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Learnable Triangulation of Human PoseMay 14 2019We present two novel solutions for multi-view 3D human pose estimation based on new learnable triangulation methods that combine 3D information from multiple 2D views. The first (baseline) solution is a basic differentiable algebraic triangulation with ... More

Growing homophilic networks are natural navigable small worldsJul 23 2015Mar 02 2016Navigability, an ability to find a logarithmically short path between elements using only local information, is one of the most fascinating properties of real-life networks. However, the exact mechanism responsible for the formation of navigation properties ... More

Newly-Discovered Anomalies in Galactic Cosmic Rays: Time for Exotic Scenarios?Mar 16 2017Recent observations of galactic cosmic rays (CR) in the 1-500 GeV energy range have revealed striking deviations from what deemed "standard." The anomalies cut across hadronic and leptonic CRs. I discuss findings that challenge physical mechanisms long ... More

Revisiting the Inverted Indices for Billion-Scale Approximate Nearest NeighborsFeb 07 2018This work addresses the problem of billion-scale nearest neighbor search. The state-of-the-art retrieval systems for billion-scale databases are currently based on the inverted multi-index, the recently proposed generalization of the inverted index structure. ... More

Off the Beaten Path: Let's Replace Term-Based Retrieval with k-NN SearchOct 31 2016Retrieval pipelines commonly rely on a term-based search to obtain candidate records, which are subsequently re-ranked. Some candidates are missed by this approach, e.g., due to a vocabulary mismatch. We address this issue by replacing the term-based ... More

Cosmic Ray Confinement and Transport Models for Probing their Putative SourcesMar 04 2015Recent efforts in cosmic ray (CR) confinement and transport theory are discussed. Three problems are addressed as being crucial for understanding the present day observations and their possible telltale signs of the CR origin. The first problem concerns ... More

Cosmic Ray Transport with Magnetic Focusing and the "Telegraph" modelFeb 06 2015Jun 24 2015Cosmic rays (CR), constrained by scattering on magnetic irregularities, are believed to propagate diffusively. But a well-known defect of diffusive approximation whereby some of the particles propagate unrealistically fast has directed interest towards ... More

Spectral universality of strong shocks accelerating charged particlesJul 09 1998As a rule, the shock compression controls the spectrum of diffusively accelerated particles. We argue that this is not so if the backreaction of these particles on the shock structure is significant. We present a self-similar solution in which the accelerated ... More

Analytic solution for nonlinear shock acceleration in the Bohm limitJul 14 1997The selfconsistent steady state solution for a strong shock, significantly modified by accelerated particles is obtained on the level of a kinetic description, assuming Bohm-type diffusion. The original problem that is commonly formulated in terms of ... More

Cosmic Ray Spectra in Supernova Remnants - I. Loss-Free Self-Similar SolutionJan 04 2019The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra should be significantly steeper than the canonical $E^{-2}$ spectrum predicted by the standard Diffusive ... More

Eigenwaves in Waveguides with Dielectric Inclusions: CompletenessSep 25 2012We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a defect. Then ... More

Eigenwaves in Waveguides with Dielectric Inclusions: SpectrumSep 24 2012We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an ... More

Geometric explanation of the rich-club phenomenon in complex networksFeb 08 2017Dec 04 2017The rich club organization (the presence of highly connected hub core in a network) influences many structural and functional characteristics of networks including topology, the efficiency of paths and distribution of load. Despite its major role, the ... More

Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphsMar 30 2016May 21 2016We present a new algorithm for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW). The proposed approach is fully graph-based, without any need for additional search structures ... More

The Hodge filtration on complements of complex coordinate subspace arrangements and integral representations of holomorphic functionsMay 12 2013We compute the Hodge filtration on cohomology groups of complements of complex coordinate subspace arrangements. By means of this result we construct integral representations of holomorphic functions such that kernels of these representations have singularities ... More

Geometry of compact complex manifolds with maximal torus actionFeb 08 2016In this present paper we study geometry of compact complex manifolds equipped with a \emph{maximal} torus $T=(S^1)^k$ action. We give two equivalent constructions providing examples of such manifolds given a simplicial fan $\Sigma$ and a compelx subgroup ... More

Even and odd plane labelled bipartite treesNov 03 2016Let $T(n,m)$ be the set of all plane labelled bipartite trees with $n$ white vertices and $m$ black. If the number $n+m$ of vertices is even, then the set $T(n,m)$ is a union of two disjoint subsets --- subset od "even" trees and subset of "odd" trees. ... More

Preferential attachment combined with random number of choicesDec 07 2016We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the following way. ... More

A remark on representations of infinite symmetric groupsApr 18 2012We simplify construction of Thoma representations of an infinite symmetric group

Schur parameters, Toeplitz matrices, and Kreĭn shorted operatorsSep 19 2011We establish connections between Schur parameters of the Schur class operator-valued functions, the corresponding simple conservative realizations, lower triangular Toeplitz matrices, and Kre\u\i n shorted operators. By means of Schur parameters or shorted ... More

Visual analytics in FCA-based clusteringApr 21 2015Visual analytics is a subdomain of data analysis which combines both human and machine analytical abilities and is applied mostly in decision-making and data mining tasks. Triclustering, based on Formal Concept Analysis (FCA), was developed to detect ... More

Direct Majorana quasiparticles heat capacity observation by $^3$He Dark Matter detectorMar 28 2013The Majorana fermion: fermion that is its own antiparticle, was predicted by Majorana in 1937. No fundamental particles are known to be Majorana fermions, although there are speculations that the neutrino is one. Many proposed theories assumes that the ... More

Gerstenhaber bracket on the Hochschild cohomology via an arbitrary resolutionOct 18 2016We prove formulas of different types that allow to calculate the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. Also we give some new formulas for the Connes' differential on ... More

Neutrino detectors for oscillation experimentsMay 17 2017A brief overview of the development of neutrino detectors for long-baseline oscillation experiments at accelerators and reactors is presented. Basic principles and main features of detectors of running accelerator experiments T2K and NOvA sensitive to ... More

Bony attractors in higher dimensionMay 16 2013In this article, we extend the phenomena of a bony attractor from a rather artificial class of step skew products to the class of diffeomorphisms on the Cartesian product of the two-dimensional torus by a sphere of arbitrary dimension.

On statistical researches of parliament elections in Russian Federation, 04.12.2011Jan 12 2012There is a lot of statistical researches of Russian elections 04.12.2011. The purpose of this activity is to give a mathematical proof of large falsifications and to estimate possible 'real results of elections'. My purpose is to show that 1. Statistical ... More

High degree vertices in the Power of Choice model combined with Preferential AttachmentAug 30 2016We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following way. At each ... More

On metric properties of maps between Hamming spaces and related graph homomorphismsMar 10 2015Apr 30 2016A mapping of $k$-bit strings into $n$-bit strings is called an $(\alpha,\beta)$-map if $k$-bit strings which are more than $\alpha k$ apart are mapped to $n$-bit strings that are more than $\beta n$ apart. This is a relaxation of the classical problem ... More

Several remarks on groups of automorphisms of free groupsJun 25 2013Let $G$ be the group of automorphisms of a free group $F_\infty$ of infinite order. Let $H$ be the stabilizer of first $m$ generators of $F_\infty$. We show that the double cosets of $\Gamma$ with respect to $H$ admit a natural semigroup structure. For ... More

On the Structure of Hermitian Manifolds with Semipositive Griffiths CurvatureApr 15 2019In this paper we establish partial structure results on the geometry of compact Hermitian manifolds of semipositive Griffiths curvature. We show that after appropriate arbitrary small deformation of the initial metric, the null spaces of the Chern-Ricci ... More

Hermitian curvature flow on manifolds with non-negative Griffiths curvatureApr 17 2016In this paper we study a particular version of the Hermitian curvature flow (HCF) over a compact complex Hermitian manifold $(M,g,J)$. We prove that if the initial metric has Griffiths positive (non-negative) Chern curvature $\Omega$, then this property ... More

On almost free torus actions and Horrocks conjectureMar 16 2012Jul 20 2012We construct a model for cohomology of a space $X$ equipped with a torus $T$ action, whose homotopy orbit space $X_{T}$ is formal. This model represents Koszul complex of its equivariant cohomology. Studying homological properties of modules over polynomial ... More

On face numbers of flag simplicial complexesOct 12 2016Denham, Suciu and Panov, Ray computed ranks of homotopy groups and Poincar\'e series of a moment-angle-complex $\mathcal Z(\mathcal K$) / Davis-Januzskiewicz space $DJ(\mathcal K)$ associated to a flag simplicial complex $\mathcal K$. In this note we ... More

Dynamics of internal envelope solitons in a rotating fluid of a variable depthMar 19 2019We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where the growth rate ... More

Dynamics of internal envelope solitons in a rotating fluid of a variable depthMar 19 2019Mar 22 2019We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where the growth rate ... More

Preferential attachment combined with random number of choicesDec 07 2016Oct 26 2017We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the following way. ... More

BV-differential on Hochschild cohomology of Frobenius algebrasMay 20 2014For a finite-dimensional Frobenius $k$-algebra $R$ with the Nakayama automorphism $\nu$ we define an algebra ${\rm HH}^*(R)^{\nu\uparrow}$. If the order of $\nu$ is not divisible by the characteristic of $k$, this algebra is isomorphic to the Hochschild ... More

On the boundary of the group of transformations leaving a measure quasi-invariantNov 11 2011May 18 2013Let $A$ be a Lebesgue measure space. We interpret measures on $A\times A\times R_+$ as 'maps' from $A$ to $A$, which spread $A$ along itself; their Radon-Nikodym derivatives also are spread. We discuss basic properties of the semigroup of such maps and ... More

The Schur problem and block operator CMV matricesJul 01 2013Jul 21 2013The CMV matrices and their sub-matrices are applied to the description of all solutions to the Schur interpolation problem for contractive analytic operator-valued functions in the unit disk (the Schur class functions).

The Kalman--Yakubovich--Popov inequality for passive discrete time-invariant systemsMay 04 2007We consider the Kalman - Yakubovich - Popov (KYP) inequality \[ \begin{pmatrix} X-A^* XA-C^*C & -A^*X B- C^*D\cr -B^*X A-D^* C & I- B^*X B-D^*D \end{pmatrix} \ge 0 \] for contractive operator matrices $ \begin{pmatrix} A&B\cr C &D \end{pmatrix}:\begin{pmatrix}\mathfrak{H}\cr\mathfrak{M} ... More

Doubling operation for polytopes and torus actionsSep 05 2009In this note we give the definition of the "doubling operation" for simple polytopes, find the formula for the h-polynomial of new polytope.As an application of this operation we establish the relationship between moment-angle manifolds and their real ... More

Preconditioned Krylov subspace methods for sixth order compact approximations of the Helmholtz equationDec 06 2012In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and preconditioned Krylov ... More

Toral rank conjecture for moment-angle complexesSep 05 2009Sep 29 2009We consider an operation K \to L(K) on the set of simplicial complexes, which we call the "doubling operation". This combinatorial operation has been recently brought into toric topology by the work of Bahri, Bendersky, Cohen and Gitler on generalised ... More

On some generalizations of the property $B$-problem of an $n$-uniform hypergraphMar 27 2019The extremal problem of hypergraph colorings related to Erd\H{o}s--Hajnal property $B$-problem is considered. Let $k$ be a natural number. The problem is to find the value of $m_k(n)$ equal to the minimal number of edges in an $n$-uniform hypergraph not ... More

Lamination exact relations and their stability under homogenizationOct 01 2012Sep 18 2013Relations between components of the effective tensors of composites that hold regardless of composite's microstructure are called exact relations. Relations between components of the effective tensors of all laminates are called lamination exact relations. ... More

Iterates of the Schur class operator-valued function and their conservative realizationsJan 28 2008Aug 19 2008Let $\mathfrak M$ and $\mathfrak N$ be separable Hilbert spaces and let $\Theta(\lambda)$ be a function from the Schur class ${\bf S}(\mathfrak M,\mathfrak N)$ of contractive functions holomorphic on the unit disk. The operator generalization of the classical ... More

UHECR Acceleration in Dark Matter Filaments of Cosmological Structure FormationJan 25 2011Apr 08 2011A mechanism for proton acceleration to ~10^21eV is suggested. It may operate in accretion flows onto thin dark matter filaments of cosmic structure formation. The flow compresses the ambient magnetic field to strongly increase and align it with the filament. ... More

Nonlinear shock acceleration beyond the Bohm limitSep 08 2005We suggest a physical mechanism whereby the acceleration time of cosmic rays by shock waves can be significantly reduced. This creates the possibility of particle acceleration beyond the knee energy at ~10^15eV. The acceleration results from a nonlinear ... More

Size dependency for the thermal physical properties of nano-sized objects in representation of Hill's nanothermodynamicsDec 19 2014Jan 09 2015We consider the problem of constructing the size dependence for the thermal physical properties of nano-sized objects, taking specific heat as an example. The base methodology is Hill's nanothermodynamics. Having to abstain from use of the additivity ... More

Partition sum in vibron model in case of non-additivity (nano-sized objects)Dec 19 2014We consider the problem of building an expression for the partition sum in case of non-additivity (nano-sized objects), in the framework of Hill's nanothermodynamics. Having to use not the additivity concept leads to the problem of building the generalised ... More

Solving Classical String Problems on Compressed TextsApr 13 2006Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing LZ-compressed texts. The ... More

Casimir interaction between gas media of excited atomsNov 19 2006The retarded dispersion interaction (Casimir interaction) between two dilute dielectric media at high temperatures is considered. The excited atoms are taken into account. It is shown that the perturbation technique can not be applied to this problem ... More

Geometry of generalized amoebasAug 22 2016Recently Krichever proposed a generalization of the amoeba and the Ronkin function of a plane algebraic curve. In our paper higher-dimensional version of this generalization is studied. We translate to the generalized case different geometric results ... More

Active Correlation Technique: Status and DevelopmentJun 06 2015During the recent years, at the FLNR a successful cycle of experiments has been accomplished on the synthesis of the superheavy elements with Z=112 to Z=118 using 48Ca ion beam. From the viewpoint of the detection of rare decays and background suppression, ... More

Difference Sturm--Liouville problems in the imaginary directionApr 11 2011We consider difference operators in $L^2$ on $\R$ of the form $$ L f(s)=p(s)f(s+i)+q(s) f(s)+r(s) f(s-i) ,$$ where $i$ is the imaginary unit. The domain of definiteness are functions holomorphic in a strip with some conditions of decreasing at infinity. ... More

Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat--Tits builldingsAug 24 2011Nov 02 2014We construct $p$-adic analogs of operator colligations and their characteristic functions. Consider a $p$-adic group $G=GL(\alpha+k\infty, Q_p)$, its subgroup $L=O(k\infty,Z_p)$, and the subgroup $K=O(\infty,Z_p)$ embedded to $L$ diagonally. We show that ... More

Existence of an invariant measure on a hypergroupDec 28 2012We prove existence of an invariant measure on a hypergroup.

Conservative discrete time-invariant systems and block operator CMV matricesAug 12 2008It is well known that an operator-valued function $\Theta$ from the Schur class ${\bf S}(\mathfrak M,\mathfrak N)$, where $\mathfrak M$ and $\mathfrak N$ are separable Hilbert spaces, can be realized as the transfer function of a simple conservative discrete ... More

Dynamics of Mesoscale Magnetic Field in Diffusive Shock AccelerationMay 15 2006We present a theory for the generation of mesoscale ($kr_{g}\ll 1$, where $r_{g}$ is the cosmic ray gyroradius) magnetic fields during diffusive shock acceleration. The decay or modulational instability of resonantly excited Alfven waves scattering off ... More

Modern theory of Fermi acceleration: a new challenge to plasma physicsFeb 21 2001One of the main features of astrophysical shocks is their ability to accelerate particles to extremely high energies. The leading acceleration mechanism, the diffusive shock acceleration is reviewed. It is demonstrated that its efficiency critically depends ... More

Anomalies in Cosmic Ray Composition: Explanation Based on Mass to Charge RatioJul 10 2017High precision spectrometry of galactic cosmic rays (CR) has revealed the lack of our understanding of how different CR elements are extracted from the supernova environments to be further accelerated in their shocks. Comparing the spectra of accelerated ... More

Various virtual structures on single file systemSep 13 2010Sep 16 2010The article provides a new approach to creating hierarchical structure of file system. First, it gives overview of the existing ways of storing files in current operating systems. Second, it describes the new way of building structures of a file system. ... More

Estimation of parameters of boundary value problems for linear ordinary differential equations with uncertain dataDec 15 2009In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear ... More

Estimation under uncertainties of acoustic and electromagnetic fields from noisy observationsOct 13 2009The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the determination ... More

Comparative analysis of modern empirical spectrophotometric atlases with multicolor photometric cataloguesAug 09 2012We present the results of the comparative analysis of the most known semi-empirical and empirical spectral atlases that was carried out using the data from the WBVR photometric catalogue. The results show that standard error of synthesized stellar magnitudes ... More

Binary Star Database (BDB): New Developments and ApplicationsNov 09 2018Binary star DataBase (BDB) is the database of binary/multiple systems of various observational types. BDB contains data on physical and positional parameters of 260,000 components of 120,000 stellar systems of multiplicity 2 to more than 20, taken from ... More

Propagating Cosmic Rays with exact Solution of Fokker-Planck EquationMar 07 2017Shortfalls in cosmic ray (CR) propagation models obscure the CR sources and acceleration mechanisms. This problem became particularly obvious after the Fermi, Pamela, and AMS-02 have discovered the electron/positron and $p/$He spectral anomalies. Most ... More

Magnetic and density spikes in cosmic ray shock precursorsOct 03 2011In shock precursors populated by accelerated cosmic rays (CR), the CR return current instability is believed to significantly enhance the pre-shock perturbations of magnetic field. We have obtained fully-nonlinear exact ideal MHD solutions supported by ... More

Magnetic states of heterophase particle in the field of mechanical stressesApr 15 2012In this paper we investigate the dependence of the magnetic states of heterophase particles on mechanical multiaxial stresses. It is shown that for such particles, there are four possible states, and the conditions of stability of these states are determined. ... More

Phase Transitions in Systems with Finite Number of AtomsJan 07 2012Feb 20 2014Properties of nanoparticles have been studied within the framework of Ising model and the method of random-field interactions: the average magnetic moment and position of critical points of the magnetic and the concentration phase transitions depending ... More

On Properties of Estimators in non Regular Situations for Poisson ProcessesMar 26 2009We consider the problem of parameter estimation by observations of inhomogeneous Poisson process. It is well-known that if the regularity conditions are fulfilled then the maximum likelihood and Bayesian estimators are consistent, asymptotically normal ... More

Holomorphic operator valued functions generated by passive selfadjoint systemsJan 31 2018In this paper we study a class $\mathcal R\mathcal S(\mathfrak M)$ of operator functions that are holomorphic in the domain $\mathbb C\setminus\{(-\infty,-1]\cup [1,+\infty)\}$ and whose values are contractive operators in a Hilbert space $(\mathfrak ... More

The degeneration level classification of algebrasOct 24 2017The aim of the paper is to develop methods that will allow to classify algebras of small levels, i.e. such algebras that all chains of nontrivial degenerations starting at them have relatively small lengths. Accordingly, the algebra under consideration ... More

On the multicolor Ramsey number of a graph with m edgesNov 21 2013Nov 24 2013The multicolor Ramsey number $r_k(F)$ of a graph $F$ is the least integer $n$ such that in every coloring of the edges of $K_n$ by $k$ colors there is a monochromatic copy of $F$. In this short note we prove an upper bound on $r_k(F)$ for a graph $F$ ... More

Topological groups and invariant measuresOct 11 2015Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures, virtual permutations, ... More

IoT-enabled Distributed Cyber-attacks on Transmission and Distribution GridsJun 22 2017The Internet of things (IoT) will make it possible to interconnect and simultaneously control distributed electrical loads. Various technical and regulatory concerns have been raised that IoT-operated loads are being deployed without appropriately considering ... More

Symmetric groups and checker triangulated surfacesOct 31 2017We consider triangulations of surfaces with edges painted three colors so that edges of each triangle have different colors. Such structures arise as Belyi data (or Grothendieck dessins d'enfant), on the other hand they enumerate pairs of permutations ... More

Multi-operator colligations and multivariate characteristic functionsJun 11 2010In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We construct characteristic ... More

Causal Scattering Matrix and the Chronological ProductNov 03 2010A causal scattering matrix is constructed by means of the mixed chronological and normal product of the free quantum fields of different variables. This scattering matrix does not contain the diverging integrals.

On topologies on Lie braid groupsJun 06 2010Jun 25 2012We discuss groups corresponding to Kohno Lie algebra of infinitesimal braids and actions of such groups. We construct homomorphisms of Lie braid groups to the group of symplectomorphisms of the space of point configurations in $R^3$ and to groups of symplectomorphisms ... More

Surface states in AlGaN/GaN high electron mobility transistors: Quantitative profiles and dynamics of the surface Fermi levelApr 18 2019Apr 19 2019We present a method to obtain quantitative profiles of surface state charge density and monitor its dynamics under various stress conditions in high electron mobility transistor (HEMT) devices. The method employs an optical spectroscopy of the channel ... More

On nonlinear TAR processes and threshold estimationOct 05 2011May 25 2012We consider the problem of threshold estimation for autoregressive time series with a "space switching" in the situation, when the regression is nonlinear and the innovations have a smooth, possibly non Gaussian, probability density. Assuming that the ... More

Hua type beta-integrals and projective systems of measures on flag spacesJun 26 2014We construct a family of measures on flag spaces (or, equivalently, on the spaces of upper-triangular matrices) compatible with respect to natural projections. We obtain an $n(n-1)/2$-parametric family of beta-integrals over space of upper-triangular ... More

The space $L^2$ on semi-infinite Grassmannian over finite fieldSep 16 2012Sep 28 2013We construct a $GL$-invariant measure on a semi-infinite Grassmannian over a finite field, describe the natural group of symmetries of this measure, and decompose the space $L^2$ over the Grassmannian on irreducible representations. The spectrum is discrete, ... More

Branching integrals and Casselman phenomenonOct 13 2007Nov 23 2007Let $G$ be a real semisimple Lie group, $K$ its maximal complex subgroup, and $G_C$ its complexification. It is known that all the $K$-finite matrix elements on $G$ admit holomorphic continuation to branching functions on $G_C$ having singularities at ... More

Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argumentNov 29 2012May 28 2016We extend the classical construction of operator colligations and characteristic functions. Consider the group $G$ of finite block unitary matrices of size $\alpha+\infty+...+\infty$ ($k$ times). Consider the subgroup $K=U(\infty)$, which consists of ... More

Minimum degrees and codegrees of minimal Ramsey 3-uniform hypergraphsFeb 04 2015A uniform hypergraph $H$ is called $k$-Ramsey for a hypergraph $F$, if no matter how one colors the edges of $H$ with $k$ colors, there is always a monochromatic copy of $F$. We say that $H$ is minimal $k$-Ramsey for $F$, if $H$ is $k$-Ramsey for $F$ ... More

On Parameter Estimation of Hidden Ergodic Ornstein-Uhlenbeck ProcessFeb 22 2019We consider the problem of parameter estimation for the partially observed linear stochastic differential equation. We assume that the unobserved Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the unobserved process and the ... More

After Plancherel formulaJan 26 2018We discuss two topics related to Fourier transforms on Lie groups and on homogeneous spaces: the operational calculus and the Gelfand--Gindikin problem (program) about separation of non-uniform spectra. Our purpose is to indicate some non-solved problems ... More

Projective toric generators in the unitary cobordism ringFeb 08 2016Feb 24 2016By the classical result of Milnor and Novikov, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $\Omega^U_*\simeq \mathbb Z[a_1,a_2,\dots]$, ${\rm deg}(a_i)=2i$. In this paper we solve a well-known problem ... More

Superconducting State and Phase TransitionsJul 16 2016Jul 26 2016From the days when superconductivity was discovered its science was entangled by the unresolved problem of the relationship between superconductive state, its crystal structure and its phase transitions. The problem was exacerbated by the adjacent scientific ... More

Modeling of the magnetic properties of nanomaterials with different crystalline structureSep 12 2012Jan 13 2013We propose a method for modeling the magnetic properties of nanomaterials with different structures. The method is based on the Ising model and the approximation of the random field interaction. It is shown that in this approximation, the magnetization ... More

Genera of non-algebraic leaves of polynomial foliations of $\mathbb C^2$Jul 29 2014Mar 20 2015In this article, we prove two results. First, we construct a dense subset in the space of polynomial foliations of degree $n$ such that each foliation from this subset has a leaf with at least $\frac{(n+1)(n+2)}2-4$ handles. Next, we prove that for a ... More

Wishart--Pickrell distributions and closures of group actionsFeb 10 2016Jun 05 2016Consider probabilistic distributions on the space of infinite Hermitian matrices $Herm(\infty)$ invariant with respect to the unitary group $U(\infty)$. We describe the closure of $U(\infty)$ in the space of spreading maps (polymorphisms) of $Herm(\infty)$, ... More

Goodness-of-Fit Tests for Perturbed Dynamical SystemsMar 26 2009We consider the goodness of fit testing problem for stochastic differential equation with small diffiusion coefficient. The basic hypothesis is always simple and it is described by the known trend coefficient. We propose several tests of the type of Cramer-von ... More

Wasserstein continuity of entropy and outer bounds for interference channelsApr 17 2015Feb 02 2016It is shown that under suitable regularity conditions, differential entropy is a Lipschitz functional on the space of distributions on $n$-dimensional Euclidean space with respect to the quadratic Wasserstein distance. Under similar conditions, (discrete) ... More

Strong data-processing inequalities for channels and Bayesian networksAug 25 2015Jul 28 2016The data-processing inequality, that is, $I(U;Y) \le I(U;X)$ for a Markov chain $U \to X \to Y$, has been the method of choice for proving impossibility (converse) results in information theory and many other disciplines. Various channel-dependent improvements ... More

Conservative algebras of $2$-dimensional algebras, IIJul 08 2015In 1990 Kantor defined the conservative algebra $W(n)$ of all algebras (i.e. bilinear maps) on the $n$-dimensional vector space. If $n>1$, then the algebra $W(n)$ does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or ... More

Generalized derivations of (color) n-ary algebrasJun 02 2015We generalize the results of Leger and Luks about generalized derivations of Lie algebras to the case of color $n$-ary $\Omega$-algebras. Particularly, we prove some properties of generalized derivations of color $n$-ary algebras; prove that a quasiderivation ... More

A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivationsJun 02 2015Sep 23 2016Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan, (-1,1)-, quasiassociative, ... More