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Predicting video saliency using crowdsourced mouse-tracking dataJun 30 2019This paper presents a new way of getting high-quality saliency maps for video, using a cheaper alternative to eye-tracking data. We designed a mouse-contingent video viewing system which simulates the viewers' peripheral vision based on the position of ... More

Video Distortion Method for VMAF Quality Values IncreasingJul 10 2019Video quality measurement takes an important role in many applications. Full-reference quality metrics which are usually used in video codecs comparisons are expected to reflect any changes in videos. In this article, we consider different colour corrections ... More

Barriers towards no-reference metrics application to compressed video quality analysis: on the example of no-reference metric NIQEJul 08 2019This paper analyses the application of no-reference metric NIQE to the task of video-codec comparison. A number of issues in the metric behaviour on videos was detected and described. The metric has outlying scores on black and solid-coloured frames. ... More

Improving Video Compression With Deep Visual-Attention ModelsMar 19 2019Recent advances in deep learning have markedly improved the quality of visual-attention modelling. In this work we apply these advances to video compression. We propose a compression method that uses a saliency model to adaptively compress frame areas ... More

Perceptually Motivated Method for Image Inpainting ComparisonJul 14 2019The field of automatic image inpainting has progressed rapidly in recent years, but no one has yet proposed a standard method of evaluating algorithms. This absence is due to the problem's challenging nature: image-inpainting algorithms strive for realism ... More

Dorronsoro's theorem and a small generalizationJun 21 2015We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

The mean value of Frobenius numbers with three argumentsMar 28 2011We prove an asymptotic formula for the mean value of Frobenius numbers with three arguments. To prove this we use a new method invented by A. Ustinov, Rodseth's algorithm an bounds for exponential sums.

D-affinity and Rational VarietiesNov 21 2018Apr 07 2019We investigate geometry of D-affine varieties. Our main result is that a D-affine uniformly rational projective variety over an algebraically closed field of zero characteristic is a generalised flag variety of a reductive group. This is a partially converse ... More

D-affinity and Rational VarietiesNov 21 2018May 02 2019We investigate geometry of D-affine varieties. Our main result is that a D-affine rational projective surface over an algebraically closed field is a generalised flag variety of a reductive group.

Global solvability of the initial boundary value problem for a model system of one-dimensional equations of polytropic flows of viscous compressible fluid mixturesOct 19 2017Oct 20 2017We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for the strong ... More

Compact domains with prescribed convex boundary metrics in quasi-Fuchsian manifoldsMay 07 2014We show the existence of a convex compact domain in a quasi-Fuchsian manifold such that the induced metric on its boundary coincides with a prescribed surface metric of curvature $K\geq-1$ in the sense of A. D. Alexandrov.

Kac-Moody Groups and Their RepresentationsDec 18 2017Feb 12 2019In this expository paper we review some recent results about representations of Kac-Moody groups. We sketch the construction of these groups. If practical, we present the ideas behind the proofs of theorems. At the end we pose open questions.

Hopf-Galois extensions with central invariantsJul 16 1997Sep 22 1997We study Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We collect general facts about them and discuss some examples arising in the study of restricted Lie algebras and quantum groups at roots of unity. Our focus ... More

The Proof of CSP Dichotomy ConjectureApr 06 2017Dec 18 2017Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The standard way to ... More

The existence of a near-unanimity function is decidableAug 08 2011We prove that the following problem is decidable: given a finite set of relations, decide whether this set admits a near-unanimity function.

A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-spaceAug 14 2012We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).

Weak integral forms and the sixth Kaplansky conjectureJul 04 2019It is a short unpublished note from 1998. I make it public because Cuadra and Meir refer to it in their paper. We precisely state and prove a folklore result that if a finite dimensional semisimple Hopf algebra admits a weak integral form then it is of ... More

D-affinity and Rational VarietiesNov 21 2018May 07 2019We investigate geometry of D-affine varieties. Our main result is that a D-affine rational projective surface over an algebraically closed field is a generalised flag variety of a reductive group.

Cyclic shifts of the van der Corput setNov 12 2008In [13], K. Roth showed that the expected value of the $L^2$ discrepancy of the cyclic shifts of the $N$ point van der Corput set is bounded by a constant multiple of $\sqrt{\log N}$, thus guaranteeing the existence of a shift with asymptotically minimal ... More

The Size of Generating Sets of PowersApr 08 2015In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. For idempotent algebras we give a simple criteria for the algebra to satisfy ... More

Key (critical) relations preserved by a weak near-unanimity functionJan 19 2015Nov 26 2016In the paper we introduce a notion of a key relation, which is similar to the notion of a critical relation introduced by Keith A.Kearnes and \'Agnes Szendrei. All clones on finite sets can be defined by only key relations. In addition there is a nice ... More

D-affinity and Rational VarietiesNov 21 2018Nov 26 2018We investigate geometry of D-affine varieties. Our main result is that a D-affine uniformly rational projective variety over an algebraically closed field of zero characteristic is a generalised flag variety of a reductive group. This is a partially converse ... More

On factorization of elements in Pimenov algebrasMar 20 2013We consider the operation of division in Pimenov algebras. We obtain necessary and sufficient conditions for prime elements in Pimenov algebras with a number of generators less than five. We adduce examples of the factorization of elements in these algebras. ... More

The proximal point method revisitedDec 17 2017In this short survey, I revisit the role of the proximal point method in large scale optimization. I focus on three recent examples: a proximally guided subgradient method for weakly convex stochastic approximation, the prox-linear algorithm for minimizing ... More

The coloring problem for classes with two small obstructionsJul 01 2013The coloring problem is studied in the paper for graph classes defined by two small forbidden induced subgraphs. We prove some sufficient conditions for effective solvability of the problem in such classes. As their corollary we determine the computational ... More

Formal Languages, Formally and CoinductivelyNov 29 2016Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and elegant proofs ... More

Formal Languages, Formally and CoinductivelyNov 29 2016Sep 18 2017Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and elegant proofs ... More

Algebraic geometry of Hopf-Galois extensionsJul 16 1997Sep 25 1997We continue the study of Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We concentrate on the geometrical side on the subject. We understand how to localize Hopf-Galois extensions and to paste them from local datum. ... More

Miscroscopic origin of de Sitter entropyJan 09 2018It has been argued recently that the entropy of black holes might be associated with soft scalar, graviton and photon states at the event horizon, as number of such possible soft states is proportional to the horizon area. However, the coefficient of ... More

Numerically explicit version of the Pólya--Vinogradov inequalityJul 02 2011In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obtained by C. Pomerance.

On a problem of Dobrowolski--WilliamsJul 02 2011In this paper we prove new upper bounds for the sum $\sum_{n=a+1}^{a+N}f(n)$, for a certain class of arithmetic functions $f$. Our results improve the previous results of G. Bachman and L. Rachakonda.

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-spaceFeb 20 2010Jan 02 2011We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.

Lie algebras in symmetric monoidal categoriesMay 16 2012Jun 18 2013We study algebras defined by identities in symmetric monoidal categories. Our focus is on Lie algebras. Besides usual Lie algebras, there are examples appearing in the study of knot invariants and Rozansky-Witten invariants. Our main result is a proof ... More

Quantum OptimizationJun 20 2000We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with randomly generated ... More

On decoherence in non-renormalizable field theories and quantum gravityAug 21 2015It was previously argued that the phenomenon of quantum gravitational decoherence described by the Wheeler-DeWitt equation is responsible for the emergence of the arrow of time. Here we show that the characteristic spatio-temporal scales of quantum gravitational ... More

Twisted Crystalline Differential OperatorsDec 15 1999May 14 2002This paper has been withdrawn by the authors.

Geometric Representation Theory of Restricted Lie Algebras of Classical TypeSep 10 1999We modify the Hochschild $\phi$-map to construct central extensions of a restricted Lie algebra. Such central extension gives rise to a group scheme which leads to a geometric construction of unrestricted representations. For a classical semisimple Lie ... More

2-Groups, 2-Characters, and Burnside RingsApr 11 2016We study 2-representations, i.e. actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended Burnside rings. Our main theorem is that the Ganter-Kapranov 2-character ... More

Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functionsFeb 08 2018We prove that the projected stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$.

Global and interior pointwise best approximation results for the gradient of Galerkin solutions for parabolic problemsJun 20 2016Mar 27 2017In this paper we establish best approximation property of fully discrete Galerkin solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method consists of ... More

Viscous compressible homogeneous multi-fluids with multiple velocities: barotropic existence theoryOct 18 2016We consider the model of viscous compressible homogeneous multi-fluids with multiple velocities. We review different formulations of the model and the existence results for boundary value problems. We analyze crucial mathematical difficulties which arise ... More

Joint Detection and Super-Resolution Estimation of Multipath Signal Parameters Using Incremental Automatic Relevance DeterminationMar 06 2015The presented work investigates a sparse Bayesian incremental automatic relevance determination (IARD) algorithm in the context of multipath parameter estimation in a super-resolution regime. The corresponding estimation problem is highly nonlinear and, ... More

A Note on Application of the Method of Approximation of Iterated Stochastic Ito integrals Based on Generalized Multiple Fourier Series to the Numerical Integration of Stochastic Partial Differential EquationsMay 09 2019Jun 24 2019We consider a way for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with respect ... More

On the volume of spherical Lambert cubeDec 21 2002The calculation of volumes of polyhedra in the three-dimensional Euclidean, spherical and hyperbolic spaces is very old and difficult problem. In particular, an elementary formula for volume of non-euclidean simplex is still unknown. One of the simplest ... More

Existence of cube terms in finite finitely generated clonesJan 15 2019We study the problem of whether a given finite clone generated by finitely many operations contains a cube term and give both structural and algorithmic results. We show that if such a clone has a cube term then it has a cube term of dimension at most ... More

Strong Numerical Methods of Order 3.0 for Ito Stochastic Differential Equations, Based on the Unified Stochastic Taylor Expansions and Multiple Fourier-Legendre SeriesJul 05 2018Sep 18 2018The article is devoted to explicit one-step numerical methods with strong order of convergence 3.0 for Ito stochastic differential equations with multidimensional non-additive noise. We consider the numerical methods, based on the unified Taylor-Ito and ... More

Numerical Simulation of 2.5-Set of Multiple Ito Stochastic Integrals of Multiplicities 1 to 5May 31 2018Jul 04 2018In this article we construct effective procedures of mean-square approximation of multiple Ito stochastic integrals of multiplicities 1-5, based on multiple Fourier-Legendre series. The results of the article can be used for realizations of numerical ... More

Expansion of Multiple Stochastic Integrals According to Martingale Poisson Measures and According to Martingales, Based on Generalized Multiple Fourier SeriesJan 19 2018May 14 2018In the article we consider some versions of the approach to expansion of multiple Ito stochastic integrals of arbitrary multiplicity, based on generalized multiple Fourier series. The expansion of multiple stochastic integrals according to martingale ... More

Expansions of multiple Stratonovich stochastic integrals, based on generalized multiple Fourier seriesDec 27 2017Sep 29 2018The article is devoted to the expansions of multiple Stratonovich stochastic integrals of multiplicities 1-4 on the basis of the method of generalized multiple Fourier series. Mean-square convergence of the expansions for the case of Legendre polynomials ... More

On deciding stability of multiclass queueing networks under buffer priority scheduling policiesAug 08 2007Nov 19 2009One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key questions related to the stability issue is how to ... More

2-Groups, 2-Characters, and Burnside RingsApr 11 2016May 03 2018We study 2-representations, i.e., actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended Burnside rings. Our main theorem is that the Ganter-Kapranov 2-character ... More

Sweeping by a tame processDec 30 2014Aug 24 2015We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions, and any such bounded trajectory must have finite length. Analogous results hold more generally for sweeping processes definable in o-minimal structures. ... More

Integration of Modules I: StabilityAug 22 2017Jan 07 2019We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for passing from ... More

QCSP monsters and the demise of the Chen ConjectureJun 29 2019We give a surprising classification for the computational complexity of Quantified Constraint Satisfaction Problems, QCSP$(\Gamma)$, where $\Gamma$ is a finite language over $3$ elements which contains all constants. In particular, such problems are either ... More

Complexity of finding near-stationary points of convex functions stochasticallyFeb 21 2018In a recent paper, we showed that the stochastic subgradient method applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. In this supplementary note, we present a stochastic subgradient method ... More

Efficiency of minimizing compositions of convex functions and smooth mapsApr 30 2016Aug 14 2017We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration solves a regularized ... More

On Boolean Control Networks with Maximal Topological EntropyJul 05 2014Boolean control networks (BCNs) are discrete-time dynamical systems with Boolean state-variables and inputs that are interconnected via Boolean functions. BCNs are recently attracting considerable interest as computational models for genetic and cellular ... More

Galois invariants of K_1-groups of Iwasawa algebrasJun 28 2010We study Galois descent of K_1 of group algebras with coefficients in certain subrings of the ring of integers of C_p, the completion of an algebraic closure of Q_p.

Towards lightweight convolutional neural networks for object detectionJul 05 2017Oct 05 2017We propose model with larger spatial size of feature maps and evaluate it on object detection task. With the goal to choose the best feature extraction network for our model we compare several popular lightweight networks. After that we conduct a set ... More

Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problem sJul 28 2017The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of linear parabolic equations with time-dependent coefficients. Such estimates ... More

Explicit One-Step Strong Numerical Methods of Order 2.5 for Ito Stochastic Differential Equations, Based on the Unified Taylor-Ito and Taylor-Stratonovich ExpansionsFeb 08 2018Aug 08 2018The article is devoted to explicit one-step numerical methods with strong order of convergence 2.5 for Ito stochastic differential equations with multidimensional non-additive noise. We consider the numerical methods, based on the unified Taylor-Ito and ... More

Integration of Modules II: ExponentialsJul 23 2018We continue our exploration of various approaches to integration of representations from a Lie algebra $\mbox{Lie} (G)$ to an algebraic group $G$ in positive characteristic. In the present paper we concentrate on an approach exploiting exponentials. This ... More

Kac-Moody Groups and CompletionsJun 26 2017May 30 2018In this paper we construct a new "pro-p-complete" topological Kac-Moody group and compare it to various known topological Kac-Moody groups. We come across this group by investigating the process of completion of groups with BN-pairs. We would like to ... More

Correlation decay and deterministic FPTAS for counting list-colorings of a graphJun 06 2006Feb 25 2007We propose a deterministic algorithm for approximately counting the number of list colorings of a graph. Under the assumption that the graph is triangle free, the size of every list is at least $\alpha \Delta$, where $\alpha$ is an arbitrary constant ... More

On the von Neumann Inequality for Linear Matrix Functions of Several VariablesNov 13 1997The theorem on the existence of three commuting contractions on a Hilbert space and of a linear homogeneous matrix function of three independent variables for which the generalized von Neumann inequality fails is proved.

Distribution of the first particle in discrete orthogonal polynomial ensemblesApr 01 2002We show that the distribution function of the first particle in a discrete orthogonal polynomial ensemble can be obtained through a certain recurrence procedure, if the (difference or q-) log-derivative of the weight function is rational. In a number ... More

Pointwise best approximation results for Galerkin finite element solutions of parabolic problemsAug 05 2015Feb 17 2016In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method uses of continuous ... More

Optimal a priori error estimates of parabolic optimal control problems with a moving point controlJan 11 2017Mar 06 2017In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear finite elements ... More

Kac-Moody Groups and Cosheaves on Davis BuildingApr 25 2017Sep 07 2018We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on projective dimension, ... More

Comparative Analysis of the Efficiency of Application of Legendre Polynomials and Trigonometric Functions to the Numerical Integration of Ito Stochastic Differential EquationsDec 30 2018Jan 09 2019The article is devoted to the comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential equations in the framework of the method of approximation ... More

Application of the Direct Combined Approach to Expansion of Double Stratonovich Stochastic IntegralsJan 21 2018Aug 31 2018The article is devoted to the expansion of double Stratonovich stochastic integrals on the base of the direct combined approach of generalized multiple Fourier series. We consider two different parts of the expansion of double Stratonovich stochastic ... More

Direct combined approach for expansion of multiple Stratonovich stochastic integrals of multiplicities 2 - 4, based on generalized multiple Fourier seriesJan 17 2018The article is devoted to the expansion of multiple Stratonovich stochastic integrals of multiplicities 2 - 4 on the base of the direct combined approach of generalized multiple Fourier series. We consider two different parts of the expansion of multiple ... More

The Hypothesis About Expansion of Multiple Stratonovich Stochastic Integrals of Arbitrary MultiplicityJan 10 2018Feb 17 2019In this review article we collected more than ten theorems about expansions of multiple Ito and Stratonovich stochastic integrals, which was formulated and proved by the author. These theorems open a new direction for study of properties of multiple stochastic ... More

Exact Calculation of Mean-Square Error of Approximation of Multiple Ito Stochastic integrals for the Method, Based on the Multiple Fourier SeriesJan 03 2018Jun 05 2018The article is devoted to the obtainment of exact and approximate expressions for mean-square error of approximation of multiple Ito stochastic integrals from the stochastic Taylor-Ito expansion for the method, based on generalized multiple Fourier series. ... More

Mean-Square Approximation of Multiple Ito and Stratonovich Stochastic Integrals from the Taylor-Ito and Taylor-Stratonovich Expansions, Using Legendre PolynomialsDec 31 2017Jan 08 2019The article is devoted to material about expansions and mean-square approximations of specific multiple Ito and Stratonovich stochastic integrals using multiple Fourier-Legendre series. Considered multiple Ito and Stratonovich integrals are included into ... More

Cascade Connections of Linear Systems and Factorizations of Holomorphic Operator Functions Around a Multiple Zero in Several VariablesFeb 04 2000We show that the factorization problem $\theta (z)=\theta_2(z)\theta_1(z)$ is solvable in the class of Hilbert space operator-valued functions holomorphic on some neighbourhood of $z=0$ in $\nspace{C}{N}$ and having a zero at $z=0$ (here $\theta (z)$ ... More

Multiparametric Dissipative Linear Stationary Dynamical Scattering Systems: Discrete CaseApr 28 1998Mar 24 1999We propose the new generalization of linear stationary dynamical systems with discrete time $t\in\mathbb{Z}$ to the case $t\in\nspace{Z}{N}$. The dynamics of such a system can be reproduced by means of its associated multiparametric Lax-Phillips semigroup. ... More

BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimensionNov 21 2014Jul 09 2015In the current paper we obtain discrepancy estimates in exponential Orlicz and BMO spaces in arbitrary dimension $d \ge 3$. In particular, we use dyadic harmonic analysis to prove that for the so-called digital nets of order $2$ the BMO${}^d$ and $\exp ... More

A Deterministic Approximation Algorithm for Computing a Permanent of a 0,1 matrixFeb 02 2007We construct a deterministic approximation algorithm for computing a permanent of a $0,1$ $n$ by $n$ matrix to within a multiplicative factor $(1+\epsilon)^n$, for arbitrary $\epsilon>0$. When the graph underlying the matrix is a constant degree expander ... More

Graphical Convergence of Subgradients in Nonconvex Optimization and LearningOct 17 2018Dec 17 2018We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such losses. We ... More

Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functionsFeb 08 2018Feb 19 2018We prove that the proximal stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. As a consequence, we resolve an open question on the convergence rate of the proximal ... More

Relative velocity of dark matter and baryonic fluids and the formation of the first structuresMay 13 2010Oct 18 2010At the time of recombination, baryons and photons decoupled and the sound speed in the baryonic fluid dropped from relativistic to the thermal velocities of the hydrogen atoms. This is less than the relative velocities of baryons and dark matter computed ... More

Correlation Functions in N=3 Superconformal TheoryJun 17 2010Jan 31 2011Using a superspace representation of the N=3 Neveau-Schwarz super Virasoro algebra, we find solutions of N=3 super Ward identities. Global transformations generated by the non-abelian supercurrent require not only superfields, but also functions of Grassmann ... More

On decoherence in quantum gravityAug 21 2015Feb 26 2017It was previously argued that the phenomenon of quantum gravitational decoherence described by the Wheeler-DeWitt equation is responsible for the emergence of the arrow of time. Here we show that the characteristic spatio-temporal scales of quantum gravitational ... More

An accelerated algorithm for minimizing convex compositionsApr 30 2016We describe a new proximal algorithm for minimizing compositions of finite-valued convex functions with smooth mappings. When applied to convex optimization problems having an additive composite form, the algorithm reduces to FISTA. The method both realizes ... More

The two-dimensional small ball inequality and binary netsNov 23 2015In the current paper we present a new proof of the small ball inequality in two dimensions. More importantly, this new argument, based on an approach inspired by lacunary Fourier series, reveals the first formal connection between this inequality and ... More

Stability of Skorokhod problem is undecidableJul 10 2010Skorokhod problem arises in studying Reflected Brownian Motion (RBM) on an non-negative orthant, specifically in the context of queueing networks in the heavy traffic regime. One of the key problems is identifying conditions for stability of a Skorokhod ... More

Regular bipartite graphs and intersecting familiesNov 09 2016Oct 18 2017In this paper we present a simple unifying approach to prove several statements about intersecting and cross-intersecting families, including the Erd\H os--Ko--Rado theorem, the Hilton--Milner theorem, a theorem due to Frankl concerning the size of intersecting ... More

Application of the Method of Approximation of Iterated Stochastic Ito Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Stochastic Partial Differential EquationsMay 09 2019Jun 26 2019We consider a method for approximation of iterated stochastic Ito integrals of multiplicity $k$ $(k\in \mathbb{N})$ with respect to infinite-dimensional Wiener process using the mean-square approximation method of iterated stochastic Ito integrals with ... More

Complexity of a Single Face in an Arrangement of s-Intersecting CurvesAug 22 2011Consider a face F in an arrangement of n Jordan curves in the plane, no two of which intersect more than s times. We prove that the combinatorial complexity of F is O(\lambda_s(n)), O(\lambda_{s+1}(n)), and O(\lambda_{s+2}(n)), when the curves are bi-infinite, ... More

Numerical Simulation of 2.5-Set of Multiple Stratonovich Stochastic Integrals of Multiplicities 1 to 5Jun 27 2018Jul 04 2018In this article we construct effective procedures of mean-square approximation of multiple Stratonovich stochastic integrals of multiplicities 1-5, based on multiple Fourier-Legendre series. The results of the article can be used for realization of numerical ... More

Ergodic Volterra Quadratic Transformations of SymplexMay 17 2012In the paper a Volterra quadratic stochastic operators of three dimensional simplex into itself is considered.The full description of ergodic properties such operators is given.

Multiparametric Passive Linear Stationary Dynamical Scattering Systems: Discrete Case, II: Existence of Conservative DilationsOct 19 1998Mar 28 1999In the present paper we introduce the notion of dilation of a multiparametric linear stationary dynamical system (systems of this type, in particular passive, and conservative scattering ones were first introduced in func-an/9804130). We establish the ... More

Solvability of a steady boundary-value problem for the equations of one-temperature viscous compressible heat-conducting bifluidsOct 18 2017We consider a boundary-value problem describing the steady motion of a two-component mixture of viscous compressible heat-conducting fluids in a bounded domain. We make no simplifying assumptions except for postulating the coincidence of phase temperatures ... More

Global unique solvability of the initial-boundary value problem for the equations of one-dimensional polytropic flows of viscous compressible multifluidsSep 18 2018We consider the equations which describe polytropic one-dimensional flows of viscous compressible multifluids. We prove global existence and uniqueness of a solution to the initial-boundary value problem which corresponds to the flow in a bounded space ... More

Switchability and collapsibility of Gap AlgebrasOct 21 2015Let A be an idempotent algebra on a 3-element domain D that omits a G-set for a factor. Suppose A is not \alpha\beta-projective (for some alpha, beta subsets of D) and is not collapsible. It follows that A is switchable. We prove that, for every finite ... More

The Connes character formula for locally compact spectral triplesMar 05 2018May 04 2018A fundamental tool in noncommutative geometry is Connes' character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterisation of manifolds. A non-compact space ... More

Dark matter in a Simplest Little Higgs with T-parity modelMar 27 2009Little Higgs models may provide a viable alternative to supersymmetry as an extension of the Standard Model. After the introduction of a discrete $Z_2$ symmetry, dubbed T-parity into Little Higgs models they also contain a promising dark matter candidate. ... More

Global and interior pointwise best approximation results for the gradient of Galerkin solutions for parabolic problemsJun 20 2016In this paper we establish best approximation property of fully discrete Galerkin solutions of the second parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method consists of ... More

Discrete maximal parabolic regularity for Galerkin finite element methodsMay 18 2015Feb 05 2016The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the time discontinuous Galerkin solution of linear parabolic equations. Such estimates have many applications. They are essential, ... More