Steklov Mathematical Institute

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.

Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems and Changes of Measures.- IV. Hellinger Processes, Absolute Continuity and Singularity of Measures.- V. Contiguity, Entire Separation, Convergence in Variation.- VI. Skorokhod Topology and Convergence of Processes.- VII. Convergence of Processes with Independent Increments.- VIII. Convergence to a Process with Independent Increments.- IX. Convergence to a Semimartingale.- X. Limit Theorems, Density Processes and Contiguity.- Bibliographical Comments.- References.- Index of Symbols.- Index of Terminology.- Index of Topics.- Index of Conditions for Limit Theorems.

The hypotheses concerning the local structure of turbulence at high Reynolds number, developed in the years 1939-41 by myself and Oboukhov (Kolmogorov 1941 a,b,c ; Oboukhov 1941 a,b ) were based physically on Richardson's idea of the existence in the turbulent flow of vortices on all possible scales l < r < L between the ‘external scales’ L and the ‘internal scale’ l and of a certain uniform mechanism of energy transfer from the coarser-scaled vortices to the finer.

This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation re

A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open quantum chains with appropriate boundary terms in the Hamiltonian. The general considerations are applied to the XXZ and XYZ models, the nonlinear Schrodinger equation and Toda chain.

It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals the maximum of the entropy bound with respect to all a priori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland, and Wootters (1996), who proved the equality for the pure state channel.

P-adic numbers p-adic analysis non-Archimedean geometry distribution theory pseudo differential operators and spectral theory p-adic quantum mechanics and representation theory quantum field theory p-adic strings.

There are two parts in this book. The first part is devoted mainly to the proper ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distribut

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from experiments, field measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning (ML) offers a wealth of techniques to extract ...Read More

The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less than 1.

Completely integrable models of quantum field theory the space of physical states the necessary properties of form factors the local commutativity theorem soliton form factors in SG model the properties of operators jm, Tmn, exp(+- i beta u/2) in SG model form factors in SU(2)-invariant Thirring model form factors in O(3)-nonlinear s-model asymptotics of form factors current algebras form factors in SU(N)-invariant Thirring model (SU(N) chiral gross-Neveau model) phenomenological reasonings.

For Re s = σ > 1, theRiemann zeta function ζ(s)is defined by $$ \zeta \left( s \right) = \sum\limits_{n = 1}^\infty {\frac{1}{{{n^s}}}} . $$ It follows from the definition that ζ(s) is an analytic function in the half-plane Re s > 1.

Purpose Therapies with novel mechanisms of action are needed for multiple myeloma (MM). T cells can be genetically modified to express chimeric antigen receptors (CARs), which are artificial proteins that target T cells to antigens. B-cell maturation antigen (BCMA) is expressed by normal and malignant plasma cells but not normal essential cells. We conducted the first-in-humans clinical trial, to our knowledge, of T cells expressing a CAR targeting BCMA (CAR-BCMA). Patients and Methods Sixteen patients received 9 × 10 6 CAR-BCMA T cells/kg at the highest dose level of the trial; we are reporting results of these 16 patients. The patients had a median of 9.5 prior lines of MM therapy. Sixty-three percent of patients had MM refractory to the last treatment regimen before protocol enrollment. T cells were transduced with a γ-retroviral vector encoding CAR-BCMA. Patients received CAR-BCMA T cells after a conditioning chemotherapy regimen of cyclophosphamide and fludarabine. Results The overall response rate was 81%, with 63% very good partial response or complete response. Median event-free survival was 31 weeks. Responses included eradication of extensive bone marrow myeloma and resolution of soft-tissue plasmacytomas. All 11 patients who obtained an anti-MM response of partial response or better and had MM evaluable for minimal residual disease obtained bone marrow minimal residual disease–negative status. High peak blood CAR + cell levels were associated with anti-MM responses. Cytokine-release syndrome toxicities were severe in some cases but were reversible. Blood CAR-BCMA T cells were predominantly highly differentiated CD8 + T cells 6 to 9 days after infusion. BCMA antigen loss from MM was observed. Conclusion CAR-BCMA T cells had substantial activity against heavily treated relapsed/refractory MM. Our results should encourage additional development of CAR T-cell therapies for MM.

To provide information about dynamic sensory stimuli, the pattern of action potentials in spiking neurons must be variable. To ensure reliability these variations must be related, reproducibly, to the stimulus. For H1, a motion-sensitive neuron in the fly's visual system, constant-velocity motion produces irregular spike firing patterns, and spike counts typically have a variance comparable to the mean, for cells in the mammalian cortex. But more natural, time-dependent input signals yield patterns of spikes that are much more reproducible, both in terms of timing and of counting precision. Variability and reproducibility are quantified with ideas from information theory, and measured spike sequences in H1 carry more than twice the amount of information they would if they followed the variance-mean relation seen with constant inputs. Thus, models that may accurately account for the neural response to static stimuli can significantly underestimate the reliability of signal transfer under more natural conditions.

Abstract The method of canonical transformations proposed by one of the authors ten years ago in connection with a microscopic theory of superfluidity for Bose systems, is generalized here to Fermi systems, and forms the basis of a method for investigating the problem of superconductivity. Starting from Fröhlich's Hamiltonian, the energy of the superconducting ground state and the one‐Fermion and collective excitations corresponding to this state are obtained. It turns out that the final formulae for the ground state and one‐Fermion excitations recently obtained by Bardeen, Cooper and Schrieffer are correct in the first approximation. The physical picture appears to be closer to the one proposed by Schafroth, Butler and Blatt. The effect on superconductivity of the Coulomb interaction between the electrons is analyzed in detail. A criterion for the superfluidity of a Fermi system with a four‐line vertex Hamiltonian is established.

The paper establishes a formula for enumeration of curves of arbitrary genus in toric surfaces. It turns out that such curves can be counted by means of certain lattice paths in the Newton polygon. The formula was announced earlier in <italic>Counting curves via lattice paths in polygons,</italic> C. R. Math. Acad. Sci. Paris <bold>336</bold> (2003), no. 8, 629–634. The result is established with the help of the so-called tropical algebraic geometry. This geometry allows one to replace complex toric varieties with the real space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R Superscript n"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb {R}^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and holomorphic curves with certain piecewise-linear graphs there.

Deep generative adversarial networks (GANs) are the emerging technology in drug discovery and biomarker development. In our recent work, we demonstrated a proof-of-concept of implementing deep generative adversarial autoencoder (AAE) to identify new molecular fingerprints with predefined anticancer properties. Another popular generative model is the variational autoencoder (VAE), which is based on deep neural architectures. In this work, we developed an advanced AAE model for molecular feature extraction problems, and demonstrated its advantages compared to VAE in terms of (a) adjustability in generating molecular fingerprints; (b) capacity of processing very large molecular data sets; and (c) efficiency in unsupervised pretraining for regression model. Our results suggest that the proposed AAE model significantly enhances the capacity and efficiency of development of the new molecules with specific anticancer properties using the deep generative models.

Let M be a closed oriented three-manifold, whose prime decomposition contains no aspherical factors. We show that for any initial riemannian metric on M the solution to the Ricci flow with surgery, defined in our previous paper math.DG/0303109, becomes extinct in finite time. The proof uses a version of the minimal disk argument from 1999 paper by Richard Hamilton, and a regularization of the curve shortening flow, worked out by Altschuler and Grayson.

By invoking the concept of twisted Poincaré symmetry of the algebra of functions on a Minkowski space–time, we demonstrate that the noncommutative space–time with the commutation relations [xμ,xν]=iθμν, where θμν is a constant real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincaré symmetry on QFT on such a space–time is briefly discussed. The presence of the twisted symmetry gives justification to all the previous treatments within NC QFT using Lorentz invariant quantities and the representations of the usual Poincaré symmetry.