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Reachability-based safe learning for optimal control problemNov 09 2018In this work we seek for an approach to integrate safety in the learning process that relies on a partly known state-space model of the system and regards the unknown dynamics as an additive bounded disturbance. We introduce a framework for safely learning ... More

Efficient Kernel-based Subsequence Search for User Identification from Walking ActivityJun 11 2019This paper presents an efficient approach for subsequence search in data streams. The problem consists in identifying coherent repetitions of a given reference time-series, eventually multi-variate, within a longer data stream. Dynamic Time Warping (DTW) ... More

Application of HUBzero platform for the educational process in astroparticle physicsDec 04 2018In the frame of the Karlsruhe-Russian Astroparticle Data Life Cycle Initiative it was proposed to deploy an educational resource astroparticle.online for the training of students in the field of astroparticle physics. This resource is based on HUBzero, ... More

A distributed data warehouse system for astroparticle physicsDec 05 2018A distributed data warehouse system is one of the actual issues in the field of astroparticle physics. Famous experiments, such as TAIGA, KASCADE-Grande, produce tens of terabytes of data measured by their instruments. It is critical to have a smart data ... More

Efficient Kernel-based Subsequence Search for User Identification from Walking ActivityJun 11 2019Jul 16 2019This paper presents an efficient approach for subsequence search in data streams. The problem consists in identifying coherent repetitions of a given reference time-series, eventually multi-variate, within a longer data stream. Dynamic Time Warping (DTW) ... More

A Discretization of the Nonholonomic Chaplygin Sphere ProblemDec 15 2006Mar 12 2007The celebrated problem of a non-homogeneous sphere rolling over a horizontal plane was proved to be integrable and was reduced to quadratures by Chaplygin. Applying the formalism of variational integrators (discrete Lagrangian systems) with nonholonomic ... More

Algebraic Closed Geodesics on a Triaxial EllipsoidJun 29 2005Oct 10 2005We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid $Q$ that are cut out by algebraic surfaces in ${\mathbb R}^3$. Such geodesics are either connected components of spatial elliptic curves or rational ... More

Schmidt decomposition for non-collinear biphoton angular wave functionsNov 08 2014Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure is described for their separation. Parameters of the Schmidt decomposition are used for evaluation of the degree of biphoton's ... More

Affine Grassmannians of group schemes and exotic principal bundles over A^1Aug 14 2013Jan 16 2014Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of triviality. To this ... More

Mountain Peak Detection in Online Social MediaAug 12 2015We present a system for the classification of mountain panoramas from user-generated photographs followed by identification and extraction of mountain peaks from those panoramas. We have developed an automatic technique that, given as input a geo-tagged ... More

On the Grothendieck-Serre conjecture on principal bundles in mixed characteristicJan 17 2015Nov 13 2016Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R contains a field. ... More

Some aspects of probability distribution for percolation of several fluids on the hexagonal latticeAug 30 2019We study random coloring of the hexagons of a honeycomb lattice into $2^{n-1}$ colors (that is the standard Potts model at infinite temperature). It may be considered as a generalization of percolation to $n$ pairwise independent, but mutually dependent ... More

Affine Grassmannians of group schemes and exotic principal bundles over A^1Aug 14 2013Nov 13 2016Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of triviality. To this ... More

Biphoton ququarts as either pure or mixed states, features and reconstruction from coincidence measurementsSep 17 2012Features of biphoton polarization-frequency ququarts are considered. Their wave functions are defined as functions of both polarization and frequency variables of photons with the symmetry obligatory for two-boson states taken into account. In experiments, ... More

Schmidt-mode analysis of quadrature entanglement in superpositions of two-mode multiphoton statesMay 13 2019The Schmidt-decomposition formalism is proposed to be used for evaluation of the degree of quadrature entanglement in two-mode multiphoton states.

Variations of Hodge structures for hypergeometric differential operators and parabolic Higgs bundlesMay 07 2015Dec 26 2015Consider the holomorphic bundle with connection on $\mathbb P^1-\{0,1,\infty\}$ corresponding to the regular hypergeometric differential operator \[ \prod_{j=1}^h(D-\alpha_j)-z\prod_{j=1}^h(D-\beta_j), \qquad D=z\frac{d}{dz}. \] If the numbers $\alpha_i$ ... More

Conservation laws in quantum field theory on graphsSep 16 2018Nov 28 2018It is shown that expected values of free scalar and vector quantum fields on graphs satisfy the same conservation laws as the classic fields. It is demonstrated that a modified version of conservation laws is satisfied for Villain action. The proofs are ... More

Entanglement of qutrits and ququartsSep 14 2010Sep 27 2010We investigate in a general form entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of collinear and, correspondingly, degenerate and non-degenerate Spontaneous Parametric Down-Conversion. Indistinguishability of photons ... More

Smoothed quantile regression processes for binary response modelsFeb 22 2013In this paper, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearization for ... More

On Some Extensions of Bernstein's Inequality for Self-adjoint OperatorsDec 22 2011Mar 12 2013We present some extensions of Bernstein's inequality for random self-adjoint operators. The main feature of these results is that they can be applied in the infinite-dimensional setting. In particular, our inequalities refine the previous results of D. ... More

Measurement of the particle production properties with the ATLAS DetectorNov 03 2017In this contribution, the results on soft hadron physics concerning the underlying event and Bose-Einsten correlations obtained using data collected in proton-proton collisions with the ATLAS experiment are presented.

On Pauli PairsSep 06 2012Feb 11 2013The state of a system in classical mechanics can be uniquely reconstructed if we know the positions and the momenta of all its parts. In 1958 Pauli has conjectured that the same holds for quantum mechanical systems. The conjecture turned out to be wrong. ... More

Spectrum of magnetohydrodynamic turbulenceNov 10 2005Feb 24 2006We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations ... More

Framed moduli spaces and tuples of operatorsMar 14 2012In this work we address the classical problem of classifying tuples of linear operators and linear functions on a finite dimensional vector space up to base change. Having adopted for the situation considered a construction of framed moduli spaces of ... More

Hypercyclic operators on topological vector spacesAug 19 2010Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\ell_1$. We extend this result. In particular, we show that there is a hypercyclic operator on the locally ... More

The Connection between the Quantum Frequency of Radiation and Frequencies of Circling of the Electron in Atom of HydrogenFeb 04 2002The connection between the quantum frequency of radiation by the transition of the electron from orbit n to orbit k and frequencies of circling of electron in these orbits for the atom of hydrogen is determined.

Moduli space of symmetric connectionsDec 28 2001The action of origin-preserving diffeomorphisms on a space of jets of symmetric connections is considered. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e series of the geometric structure of symmetric connection is constructed, ... More

On numerically hypercyclic operatorsFeb 11 2013According to Kim, Peris and Song, a continuous linear operator $T$ on a complex Banach space $X$ is called {\it numerically hypercyclic} if the numerical orbit $\{f(T^nx):n\in\N\}$ is dense in $\C$ for some $x\in X$ and $f\in X^*$ satisfying $\|x\|=\|f\|=f(x)=1$. ... More

A weighted bilateral shift with cyclic square is supercyclicSep 07 2012It is shown that for a bounded weighted bilateral shift $T$ acting on $\ell_p(\Z)$ for $1\leq p\leq 2$ supercyclicity of $T$, weak supercyclicity of $T$, cyclicity of $T\oplus T$ and cyclicity of $T^2$ are equivalent. A new sufficient condition for cyclicity ... More

On the set of hypercyclic vectors for the differentiation operatorSep 05 2012Let $D$ be the differentiation operator $Df=f'$ acting on the Fr\'echet space $\H$ of all entire functions in one variable with the standard (compact-open) topology. It is known since 1950's that the set $H(D)$ of hypercyclic vectors for the operator ... More

Towards conformal invariance of 2D lattice modelsJul 31 2007Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and ... More

Halfspace depth does not characterize probability distributionsOct 22 2018We give examples of different multivariate probability distributions whose halfspace depths coincide at all points of the sample space.

B-spline normal multi-scale transforms for planar curvesNov 18 2013Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the approximating subdivision ... More

Formation of Cooper Pairs as a Consequence of Exchange InteractionJan 15 2015Aug 03 2016Analyzing the exchange energy of two conduction electrons in the crystal at a many-body approach we find, that the exchange energy may be negative and, thus, the singlet state may be favorable. A full overlap in the real space of the wave functions of ... More

Uniform bounds for robust mean estimatorsDec 09 2018Dec 29 2018Median-of-means technique is an elegant and general method for estimating the expectation of a random variable that provides strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. We consider generalizations of the ... More

Gaussian Prototypical Networks for Few-Shot Learning on OmniglotAug 09 2017We propose a novel architecture for $k$-shot classification on the Omniglot dataset. Building on prototypical networks, we extend their architecture to what we call Gaussian prototypical networks. Prototypical networks learn a map between images and embedding ... More

Quantum Cherenkov radiation by spinless and spin-1/2 particlesNov 17 2015In this paper, the Cherenkov radiation process is investigated in the frame of the Quantum Field Theory, both for the spinless and spin-1/2 charged particles. In the latter case, the polarization density matrix technique was used to account for the spin ... More

Universal deformation of particle momenta space in perturbation theoryApr 11 2018We define an embedding of the space of complex momenta and masses in perturbation theory into a universal projective space. This embedding is natural in the sense of properties of the vector bundle defined by Feynman integrals on the complement to Landau ... More

Rings: an efficient Java/Scala library for polynomial ringsDec 06 2017Sep 21 2018In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast algorithms. \Rings ... More

Classification of Realizations of Lie Algebras of Vector Fields on a CircleApr 08 2013Oct 23 2018Finite-dimensional subalgebras of a Lie algebra of smooth vector fields on a circle, as well as piecewise-smooth global transformations of a circle on itself, are considered. A canonical forms of realizations of two- and three-dimensional noncommutative ... More

Rational Witt classes of pretzel knotsJun 19 2008In his pioneering work from 1969, Jerry Levine introduced a complete set of invariants of algebraic concordance of knots. The evaluation of these invariants requires a factorization of the Alexander polynomial of the knot, and is therefore in practice ... More

Translocation of Polymers through Nanopores at Weak External Field, Direct Approach with Monte Carlo SimulationsJun 17 2008I did off-lattice 3D Monte Carlo simulations for polymer translocation through a narrow pore at low external field, trying to be as close to a direct approach as possible. The process was found non equilibrium globally, but dynamics of the monomers close ... More

Building a stochastic template bank for detecting massive black hole binariesJan 26 2008Coalescence of two massive black holes is the strongest and most promising source for LISA. In fact, gravitational signal from the end of inspiral and merger will be detectable throughout the Universe. In this article we describe the first step in the ... More

An extension of Kracht's theorem to generalized Sahlqvist formulasMar 12 2010Sahlqvist formulas are a syntactically specified class of modal formulas proposed by Hendrik Sahlqvist in 1975. They are important because of their first-order definability and canonicity, and hence axiomatize complete modal logics. The first-order properties ... More

Fullerene Faraday Cage Keeps Magnetic Properties of Inner Cluster PristineJan 11 2018Feb 25 2018Any single molecular magnets (SMM) perspective for application is as good as its magnetization stability in ambient conditions. Endohedral metallofullerenes (EMFs) provide a solid basis for promising SMMs. In this study, we investigated the behavior of ... More

*-Doubles and embedding of associative algebras in B(H)Nov 18 2007Apr 08 2009We study the *-double functor between the categories of associative and involutive algebras. It is proved that an associative algebra is isomorphic to a subalgebra of a $C\sp*$-algebra if and only if its *-double is *-isomorphic to a *-subalgebra of a ... More

On the spectrum of frequently hypercyclic operatorsSep 06 2012A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised ... More

Hypercyclic and mixing operator semigroupsSep 05 2012We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group ${T_t}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also describe a class ... More

The Kitai Criterion and backward shiftsSep 07 2012It is proved that for any separable infinite dimensional Banach space $X$, there is a bounded linear operator $T$ on $X$ such that $T$ satisfies the Kitai Criterion. The proof is based on quasisimilarity argument and on showing that $I+T$ satisfies the ... More

Universal elements for non-linear operators and their applicationsSep 06 2012We prove that under certain topological conditions on the set of universal elements of a continuous map $T$ acting on a topological space $X$, that the direct sum $T\oplus M_g$ is universal, where $M_g$ is multiplication by a generating element of a compact ... More

A short proof of the existence of disjoint hypercyclic operatorsSep 06 2012We give a short proof of the existence of disjoint hypercyclic tuples of operators of any given length on any separable infinite dimensional Frechet space. A similar argument provides disjoint dual hypercyclic tuples of operators of any length on any ... More

On supercyclicity of operators from a supercyclic semigroupSep 05 2012We show that for every supercyclic strongly continuous operator semigroup ${T_t}_{t\geq 0}$ acting on a complex $\F$-space, every $T_t$ with $t>0$ is supercyclic. Moreover, the set of supercyclic vectors of each $T_t$ with $t>0$ is exactly the set of ... More

Critical percolation in the planeSep 24 2009We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case ... More

Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entriesMay 23 2016Jun 17 2018Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical covariance estimator ... More

Stokes Theorem for Lipschitz forms on a smooth manifoldMay 27 2008Stokes theorem holds for Lipschitz forms on a smooth manifold.

Smoothed quantile regression processes for binary response modelsFeb 22 2013Apr 04 2019In this paper, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearisation for ... More

Compact operators without extended eigenvaluesSep 07 2012A complex number $\lambda$ is called an extended eigenvalue of a bounded linear operator $T$ on a Banach space $\B$ if there exists a non-zero bounded linear operator $X$ acting on $\B$ such that $XT=\lambda TX$. We show that there are compact quasinilpotent ... More

Electrodynamics of accelerated charges or Why electron does not radiate in Rutherford's atomMar 20 2000It is shown, that the radiation of the charge, moving with uniform acceleration or uniformly moving round a circle and also freely moving in a gravitational field, contradicts the principle of equivalence. It is also shown, that the interaction of the ... More

Chaotic Banach algebrasAug 19 2010We construct an infinite dimensional non-unital Banach algebra $A$ and $a\in A$ such that the sets $\{za^n:z\in\C,\ n\in\N\}$ and $\{({\bf 1}+a)^na:n\in\N\}$ are both dense in $A$, where $\bf 1$ is the unity in the unitalization $A^{\#}=A\oplus \spann\{{\bf ... More

Nice Banach Modules and Invariant SubspacesSep 05 2012Let $\A$ be a semisimple unital commutative Banach algebra. We say that a Banach $\A$-module $M$ is nice if every proper closed submodule of $M$ is contained in a closed submodule of $M$ of codimension 1. We provide examples of nice and non-nice modules. ... More

Forest fires on $\Z_+$ with ignition only at 0Jul 10 2009Sep 15 2009We consider a version of the forest fire model on graph $G$, where each vertex of a graph becomes occupied with rate one. A fixed vertex $v_0$ is hit by lightning with the same rate, and when this occurs, the whole cluster of occupied vertices containing ... More

On Some Extensions of Bernstein's Inequality for Self-adjoint OperatorsDec 22 2011Apr 14 2017We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main feature of our ... More

Partial fractioning reduction of perturbative amplitudesDec 23 2011A new method is presented for the simplification of loop integrals in one particle irreducible diagrams with large numbers of external lines, based on the partial fractioning of products of propagators. Whenever a loop diagram in $d$ dimensions has $d+1$ ... More

Top Quark Properties at the TevatronFeb 11 2017I report on the status of the studies of top-quark properties carried out by the Tevatron experiments CDF and D0.

The role of environment in the observed Fundamental Plane of radio Active Galactic NucleiMay 17 2018The optical Fundamental Plane of black hole activity relates radio continuum luminosity of Active Galactic Nuclei to [O III] luminosity and black hole mass. We examine the environments of low redshift ($z<0.2$) radio-selected AGN, quantified through galaxy ... More

Towards understanding feedback from supermassive black holes using convolutional neural networksDec 02 2017Supermassive black holes at centers of clusters of galaxies strongly interact with their host environment via AGN feedback. Key tracers of such activity are X-ray cavities -- regions of lower X-ray brightness within the cluster. We present an automatic ... More

Approximation of Bergman kernels by rational functions with fixed polesOct 10 2017Nov 14 2017We solved the problem of the best rational approximation of the Bergman kernels on the unit circle of the complex plane in the quadratic and uniform metrics.

Formation of Cooper Pairs as a Consequence of Exchange InteractionJan 15 2015Sep 18 2018Analyzing the exchange energy of two conduction electrons in a crystal at many-body approach we find that the exchange energy may be negative and, thus, the singlet state may be favorable. A full overlap in the real space of the wave functions of two ... More

Existence of Nontrivial Negative Resonances for Polynomial Ordinary Differential Equations With Painlevé PropertyDec 30 2014The Painlev\'e classification is one of the central problems in analytics theory of differential equations rooted in the XIX century. Although it saw many significant advances in analyzing certain classes of equations, the classification still remains ... More

Non-sequential weak supercyclicity and hypercyclicitySep 07 2012A bounded linear operator $T$ acting on a Banach space $\B$ is called weakly hypercyclic if there exists $x\in \B$ such that the orbit ${T^n x: n=0,1,...}$ is weakly dense in $\B$ and $T$ is called weakly supercyclic if there is $x\in \B$ for which the ... More

Hypercyclic tuples of operators on $C^n$ and $R^n$Aug 20 2010A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept ... More

Self-detection of x-ray Fresnel transmissivity using photoelectron-induced gas ionizationMay 27 2015Jan 18 2016Electric response of an x-ray mirror enclosed in a gas flow ionization chamber was studied under the conditions of total external reflection for hard x-rays. It is shown that the electric response of the system as a function of the incidence angle is ... More

Painleve Classification of Polynomial Ordinary Differential Equations of Arbitrary Order and Second DegreeOct 09 2014The problem of Painleve classification of ordinary differential equations lasting since the end of XIX century saw significant advances for the limited equation order, however not that much for the equations of higher orders. In this work we propose the ... More

On the Spectrum of Magnetohydrodynamic TurbulenceMar 02 2005Jun 17 2005We propose a phenomenological model for incompressible magnetohydrodynamic turbulence. We argue that nonlinear-wave interaction weakens as the energy cascade proceeds to small scales, however, the anisotropy of fluctuations along the large-scale magnetic ... More

Powers of sets in free groupsMay 11 2010Nov 23 2012We prove that |A^n| > c_n |A|^{[\frac{n+1}{2}]} for any finite subset A of a free group if A contains at least two noncommuting elements, where c_n>0 are constants not depending on A. Simple examples show that the order of these estimates are the best ... More

Concordance invariants from higher order coversSep 05 2008We generalize the Manolescu-Owens smooth concordance invariant delta(K) of knots K in the 3-sphere to invariants delta_{p^n}(K) obtained by considering covers of order p^n, with p prime. Our main result shows that for any odd prime p, the direct sum of ... More

Adaptive quantum tomographyOct 10 2016We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We argue in favor ... More

The signature of an even symmetric form with vanishing associated linking formApr 23 2012Apr 25 2012We prove that the signature of an even, symmetric form on a finite rank integral lattice, has signature divisible by 8, provided its associated linking form vanishes in the Witt group of linking forms. Our result generalizes the well know fact that an ... More

Operators Similar to Contractions and Their Similarity to a Normal OperatorNov 10 2001It is proved recently by Benamara-Nikolski that a contraction having finite defects and spectrum not filling in the closed unit disc, is similar to a normal operator if and only if it has the so-called linear resolvent growth property. We obtain results ... More

The rational Witt class and the unknotting number of a knotJul 14 2009We use the rational Witt class of a knot in the 3-sphere as a tool for addressing questions about its unknotting number. We apply these tools to several low crossing knots (151 knots with 11 crossing and 100 knots with 12 crossings) and to the family ... More

Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entriesMay 23 2016Jun 29 2016Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical covariance estimator ... More

Generalized Hermitian Codes over GF(2^r)Nov 08 2005In this paper we studied generalization of Hermitian function field proposed by A.Garcia and H.Stichtenoth. We calculated a Weierstrass semigroup of the point at infinity for the case q=2, r>=3. It turned out that unlike Hermitian case, we have already ... More

Orbital and strongly orbital spacesSep 05 2012We say that a (countably dimensional) topological vector space $X$ is orbital if there is $T\in L(X)$ and a vector $x\in X$ such that $X$ is the linear span of the orbit ${T^nx:n=0,1,...}$. We say that $X$ is strongly orbital if, additionally, $x$ can ... More

Symplectic surfaces and generic J-holomorphic structures on 4-manifoldsJul 04 2002Feb 12 2004It is a well known fact that every embedded symplectic surface $\Sigma$ in a symplectic 4-manifold $(X^4,\omega)$ can be made $J$-holomorphic for some almost-complex structure $J$ compatible with $\omega$. In this paper we investigate when such a $J$ ... More

Uniform bounds for robust mean estimatorsDec 09 2018May 03 2019This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of symmetry and robustness. ... More

Random geometric subdivisionsDec 05 2011We study several models of random geometric subdivisions arising from the model of Diaconis and Miclo (2011). In particular, we show that the limiting shape of an indefinite subdivision of a quadrilateral is a.s.\ a parallelogram. We also show that the ... More

Discrete Complex Analysis and ProbabilitySep 30 2010We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo Duminil-Copin and Cl\'ement Hongler.

Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising modelJul 31 2007We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel those observables are used to construct conformally invariant ... More

Dimension of quasicirclesApr 07 2009We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala's conjecture that the Hausdorff dimension of a $k$-quasicircle ... More

Rapid growth sequencesFeb 01 2002Feb 02 2002Studying Fermat sequence we can simply find infinitely many other rapidly growing sequences of similar properties. On the other hand this approach allows us simple construction of such sequences.

A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fieldsNov 12 2012Nov 12 2015Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.

Azimuthal entanglement and multichannel Schmidt-type decomposition of non-collinear biphotonsJan 08 2016Purely azimuthal entanglement is analyzed for noncollinear frequency-degenerate biphoton states. The degree of azimuthal entanglement is found to be very high, with the Schmidt parameter $K$ on the order of the ratio of the pump waist to its wavelength. ... More

Feedback control for damping a system of linear oscillatorsSep 20 2015Nov 13 2015The paper is devoted to a design of a common bounded feedback control steering a system of an arbitrary number of linear oscillators to the equilibrium. At high energies, the control is based on the asymptotic theory of reachable sets of linear systems. ... More

Asymptotically optimal feedback control for a system of linear oscillatorsNov 29 2016Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the ratio of motion ... More

Schmidt modes and entanglement of biphoton polarization qutritsAug 12 2013Polarization features and entanglement of biphoton polarization qutrits are briefly outlined. Schmidt modes of qutrits are found analytically and in a general form by the method different from the standard one and based on the original approach of Erhard ... More

Mutual information-energy inequality for thermal states of a bipartite quantum systemDec 18 2014Mar 19 2015In this work, we consider an upper bound for the quantum mutual information in thermal states of a bipartite quantum system. This bound is related with the interaction energy and logarithm of the partition function of the system. We demonstrate the connection ... More

Frobenius manifold structures on the spaces of abelian integralsJan 21 2007Dec 26 2010Frobenius manifold structures on the spaces of abelian integrals were constructed by I. Krichever. We use D-modules, deformation theory, and homological algebra to give a coordinate-free description of these structures. It turns out that the tangent sheaf ... More

Integrable flows and Backlund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3)May 18 2005We show that the $m$-dimensional Euler--Manakov top on $so^*(m)$ can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety $\bar{\cal V}(k,m)$, and present its Lax representation with a rational ... More

Logical methods of object recognition on satellite images using spatial constraintsApr 27 2010A logical approach to object recognition on image is proposed. The main idea of the approach is to perform the object recognition as a logical inference on a set of rules describing an object shape.

An example of the Langlands correspondence for irregular rank two connections on P^1Mar 31 2010May 02 2012Special kinds of rank 2 vector bundles with (possibly irregular) connections on P^1 are considered. We construct an equivalence between the derived category of quasi-coherent sheaves on the moduli stack of such bundles and the derived category of modules ... More