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On the equivalence between multiclass processor sharing and random order scheduling policiesApr 06 2017Apr 11 2018Consider a single server system serving a multiclass population. Some popular scheduling policies for such system are the discriminatory processor sharing (DPS), discriminatory random order service (DROS), generalized processor sharing (GPS) and weighted ... 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

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

Metastability in Stochastic Replicator DynamicsJan 07 2018May 07 2018We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed due to non-uniqueness ... More

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

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

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

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

Distributed Cooperative Caching for VoD with Geographic ConstraintsMar 05 2019We consider caching of video streams in a cellular network in which each base station is equipped with a cache. Video streams are partitioned into multiple substreams and the goal is to place substreams in caches such that the residual backhaul load is ... More

Hamiltonian System Approach to Distributed Spectral Decomposition in NetworksApr 04 2017Nov 23 2017Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper we develop efficient ... 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

Similarities on Graphs: Kernels versus Proximity MeasuresFeb 17 2018We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of specific similarity ... 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

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

Impulsive Control for G-AIMD Dynamics with Relaxed and Hard ConstraintsMar 19 2018Motivated by various applications from Internet congestion control to power control in smart grids and electric vehicle charging, we study Generalized Additive Increase Multiplicative Decrease (G-AIMD) dynamics under impulsive control in continuous time ... 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

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

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

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

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

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

Linearly Convergent Asynchronous Distributed ADMM via Markov SamplingOct 11 2018We consider the consensual distributed optimization problem and propose an asynchronous version of the Alternating Direction Method of Multipliers (ADMM) algorithm to solve it. The `asynchronous' part here refers to the fact that only one node/processor ... 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

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

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

The Power of Side-information in Subgraph DetectionNov 10 2016Mar 06 2017In this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erd\H{o}s-R\'enyi (ER) graph embedded in a larger and sparser ER graph, in the presence of side-information. ... 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

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

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

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

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

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

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

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

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

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

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

PageRank in Undirected Random GraphsMar 23 2017PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning. In this paper, we study PageRank in undirected random graphs with an expansion property. The Chung-Lu random graph is an example ... 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

Real-Time Fair Resource Allocation in Distributed Software Defined NetworksNov 27 2017The performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time.To address this issue, bandwidth sharing techniques that quickly ... More

Multi-Path Alpha-Fair Resource Allocation at Scale in Distributed Software Defined NetworksSep 04 2018Sep 12 2018The performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time. To address this issue, bandwidth sharing techniques that quickly ... More

Graphlet Count Estimation via Convolutional Neural NetworksOct 07 2018Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two possible 4-node ... 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

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

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

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

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

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

Computing Entanglement PolytopesAug 09 2018In arXiv:1208.0365 entanglement polytopes where introduced as a coarsening of the SLOCC classification of multipartite entanglement. The advantages of classifying entanglement by entanglement polytopes are a finite hierarchy for all dimensions and a number ... 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

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

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

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

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

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.

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

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 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

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

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.

Strengthening of copper by carbon nanotubesOct 18 2018The influence of a modifier based on multi walled carbon nanotubes (MWCNT) is investigated using C11000 copper alloy. The influence of the modifier addition into the melt was investigated using tensile test, hardness measurements, X-ray diffraction method ... 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.

Pseudoscalar flavor-singlet mesons from lattice QCDMay 20 2019We investigate the masses and mixing of $\eta$, $\eta'$ mesons in the framework of twisted mass lattice QCD with $N_f=2+1+1$ dynamical quark flavors. For the first time we perform a controlled chiral and continuum extrapolation to obtain physical results. ... More

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 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

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

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

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

Eigenvalue inequalities and absence of threshold resonances for waveguide junctionsJun 30 2016Sep 27 2016Let $\Lambda\subset \mathbb{R}^d$ be a domain consisting of several cylinders attached to a bounded center. One says that $\Lambda$ admits a threshold resonance if there exists a non-trivial bounded function $u$ solving $-\Delta u=\nu u$ in $\Lambda$ ... More

Variational proof of the existence of eigenvalues for star graphsNov 30 2015We provide a purely variational proof of the existence of eigenvalues below the bottom of the essential spectrum for the Schr\"odinger operator with an attractive $\delta$-potential supported by a star graph, i.e. by a finite union of rays emanating from ... 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.

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

Equivalence of Wilson Loops in ABJM and N = 4 SYM TheoryOct 06 2011Oct 27 2011In previous investigations, it was found that four-sided polygonal light-like Wilson loops in ABJM theory calculated to two-loop order have the same form as the corresponding Wilson loop in N = 4 SYM at one-loop order. Here we study light-like polygonal ... More

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

Classification of Rigid Irregular $G_2$-ConnectionsSep 12 2016Jul 16 2018Using the Katz-Arinkin algorithm we give a 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, and slopes having numerator ... More

D-modules on rigid analytic spacesJul 21 2014We give an overview of the theory of $\wideparen{\mathcal{D}}$-modules on rigid analytic spaces and its applications to admissible locally analytic representations of $p$-adic Lie groups.

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.

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

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.

An Efficient Local Approach to Convexity Testing of Piecewise-Linear HypersurfacesMar 07 2007We show that a closed piecewise-linear hypersurface immersed in $R^n$ ($n\ge 3$) is the boundary of a convex body if and only if every point in the interior of each $(n-3)$-face has a neighborhood that lies on the boundary of some convex body; no assumptions ... 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

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

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

Graev ultrametrics and free products of Polish groupsDec 12 2012Oct 10 2013We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two Polish groups ... More