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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

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

The Goldilocks zone: Towards better understanding of neural network loss landscapesJul 06 2018Nov 12 2018We explore the loss landscape of fully-connected and convolutional neural networks using random, low-dimensional hyperplanes and hyperspheres. Evaluating the Hessian, $H$, of the loss function on these hypersurfaces, we observe 1) an unusual excess of ... More

Large Scale Structure of Neural Network Loss LandscapesJun 11 2019There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High dimensionality ... More

On Evolutionary Spatial Heterogeneous GamesDec 20 2007How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model to take into ... More

Stiffness: A New Perspective on Generalization in Neural NetworksJan 28 2019We investigate neural network training and generalization using the concept of stiffness. We measure how stiff a network is by looking at how a small gradient step on one example affects the loss on another example. In particular, we study how stiffness ... More

Adaptive Quantum State Tomography with Neural NetworksDec 17 2018Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements -- as well as ... More

Exploring the cooperative regimes in a model of agents without memory or "tags": indirect reciprocity vs. selfish incentivesNov 15 2002The self-organization in cooperative regimes in a simple mean-field version of a model based on "selfish" agents which play the Prisoner's Dilemma (PD) game is studied. The agents have no memory and use strategies not based on direct reciprocity nor 'tags'. ... More

Cooperation and Self-Regulation in a Model of Agents Playing Different GamesJun 23 2003A simple model for cooperation between "selfish" agents, which play an extended version of the Prisoner's Dilemma(PD) game, in which they use arbitrary payoffs, is presented and studied. A continuous variable, representing the probability of cooperation, ... More

Distribution of galaxies at large redshift and cosmological parameters from the magnification bias in Cl0024+1654Jun 06 1996We analyse the surface density of very faint galaxies at the limit of the sky background noise in the field of the cluster of galaxies Cl0024+1654. The radial variation of their number density in the magnitude bins $B=26-28$ and $I=24-26.5$ displays an ... More

Fractional Statistics in Three Dimensions: Compact Maxwell-Higgs SystemSep 21 1995We show that a (3+1)-dimensional system composed of an open magnetic vortex and an electrical point charge exhibits the phenomenon of Fermi-Bose transmutation. In order to provide the physical realization of this system we focus on the lattice compact ... More

Gravitational Lensing and Tests of the Cosmological ConstantFeb 01 1998The case for a flat Cold Dark Matter model with a positive cosmological constant $\Lambda$ has been recently strongly advocated by some theoreticians. In this paper we give the observers point of view to the light of the most recent observations with ... More

Limit theorems for some adaptive MCMC algorithms with subgeometric kernelsJul 18 2008Sep 03 2009This paper deals with the ergodicity and the existence of a strong law of large numbers for adaptive Markov Chain Monte Carlo. We show that a diminishing adaptation assumption together with a drift condition for positive recurrence is enough to imply ... More

Fixed boundary conditions and phase transitions in pure gauge compact QEDJun 02 1994We have simulated the pure gauge compact QED with fixed boundary conditions, on lattices from $6^4$ to $16^4$. We argue that a lattice with this fixed boundary imposition corresponds actually to a lattice with spherical topology. We have found the presence ... More

The Effect of Large Amplitude Fluctuations in the Ginzburg-Landau Phase TransitionOct 09 2000The lattice Ginzburg-Landau model in d=3 and d=2 is simulated, for different values of the coherence length $\xi$ in units of the lattice spacing $a$, using a Monte Carlo method. The energy, specific heat, vortex density $v$, helicity modulus $\Gamma_\mu$ ... More

Catastrophic Phase Transitions and Early Warnings in a Spatial Ecological ModelOct 06 2009Gradual changes in exploitation, nutrient loading, etc. produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts are fundamental ... More

Trajectory eigenmodes of an orbiting wave sourceJul 23 2013Resonances usually result from wave superpositions in cavities where they are due to the wave spatio-temporal folding imposed by the boundaries. These energy accumulations are the signature of the cavity eigenmodes. Here we study a situation in which ... More

Weak lensing at the limit of the sky background noiseAug 16 1996Recent weak lensing observations have pushed the use of 4 meter-class telescopes to the limits of their capabilities with exposure times exceeding several hours. The leading idea is that the surface density of faint galaxies up to very faint magnitude ... More

Online Expectation Maximization based algorithms for inference in hidden Markov modelsAug 19 2011Oct 16 2012The Expectation Maximization (EM) algorithm is a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be available at ... More

State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chainsJan 16 2009Sep 03 2009We consider a form of state-dependent drift condition for a general Markov chain, whereby the chain subsampled at some deterministic time satisfies a geometric Foster-Lyapunov condition. We present sufficient criteria for such a drift condition to exist, ... More

Loop Representation of the Partition Function of Lattice U(1) Gauge TheoryFeb 17 1994We introduce in a natural and straigthforward way the $loop$ (Lagrangian) $representation$ for the partition function of pure compact lattice QED. The corresponding classical lattice loop action is proportional to the quadratic area of the loop world ... More

V- and I-band observations of the halo of NGC 5907Jun 28 1996Using long exposures taken in the V and I bands with a 4096$\times$4096 pixel CCD array at the prime focus of the Canada-France-Hawaii telescope, we have confirmed the discovery by Sackett et al. (1994) of a flat, faint luminous halo around the edge-on ... 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

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.

Cyclically regular semigroupsMar 16 2011We study varieties of semigroups related to completely 0-simple semigroup. We present here an algorithmic descriptions of these varieties interms of "forbidden" semigroups.

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

Kolmogorov-Burgers Model for Star Forming TurbulenceAug 18 2001Oct 23 2001The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range such turbulence obeys the Kolmogorov law, while in the dissipative range ... 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

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.

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

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

Heegaard Floer groups of Dehn surgeriesSep 22 2014We use an algorithm by Ozsvath and Szabo to find closed formulae for the ranks of the hat version of the Heegaard Floer homology groups for non-zero Dehn surgeries on knots in the 3-sphere. As applications we provide new bounds on the number of distinct ... More

Effect of slip boundary conditions on interfacial stability of two-layer viscous fluids under shearJun 06 2015Jun 09 2015The traditional approach in the study of hydrodynamic stability of stratified fluids includes the stick boundary conditions between layers. However, this rule may be violated in polymer systems and as a consequence various instabilities may arise. The ... More

A complete locally convex space of countable dimension admitting an operator with no invariant subspacesSep 14 2010We construct a complete locally convex topological vector space $X$ of countable algebraic dimension and a continuous linear operator $T:X\to X$ such that $T$ has no non-trivial closed invariant subspaces.

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

On The Painleve Property For A Class Of Quasilinear Partial Differential EquationsSep 11 2018The last decades saw growing interest across multiple disciplines in nonlinear phenomena described by partial differential equations (PDE). Integrability of such equations is tightly related with the Painleve property - solutions being free from moveable ... More

Positivstellensatz and flat functionals on path *-algebrasApr 06 2009Jun 07 2009We consider the class of non-commutative *-algebras which are path algebras of doubles of quivers with the natural involutions. We study the problem of extending positive truncated functionals on such *-algebras. An analog of the solution of the truncated ... More

Inferring hierarchical structure of spatial and generic complex networks through a modeling frameworkDec 15 2017Our recent paper [Grauwin et al. Sci. Rep. 7 (2017)] demonstrates that community and hierarchical structure of the networks of human interactions largely determines the least and should be taken into account while modeling them. In the present proof-of-concept ... 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

Remarks on common hypercyclic vectorsSep 06 2012We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator $T$ on a complex Fr\'echet space $X$ and a set $\Lambda\subseteq \R_+\times\C$ which is not ... More

Operators commuting with the Volterra operator are not weakly supercyclicMar 10 2009We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p<\infty$, commuting with the Volterra operator $V$, is not weakly supercyclic, which answers affirmatively a question raised by L\'eon-Saavedra and Piqueras-Lerena. It is achieved by ... More

The Spectral Problem and Algebras Associated with Extended Dynkin GraphsApr 06 2009The Spectral Problem is to describe possible spectra $\sigma (A_j)$ for an irreducible $n$-tuple of Hermitian operators s.t. $A_1+...+A_n$ is a scalar operator. In case when $m_j= | \sigma (A_j)|$ are finite and a rooted tree ${\rm T}_{m_1,..., m_n}$ ... 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

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

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

On O^*-representability and C^*-representability of *-algebrasSep 24 2007May 10 2008Characterization of the *-subalgebras in the algebra of bounded operators acting on Hilbert space is presented. Sufficient conditions for the existence of a faithful representation in pre-Hilbert space of a *-algebra in terms of its Groebner basis are ... More

Chosen-ciphertext attack on noncommutative Polly CrackerAug 02 2005Nov 08 2005We propose a chosen-ciphertext attack on recently presented noncommutative variant of the well-known Polly Cracker cryptosystem. We show that if one chooses parameters for this noncommutative Polly Cracker as initially proposed, than the system should ... More

Top-quark mass at ATLAS and CMSJan 15 2019The top-quark mass measurements carried out by the LHC experiments, ATLAS and CMS, are summarized. Results of different approaches to the top-quark mass reconstruction are presented. Masses from different measurements are in good agreement within uncertainties. ... More

Feynman integrals as flat bundles over the complement of Landau varietiesOct 25 2017We demonstrate that Feynman integrals of a fixed diagram form a flat vector bundle over the complement of Landau varieties that possesses a connection \begin{equation} \frac{\partial}{\partial p_{i,\mu}}f_\beta(p_{i,\mu})=\sum_{\beta'} \sum_k \sum_{I_1,...,I_k} ... More

Plug-in Approach to Active LearningApr 07 2011Nov 02 2011We present a new active learning algorithm based on nonparametric estimators of the regression function. Our investigation provides probabilistic bounds for the rates of convergence of the generalization error achievable by proposed method over a broad ... More

A hypercyclic finite rank perturbation of a unitary operatorAug 20 2010A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space $\H$ are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic. ... More

Approximations of Periodic Functions by Analogue of Zigmund's Sums in the Spaces $L^{p(\cdot)}$Jan 12 2015In this work we found order estimates for the upper bounds of the deviations of analogue of Zigmund's sums on the classes of $(\psi;\beta)$-differentiable functions in the metrics of generalized Lebesgue spaces with variable exponent.

Geometric median and robust estimation in Banach spacesAug 06 2013Sep 29 2015In many real-world applications, collected data are contaminated by noise with heavy-tailed distribution and might contain outliers of large magnitude. In this situation, it is necessary to apply methods which produce reliable outcomes even if the input ... 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

On the Rees-Sushkevich varietySep 15 2010May 31 2011We study varieties of semigroups related to completely 0-simple semigroup. We present here an algorithmic descriptions of these varieties in terms of "forbidden" semigroups. We also describe residually completely 0-simple varieties of semigroups in terms ... 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

Mixing operators on spaces with weak topologySep 05 2012We prove that a continuous linear operator $T$ on a topological vector space $X$ with weak topology is mixing if and only if the dual operator $T'$ has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic ... 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

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

On similarity of quasinilpotent operatorsSep 07 2012Bounded linear operators on separable Banach spaces algebraically similar to the classical Volterra operator $V$ acting on $C[0,1]$ are characterized. From this characterization it follows that $V$ does not determine the topology of $C[0,1]$, which answers ... More

Norm attaining operators and pseudospectrumSep 06 2012It is shown that if $1<p<\infty$ and $X$ is a subspace or a quotient of an $\ell_p$-direct sum of finite dimensional Banach spaces, then for any compact operator $T$ on $X$ such that $\|I+T\|>1$, the operator $I+T$ attains its norm. A reflexive Banach ... More

Framed moduli and Grassmannians of submodulesOct 22 2010Dec 20 2010In this work we study a realization of moduli spaces of framed quiver representations as Grassmannians of submodules devised by Marcus Reineke. Obtained is a generalization of this construction for finite dimensional associative algebras and for quivers ... More

Grafting Seiberg-Witten monopolesOct 26 2001Feb 23 2003We demonstrate that the operation of taking disjoint unions of J-holomorphic curves (and thus obtaining new J-holomorphic curves) has a Seiberg-Witten counterpart. The main theorem asserts that, given two solutions (A_i, psi_i), i=0,1 of the Seiberg-Witten ... 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

Aproximation of periodical function in weighted Orlicz spacesJan 12 2015In this paper we obtained some direct and inverse theorems of approximation theory for $\psi$-differentiable functions in the metric weighted Orlicz spaces with weights, which belong to the class of Muckenhoupt.

Supplement paper to "Online Expectation Maximization based algorithms for inference in hidden Markov models"Aug 20 2011Oct 16 2012This is a supplementary material to the paper "Online Expectation Maximization based algorithms for inference in hidden Markov models". It contains further technical derivations and additional simulation results.

New Fréchet features for random distributions and associated sensitivity indicesMar 30 2015In this article we define new Fr\`Echet features for random cumulative distribution functions using contrast. These contrasts allow to construct Wasserstein costs and our new features minimize the average costs as the Fr\`Echet mean minimizes the mean ... More

Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part IINov 02 2009We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We discuss in detail the special case of stochastic approximation. We use the result to analyze the ... 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

From Quenched Disorder to Continuous Time Random WalkJul 17 2017Aug 21 2017This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to t/\Lambda^{1/\alpha}$ for transient ... More

Destabilization of the EW vacuum in non-minimally coupled inflationNov 26 2018Current cosmological data favour inflationary models non-minimally coupled to gravity. In this work we study the implications of the metastability of the electroweak vacuum in this framework. We consider an inflaton field with a non-minimal coupling to ... More

On orbits of truncated convolution operatorsAug 20 2010We prove that a semigroup generated by a finitely many truncated convolution operators on $L^p[0,1]$ with $1\leq p<\infty$ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.

Semi-invariants of 2-representations of quiversSep 24 2009In this work we obtain a version of the Procesi-Rasmyslov Theorem for the algebra of semi-invariants of representations of an arbitrary quiver with dimension vector (2,2,...,2).