov approach and alternative technique based on averaging of the equation, together with further necessary improvements of the arising scheme for $n\geq 2$. The alternative technique is applicable to other types of PDEs including parabolic and time-dependent Schr\"{o}dinger ones. The schemes are implicit and three-point in each spatial direction and time and include a scheme with a splitting operator for $n\geq 2$. For $n=1$ and the mesh on characteristics, the 4th order scheme becomes explicit and close to an exact four-point scheme. We present a conditional stability theorem covering the cases of stability in strong and weak energy norms with respect to both initial functions and free term in the equation. Its corollary ensures the 4th order error bound in the case of smooth solutions to the IBVP. The main schemes are generalized for non-uniform rectangular meshes. We also give results of numerical experiments showing the sensitive dependence of the error orders in three norms on the weak smoothness order of the initial functions and free term and essential advantages over the 2nd approximation order schemes in the non-smooth case as well.

We study family of dynamical systems on 2-torus modeling over-damped Josephson junction in superconductivity. It depends on three parameters (B,A;ω): B (abscissa), A(ordinate), ω (a fixed frequency).We study the rotation numberρ(B,A;ω) as a function of (B,A) withfixedω. Aphase-lock areais the level set Lr:={ρ=r}, if it has an on-empty interior. This holds for r∈Z (a result by V.M.Buchstaber, O.V.Karpov and S.I.Tertychnyi). It is known that each phase-lock area is an infinite garland of domains going to infinity in the vertical direction and separated by points called constrictions (expect for the separation points with A= 0). We show that all the constrictions in Lr lie in its axis {B=ωr}, confirming an experimental fact (conjecture) observed numerically by S.I.Tertychnyi, V.A.Kleptsyn, D.A.Filimonov, I.V.Schurov. We prove that each constriction is positive: the phase-lock area germ contains the vertical line germ (confirming another conjecture). To do this, we study family of linear systems on the Riemann sphere equivalently describing the model: the Josephson type systems.We study their Jimbo isomonodromic deformations described by solutions of Painleve 3 equations. Using results of this study and a Riemann–Hilbert approach, we show that each constriction can be analytically deformed to constrictions with the same l:=Bω and arbitrarily small ω. Then non-existence of ”ghost” constrictions (nonpositive or with ρ not equal to l) with a given l for small ω is proved by slow-fast methods.

Real-time estimation of the parameters characterising infectious disease transmission is important for optimization quarantine interventions during outbreaks. One of the most significant parameters is the effective reproduction number - number of secondary cases produced by a single infection. The current study presents an approach for estimating the effective reproduction number and its application to COVID-19 outbreak. The method is based on fitting SIR epidemic model to observation data in a sliding time window and allows to show real-time dynamics of reproduction number at any phase of epidemic for countries globally. Online data on COVID-19 daily cases of infections, recoveries, deaths are used.Finally, time-dependent reproduction number is explored in connection with dynamics of peoples mobility. The method allows to assess the disease transmission potential and understand the effect of interventions on epidemics spread. It also can be easily adapted to future outbreaks of different pathogens. The tool is available online as Python code from the Github repository.

For Milnor, statistical, and minimal attractors, we construct examples of smooth flows φ on S^2 for which the attractor of the Cartesian square of φ is smaller than the Cartesian square of the attractor of φ. In the example for the minimal attractors, the flow φ also has an SRB-measure such that its square does not coincide with an SRB-measure of the square of φ.

The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples, which are not multiple zeta series, are Tornheim sums. We show that convergent big zeta values are periods of the moduli space of stable curves of genus zero on one hand and multiple zeta values on the other hand. It gives an alternative way to prove that any such period may be expressed as a rational linear combination of multiple zeta values and a simple algorithm for finding such an expression.

Electroencephalography (EEG) is a well-established non-invasive technique to measure the brain activity, albeit with a limited spatial resolution. Variations in electric conductivity between different tissues distort the electric fields generated by cortical sources, resulting in smeared potential measurements on the scalp. One needs to solve an ill-posed inverse problem to recover the original neural activity. In this article, we present a generic method of recovering the cortical potentials from the EEG measurement by introducing a new inverse-problem solver based on deep Convolutional Neural Networks (CNN) in paired (U-Net) and unpaired (DualGAN) configurations. The solvers were trained on synthetic EEG-ECoG pairs that were generated using a head conductivity model computed using the Finite Element Method (FEM). These solvers are the first of their kind, that provide robust translation of EEG data to the cortex surface using deep learning. Providing a fast and accurate interpretation of the tracked EEG signal, our approach promises a boost to the spatial resolution of the future EEG devices.  

Missing genotypes can affect the effcacy of machine learning approaches to identify the risk genetic variants of common diseases and traits. The problem occurs when genotypic data are collected from different experiments with different DNA microarrays, each being characterised by its pattern of uncalled (missing) genotypes. This can prevent the machine learning classifier from assigning the classes correctly. To tackle this issue, we used well-developed notions of object-attribute biclusters and formal concepts that correspond to dense subrelations in the binary relation patients x SNPs. The paper contains experimental results on applying a biclustering algorithm to a large real-world dataset collected for studying the genetic bases of ischemic stroke. The algorithm could identify large dense biclusters in the genotypic matrix for further processing, which in return significantly improved the quality of machine learning classifiers. The proposed algorithm was also able to generate biclusters for the whole dataset without size constraints in comparison to the In-Close4 algorithm for generation of formal concepts.

In this paper, we describe versions of triclustering algorithms adapted for efficient calculations in distributed environments with MapReduce model or parallelisation mechanism provided by modern programming languages. OAC-family of triclustering algorithms shows good parallelisation capabilities due to the independent processing of triples of a triadic formal context. We provide the time and space complexity of the algorithms and justify their relevance. We also compare performance gain from using a distributed system and scalability.