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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

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

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 Spectrum Steepening in Supernova Remnants -- I. Loss-Free Self-Similar SolutionJan 04 2019Jul 02 2019The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra are likely to be significantly steeper than the canonical $E^{-2}$ spectrum predicted by the standard ... 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: 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

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

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

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

Resonance oscillations of non-reciprocal long-range van der Waals forces between atoms in electromagnetic fieldsNov 03 2017Feb 28 2018We study theoretically the van der Waals interaction between two atoms out of equilibrium with isotropic electromagnetic field. We demonstrate that at large interatomic separations, the van der Waals forces are resonant, spatially oscillating and non-reciprocal ... More

Casimir interaction between excited media in electromagnetic fieldApr 07 2006We investigate the Casimir-Polder interaction between two atoms one of which is excited. We show that the perturbation theory results in divergence of integrals for the interaction between an excited atom and a media of dilute gas. We considered the interaction ... 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

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

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

Casimir-Polder interaction between an excited atom and a gas dielectric mediumJun 15 2006Oct 09 2006The Casimir-Polder potential for interaction between an excited atom and a ground-state one in the retarded case obtained with the help of perturbation technique drops as R^-2 with the distance between the atoms [E.A. Power, T.Thirunamachandran, Phys. ... More

A Chance-Constrained Stochastic Electricity MarketJun 17 2019Efficiently accommodating uncertain renewable resources in wholesale electricity markets is among the foremost priorities of market regulators in the US, UK and EU nations. However, existing deterministic market designs fail to internalize the uncertainty ... More

On the derived category of quasi-hereditary algebras with two simple modulesDec 02 2018We describe the derived Picard groups and two-term silting complexes for quasi-hereditary algebras with two simple modules. We also describe by quivers with relations all algebras derived equivalent to a quasi-hereditary algebra with two simple modules. ... 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 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

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

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

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

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

Gerstenhaber bracket on the Hochschild cohomology via an arbitrary resolutionOct 18 2016Nov 15 2018We 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. Using one of these formulas, we give a new short proof of 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

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

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

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

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

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

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

The near neutrino detector for the T2K experimentMay 04 2008The T2K experiment is a second generation long baseline neutrino oscillation experiment designed as a sensitive search for nu_e appearance. The T2K near neutrino detector complex is located 280 meters from the pion production target and will measure both ... 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

Dispersion interaction between two atoms in electromagnetic fieldsJun 16 2008We present a new theory of atom-atom dispersion interaction in the presence of electromagnetic fields. The theory takes into account the absorption and emission of virtual photons leading to the resonance contributions to the interaction potential in ... More

A Chance-Constrained Stochastic Electricity MarketJun 17 2019Jul 06 2019Efficiently accommodating uncertain renewable resources in wholesale electricity markets is among the foremost priorities of market regulators in the US, UK and EU nations. However, existing deterministic market designs fail to internalize the uncertainty ... 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

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

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

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

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).

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

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

Degenerations of binary Lie and nilpotent Malcev algebrasSep 23 2016We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over \mathbb{C}. In particular, we describe all irreducible components of these varieties.

Dimension Reduction for the Hyperbolic SpaceOct 06 2007A dimension reduction for the hyperbolic space is established. When points are far apart an embedding with bounded distortion into the hyperbolic plane is achieved.

How to Play Unique Games on ExpandersMar 02 2009In this note we improve a recent result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a $(1-\varepsilon)$-satisfiable instance of Unique Games with the constraint graph $G$, our algorithm ... More

The mixed Hodge structure on complements of complex coordinate subspace arrangementsDec 16 2014We compute the mixed Hodge structure on the cohomology ring of complements of complex coordinate subspace arrangements. The mixed Hodge structure can be described in terms of the special bigrading on the cohomology ring of complements of complex coordinate ... More

Real-time operating mode with DSSSD detector to search for short correlation ER-alpha chainsJun 05 2015Real-time PC based algorithm is developed for DSSSD detector. Complete fusion nuclear reaction natYb+48Ca->217Th is used to test this algorithm at 48Ca beam. Example of successful application of a former algorithm for resistive strip PIPS detector in ... 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

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

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.

Classification of generalized Kähler-Ricci solitons on complex surfacesJul 08 2019Using toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in arXiv:1802.00170. This construction also reveals that these solitons are generalized K\"ahler in two distinct ways, with vanishing ... 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

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

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

Enhancing Distribution Resilience with Mobile Energy Storage: A Progressive Hedging ApproachMar 03 2018Electrochemical energy storage (ES) units (e.g. batteries) have been field-validated as an efficient back-up resource that enhance resilience of the distribution system in case of natural disasters. However, using these units for resilience is not sufficient ... 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

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

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

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

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

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

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

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

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

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

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

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

Coherent multiple-antenna block-fading channels at finite blocklengthApr 23 2017Jun 26 2018In this paper we consider a channel model that is often used to describe the mobile wireless scenario: multiple-antenna additive white Gaussian noise channels subject to random (fading) gain with full channel state information at the receiver. Dynamics ... More

Pseudoenergy, Superenergy, and Energy Radiation via Gravitational Waves in General RelativityMay 27 2003For slowly spinning matter the rate of energy loss via radiation of gravitational waves is estimated in General Relativity (GR) within a generally covariant superenergy approach. This estimation differs from Einstein's Quadrupole Formula (EQF) by a suppression ... More