This special conference starts the new series, and therefore, it launches a tradition to follow, and an opportunity for a rapid spin up. This ICCQ conference was organized by the HSE and leading IT innovative companies such Huawei and Yandex. The ICCQ 2021 attracted a number of renowned experts including Jens Palsberg, Anders Møller, and David West. The papers were submitted from the world over. The conference attracted speakers and attendees from the USA, Europe, and Asia; therefore, this is truly an international event. Although ICCQ started as a relatively small single-day conference, it immediately gained the IEEE support. The plan for the next years is to embrace the world while keeping high quality standards.

This book constitutes revised selected papers of the 9th International Conference on Analysis of Images, Social Networks and Texts, AIST 2020, held in Moscow, Russia, in october 2020. Due to the COVID-19 pandemic the conference was held online. 

The 14 full papers, 9 short papers and 4 poster papers were carefully reviewed and selected from 108 qualified submissions. The papers are organized in topical sections on ​natural language processing; computer vision; social network analysis; data analysis and machine learning; theoretical machine learning and optimization; process mining; posters.

We discuss the applicability of multiphase lattice Boltzmann method for the simulation of the drop oscillation. We demonstrate that the simulation of the single drop excited to the first eigenmode does follow Rayleigh formula. Simulations show no sensitivity to the number of the discrete velocities with D3Q19 and D3Q27 representations of the distribution function in three dimensions. The boundaries do influent the motion of the drop—division of the computational area by the even and the odd number of cells comes out important and leads to symmetry violence. The second part of the chapter describes the oscillations of the ensemble of three drops due to the excitation of the central drop in the first eigenmode. The motion of the backdrops does strongly depend on the viscosity of the fluid. We provide future details of simulations.

The relevance of studying the regulation of protein-ligand interactions is due to the emergence of new views on the role of metabolites and their key importance in vital processes. To study the protein-ligand interaction, the AB0 antigen-antibody blood system and the enzyme-substrate system of dehydrogenases were used as a test system, and ethanol was used as an influencing factor. In experiments performed with A and B blood erythrocyte antigens, natural AB0 system antibodies and monoclonal antibodies under the influence of ethanol performed change of the degree of agglutination and the time to onset of erythrocyte agglutination. It was found that ethanol can regulate the enzyme-substrate interactions of dehydrogenases: lactate dehydrogenase (EC 1.1.1.27), glyceraldehyde phosphate dehydrogenase (EC 1.1.1.12), and α-glycerol phosphate dehydrogenase (EC 1.1.1.8). The increase in the activity of studied enzymes under the influence of ethanol in the whole blood hemolysate was 2.5 - 3 times higher than in the isolated medium (with pure enzyme preparations).

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.

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.

This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.

The Volume includes a Special Section on "Analytical and Computational Methods in Probability"

The materials of the 5th International conference on stochastic methods are presented including the following directions: probability and statistics (analytic modelling, asymptotic methods and limit theorems, stochastic analysis, Markov processes and martingales, actuarial and financial mathematics, et al.); applications of stochastic methods (queueing theory and stochastic networks, reliability theory and risk analysis, probability in indistry, economics and other areas, computer science and computer networks, machine learning and data analysis, etc.).

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.

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

In the paper, three algorithms for predicting protein side-chain conformations are suggested and discussed. All proposed approaches analyze the local neighborhood of the target residue to avoid'steric clashes'. Strong and weak points of the algorithms are described, and ways of improving their outcomes are suggested. The approach based on predicting conformations for all residues in a protein chain segment appears to be the most promising.

We derive a quadratic recursion relation for the linear Hodge integrals of the form $⟨τ_2^nλ_k⟩$. These numbers are used in a formula for Masur-Veech volumes of moduli spaces of quadratic differentials discovered by Chen, Möller and Sauvaget. Therefore, our recursion provides an efficient way of computing these volumes.

A novel method for finding roots of polynomials over finite fields has been proposed. This method is based on the cyclotomic discrete Fourier transform algorithm. The improvement is achieved by using the normalized cyclic convolutions, which have a small complexity and allow matrix decomposition, as well as methods of adapting the truncated normalized cyclic convolutions calculation. For small values of degree of the error-locator polynomial the novel method has not only the smallest multiplicative complexity, but the full computational complexity of this method is also less than with other methods. Thus, the multiplicative complexity of the novel method in comparison to the method of affine decomposition (the Fedorenko-Trifonov method) is up to ten times less, although the additive complexity is approximately 10-15\% more. The novel method has matrix representation convenient for implementation.

A complete description of trees with maximal possible number of maximum independent setsamong all 𝑛-vertex trees with exactly 𝑙 leaves is obtained. For all values of the parameters 𝑛 and 𝑙, the extremal tree is unique and is the result of merging the endpoints of 𝑙 simple paths.

A systematic study of the phosphine additives influence on the activity of a ruthenium catalyst in reductive amination without an external hydrogen source was carried out. [CymeneRuCl2]2 was used as a reference catalyst, and a broad set of phosphines including Alk3P, Alk2ArP, Ar3P and X3P was screened. Three complexes of general formula (Cymene)RuCl2PR3 were isolated in a pure form, and their catalytic activity was compared with the in situ generated complexes. Nonhindered triarylphosphines with electron acceptor groups were found to be the most perspective activating agents, increasing the activity of the catalyst approx. six times, Alk2ArP ligands have less noticeable influence, while trialkylphosphines strongly deactivate the ruthenium catalyst.

A systematic study of the phosphine additives influence on the activity of a ruthenium catalyst in reductive amination without an external hydrogen source was carried out. [CymeneRuCl2]2 was used as a reference catalyst, and a broad set of phosphines including Alk3P, Alk2ArP, Ar3P and X3P was screened. Three complexes of general formula (Cymene)RuCl2PR3 were isolated in a pure form, and their catalytic activity was compared with the in situ generated complexes. Nonhindered triarylphosphines with electron acceptor groups were found to be the most perspective activating agents, increasing the activity of the catalyst approx. six times, Alk2ArP ligands have less noticeable influence, while trialkylphosphines strongly deactivate the ruthenium catalyst.

The Keap1-Nrf2 signaling axis is a validated and promising target for cellular defense and survival pathways. This minireview discusses the potential off-target effects and their impact on future drug development originating from Keap1-targeting small molecules that function as displacement activators of the redox-sensitive transcription factor Nrf2. We argue that small-molecule displacement activators, similarly to electrophiles, will release both Nrf2 and other Keap1 client proteins from the ubiquitin ligase complex. This non-specificity is likely unavoidable and may result in off-target effects during Nrf2 activation by targeting Keap1. The small molecule displacement activators may also target Kelch domains in proteins other than Keap1, causing additional off-target effects unless designed to ensure specificity for the Kelch domain only in Keap1. A potentially promising and alternative therapeutic approach to overcome this non-specificity emerging from targeting Keap1 is to inhibit the Nrf2 repressor Bach1 for constitutive activation of the Nrf2 pathway and bypass the Keap1-Nrf2 complex.

We investigate a well-known phenomenon of the appearance of the crossover points, corresponding to the intersections of the solubility isotherms of the solid compound in supercritical fluid. Opposed to the accepted understanding of the existence of two fixed crossover points, which confine the region of the inverse isobaric temperature dependence of the solubility, we have found that these points tend to shift with the change of the temperature and in the limit of the certain threshold value they converge to a single point. We demonstrate this analyzing the solubility data of a set of poorly soluble drug compounds, which have been computed in a wide area of the phase diagram via the approach, based on the classical density functional theory. Thorough analysis of the available in the literature experimental solubility data is found to be in an agreement with our conclusions, as one can find that the wider temperature region of the experimental study is, the more pronounced effect of the crossover points drift can be observed.

We study singularities of optimal solutions in a problem of controlling the Timoshenko beam vibrations. The Timoshenko beam vibrations are described by a system of two coupled hyperbolic equations. Controls are introduced as external bounded forces. We consider the problem of minimizing the mean square deviation of the Timoshenko beam from the equilibrium position. For some initial conditions we reduce this problem to the optimal control problem for ordinary differential equations. We study the case of two-dimensional controls. For some initial positions of the beam, we prove that the optimal solutions have a Fuller type singularity. We give an asymptotic representation of the corresponding family of optimal trajectories.

The guarantee of an anonymous mechanism is the worst case welfare an agent can secure against unanimously adversarial others. How high can such a guarantee be, and what type of mechanism achieves it? We address the worst case design question in the n-person probabilistic voting/bargaining model with p deterministic outcomes. If n is no less than p the uniform lottery is the only maximal (unimprovable) guarantee; there are many more if p>n, in particular the ones inspired by the random dictator mechanism and by voting by veto. If n=2 the maximal set M(n,p) is a simple polytope where each vertex combines a round of vetoes with one of random dictatorship. For p>n>2, we show that the dual veto and random dictator guarantees, together with the uniform one, are the building blocks of 2 to the power d simplices of dimension d in M(n,p), where d is the quotient of p-1 by n. Their vertices are guarantees easy to interpret and implement. The set M(n,p) may contain other guarantees as well; what we can say in full generality is that it is a finite union of polytopes, all sharing the uniform guarantee.

Convergence of order O(1/ √ n) is obtained for the distance in total variation between the Poisson distribution and the distribution of the number of fixed size cycles in generalized random graphs with random vertex weights. The weights are assumed to be independent identically distributed random variables which have a power-law distribution. The proof is based on the Chen–Stein approach and on the derived properties of the ratio of the sum of squares of random variables and the sum of these variables. These properties can be applied to other asymptotic problems related to generalized random graphs

A general scenario for an N-sequential conclusive state discrimination introduced recently in Loubenets and Namkung [arXiv:2102.04747] can provide a multipartite quantum communication realizable in the presence of a noise. In the present article, we propose a new experimental scheme for the implementation of a sequential conclusive discrimination between binary coherent states via indirect measurements within the Jaynes-Cummings interaction model. We find that if the mean photon number is less than 1.6, then, for our two-sequential state discrimination scheme, the optimal success probability is larger than the one presented in Fields, Varga, and Bergou [2020, IEEE Int. Conf. Quant. Eng. Comp.]. We also show that, if the mean photon number is almost equal to 1.2, then the optimal success probability nearly approaches the Helstrom bound.

In the present article, we consistently develop the main issues of the Bloch vectors formalism for an arbitrary finite-dimensional quantum system. In the frame of this formalism, qudit states and their evolution in time, qudit observables and their expectations, entanglement and nonlocality, etc. are expressed in terms of the Bloch vectors -- the vectors in the Euclidean space R^{d²-1}, arising under decompositions of observables and states in different operator bases. Within this formalism, we specify for all d≥2 the set of Bloch vectors of traceless qudit observables and describe its properties; also, find for the sets of the Bloch vectors of qudit states, pure and mixed, the new compact expressions in terms of the operator norms that explicitly reveal the general properties of these sets and have the unified form for all d≥2. For the sets of the Bloch vectors of qudit states under the generalized Gell-Mann representation, these general properties cannot be analytically extracted from the known equivalent specifications of these sets via the system of algebraic equations. We derive the general equations describing the time evolution of the Bloch vector of a qudit state if a qudit system is isolated and if it is open and find for both cases the main properties of the Bloch vector evolution in time. For a pure bipartite state of a dimension d₁×d₂, we quantify its entanglement via the characteristics of the Bloch vectors for its reduced states. The introduced general formalism is important both for the theoretical analysis of quantum system properties and for quantum applications, in particular, for optimal quantum control, since, for systems where states are described by vectors in the Euclidean space, the methods of optimal control, analytical and numerical, are well developed.

We estimate the n-gram entropies of English- language texts, using dictionaries and taking into account punctuation, and find a heuristic method for estimating the marginal entropy. We propose a method for evaluating the coverage of empirically generated dictionaries and an ap- proach to address the disadvantage of low coverage. In ad- dition, we compare the probability of obtaining a meaning- ful text by directly iterating through all possible n-grams of the alphabet and conclude that this is only possible for very short text segments.

Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.

We show existence of a natural rational structure on periodic cyclic homology, conjectured by L. Katzarkov, M. Kontsevich, T. Pantev, for several classes of dg-categories, including proper connective C-dg-algebras and dg-categories of local systems. The main ingredient is derived nilpotent invariance of A. Blanc's semi-topological K-theory, which we establish along the way.

Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest caliber. Here we study population annealing using as the main example the two-dimensional Ising model which allows for particularly clean comparisons due to the available exact results and the wealth of published simulational studies employing other approaches. We analyze in depth the accuracy and precision of the method, highlighting its relation to older techniques such as simulated annealing and thermodynamic integration. We introduce intrinsic approaches for the analysis of statistical and systematic errors and provide a detailed picture of the dependence of such errors on the simulation parameters. The results are benchmarked against canonical and parallel tempering simulations.

Recent chain-like structured materials have shown a robust superconducting phase. These materials exhibit the presence of quasi-one-dimensional bands (q1D) coupled to conventional higher-dimensional bands. On the mean-field level such systems have a high critical temperature when the chemical potential is close to the edge of a q1D band and the related Lifshitz transition is approached. However, the impact of the pair fluctuations compromises the mean-field results. Recently it has been demonstrated that these fluctuations can be suppressed (screened) by a specific multiband mechanism based on the pair-exchange coupling of the q1D condensate to a stable higher-dimensional one. In the present work we demonstrate that strikingly enough, this mechanism is not very sensitive to the basic parameters of the stable condensate such as its strength and dimensionality. For example, even the presence of a passive higher-dimensional band, which does not exhibit any superconducting correlations when taken as a separate superconductor, results in suppression of the pair fluctuations.

We prove that a finite 3-group in the Cremona group Cr_3(ℂ) can be generated by at most 4 elements. This provides the last missing piece in bounding the ranks of finite p-subgroups in the space Cremona group.

We consider an initial-boundary value problem for the $n$-dimensional wave equation with the variable sound speed, $n\geq 1$. We construct three-level implicit in time compact in space (three-point in each space direction) 4th order finite-difference schemes on the uniform rectangular meshes including their one-parameter (for $n=2$) and three-parameter (for $n=3$) families. They are closely connected to some methods and schemes constructed recently by several authors. In a unified manner, we prove the conditional stability of schemes in the strong and weak energy norms together with the 4th order error estimate under natural conditions on the time step. We also give an example of extending a compact scheme for non-uniform in space and time rectangular meshes. We suggest simple effective iterative methods based on FFT to implement the schemes whose convergence rate, under the stability condition, is fast and independent on both the meshes and variable sound speed. A new effective initial guess to start iterations is given too. We also present promising results of numerical experiments.

We present the construction of an original stochastic model for the instantaneous turbulent kinetic energy at a given point of a flow, and we validate estimator methods on this model with observational data examples. Motivated by the need for wind energy industry of acquiring relevant statistical information of air motion at a local place, we adopt the Lagrangian description of fluid flows to derive, from the 3D+time equations of the physics, a 0D+time-stochastic model for the time series of the instantaneous turbulent kinetic energy at a given position. Specifically, based on the Lagrangian stochastic description of a generic fluid-particles, we derive a family of mean-field dynamics featuring the square norm of the turbulent velocity. By approximating at equilibrium the characteristic nonlinear terms of the dynamics, we recover the so called Cox-Ingersoll-Ross process, which was previously suggested in the literature for modelling wind speed. We then propose a calibration procedure for the parameters employing both direct methods and Bayesian inference. In particular, we show the consistency of the estimators and validate the model through the quantification of uncertainty, with respect to the range of values given in the literature for some physical constants of turbulence modelling.

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.

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.

We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. These graphs encode degenerations of curves to rational curves, and graph potentials encode degenerations of the moduli space of rank 2 bundles with fixed determinant. We show that the birational type of the graph potential only depends on the homotopy type of the colored graph, and thus define a topological quantum field theory. By analyzing toric degenerations of the moduli spaces we explain how graph potentials are related to these moduli spaces in the setting of mirror symmetry for Fano varieties.  On the level of enumerative mirror symmetry this shows how invariants of graph potentials are related to Gromov-Witten invariants of the moduli space. In the context of homological mirror symmetry we formulate a conjecture regarding the shape of semiorthogonal decompositions for the derived category. Studying the properties of graph potentials we provide evidence for this conjecture. Finally, by studying the Grothendieck rings of varieties and categories we will give further geometric evidence.

The aim of this note is to investigate the relation between two types of non-singular projective varieties of Picard rank 2, namely the Projective bundles over Projective spaces and certain Blow-up of Projective spaces.

We provide a variant of an axiomatization of elementary geometry based on logical axioms in the spirit of Huzita--Justin axioms for the Origami constructions. We isolate the fragments corresponding to natural classes of Origami constructions such as Pythagorean, Euclidean, and full Origami constructions. The sets of Origami constructible points for each of the classes of constructions provides the minimal model of the corresponding set of logical axioms. Our axiomatizations are based on Wu's axioms for orthogonal geometry and some modifications of Huzita--Justin axioms. We work out bi-interpretations between these logical theories and theories of fields as described in J.A. Makowsky (2018). Using a theorem of M. Ziegler (1982) which implies that the first order theory of Vieta fields is undecidable, we conclude that the first order theory of our axiomatization of Origami is also undecidable.

The injection of a long piece of flexible rod into a two-dimensional domain yields a complex pattern commonly studied through elasticity theory, packing analysis, and fractal geometries. "Loop" is an one-vertex entity which which is naturally formed in this system. The role of the elastic features of each individual loop in 2D packing has not yet been discussed. In this work we point out how the shape of a given loop in the complex structure allows to estimate local deformations and forces. First, we build sets of symmetric free loops and performed compression experiments. Then, tight packing configurations are analyzed by using image processing. We found that the dimensions of the loops, confined or not, obey the same dependence on the deformation. The result is consistent with a simple model based on 2D elastic theory for filaments, where the rod adopts the shape of Euler's elasticas between its contact points. The force and the stored energy are obtained from numerical integration of the analytic expressions. In an additional experiment, we obtain that the compression force for deformed loops corroborates the theoretical findings. The importance of the shape of the loop is discussed and we hope that the theoretical curves may allow statistical considerations in future investigations.