St. Petersburg Department of Steklov Institute of Mathematics

The lion's share of bacteria in various environments cannot be cloned in the laboratory and thus cannot be sequenced using existing technologies. A major goal of single-cell genomics is to complement gene-centric metagenomic data with whole-genome assemblies of uncultivated organisms. Assembly of single-cell data is challenging because of highly non-uniform read coverage as well as elevated levels of sequencing errors and chimeric reads. We describe SPAdes, a new assembler for both single-cell and standard (multicell) assembly, and demonstrate that it improves on the recently released E+V-SC assembler (specialized for single-cell data) and on popular assemblers Velvet and SoapDeNovo (for multicell data). SPAdes generates single-cell assemblies, providing information about genomes of uncultivatable bacteria that vastly exceeds what may be obtained via traditional metagenomics studies. SPAdes is available online ( http://bioinf.spbau.ru/spades ). It is distributed as open source software.

Metric Spaces Length Spaces Constructions Spaces of Bounded Curvature Smooth Length Structures Curvature of Riemannian Metrics Space of Metric Spaces Large-scale Geometry Spaces of Curvature Bounded Above Spaces of Curvature Bounded Below Bibliography Index.

The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Gordon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians. The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results. The book will be essential reading for all mathematical physicists working in field theory and statistical physics.

The book contain detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well. Main Models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models. Heisenberg Antiferromagnet and Hubbard models. It is explained in detail, how to calculate correlation functions.

The impact of the marketing function on firm performance has been the focus of much recent research in marketing. Thus, the effect of marketing capability on firm performance, compared with that of other capabilities, such as research and development and operations, is an issue of importance to managers. To examine this issue and generate empirical generalizations, the authors conduct a meta-analysis of the firm capability–performance relationship using a mixed-effects model. The results show that, in general, marketing capability has a stronger impact on firm performance than research-and-development and operations capabilities. The results provide guidelines for managers and generate directions for further research.

OBJECTIVES: Analysis of dental radiographs is an important part of the diagnostic process in daily clinical practice. Interpretation by an expert includes teeth detection and numbering. In this project, a novel solution based on convolutional neural networks (CNNs) is proposed that performs this task automatically for panoramic radiographs. METHODS: A data set of 1352 randomly chosen panoramic radiographs of adults was used to train the system. The CNN-based architectures for both teeth detection and numbering tasks were analyzed. The teeth detection module processes the radiograph to define the boundaries of each tooth. It is based on the state-of-the-art Faster R-CNN architecture. The teeth numbering module classifies detected teeth images according to the FDI notation. It utilizes the classical VGG-16 CNN together with the heuristic algorithm to improve results according to the rules for spatial arrangement of teeth. A separate testing set of 222 images was used to evaluate the performance of the system and to compare it to the expert level. RESULTS: For the teeth detection task, the system achieves the following performance metrics: a sensitivity of 0.9941 and a precision of 0.9945. For teeth numbering, its sensitivity is 0.9800 and specificity is 0.9994. Experts detect teeth with a sensitivity of 0.9980 and a precision of 0.9998. Their sensitivity for tooth numbering is 0.9893 and specificity is 0.9997. The detailed error analysis showed that the developed software system makes errors caused by similar factors as those for experts. CONCLUSIONS: The performance of the proposed computer-aided diagnosis solution is comparable to the level of experts. Based on these findings, the method has the potential for practical application and further evaluation for automated dental radiograph analysis. Computer-aided teeth detection and numbering simplifies the process of filling out digital dental charts. Automation could help to save time and improve the completeness of electronic dental records.

This book describes the theory and selected applications of one of the most important mathematical tools used in the theoretical investigation of collective excitations in statistical physics, such as occur in superfluidity, superconductivity, plasma dynamics, superradiation, and in phase transitions. The author, who is a distinguished physicist and leading researcher in this area, begins with an introduction to functional integral techniques in equilibrium statistical thermodynamics, and discusses the expression of partition functions and Green functions in terms of functional integrals. Subsequent sections deal with the application of functional integrals in superfluid Bose systems, systems with Coulomb interaction, and superfluid Fermi systems. The final section considers the application of the concept of Bose-condensation of auxiliary fields to the theory of crystals, heavy atoms and also to the theory of model Hamiltonians (BCS and Dicke models).

// Artur Kadurin 1, 2, 3, 4 , Alexander Aliper 2 , Andrey Kazennov 2, 7 , Polina Mamoshina 2, 5 , Quentin Vanhaelen 2 , Kuzma Khrabrov 1 , Alex Zhavoronkov 2, 6, 7 1 Search Department, Mail.Ru Group Ltd., Moscow, Russia 2 Pharmaceutical Artificial Intelligence Department, Insilico Medicine, Inc., Emerging Technology Centers, Johns Hopkins University at Eastern, Baltimore, Maryland, USA 3 Big Data and Text Analysis Laboratory, Kazan Federal University, Kazan, Republic of Tatarstan, Russia 4 St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, Petersburg, Russia 5 Department of Computer Science, University of Oxford, Oxford, UK 6 The Biogerontology Research Foundation, Trevissome Park, Truro TR4 8UN, UK 7 Moscow Institute of Physics and Technology, Dolgoprudny, Russia Correspondence to: Alex Zhavoronkov, email: alex@insilicomedicine.com Keywords: generative adversarian networks, adversarial autoencoder, deep learning, drug discovery, artificial intelligence Received: June 14, 2016      Accepted: November 24, 2016      Published: December 22, 2016 ABSTRACT Recent advances in deep learning and specifically in generative adversarial networks have demonstrated surprising results in generating new images and videos upon request even using natural language as input. In this paper we present the first application of generative adversarial autoencoders (AAE) for generating novel molecular fingerprints with a defined set of parameters. We developed a 7-layer AAE architecture with the latent middle layer serving as a discriminator. As an input and output the AAE uses a vector of binary fingerprints and concentration of the molecule. In the latent layer we also introduced a neuron responsible for growth inhibition percentage, which when negative indicates the reduction in the number of tumor cells after the treatment. To train the AAE we used the NCI-60 cell line assay data for 6252 compounds profiled on MCF-7 cell line. The output of the AAE was used to screen 72 million compounds in PubChem and select candidate molecules with potential anti-cancer properties. This approach is a proof of concept of an artificially-intelligent drug discovery engine, where AAEs are used to generate new molecular fingerprints with the desired molecular properties.

Asymptotic geometry is the study of metric spaces from a large scale point of view, where the local geometry does not come into play. An important class of model spaces are the hyperbolic spaces (in the sense of Gromov), for which the asymptotic geometry is nicely encoded in the boundary at infinity.
\n In the first part of this book, in analogy with the concepts of classical hyperbolic geometry, the authors provide a systematic account of the basic theory of Gromov hyperbolic spaces. These spaces have been studied extensively in the last twenty years, and have found applications in group theory, geometric topology, Kleinian groups, as well as dynamics and rigidity theory. In the second part of the book, various aspects of the asymptotic geometry of arbitrary metric spaces are considered. It turns out that the boundary at infinity approach is not appropriate in the general case, but dimension theory proves useful for finding interesting results and applications.
\n The text leads concisely to some central aspects of the theory. Each chapter concludes with a separate section containing supplementary results and bibliographical notes. Here the theory is also illustrated with numerous examples as well as relations to the neighboring fields of comparison geometry and geometric group theory.
\n The book is based on lectures the authors presented at the Steklov Institute in St. Petersburg and the University of Zurich. It addressed to graduate students and researchers working in geometry, topology, and geometric group theory.

The partition function of a six-vertex model with domain wall boundary conditions is considered on the finite lattice. The authors show that the partition function satisfies a recursive relation. They solve the recursion relation by a determinant formula. This gives a determinant representation for the partition function. They use the Quantum Inverse Scattering Method (QISM).

Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

Recent research has shown the advantages of using autoencoders based on deep neural networks for collaborative filtering. In particular, the recently proposed Mult-VAE model, which used the multinomial likelihood variational autoencoders, has shown excellent results for top-N recommendations. In this work, we propose the Recommender VAE (RecVAE) model that originates from our research on regularization techniques for variational autoencoders. RecVAE introduces several novel ideas to improve Mult-VAE, including a novel composite prior distribution for the latent codes, a new approach to setting the beta hyperparameter for the beta-VAE framework, and a new approach to training based on alternating updates. In experimental evaluation, we show that RecVAE significantly outperforms previously proposed autoencoder-based models, including Mult-VAE and RaCT, across classical collaborative filtering datasets, and present a detailed ablation study to assess our new developments. Code and models are available at https://github.com/ilya-shenbin/RecVAE.

With hundreds of worked examples, exercises and illustrations, this detailed exposition of the theory of Vassiliev knot invariants opens the field to students with little or no knowledge in this area. It also serves as a guide to more advanced material. The book begins with a basic and informal introduction to knot theory, giving many examples of knot invariants before the class of Vassiliev invariants is introduced. This is followed by a detailed study of the algebras of Jacobi diagrams and 3-graphs, and the construction of functions on these algebras via Lie algebras. The authors then describe two constructions of a universal invariant with values in the algebra of Jacobi diagrams: via iterated integrals and via the Drinfeld associator, and extend the theory to framed knots. Various other topics are then discussed, such as Gauss diagram formulae, before the book ends with Vassiliev's original construction.

We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schrammʼs SLE curves with parameters <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>κ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>κ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>16</mml:mn> <mml:mo stretchy="false">/</mml:mo> <mml:mn>3</mml:mn> </mml:math> , respectively.

Abstract Seismic depth migration aims to produce an image of seismic reflection interfaces. Ray methods are suitable for subsurface target-oriented imaging and are less costly compared to two-way wave-equation-based migration, but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way wave equation, referred to as reverse-time migration, are known to be capable of dealing with these problems. However, they are very expensive, especially in the 3D case. It can be prohibitive if many iterations are needed, such as for velocity-model building. Our method relies on the calculation of the Green functions for the classical wave equation by per-forming a summation of Gaussian beams for the direct and back-propagated wavefields. The subsurface image is obtained by cal-culating the coherence between the direct and backpropagated wavefields. To a large extent, our method combines the advantages of the high computational speed of ray-based migration with the high accuracy of reverse-time wave-equation migration because it can overcome problems with caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. We have demonstrated the quality of our method with several state-of-the-art benchmark subsurface models, which have velocity variations up to a high degree of complexity. Our algorithm is especially suited for efficient imaging of selected subsurface subdomains, which is a large advantage particularly for 3D imaging and velocity-model refinement applications such as subsalt velocity-model improvement. Because our method is also capable of providing highly accurate migration results in structurally complex subsurface settings, we have also included the concept of true-amplitude imaging in our migration technique.

Abstract It has been widely reported that tree leaves have tended to appear earlier in many regions of the northern hemisphere in the last few decades, reflecting climate warming. Satellite observations revealed an 8‐day advance in leaf appearance date between 1982 and 1991 in northern latitudes. In situ observations show that leaf appearance dates in Europe have advanced by an average of 6.3 days from 1959 to 1996. Modelling of leaf appearance on the basis of temperature also shows a marked advance in temperate and boreal regions from 1955 to 2002. However, before 1955, reported studies of phenological variations are restricted to local scale. Modelling, ground observations and satellite observations are here combined to analyse phenological variations in Eurasian taiga over nearly a century. The trend observed by remote sensing consists mainly in a shift at the end of the 1980s, reflecting a shift in winter and spring temperature. In western boreal Eurasia, a trend to earlier leaf appearance is evident since the mid‐1930s, although it is discontinuous. In contrast, the strong advance in leaf appearance detected over Central Siberia using satellite data in 1982–1991 is strengthened by late springs in 1983–1984; moreover, in this region the green‐up timing has displayed successive trends with opposite signs since 1920. Thus, such strong trend is not unusual if considered locally. However, the recent advance is unique in simultaneously affecting most of the Eurasian taiga, the leaf appearance dates after 1990 being the earliest in nearly a century in most of the area.

<ja:p>Due to the unprecedented loss of old-growth forests to harvesting throughout circumboreal regions an understanding of similarities and differences in old-growth dynamics is needed to design effective restoration, management and conservation efforts. This paper reviews concepts, prevalence and variability of old-growth forests across landscapes, and evaluates different stand scale dynamics at the old-growth stage across the circumboreal zone. Old-growth historically dominated many boreal forest landscapes in both Eurasia and North America. Throughout much of North America, and to some extent in western Siberia, the natural prevalence and development of old-growth forests are regulated by the occurrence of stand-replacing fires. In eastern North America and Siberia, insect outbreaks may, however, be more important. Insect outbreaks as well as recurrent non-stand replacing surface fires and windthrows, when occurring at the old-growth stage, often form stands characterized by several tree age-class cohorts. This multi age-class forest development type is common in Europe and eastern Siberia but its prevalence and importance in boreal North-America is not well documented. Similarities in successional dynamics across the circumboreal region are found in the development of mono-dominant even-aged stands, the replacement of shade intolerant tree species by shade tolerant species, as well as in all-aged stands driven by small-scale gap dynamics. The message to land managers is that the focus should not only be on setting aside remaining old-growth forests or in restoring static old-growth attributes, but also in emulating natural disturbances and successional dynamics at landscape and regional scales to maintain natural variability in old-growth attributes through time.</ja:p>

This survey consists of two parts. Part 1 is devoted to amoebas. These are images of algebraic subvarieties in the complex torus under the logarithmic moment map. The amoebas have essentially piecewise-linear shape if viewed at large. Furthermore, they degenerate to certain piecewise-linear objects called tropical varieties whose behavior is governed by algebraic geometry over the so-called tropical semifield. Geometric aspects of tropical algebraic geometry are the content of Part 2. We pay special attention to tropical curves. Both parts also include relevant applications of the theories. Part 1 of this survey is a revised and updated version of an earlier prepreint of 2001.

We compare two natural types of fractional Laplacians (− Δ) s , namely, the “Navier” and the “Dirichlet” ones. We show that for 0 < s < 1 their difference is positive definite and positivity preserving. Then we prove the coincidence of the Sobolev constants for these two fractional Laplacians.

Convolutional neural networks (CNN) have been successfully used to handle three-dimensional data and are a natural match for data with spatial structure such as 3D molecular structures. However, a direct 3D representation of a molecule with atoms localized at voxels is too sparse, which leads to poor performance of the CNNs. In this work, we present a novel approach where atoms are extended to fill other nearby voxels with a transformation based on the wave transform. Experimenting on 4.5 million molecules from the Zinc database, we show that our proposed representation leads to better performance of CNN-based autoencoders than either the voxel-based representation or the previously used Gaussian blur of atoms and then successfully apply the new representation to classification tasks such as MACCS fingerprint prediction.