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Stochastic Coalitional Better-response Dynamics and Strong Nash EquilibriumJun 10 2015We consider coalition formation among players in an n-player finite strategic game over infinite horizon. At each time a randomly formed coalition makes a joint deviation from a current action profile such that at new action profile all players from the ... More

Lower Bounds for the Fair Resource Allocation ProblemFeb 08 2018The $\alpha$-fair resource allocation problem has received remarkable attention and has been studied in numerous application fields. Several algorithms have been proposed in the context of $\alpha$-fair resource sharing to distributively compute its value. ... More

Whittle Index Policy for Crawling Ephemeral ContentMar 30 2015We consider a task of scheduling a crawler to retrieve content from several sites with ephemeral content. A user typically loses interest in ephemeral content, like news or posts at social network groups, after several days or hours. Thus, development ... More

Stability Analysis of GI/G/c/K Retrial Queue with Constant Retrial RateJul 09 2010We consider a GI/G/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has $c$ identical servers and can accommodate the maximal number of $K$ jobs. If a newly arriving ... More

Closed form solutions for symmetric water filling gamesJul 26 2007Jul 30 2007We study power control in optimization and game frameworks. In the optimization framework there is a single decision maker who assigns network resources and in the game framework users share the network resources according to Nash equilibrium. The solution ... More

Convergence and Optimal Buffer Sizing for Window Based AIMD Congestion ControlMar 13 2007We study the interaction between the AIMD (Additive Increase Multiplicative Decrease) congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. First, we show that the hybrid ... More

Parallel and Distributed Approaches for Graph Based Semi-supervised LearningSep 04 2015Two approaches for graph based semi-supervised learning are proposed. The firstapproach is based on iteration of an affine map. A key element of the affine map iteration is sparsematrix-vector multiplication, which has several very efficient parallel ... More

Coding for Caches in the PlaneSep 03 2013We consider wireless caches located in the plane according to general point process and specialize the results for the homogeneous Poisson process. A large data file is stored at the caches, which have limited storage capabilities. Hence, they can only ... More

A singular perturbation approach for choosing PageRank damping factorDec 04 2006The choice of the PageRank damping factor is not evident. The Google's choice for the value c=0.85 was a compromise between the true reflection of the Web structure and numerical efficiency. However, the Markov random walk on the original Web Graph does ... More

A retrial system with two input streams and two orbit queuesJun 22 2012Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i=1,2) finds the server busy, it is blocked and routed to a separate type-i retrial (orbit) ... More

Distributed Weight Selection in Consensus Protocols by Schatten Norm MinimizationJun 16 2014Jul 18 2014In average consensus protocols, nodes in a network perform an iterative weighted average of their estimates and those of their neighbors. The protocol converges to the average of initial estimates of all nodes found in the network. The speed of convergence ... More

Hitting with Restart: A Reason for Sisyphus LabourMar 30 2015Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process with restart in the Borel state space. At each step the process either with a positive probability restarts from a given distribution, ... More

Optimal Choice of Threshold in Two Level Processor SharingJun 12 2007Jun 13 2007We analyze the Two Level Processor Sharing (TLPS) scheduling discipline with the hyper-exponential job size distribution and with the Poisson arrival process. TLPS is a convenient model to study the benefit of the file size based differentiation in TCP/IP ... More

Semi-supervised Learning with Regularized LaplacianAug 20 2015We study a semi-supervised learning method based on the similarity graph and RegularizedLaplacian. We give convenient optimization formulation of the Regularized Laplacian method and establishits various properties. In particular, we show that the kernel ... More

Optimization of Caching Devices with Geometric ConstraintsFeb 11 2016It has been recently advocated that in large communication systems it is beneficial both for the users and for the network as a whole to store content closer to users. One particular implementation of such an approach is to co-locate caches with wireless ... More

Bayesian Inference of Online Social Network Statistics via Lightweight Random Walk CrawlsOct 19 2015Dec 18 2015Online social networks (OSN) contain extensive amount of information about the underlying society that is yet to be explored. One of the most feasible technique to fetch information from OSN, crawling through Application Programming Interface (API) requests, ... More

Quasi-stationary distributions as centrality measures of reducible graphsAug 03 2007Aug 08 2007Random walk can be used as a centrality measure of a directed graph. However, if the graph is reducible the random walk will be absorbed in some subset of nodes and will never visit the rest of the graph. In Google PageRank the problem was solved by introduction ... More

Distribution of PageRank Mass Among Principle Components of the WebSep 13 2007We study the PageRank mass of principal components in a bow-tie Web Graph, as a function of the damping factor c. Using a singular perturbation approach, we show that the PageRank share of IN and SCC components remains high even for very large values ... More

On Mixing in Pairwise Markov Random Fields with Application to Social NetworksNov 28 2016We consider pairwise Markov random fields which have a number of important applications in statistical physics, image processing and machine learning such as Ising model and labeling problem to name a couple. Our own motivation comes from the need to ... More

Markov Processes with RestartJun 22 2012We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such processes comes ... More

PageRank in undirected random graphsNov 16 2015PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning .In this paper, we study PageRank in undirected random graphs with expansion property. The Chung-Lu random graph represents an example ... More

Information dissemination processes in directed social networksOct 25 2013Social networks can have asymmetric relationships. In the online social network Twitter, a follower receives tweets from a followed person but the followed person is not obliged to subscribe to the channel of the follower. Thus, it is natural to consider ... More

Optimal Threshold Control by the Robots of Web Search Engines with Obsolescence of DocumentsJan 19 2012A typical web search engine consists of three principal parts: crawling engine, indexing engine, and searching engine. The present work aims to optimize the performance of the crawling engine. The crawling engine finds new web pages and updates web pages ... More

Personalized PageRank with Node-dependent RestartAug 04 2014Personalized PageRank is an algorithm to classify the improtance of web pages on a user-dependent basis. We introduce two generalizations of Personalized PageRank with node-dependent restart. The first generalization is based on the proportion of visits ... More

Quick Detection of Nodes with Large DegreesFeb 15 2012Our goal is to quickly find top $k$ lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find a node with the largest degree ... More

Quick Detection of High-degree Entities in Large Directed NetworksOct 02 2014Oct 23 2014In this paper, we address the problem of quick detection of high-degree entities in large online social networks. Practical importance of this problem is attested by a large number of companies that continuously collect and update statistics about popular ... More

Distribution and Dependence of Extremes in Network Sampling ProcessesAug 11 2014Feb 24 2015We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, ... More

Subgraph Detection with cues using Belief PropagationNov 10 2016We consider an Erdos-Renyi graph with $n$ nodes and edge probability $q$ that is embedded with a random subgraph of size $K$ with edge probabilities $p$ such that $p>q$. We address the problem of detecting the subgraph nodes when only the graph edges ... More

Generalized Optimization Framework for Graph-based Semi-supervised LearningOct 19 2011We develop a generalized optimization framework for graph-based semi-supervised learning. The framework gives as particular cases the Standard Laplacian, Normalized Laplacian and PageRank based methods. We have also provided new probabilistic interpretation ... More

Infinite Horizon Optimal Impulsive Control Theory with Application to Internet Congestion ControlNov 27 2013We develop Bellman equation based approach for infinite time horizon optimal impulsive control problems. Both discounted and time average criteria are considered. We establish very general and at the same time natural conditions under which a canonical ... More

PageRank in undirected random graphsNov 16 2015Nov 25 2016PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning.In this paper, we study PageRank in undirected random graphs with expansion property. The Chung-Lu random graph representsan example ... More

Alpha current flow betweenness centralityAug 12 2013A class of centrality measures called betweenness centralities reflects degree of participation of edges or nodes in communication between different parts of the network. The original shortest-path betweenness centrality is based on counting shortest ... More

Subgraph Detection with cues using Belief PropagationNov 10 2016Nov 23 2016We consider an Erdos-Renyi graph with $n$ nodes and edge probability $q$ that is embedded with a random subgraph of size $K$ with edge probabilities $p$ such that $p\textgreater{}q.$ We address the problem of detecting the subgraph nodes when only the ... More

Online Myopic Network CoveringDec 20 2012Efficient marketing or awareness-raising campaigns seek to recruit $n$ influential individuals -- where $n$ is the campaign budget -- that are able to cover a large target audience through their social connections. So far most of the related literature ... More

Singularly perturbed linear programs and Markov decision processesNov 21 2016Linear programming formulations for the discounted and long-run average MDPs have evolved along separate trajectories. In 2006, E. Altman conjectured that the two linear programming formulations of discounted and long-run average MDPs are, most likely, ... More

Monte Carlo Methods for Top-k Personalized PageRank Lists and Name DisambiguationAug 23 2010We study a problem of quick detection of top-k Personalized PageRank lists. This problem has a number of important applications such as finding local cuts in large graphs, estimation of similarity distance and name disambiguation. In particular, we apply ... More

Localization and AdS/CFT CorrespondenceAug 09 2016Aug 14 2016An interplay between localization and holography is reviewed with the emphasis on the AdS_5/CFT_4 correspondence.

Cross sections of Borel flows with restrictions on the distance setApr 08 2016Given a set of positive reals, we provide a necessary and sufficient condition for a free Borel flow to admit a cross section with all distances between adjacent points coming from this set.

Localization and AdS/CFT CorrespondenceAug 09 2016Oct 15 2016An interplay between localization and holography is reviewed with the emphasis on the AdS_5/CFT_4 correspondence.

A Primordial Origin for Misalignments Between Stellar Spin Axes and Planetary OrbitsApr 18 2013The presence of gaseous giant planets whose orbits lie in extreme proximity to their host stars ("hot Jupiters"), can largely be accounted for by planetary migration, associated with viscous evolution of proto-planetary nebulae. Recently, observations ... More

Stellar black hole mass function: determination and possible implications for fundamental gravityJul 10 2003We discuss masses of stellar black holes found in binary systems and errors in their determination. The observed mass distribution has a broad shape within the range $4-16 M_\odot$ without visible concentration to some preferred value. On the other hand, ... More

On the lowest energy excitations of one-dimensional strongly correlated electronsMar 06 1998Aug 28 1999It is proven that the lowest excitations $E_{low}(k)$ of one-dimensional half-integer spin generalized Heisenberg models and half-filled extended Hubbard models are $\pi$-periodic functions. For Hubbard models at fractional fillings $E_{low}{(k+ 2 k_f)} ... More

Resolvents of self-adjoint extensions with mixed boundary conditionsDec 21 2004Mar 30 2006We prove a variant of Krein's resolvent formula expressing the resolvents of self-adjoint extensions through the associated boundary conditions. Applications to solvable quantum-mechanical problems are discussed.

On the discrete spectrum of Robin Laplacians in conical domainsJul 31 2015We discuss several geometric conditions guaranteeing the finiteness or the infiniteness of the discrete spectrum for Robin Laplacians on conical domains.

Dimensional reduction of Lattice Gauge Theory in (2+1)DNov 15 2002This is my Ph.D. thesis defended earlier this year. It contains mostly information already presented in previous Bielefeld/Saclay papers on this subject, though in more detailed form. It also includes actual calculations and some unpublished material ... More

On signal and extraneous roots in Singular Spectrum AnalysisJun 17 2010In the present paper we study properties of roots of characteristic polynomials for the linear recurrent formulae (LRF) that govern time series. We also investigate how the values of these roots affect Singular Spectrum Analysis implications, in what ... More

On semiclassical dispersion relations of Harper-like operatorsJan 28 2004Oct 20 2004We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical Hamiltonian is studied ... More

Illumination of convex bodies with many symmetriesJun 29 2016Oct 05 2016Let $n\geq C$ for a large universal constant $C>0$, and let $B$ be a convex body in $R^n$ such that for any $(x_1,x_2,\dots,x_n)\in B$, any choice of signs $\varepsilon_1,\varepsilon_2,\dots,\varepsilon_n\in\{-1,1\}$ and for any permutation $\sigma$ on ... More

Coupled mass-momenta balance for modeling material failureOct 27 2016Cracks are created by massive breakage of molecular or atomic bonds. The latter, in its turn, leads to the highly localized loss of material, which is the reason why even closed cracks are visible by a naked eye. Thus, fracture can be interpreted as the ... More

Localization in a quasiperiodic model on quantum graphsJul 13 2007We show the presence of a dense pure point spectrum on quantum graphs with Maryland-type quasiperiodic Kirchhoff coupling constants at the vertices.

A remark on the discriminant of Hill's equation and Herglotz functionsJan 08 2014We establish a link between the basic properties of the discriminant of periodic second-order differential equations and an elementary analysis of Herglotz functions. Some generalizations are presented using the language of self-adjoint extensions.

An example of unitary equivalence between self-adjoint extensions and their parametersDec 31 2012Jan 08 2013The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of operator-valued ... More

Localization effects in a periodic quantum graph with magnetic field and spin-orbit interactionJul 18 2006Aug 08 2006A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in ... More

CMS results on soft diffractionOct 09 2013We present measurements of soft single- and double-diffractive cross sections, as well as of forward rapidity gap cross sections at 7 TeV at the LHC, and compare the results to other measurements and to theoretical predictions implemented in various Monte ... More

Subset Simulation Method for Rare Event Estimation: An IntroductionMay 13 2015This paper provides a detailed introductory description of Subset Simulation, an advanced stochastic simulation method for estimation of small probabilities of rare failure events. A simple and intuitive derivation of the method is given along with the ... More

On the orientation of graphsDec 27 2000In this short notice we give a universal definition of $\Z_2$-module $Or(\Gamma)$ of orientations of a graph $\Gamma$ and construct a method, by means of which one can easily verify whenever two such special definitions coincide.

Smirnov's observable for free boundary conditions, interfaces and crossing probabilitiesApr 01 2014Dec 11 2014We prove convergence results for variants of Smirnov's fermionic observable in the critical Ising model in presence of free boundary conditions. One application of our analysis is a simple proof of a theorem by Hongler and Kyt\"ol\"a on convergence of ... More

On one uniqueness theorem for M. Rietz potentialsDec 12 2007We prove that there exists a nonzero holderian real-to-real function vanishing together with its M. Rietz potential in all points of some set of positive length. This result improves the one of D. Beliaev and V. Havin. We also extend the results to multidimensional ... More

Convexity of Hypersurfaces in Spherical SpacesAug 23 2007Oct 02 2007A spherical set is called convex if for every pair of its points there is at least one minimal geodesic segment that joins these points and lies in the set. We prove that for n >= 3 a complete locally-convex (topological) immersion of a connected (n-1)-manifold ... More

On locally convex PL-manifolds and fast verification of convexitySep 23 2003Nov 24 2003We show that a realization of a closed connected PL-manifold of dimension n-1 in Euclidean n-space (n>2) is the boundary of a convex polyhedron if and only if the interior of each (n-3)-face has a point, which has a neighborhood lying on the boundary ... More

A Fast Audio Clustering Using Vector Quantization and Second Order StatisticsSep 23 2010This paper describes an effective unsupervised speaker indexing approach. We suggest a two stage algorithm to speed-up the state-of-the-art algorithm based on the Bayesian Information Criterion (BIC). In the first stage of the merging process a computationally ... More

Stellar explosions: from supernovae to gamma-ray burstsOct 14 2004Current understanding of core collapse and thermonuclear supernovae is reviewed. Recent progress in unveiling the nature of cosmic gamma-ray bursts (GRB) is discussed, with the focus on the apparent link of several GRBs with an energetic subclass of stellar ... More

Einstein-Podolsky-Rosen paradox and measurement of quantum systemFeb 13 1999Einstein-Podolsky-Rosen (EPR) paradox is considered in a relation to a measurement of an arbitrary quantum system . It is shown that the EPR paradox always appears in a gedanken experiment with two successively joined measuring devices.

On the Robin eigenvalues of the Laplacian in the exterior of a convex polygonNov 07 2014Jan 26 2015Let $\Omega\subset \mathbb{R}^2$ be the exterior of a convex polygon whose side lengths are $\ell_1,...,\ell_M$. For $\alpha>0$, let $H^\Omega_\alpha$ denote the Laplacian in $\Omega$, $u\mapsto -\Delta u$, with the Robin boundary conditions $\partial ... More

Spectra of Schroedinger operators on equilateral quantum graphsDec 28 2005Jan 05 2006We consider magnetic Schroedinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator. In particular, ... More

Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structuresSep 04 2011We consider a class of self-adjoint extensions using the boundary triple technique. Assuming that the associated Weyl function has the special form $M(z)=\big(m(z)\Id-T\big) n(z)^{-1}$ with a bounded self-adjoint operator $T$ and scalar functions $m,n$ ... More

Singlet Free Energies of a Static Quark-Antiquark PairSep 01 2004We study the singlet part of the free energy of a static quark anti-quark pair at finite temperature in three flavor QCD with degenerate quark masses using $N_{\tau}=4$ and 6 lattices with Asqtad staggered fermion action. We look at thermodynamics of ... More

Statistically self-similar fractal setsDec 24 2001In the present paper we define statistically self-similar sets, and, using a modification of method described K.J.Falconer find a Hausdorff dimension of a statistically self-similar set.

Particle Dark Matter from Physics Beyond the Standard ModelFeb 09 2004In this talk I contrast three different particle dark matter candidates, all motivated by new physics beyond the Standard Model: supersymmetric dark matter, Kaluza-Klein dark matter, and scalar dark matter. I then discuss the prospects for their discovery ... More

Critical Ising interfaces in multiply-connected domainsSep 20 2013Mar 13 2015We prove a general result on convergence of interfaces in the critical planar Ising model to conformally invariant curves absolutely continuous with respect to SLE(3). Our setup includes multiple interfaces on arbitrary finitely connected domains, and ... More

Fast Verification of Convexity of Piecewise-linear SurfacesSep 23 2003Nov 24 2003We show that a realization of a closed connected PL-manifold of dimension n-1 in n-dimensional Euclidean space (n>2) is the boundary of a convex polyhedron (finite or infinite) if and only if the interior of each (n-3)-face has a point, which has a neighborhood ... More

On approximation of homeomorphisms of a Cantor setOct 03 2005Jan 24 2007We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology tau, which was started in the paper (S. Bezuglyi, A.H. Dooley, and J. Kwiatkowski, Topologies on the group of ... More

Centres of skewfields and completely faithful Iwasawa modulesOct 29 2007Let H be a torsionfree compact p-adic analytic group whose Lie algebra is split semisimple. We show that the quotient skewfield of fractions of the Iwasawa algebra \Lambda_H of H has trivial centre and use this result to classify the prime c-ideals in ... More

Measurements of Diffractive Processes at CDFJun 10 2003We review the results of measurements on hard diffractive processes performed by the CDF Collaboration and report preliminary CDF results on two soft diffractive processes with a leading antiproton and a rapidity gap in addition to that associated with ... More

Aspects of Diffraction at the TevatronAug 18 2003Results on soft and hard diffraction obtained by the CDF Collaboration at the Fermilab Tevatron proton-antiproton Collider are reviewed with emphasis on aspects of the data that point to the underlying QCD mechanism for diffraction. The results are interpreted ... More

Surface Curvature Effects on Reflectance from Translucent MaterialsOct 13 2010Nov 15 2010Most of the physically based techniques for rendering translucent objects use the diffusion theory of light scattering in turbid media. The widely used dipole diffusion model (Jensen et al. 2001) applies the diffusion-theory formula derived for a planar ... More

Sample covariance matrices of heavy-tailed distributionsJun 11 2016Let $p>2$, $B\geq 1$, $N\geq n$ and let $X$ be a centered $n$-dimensional random vector with the identity covariance matrix such that $\sup\limits_{a\in S^{n-1}}{\mathrm E}|\langle X,a\rangle|^p\leq B$. Further, let $X_1,X_2,\dots,X_N$ be independent ... More

Capture of Planets Into Mean Motion Resonances and the Origins of Extrasolar Orbital ArchitecturesMay 07 2015The early stages of dynamical evolution of planetary systems are often shaped by dissipative processes that drive orbital migration. In multi-planet systems, convergent amassing of orbits inevitably leads to encounters with rational period ratios, which ... More

On the spectrum of a waveguide with periodic cracksJul 21 2010The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small.

Theory of 2D metal-insulator transition I: Zero Magnetic fieldDec 26 2000We propose a scaling theory of 2D metal insulator transition discovered by Kravchenko and coworkers. In this theory conductance/resistance duality is an exact relation. The exponent of the stretched exponential in $\sigma(T)$ is determined by the temperature ... More

On some upper bounds for spin velocity and instability of gapless state of 1-d Heisenberg chainsOct 19 1999We derive upper bounds for spin velocity in half-integer-spin Heisenberg antiferromagnetic chains. We relate these upper bounds to the instability of the gapless state, which is observed in frustrated systems.

Statistical InferenceMar 16 2016What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly reporting p-values ... More

Reducible boundary conditions in coupled channelsJun 03 2005Sep 07 2005We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs we describe a class of the operators which can be reduced to the direct sum of several one-dimensional problems. ... More

Prime ideals in nilpotent Iwasawa algebrasAug 01 2011Let G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of G, and use this to show that the prime spectrum of ... More

Strongly normal cones and the midpoint locally uniform rotundityDec 06 2011We give the method of construction of normal but not strongly normal positive cones in Banach space.

TASI Lectures on Precision Electroweak PhysicsFeb 03 2004These notes are a written version of a set of lectures given at TASI-02 on the topic of precision electroweak physics.

The Classification of Rigid Irregular $G_2$-ConnectionsSep 12 2016Sep 28 2016Using the Katz-Arinkin algorithm we give a complete classification of irreducible rigid irregular connections on a punctured $\mathbb{P}^1_{\mathbb{C}}$ having differential Galois group $G_2$, the exceptional simple algebraic group. In addition to hypergeometric ... More

Bordism classes of the multiple points manifoldsAug 07 2000Let $f:V^n\looparrowright M^m$ be a smooth generic immersion. Then the set of points, that have at least $k$ preimages is an image of a (non-generic) immersion. If the manifolds $V^n$ and $M^m$ are oriented and $m-n$ is even, then the manifold of $k$-fold ... More

Dynamics of infinite-multivalued transformationsDec 08 2004We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of $m$-transformations we ... More

Variational principle for Hamiltonians with degenerate bottomOct 25 2007We consider perturbations of Hamiltonians whose Fourier symbol attains its minimum along a hypersurface. Such operators arise in several domains, like spintronics, theory of supercondictivity, or theory of superfluidity. Variational estimates for the ... More

An inequality for the maximum curvature through a geometric flowJan 15 2015Jul 29 2015We provide a new proof of the following inequality: the maximum curvature $k_\mathrm{max}$ and the enclosed area $A$ of a smooth Jordan curve satisfy $k_\mathrm{max}\ge \sqrt{\pi/A}$. The feature of our proof is the use of the curve shortening flow.

A high speed unsupervised speaker retrieval using vector quantization and second-order statisticsAug 27 2010Sep 09 2010This paper describes an effective unsupervised method for query-by-example speaker retrieval. We suppose that only one speaker is in each audio file or in audio segment. The audio data are modeled using a common universal codebook. The codebook is based ... More

On time change equivalence of Borel flowsSep 19 2016This paper addresses the notion of time change equivalence for Borel multidimensional flows. We show that all free flows are time change equivalent up to a compressible set. An appropriate version of this result for non-free flows is also given.

Note on the question of SikoraNov 01 2007A natural topology on the set of left orderings on free abelian groups and free groups $F_n$, $n>1$ has studied in [1]. It has been proven already that in the abelian case the resulted topological space is a Cantor set. There was a conjecture: this is ... More

On the asymptotics of the principal eigenvalue for a Robin problem with a large parameter in planar domainsMay 14 2013Let $\Omega\subset \RR^2$ be a domain having a compact boundary $\Sigma$ which is Lipschitz and piecewise $C^4$ smooth, and let $\nu$ denote the inward unit normal vector on $\Sigma$. We study the principal eigenvalue $E(\beta)$ of the Laplacian in $\Omega$ ... More

Quasiperiodic surface Maryland models on quantum graphsNov 20 2008We study quantum graphs corresponding to isotropic lattices with quasiperiodic coupling constants given by the same expressions as the coefficients of the discrete surface Maryland model. The absolutely continuous and the pure point spectra are described. ... More

On the distribution of the Brownian motion process on its way to hitting zeroJan 05 2010Apr 07 2010We present functional versions of recent results on the univariate distributions of the process $V_{x,u} = x + W_{u\tau(x)},$ $0\le u\le 1$, where $W_\bullet$ is the standard Brownian motion process, $x>0$ and $\tau (x) =\inf\{t>0 : W_{t}=-x\}$.

Tame Decompositions and CollisionsFeb 24 2014A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The tame case, where ... More

On the chromatic number of a simplicial complexJun 20 2013Nov 17 2015In [Ho] A.J. Hoffman proved a lower bound on the chromatic number of a graph in the terms of the largest and the smallest eigenvalues of its adjacency matrix. In this paper, we prove a higher dimensional version of this result and give a lower bound on ... More

Full Groups and Orbit Equivalence in Cantor DynamicsJun 06 2010Jul 15 2010In this note we consider dynamical systems $(X,G)$ on a Cantor set $X$ satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems $(X_1,G_1)$ and $(X_2,G_2)$ ... More