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Machine Learning at Microsoft with ML .NETMay 14 2019May 15 2019Machine Learning is transitioning from an art and science into a technology available to every developer. In the near future, every application on every platform will incorporate trained models to encode data-based decisions that would be impossible for ... More

Triangulated endofunctors of the derived category of coherent sheaves which do not admit DG liftingsApr 29 2016Recently, Rizzardo and Van den Bergh constructed an example of a triangulated functor between the derived categories of coherent sheaves on smooth projective varieties over a field $k$ of characteristic $0$ which is not of the Fourier-Mukai type. The ... More

On the properties of nodal price response matrix in electricity marketsApr 14 2014Jan 24 2015We establish sufficient conditions for nodal price response matrix in electric power system to be symmetric and negative (semi-)definite. The results are applicable for electricity markets with nonlinear and intertemporal constraints.

Remarks on formal deformations and Batalin-Vilkovisky algebrasFeb 02 1998Feb 10 1998This note consists of two parts. Part I is an exposition of (a part of) the V.Drinfeld's letter, [D]. The sheaf of algebras of polyvector fields on a Calabi-Yau manifold, equipped with the Schouten bracket, admits a structure of a Batalin-Vilkovisky algebra. ... More

On the possibility to measure nuclear matrix element for neutrinoless double beta decay of Ca48Aug 25 2011As shown in Ref. \cite{Rod09}, the Fermi part $M_{F}^{0\nu}$ of the total $0\nu\beta\beta$-decay nuclear matrix element $M^{0\nu}$ can be related to the single Fermi transition matrix element between the isobaric analog state (IAS) of the ground state ... More

Explicit Solutions to Boundary Problems for 2+1-Dimensional Integrable SystemsDec 16 2010Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within the framework ... More

Guided Grammar ConvergenceMar 29 2015Relating formal grammars is a hard problem that balances between language equivalence (which is known to be undecidable) and grammar identity (which is trivial). In this paper, we investigate several milestones between those two extremes and propose a ... More

Translating photobiology to electrophysiology: A brief overview of several photobiological processes with accent on electrophysiologyJun 28 2013The mini-review gives special attention to holistic approach and mechanisms of processes. The physical and chemical frames and background for visual perception and signalling are discussed. Perception of photons by retinal rod cells is described in more ... More

Simplicissimus' InquiriesJun 27 2009This is a kind of essay dedicated to Lev Borisovich Okun. I would like to ask some questions which I can not answer. However I suspect I know how to answer them. Questions are as follows: 1. Particle identity. 2. Information storage. 3. Information read-out ... More

Non-colliding Jacobi processes as limits of Markov chains on Gelfand-Tsetlin graphDec 16 2008We introduce a stochastic dynamics related to the measures that arise in harmonic analysis on the infinite-dimensional unitary group. Our dynamics is obtained as a limit of a sequence of natural Markov chains on Gelfand-Tsetlin graph. We compute finite-dimensional ... More

Non-intersecting paths and Hahn orthogonal polynomial ensembleAug 17 2007We compute the bulk limit of the correlation functions for the uniform measure on lozenge tilings of a hexagon. The limiting determinantal process is a translation invariant extension of the discrete sine process, which also describes the ergodic Gibbs ... More

Information Planning for Text DataFeb 09 2018Mar 21 2018Information planning enables faster learning with fewer training examples. It is particularly applicable when training examples are costly to obtain. This work examines the advantages of information planning for text data by focusing on three supervised ... More

On generalized resolvents and characteristic matrices of differential operatorsSep 21 2009The main objects of our considerations are differential operators generated by a formally selfadjoint differential expression of an even order on the interval $[0,b> (b\leq \infty)$ with operator valued coefficients. We complement and develop the known ... More

Forecasting using incomplete modelsMay 12 2017Nov 29 2018We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of incomplete models, i.e. ... More

$\Ughr$ invariant quantization on some homogeneous manifoldsNov 05 2002We consider a class of homogeneous manifolds over a simple Lie group which appears in the problem of classification of homogeneous manifolds with reductive subgroups of maximal rank as stabilizer of a point. We prove that any manifold of this class possesses ... More

The Hilbert 16-th problem and an estimate for cyclicity of an elementary polycycleOct 17 2000Hilbert-Arnold (HA) problem, motivated by Hilbert 16-th problem, is to prove that for a generic k-parameter family of smooth vector fields {\dot x=v(x,\eps)}_{\eps\in B^k} on the 2-dimensional sphere S^2 has uniformly bounded number of limit cycles (isolated ... More

Generic Diffeomorphisms with Superexponential Growth of Number of Periodic OrbitsFeb 26 1999Consider a compact manifold M of dimension at least 2 and the space of C^r-smooth diffeomorphisms Diff^r(M). The classical Artin-Mazur theorem says that for a dense subset D of Diff^r(M) the number of isolated periodic points grows at most exponentially ... More

Fisher information and quantum mechanical models for financeApr 15 2015The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models ... More

Moments of the ARPES spectral function of an undoped Mott insulatorMar 15 2000We derive analytic expressions for the first three frequency moments of the single particle spectral function for one hole in a Mott insulator in terms of equilibrium spin correlation functions of the insulating state. We show that the ``remnant Fermi ... More

Hilbert series and Berezin-Gelfand dualityAug 31 2009Mar 13 2010We give an example showing how Jacobi polynomials and their discrete counterparts (Hahn polynomials) appear in the Hilbert series of some homogeneous spaces.

On hypergeometric functions connected with quantum cohomology of flag spacesDec 20 1997Givental's recursion relations for the flag varieties $G/B$ are established.

MediaWiki Grammar RecoveryJul 23 2011The paper describes in detail the recovery effort of one of the official MediaWiki grammars. Over two hundred grammar transformation steps are reported and annotated, leading to delivery of a level 2 grammar, semi-automatically extracted from a community ... More

Induced Magnetic Field in a Finite Fermion Density Maxwell QED$_{2+1}$Jan 20 1997Jan 22 1997We are studying finite fermion density states in Maxwell QED$_{2+1}$ with external magnetic field. It is shown that at any fermion density the energy of some magnetized states may be less than that of the state with the same density, but no magnetic field. ... More

Disjointness of representations arising in harmonic analysis on the infinite-dimensional unitary groupMay 17 2008Nov 07 2008We prove pairwise disjointness of representations T_{z,w} of the infinite-dimensional unitary group. These representations provide a natural generalization of the regular representation for the case of "big" group U(\infty). They were introduced and studied ... More

The Grammar Hammer of 2012Dec 17 2012This document is a case study in aggressive self-archiving. It collects all initiatives undertaken by its author in 2012, including unpublished ones, explains their relevance and relation with one another. Discussed topics include guided convergence of ... More

Symmetric operators with real defect subspaces of the maximal dimension. Applications to differential operatorsDec 17 2010Let $\gH$ be a Hilbert space and let $A$ be a simple symmetric operator in $\gH$ with equal deficiency indices $d:=n_\pm(A)<\infty$. We show that if, for all $\l$ in an open interval $I\subset\bR$, the dimension of defect subspaces $\gN_\l(A)(=\Ker (A^*-\l))$ ... More

Borel Reductions and Cub GamesJul 09 2012It is shown that the power set of $\k$ ordered by the subset relation modulo various versions of the non-stationary deal can be embedded into the partial order of Borel equivalence relations on $2^\k$ under Borel reducibility. Here $\k$ is uncountable ... More

Development of charge-exchange injection at the Novosibirsk Institute of Nuclear Physics and around the WorldAug 17 2018The study of charge-exchange injection of protons into accelerators started in 1960 at the Institute of Nuclear Physics of the Siberian Branch of Russian Academy of Science, as proposed by G. I. Budker in connection with the development of the program ... More

On Geometry and Symmetries in Classical and Quantum Theories of Gauge GravityMay 16 2019Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes that are required to satisfy certain conditions, in order ... More

The Class of Purely Unrectifiable Sets in the Hilbert Space is coanalytic-completeMar 14 2013The space $F(\ell_2)$ of all closed subsets of $\ell_2$ is a Polish space. We show that the subset $P\subset F(\ell_2)$ consisting of the purely 1-unrectifiable sets is $\Pii$-complete.

On the derived DG functorsApr 12 2010Jan 05 2011Assume that abelian categories $A, B$ over a field admit countable direct limits and that these limits are exact. Let $F: D^+_{dg}(A) --> D^+_{dg}(B)$ be a DG quasi-functor such that the functor $Ho(F): D^+(A) \to D^+(B)$ carries $D^{\geq 0}(A)$ to $D^{\geq ... More

Around Hilbert-Arnold ProblemNov 06 2001This lectures notes consists of four lectures. The first lecture discusses questions around Hilbert-Arnold Problem which is naturally arises from Quantitative Hilbert 16-th problem. In the second lecture we outline author's solution of a weak form of ... More

Ideal DatabasesDec 30 2015From algebraic geometry perspective database relations are succinctly defined as Finite Varieties. After establishing basic framework, we give analytic proof of Heath theorem from Database Dependency theory. Next, we leverage Algebra/Geometry dictionary ... More

Algorithm for multivariate data standardization up to third momentApr 18 2012An algorithm for transforming multivariate data to a form with normalized first, second and third moments is presented.

Kondo resonance in the case of strong Coulomb screeningNov 05 1995The effect of Coulomb screening on the magnetic impurity behavior is analysed. Two types of the behavior corresponding to either integer or fractional occupation numbers of the low lying magnetic level are described. The features in the dependence of ... More

Pentagramma Mirificum and elliptic functionsJun 18 2011We give an exposition of fragments from Gauss [G] where he discovered, with the help of some work of Jacobi, a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in ... More

Local structure of moduli spacesAug 05 1997Aug 06 1997We describe the algebra of a universal formal deformation as the zeroth cohomology of the dg Lie algebra corresponding to this deformation problem. A report at Arbeitstagung 1997 on the joint work with V.Hinich.

A remark on virtual orientations for complete intersectionsAug 03 1997The aim of this note is to give a simple definition of genus zero virtual orientation classes (or fundamental classes) for projective complete intersections or, more generally, for complete intersections in convex varieties, and to prove a push forward ... More

Nuclear matrix elements for double beta decayOct 30 2009The present status of calculations of the nuclear matrix elements for neutrinoless double beta decay is reviewed. A proposal which allows in principle to measure the neutrinoless double beta decay Fermi matrix element is briefly described.

Quantitative description of ion transport via plasma membrane of yeast and small cellsDec 18 2012Jan 16 2016Modeling of ion transport via plasma membrane needs identification and quantitative understanding of the involved processes. Brief characterization of main ion transport systems of a yeast cell (Pma1, Ena1, TOK1, Nha1, Trk1, Trk2, non-selective cation ... More

Formation of filament-like structures in the pulsar magnetosphere and the short-term variability of pulsar emissionJan 10 2014Magnetohydrodynamic (MHD) instabilities can play an important role in the dynamics of the pulsar magnetosphere and can be responsible for the formation of various structures. We consider the instability caused by a gradient of the magnetic pressure which ... More

Minimal spectral functions of an ordinary differential operatorOct 06 2010Oct 12 2010Let $l[y]$ be a formally selfadjoint differential expression of an even order on the interval $[0,b> \;(b\leq \infty)$ and let $L_0$ be the corresponding minimal operator. By using the concept of a decomposing boundary triplet we consider the boundary ... More

Low-Temperature QED with External Magnetic FieldDec 01 1994Low-temperature expansion of the effective Lagrangian of the QED$_{3+1}$ with a uniform magnetic field and a finite chemical potential is performed. Temperature corrections, as well as zero-temperature expression for the effective Lagrangian are presented ... More

Integrality of instanton numbersJul 31 2007Sep 17 2008We prove the results announced in a joint paper (arXiv:hep-th/0603106) with Maxim Kontsevich and Albert Schwarz.

Reconstruction of piecewise constant functions from X-ray dataJan 07 2019Apr 08 2019We show that on a two-dimensional compact nontrapping Riemannian manifold with strictly convex boundary, a piecewise constant function can be recovered from its integrals over geodesics. We adapt the injectivity proof which uses variations through geodesics ... More

Sur les algèbres vertex attachées aux variétés algébriquesApr 21 2003Sganarelle: ... Mais encore faut-il croire quelque chose dans le monde: qu'est-ce donc que vous croyez? Dom Juan: Ce que je crois? Sganarelle: Oui. Dom Juan: Je crois que deux et deux sont quatre, Sganarelle, et que quatre et quatre sont huit. [Moli\`ere, ... More

Boundary relations and boundary conditions for general (not necessarily definite) canonical systems with possibly unequal deficiency indicesSep 10 2011Sep 13 2011We investigate in the paper general (not necessarily definite) canonical systems of differential equation in the framework of extension theory of symmetric linear relations. For this aim we first introduce the new notion of a boundary relation $\G:\gH^2\to\HH$ ... More

On spectral and pseudospectral functions of first-order symmetric systemsJul 21 2014We consider general (not necessarily Hamiltonian) first-order symmetric system $J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b) $ with the regular endpoint $a$. A distribution matrix-valued function $\Si(s), \; s\in\bR,$ is called a spectral (pseudospectral) ... More

On generalized resolvents and characteristic matrices of first-order symmetric systemsMar 16 2014We study general (not necessarily Hamiltonian) first-order symmetric system $J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b) $ with the regular endpoint $a$ and singular endpoint $b$. It is assumed that the deficiency indices $n_\pm(\Tmi)$ of the corresponding ... More

Controlling passively-quenched single photon detectors by bright lightJul 26 2007Apr 17 2009Single photon detectors based on passively-quenched avalanche photodiodes can be temporarily blinded by relatively bright light, of intensity less than a nanowatt. I describe a bright-light regime suitable for attacking a quantum key distribution system ... More

On compressions of self-adjoint extensions of a symmetric linear relationDec 01 2018Let $A$ be a symmetric linear relation in the Hilbert space $\gH$ with equal deficiency indices $n_\pm (A)\leq\infty$. A self-adjoint linear relation $\wt A\supset A$ in some Hilbert space $\wt\gH\supset \gH$ is called an exit space extension of $A$; ... More

Some applications of weight structures of BondarkoFeb 02 2011Dec 10 2011We construct a functor from the triangulated category of Voevodsky motives to a certain derived category of mixed Hodge structures enriched with integral weight filtration. We use this construction to prove a strong integral version of the Deligne conjecture ... More

Investigation of heavy ions diffusion under the influence of current-driven mechanism and compositional waves in plasmaMay 25 2016We consider diffusion caused by a combined influence of the Hall effect and electric currents, and argue that such diffusion forms chemical inhomogeneities in plasma. The considered mechanism can be responsible for the formation of element spots in laboratory ... More

Diffusion in plasma: the Hall effect, compositional waves, and chemical spotsSep 12 2016We consider diffusion caused by a combined influence of the electric current and the Hall effect, and argue that such diffusion can form inhomogeneities of the chemical composition in plasma. The considered mechanism can be responsible for a formation ... More

Effective Lagrangian of Thermal QED with External Magnetic Field and the Static Limit of the Polarization OperatorJul 25 1995A low-temperature expansion of QED one-loop effective Lagrangian valid for a wide range of parameters is presented in a form of finite sums of elementary functions. Starting from the effective action components of the one-loop polarization operator responsible ... More

QED$_{2+1}$ with Nonzero Fermion Density and Quantum Hall EffectOct 10 1994A general expression for the conductivity in the QED$_{2+1}$ with nonzero fermion density in the uniform magnetic field is derived. It is shown that the conductivity is entirely determined by the Chern-Simons coefficient: $\sigma_{ij}=\varepsilon_{ij}~{\cal ... More

Antimonopoly regulation method based on perfect price discriminationJul 16 2015We propose a method of antimonopoly regulation in a day-ahead power market with locational marginal pricing which forms economic incentives for a producer, operating a portfolio of generating units, to submit an offer indicating its true cost and faithful ... More

Optimal Polynomial-Time Estimators: A Bayesian Notion of Approximation AlgorithmAug 14 2016Sep 15 2016The concept of an "approximation algorithm" is usually only applied to optimization problems since in optimization problems the performance of the algorithm on any given input is a continuous parameter. We introduce a new concept of approximation applicable ... More

Emergent quantum mechanics of financesDec 11 2013This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability ... More

Dynamics of Inhomogeneous Tomonaga-Luttinger Liquid WireNov 05 1995Dynamics of the 1D electron transport between two reservoirs are studied based on the inhomogeneous Tomonaga- Luttinger Liquid (ITLL) model in the case when the effect of the electron backscattering on the impurities is negligible. The inhomogeneities ... More

Umklapp scattering in transport through a 1D wire of finite lengthJul 05 1999Suppression of electron current $ \Delta I$ through a 1D channel of length $L$ connecting two Fermi liquid reservoirs is studied taking into account the Umklapp interaction induced by a periodic potential. This interaction opens band gaps at the integer ... More

Vertex algebras and elliptic generaJun 27 1999A report at Arbeitstagung, June 1999, Bonn, on the joint work with V.Gorbounov, F.Malikov and A.Vaintrob.

ERRATA for "One-Loop Threshold Effects in String Unification"May 19 1992The original paper, as published in Nuclear Physics B in 1988, had a few factor-of-two errors. Some people got confused by those errors. The purpose of these errata is to make things clear. The revised version of the complete article is also posted to ... More

Relation of isospin-symmetry breaking correction for superallowed beta decay to energy of charge-exchange giant monopole resonanceJun 03 2012Dec 15 2013After application of an analytical transformation, a new exact representation for the nuclear isospin-symmetry breaking correction $\delta_C$ to superallowed beta decay is obtained. The correction is shown to be essentially the reciprocal of the square ... More

Guided Grammar Convergence. Full Case Study Report. Generated by converge::GuidedJul 27 2012This report is meant to be used as auxiliary material for the guided grammar convergence technique proposed earlier as problem-specific improvement in the topic of convergence of grammars. It contains a narrated MegaL megamodel, as well as full results ... More

Salinity tolerance in plants: attempts to manipulate ion transportNov 06 2014Ion transport is the major determining factor of salinity tolerance in plants. A simple scheme of a plant cell with ion fluxes provides basic understanding of ion transport and the corresponding changes of ion concentrations under salinity. The review ... More

Reconstruction of piecewise constant functions from X-ray dataJan 07 2019We show that on a two-dimensional compact nontrapping Riemannian manifold with strictly convex boundary, a piecewise constant function can be recovered from its integrals over geodesics. We adapt the injectivity proof which uses variations through geodesics ... More

Spectral and pseudospectral functions of various dimensions for symmetric systemsNov 10 2016The main object of the paper is a symmetric system $J y'-B(t)y=\l\D(t) y$ defined on an interval $\cI=[a,b) $ with the regular endpoint $a$. Let $\f(\cd,\l)$ be a matrix solution of this system of an arbitrary dimension and let $(Vf)(s)=\int\limits_\cI ... More

On eigenfunction expansions of first-order symmetric systems and ordinary differential operators of an odd orderJul 25 2013We study general (not necessarily Hamiltonian) first-order symmetric systems $J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b\rangle $ with the regular endpoint $a$. It is assumed that the deficiency indices $n_\pm(\Tmi)$ of the minimal relation $\Tmi$ ... More

Vacuum and spacetime signature in the theory of superalgebraic spinorsMar 21 2019May 08 2019We investigated action of operator analogs of Dirac gamma matrices (we called them gamma operators) on a vacuum. We derived formulas for vacuum state vector and operators of the Lorentz transformations of spinors in the superalgebraic representation of ... More

Classification and Non-classification of Homeomorphism RelationsJul 26 2014Jan 14 2015The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group action (Kechris-Solecki). ... More

Concavity of Eigenvalue Sums and the Spectral Shift FunctionDec 26 2001It is well known that the sum of negative (positive) eigenvalues of some finite Hermitian matrix $V$ is concave (convex) with respect to $V$. Using the theory of the spectral shift function we generalize this property to self-adjoint operators on a separable ... More

Compositional waves and variations in the atmospheric abundances of magnetic starsFeb 01 2016The stars of the middle main sequence often have relatively quiescent outer layers and spot-like chemical structures may develope in their atmospheres. Recent observations show that abundance peculiarities can change as stars evolve on the main sequence ... More

Element spots in Ap- and HgMn-stars from current-driven diffusionJan 25 2016The stars of the middle main sequence often have spot-like chemical structures at their surfaces. We consider the diffusion process caused by electric currents that can lead to the formation of such chemical spots. Diffusion is considered using the partial ... More

Comment on "Dynamical Chern-Simons term generation at finite density" and "Chern-Simons term at finite density"Dec 23 1996We comment on the calculation of the Chern-Simons coefficient in (2+1)-dimensional gauge theories at finite chemical potential made by A.N.Sissakian, O.Yu.Shevchenko and S.B.Solganik (hep-th/9608159 and hep-th/9612140).

Spontaneous Magnetization in Maxwell QED$_{2+1}$May 28 1996Nov 10 1996Spontaneous magnetization in the Maxwell QED$_{2+1}$ at finite fermion density is studied. It is shown that at low fermion densities the one-loop free energy has its minimum at some nonvanishing value of the magnetic field. The magnetization is due to ... More

Bulk universality for random lozenge tilings near straight boundaries and for tensor productsMar 08 2016We prove that the asymptotic of the bulk local statistics in models of random lozenge tilings is universal in the vicinity of straight boundaries of the tiled domains. The result applies to uniformly random lozenge tilings of large polygonal domains on ... More

A geometric proof of the existence of Whitney stratificationsOct 13 2000A stratification of a singular set, e.g. an algebraic or analytic variety, is, roughly, a partition of it into manifolds so that these manifolds fit together "regularly". A classical theorem of Whitney says that any complex analytic set has a stratification. ... More

Cepheid Kinematics and the Galactic WarpOct 27 2013The space velocities of 200 long-period ($P>5$ days) classical Cepheids with known proper motions and line-of-sight velocities whose distances were estimated from the period--luminosity relation have been analyzed. The linear Ogorodnikov-Milne model has ... More

Orientation Parameters of the Cepheid System in the GalaxyOct 27 2013Based on the distribution of long-period Cepheids, we have redetermined the orientation parameters of their principal plane in the Galaxy. Based on 299 Cepheids with heliocentric distances $r<20$ kpc and pulsation periods $P\geq5^d$, we have found the ... More

Neutron Skin and Giant Resonances in NucleiApr 02 2007Some aspects, both experimental and theoretical, of extracting the neutron skin $\Delta R$ from properties of isovector giant resonances are discussed. Existing proposals are critically reviewed. The method relying on the energy difference between the ... More

One-Loop Threshold Effects in String UnificationMay 19 1992Like grand unification of old, string unification predicts simple tree-level relations between the couplings of all unbroken gauge groups such as $SU(3)_C$ or $SU(2)_W\)$. I show here how to compute one-loop corrections to these relations for any four-dimensional ... More

Pseudo-random number generators for Monte Carlo simulations on Graphics Processing UnitsMar 09 2010Basic uniform pseudo-random number generators are implemented on ATI Graphics Processing Units (GPU). The performance results of the realized generators (multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR, RANLUX and Mersenne ... More

Pion reactions with few-nucleon systemsOct 08 2009We report about the recent results for s- and p-wave pion production in NN -> NNpi within effective field theory and discuss how the charge symmetry breaking in pn -> d pi^0 can be used to extract the strong contribution to the neutron-proton mass difference. ... More

Cosmology and semi-conservation of computations in the universeApr 30 2007Resent works of Hawking and Susskind suggested that information is conserved in the universe. We extend this thesis and propose that dynamics of information - computations can conserve in Anti-de-Sitter cosmological model. Information geometry formalism ... More

Graph Parameters and Ramsey TheoryAug 27 2016Ramsey's Theorem tells us that there are exactly two minimal hereditary classes containing graphs with arbitrarily many vertices: the class of complete graphs and the class of edgeless graphs. In other words, Ramsey's Theorem characterizes the graph vertex ... More

From Alternating Sign Matrices to the Gaussian Unitary EnsembleJun 26 2013Jan 05 2014The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the six-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian Unitary Ensemble ... More

The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matricesNov 08 2010Aug 14 2012The problem of the description of finite factor representations of the infinite-dimensional unitary group, investigated by Voiculescu in 1976, is equivalent to the description of all totally positive Toeplitz matrices. Vershik-Kerov showed that this problem ... More

Bulk universality for random lozenge tilings near straight boundaries and for tensor productsMar 08 2016Dec 28 2017We prove that the asymptotic of the bulk local statistics in models of random lozenge tilings is universal in the vicinity of straight boundaries of the tiled domains. The result applies to uniformly random lozenge tilings of large polygonal domains on ... More

Using Information Semantic Systems for Absolutely Secure ProcessingFeb 24 2010Propose a new cryptographic information concept. It allows : - to create absolutely algorithmic unbreakable ciphers for communication through open digital channels; - to create new code-breaking methods. They will be the most efficient decoding methods ... More

Vacuum and spacetime signature in the theory of superalgebraic spinorsMar 21 2019Formulas for vacuum state vector and operators of the Lorentz transformations and gauge charge transformations of spinors are derived in the superalgebraic representation of spinors. Five operator analogs of five Dirac gamma matrices exist in the superalgebraic ... More

Modern High Intensity H- Accelerator SourcesJun 09 2018A review of modern high intensity H- ion sources for accelerators is presented. The cesiation effect, a significant enhancement of negative ion emission from gas discharges with decrease of co-extracted electron current below negative ion current, was ... More

De Rham complex of a Gerstenhaber algebraJul 07 2015We introduce a notion of the De Rham complex of a Gerstenhaber algebra which produces a notion of a "quasi-BV structure", and allows to classify these structures, generalizing the classical results for polyvector fields.

Hodge realizations of 1-motives and the derived AlbaneseSep 17 2008Dec 08 2011We prove that the embedding of the derived category of 1-motives into the triangulated category of effective Voevodsky motives, as well as its left adjoint functor $LAlb$, commute with the Hodge realization.

On the first continuous $L^2$-cohomology of free group factorsDec 19 2013Jan 06 2014We prove that the first continuous $L^2$-cohomology of free group factors vanishes. This answers a question by Andreas Thom regarding continuity properties of free difference quotients and shows that one can not distinguish free group factors by means ... More

A Non-classification Result for Wild KnotsApr 09 2015Apr 21 2016Using methods of descriptive theory it is shown that the classification problem for wild knots is strictly harder than that for countable structures.

Magnetostriction and magnetoelastic domains in antiferromagnetsOct 18 2000The problem of the observable equilibrium domain structure in pure antiferromagnets (and other thermoelastics) is investigated with the use of continuous elasticity theory. It is shown that completely rigid surface produces the imaginary ``incompatibility ... More

Chiral Poincaré dualityMay 03 1999May 12 1999The aim of this note is to prove the analogue of Poincar\'e duality in the chiral Hodge cohomology.

Localization of modules over small quantum groupsApr 03 1996Apr 25 1996A report on the works hep-th/9411050, q-alg/9412017, q-alg/9503013, q-alg/9506011 and a joint work with R.Bezrukavnikov.

Coulomb drag between one-dimensional conductorsMar 08 2000Aug 07 2000We have analyzed Coulomb drag between currents of interacting electrons in two parallel one-dimensional conductors of finite length $L$ attached to external reservoirs. For strong coupling, the relative fluctuations of electron density in the conductors ... More