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Bounding the error of discretized Langevin algorithms for non-strongly log-concave targetsJun 20 2019In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the Langevin Monte Carlo (LMC) algorithm, the Euler discretization of the ... More

Theoretical guarantees for approximate sampling from smooth and log-concave densitiesDec 23 2014Feb 19 2016Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling from a given ... More

On estimation of the diagonal elements of a sparse precision matrixApr 18 2015May 25 2016In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision matrix. It is ... More

Outlier-robust estimation of a sparse linear model using $\ell_1$-penalized Huber's $M$-estimatorApr 12 2019May 22 2019We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the $\ell_1$-penalized Huber's ... More

Minimax rates in permutation estimation for feature matchingOct 17 2013Feb 02 2015The problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation. We address this problem from a statistical point of view and provide a theoretical analysis of ... More

Restricted eigenvalue property for corrupted Gaussian designsMay 21 2018Nov 30 2018Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eigenvalue-type condition for Gaussian designs. Such a notion is suitable for ... More

Minimax estimation of a p-dimensional linear functional in sparse Gaussian models and robust estimation of the meanDec 15 2017Nov 08 2018We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of $n$ independent $p$-dimensional Gaussian vectors, under the assumption that most of these means are ... More

Optimal Kullback-Leibler Aggregation in Mixture Density Estimation by Maximum LikelihoodJan 18 2017We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect to the Kullback-Leibler ... More

Outlier-robust estimation of a sparse linear model using $\ell_1$-penalized Huber's $M$-estimatorApr 12 2019We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the $\ell_1$-penalized Huber's ... More

Sharp adaptive estimation of the drift function for ergodic diffusionsFeb 28 2006The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the value of $k$ ... More

On the Prediction Performance of the LassoFeb 07 2014Nov 08 2016Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context of multiple ... More

On the Prediction Performance of the LassoFeb 07 2014Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context of multiple ... More

On the Exponentially Weighted Aggregate with the Laplace PriorNov 25 2016In this paper, we study the statistical behaviour of the Exponentially Weighted Aggregate (EWA) in the problem of high-dimensional regression with fixed design. Under the assumption that the underlying regression vector is sparse, it is reasonable to ... More

Stein Shrinkage and Second-Order Efficiency for semiparametric estimation of the shiftSep 10 2005Feb 26 2007The problem of estimating the shift (or, equivalently, the center of symmetry) of an unknown symmetric and periodic function $f$ observed in Gaussian white noise is considered. Using the blockwise Stein method, a penalized profile likelihood with a data-driven ... More

Minimax rates in outlier-robust estimation of discrete modelsFeb 12 2019We consider the problem of estimating the probability distribution of a discrete random variable in the setting where the observations are corrupted by outliers. Assuming that the discrete variable takes k values, the unknown parameter p is a k-dimensional ... More

Mirror averaging with sparsity priorsMar 05 2010Aug 17 2012We consider the problem of aggregating the elements of a possibly infinite dictionary for building a decision procedure that aims at minimizing a given criterion. Along with the dictionary, an independent identically distributed training sample is available, ... More

Tight conditions for consistent variable selection in high dimensional nonparametric regressionFeb 17 2011We address the issue of variable selection in the regression model with very high ambient dimension, i.e., when the number of covariates is very large. The main focus is on the situation where the number of relevant covariates, called intrinsic dimension, ... More

Estimating linear functionals of a sparse family of Poisson meansDec 05 2017Jan 17 2018Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown intensity ... More

Asymptotic statistical equivalence for ergodic diffusions: the multidimensional caseMay 03 2005May 06 2005Asymptotic local equivalence in the sense of Le Cam is established for inference on the drift in multidimensional ergodic diffusions and an accompanying sequence of Gaussian shift experiments. The nonparametric local neighbourhoods can be attained for ... More

Convex programming approach to robust estimation of a multivariate Gaussian modelDec 15 2015Feb 06 2016Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often considered as ... More

Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsityMar 19 2008Mar 22 2013We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of ... More

Second-order asymptotic expansion for a non-synchronous covariation estimatorApr 04 2008Aug 02 2010In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers \cite{Hay-Yos03, Hay-Yos04}, we derive second-order asymptotic expansions for ... More

On the prediction loss of the lasso in the partially labeled settingJun 20 2016In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling. The main goal ... More

Sharp Oracle Inequalities for Aggregation of Affine EstimatorsApr 20 2011Feb 01 2013We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a PAC-Bayesian type inequality ... More

Tight conditions for consistency of variable selection in the context of high dimensionalityJun 21 2011Feb 19 2013We address the issue of variable selection in the regression model with very high ambient dimension, that is, when the number of variables is very large. The main focus is on the situation where the number of relevant variables, called intrinsic dimension, ... More

On the prediction loss of the lasso in the partially labeled settingJun 20 2016Nov 08 2016In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling. The main goal ... More

Minimax testing of a composite null hypothesis defined via a quadratic functional in the model of regressionAug 09 2012Jan 04 2013We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the null hypothesis states that the regression function $f$ satisfies the constraint ... More

Penalized maximum likelihood and semiparametric second-order efficiencyMay 16 2006We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order ... More

Learning Heteroscedastic Models by Convex Programming under Group SparsityApr 16 2013Popular sparse estimation methods based on $\ell_1$-relaxation, such as the Lasso and the Dantzig selector, require the knowledge of the variance of the noise in order to properly tune the regularization parameter. This constitutes a major obstacle in ... More

A nonasymptotic law of iterated logarithm for robust online estimatorsMar 15 2019In this paper, we provide tight deviation bounds for M-estimators, which are valid with a prescribed probability for every sample size. M-estimators are ubiquitous in machine learning and statistical learning theory. They are used both for defining prediction ... More

A nonasymptotic law of iterated logarithm for general M-estimatorsMar 15 2019May 24 2019M-estimators are ubiquitous in machine learning and statistical learning theory. They are used both for defining prediction strategies and for evaluating their precision. In this paper, we propose the first non-asymptotic "any-time" deviation bounds for ... More

Sparse Regression Learning by Aggregation and Langevin Monte-CarloMar 06 2009Feb 16 2010We consider the problem of regression learning for deterministic design and independent random errors. We start by proving a sharp PAC-Bayesian type bound for the exponentially weighted aggregate (EWA) under the expected squared empirical loss. For a ... More

Statistical inference in compound functional modelsAug 31 2012Jan 02 2013We consider a general nonparametric regression model called the compound model. It includes, as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant covariates. ... More

A new algorithm for estimating the effective dimension-reduction subspaceJan 30 2007The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR subspace is ... More

Structures induced on transversals to a subgroup of a group and hypergroups over the groupJul 31 2015Aug 10 2015On the transversals of a subgroup of a group, using the binary operation of the group, structural mappings are defined. Based on these mappings, the notion of the hypergroup over the group is introduced, which generalizes the notion of the quotient-group ... More

An algorithm for determining the irreducible polynomials over finite fieldsMay 02 2015We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.

Hypergroups over the group and generalizations of Schreier's theorem on group extensionsMar 24 2014Let $H$ be a group, $m$ be a positive integer, $Ext_m H$ be the set of all isomorphic in $G$ classes of group monomorphisms $\varphi: H \rightarrow G$ such that index of $\varphi(H)$ in $G$ is $m$. The main goal of this paper is to describe the elements ... More

NNLO classical solution for Lipatov's effective action for reggeized gluonsFeb 15 2018Mar 19 2018We consider the formalism of small-x effective action for reggeized gluons, Gribov (Sov Phys JETP 26:414, 1968), Lipatov (Nucl Phys B 452:369, 1995; Phys Rep 286:131, 1997; Subnucl Ser 49:131, 2013, Int J Mod Phys Conf Ser 39:1560082, 2015; Int J Mod ... More

Band insulator to Mott insulator transition in a bilayer Hubbard modelMar 27 2007The ground state phase diagram of the half-filled repulsive Hubbard model in a bilayer is investigated using cluster dynamical mean field theory. For weak to intermediate values of Coulomb repulsion $U$, the system undergoes a transition from a Mott insulating ... More

Tunneling system coupled to phonon: an analytical treatmentOct 01 2004Oct 28 2004This paper was withdrawn by the authors.

The flavor universality of some mass splittings in hadronsOct 08 2014The approximate chiral invariance of the two-flavor QCD is known to be spontaneously broken. This effect explains the relatively small pion mass and, as is widely believed, the mass splittings of would-be chiral partners --- the hadrons of equal spin ... More

Implications of the Crystal Barrel data for meson-baryon symmetriesJul 09 2007Sep 10 2008Making use of numerous resonances discovered by the Crystal Barrel Collaboration we discuss some possible relations between the baryon and meson spectra of resonances composed of the light non-strange quarks. Our goal is to indicate new features that ... More

Parity doubling in particle physicsApr 12 2007Sep 07 2007Parity doubling in excited hadrons is reviewed. Parity degeneracy in hadrons was first experimentally observed 40 years ago. Recently new experimental data on light mesons caused much excitement and renewed interest to the phenomenon, which still remains ... More

Experimental indication on chiral symmetry restoration in meson spectrumMar 21 2006Jun 27 2006The spectroscopic predictions of the Ademollo-Veneziano-Weinberg dual model are critically tested in view of the modern experimental data. The predicted equidistance of masses squared for chiral partners is shown to be violated high in energies, instead ... More

Regge spectrum from holographic models inspired by OPEFeb 23 2009Jun 29 2009The problem of obtaining the Regge-like behaviour for meson mass spectrum in the hard-wall AdS/QCD models is addressed. We show that the problem can be solved by a simple incorporation of the effects of local vacuum condensates into such models. The slope ... More

Towards understanding broad degeneracy in non-strange mesonsJan 11 2007Jul 06 2007The spectroscopic regularities of modern empirical data on the non-strange mesons up to 2.4 GeV can be summarized as a systematic clustering of states near certain values of energy. It is getting evident that some unknown X-symmetry triggers the phenomenon. ... More

A Simple Method to Mix Granular MaterialsOct 06 1999We show that a mixture of two species of granular particles with equal sizes but differing densities can be either segregated or mixed by adjusting the granular temperature gradient and the magnitude of the gravitational force. In the absence of gravity, ... More

Interplay of gas and ice during cloud evolutionAug 21 2014Jan 20 2015During the evolution of diffuse clouds to molecular clouds, gas-phase molecules freeze out on surfaces of small dust particles to form ices. On dust surfaces, water is the main constituent of the icy mantle in which a complex chemistry is taking place. ... More

Competing Glauber and Kawasaki DynamicsAug 17 1998Using a quantum formulation of the master equation we study a kinetic Ising model with competing stochastic processes: the Glauber dynamics with probability $p$ and the Kawasaki dynamics with probability $1 - p$. Introducing explicitely the coupling to ... More

Limit shocks of relativistic magnetohydrodynamics, Punsly's waveguide and the Blandford-Znajek solutionJun 05 2002Sep 11 2002In this paper we examine various issues closely related to the ongoing discussion on the nature of the Blandford-Znajek mechanism of extraction of rotational energy of black holes. In particular, we show that switch-on and switch-off shocks are allowed ... More

Simulations of Axisymmetric Magnetospheres of Neutron StarsOct 11 2005Nov 28 2005In this paper we present the results of time-dependent simulations of dipolar axisymmetric magnetospheres of neutron stars carried out both within the framework of relativistic magnetohydrodynamics and within the framework of resistive force-free electrodynamics. ... More

On the nature of the Blandford-Znajek mechanismNov 07 2002It is widely accepted in the astrophysical community that the event horizon plays crucial role in the Blandford-Znajek mechanism of extraction of rotational energy of black holes. In fact, this view is a quintessence of the Membrane Paradigm of black ... More

Planetary nebula or symbiotic Mira? Near infrared colours mark the differenceAug 21 2001Nebulae around symbiotic Miras look very much like genuine planetary nebulae, although they are formed in a slightly different way. We present near infrared photometry of known and suspected symbiotic nebulae obtained with the Deep Near Infrared Southern ... More

A catalogue of IJK photometry of Planetary Nebulae with DENISMay 15 2001Near-infrared photometry of planetary nebulae (PNe) allows the classification of those objects. We present the largest homogeneous sample so far, obtained with the Deep Near Infrared Southern Sky Survey (DENIS).

Spin Injection and Nonlocal Spin Transport in Magnetic NanostructuresSep 20 2006We theoretically study the nonlocal spin transport in a device consisting of a nonmagnetic metal (N) and ferromagnetic injector (F1) and detector (F2) electrodes connected to N. We solve the spin-dependent transport equations in a device with arbitrary ... More

Towards spin turbulence of light: Spontaneous disorder and chaos in cavity-polariton systemsNov 23 2015Nov 02 2016Recent advances in nanophotonics have brought about coherent light sources with chaotic circular polarization; a low-dimensional chaotic evolution of optical spin was evidenced in laser diodes. Here we propose a mechanism that gives rise to light with ... More

Spectral curves and parameterizations of a discrete integrable 3-dimensional modelSep 09 2002We consider a discrete classical integrable model on the 3-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of the different 3-dimensional spin models. We have found the general solution of this ... More

Relativistic Toda chain at root of unity II. Modified Q-operatorJul 27 2001Matrix elements of quantum intertwiner as well as the modified Q-operator for the quantum relativistic Toda chain at root of unity are constructed explicitly. Modified Q-operators make isospectrality transformations of quantum transfer matrices so that ... More

On Special Cases of General Geometry: geometries with changing length of vectorsJun 01 2006We find relations between quantities defining geometry and quantities defining the length of a curve in geometries underlying Electromagnetism and unified model of Electromagnetism and Gravitation. We show that the length of a vector changes along a curve ... More

Multi-black holes and instantons in effective string theoryJul 16 1996The effective action for string theory which takes into account non-minimal coupling of moduli admits multi-black hole solutions. The euclidean continuation of these solutions can be interpreted as an instanton mediating the splitting and recombination ... More

Large-Scale Magnetic Field Re-generation by Resonant MHD Wave InteractionsOct 24 2007We investigate numerically the long-time behavior of balanced Alfven wave turbulence forced at intermediate scales. Whereas the usual constant-flux solution is found at the smallest scales, two new scalings are obtained at the forcing scales and at the ... More

Dynamical mean field theory of small polaron transportJun 24 2003We present a unified view of the transport properties of small-polarons in the Holstein model at low carrier densities, based on the Dynamical Mean Field Theory. The nonperturbative nature of the approach allows us to study the crossover from classical ... More

Dynamical Systems and Topological SurgeryDec 12 2008In this paper we try to establish a connection between a three-dimensional Lotka--Volterra dynamical system and two-dimensional topological surgery. There are many physical phenomena exhibiting two-dimensional topological surgery through a `hole drilling' ... More

Reptation Quantum Monte CarloAug 19 1998We present an elementary and self-contained account of the analogies existing between classical diffusion and the imaginary-time evolution of quantum systems. These analogies are used to develop a new quantum simulation method which allows to calculate ... More

A special chain theorem for the embedding dimensionOct 01 2014This paper establishes an analogue of the special chain theorem for the embedding dimension of polynomial rings, with direct application on the (embedding) codimension. In particular, we recover a classic result on the transfer of regularity to polynomial ... More

The Cauchy problem for f(R)-gravity: an overviewMar 11 2011We review the Cauchy problem for f(R) theories of gravity, in metric and metric-affine for- mulations, pointing out analogies and differences with respect to General Relativity. The role of conformal transformations, effective scalar fields and sources ... More

Distinguishing WH and WBBbar production at the Fermilab TevatronMar 02 1999The production of a Higgs boson in association with a W-boson is the most likely process for the discovery of a light Higgs at the Fermilab Tevatron. Since it decays primarily to b-quark pairs, the principal background for this associated Higgs production ... More

Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributionsNov 10 2008Jan 18 2009We study the perturbative QCD corrections to heavy-quark structure functions of charged-lepton deep-inelastic scattering and their impact on global fits of parton distributions. We include the logarithmically enhanced terms near threshold due to soft ... More

A New Metallicity Calibration for Dwarfs for the RGU-PhotometryMar 20 2003We adopted the procedure of Carney to obtain a metallicity calibration for dwarfs for the RGU-photometry. For this purpose we selected 76 dwarfs of different metallicities from Carney, and Strobel et al., and evaluated their \delta(U-G) ultra-violet excess ... More

An information theoretical analysis of quantum optimal controlJan 20 2014We show that if an efficient classical representation of the dynamics exists, optimal control problems on many-body quantum systems can be solved efficiently with finite precision. We show that the size of the space of parameters necessary to solve quantum ... More

Sub-Poissonian Shot Noise in Molecular WiresSep 05 2002We investigate the transport behavior of polyene molecules sandwiched between two metallic contacts using the non-equilibrium Green's function formalism. We calculate both current and noise power as a function of applied voltage and show that they decrease ... More

Numerical solution of moving plate problem with uncertain parametersMar 14 2015This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently developed ... More

Dynamical mechanisms of DC current generation in driven Hamiltonian systemsApr 03 2001Recent symmetry considerations (Phys. Rev. Lett. {\bf 84} 2358 (2000)) have shown that dc currents may be generated in the stochastic layer of a system describing the motion of a particle in a one-dimensional potential in the presence of an ac time-periodic ... More

On reggeization of vertex of triple reggeized gluons in high energy QCDMay 13 2019We calculate one loop QCD Regge Field Theory (RFT) correction to the $A_{+}A_{+} A_{-}$ vertex of three reggeized gluons to one QCD loop precision. We demonstrate, that all loop leading logarithmic corrections to the vertex can be summed through the integro-differential ... More

Subsurface diffusion in crystals and effect of surface permeability on the atomic step motionApr 01 2019Apr 17 2019Atomic mechanism of the bulk and surface point defect generation and annihilation on surface sinks is considered theoretically on the base of the Burton, Cabrera and Frank model. We show that the creation and annihilation of self-interstitials and vacancies ... More

Can we have another light (~ 145 GeV) Higgs boson?Oct 20 2015A second light Higgs boson, with mass of approximately 145 GeV, is predicted by non-minimal Supersymmetric models. This new particle can account for an apparent \sim 3 \sigma excess recorded by the CMS experiment at the Large Hadron Collider (LHC) during ... More

Supersymmetric Magnetic Moments Sum Rules and Spontaneous Supersymmetry BreakingNov 22 1994In supersymmetry the anomalous magnetic moment of particles belonging to the same supermultiplet is related by simple sum rules. We study the modification of these sum rules in the case of spontaneously broken N=1 global supersymmetry.

Apology of EuclidJul 11 2005This is a short apology of the style of the Elements by Euclid and Bourbaki.

On reggeization of vertex of three reggeized gluons in high energy QCDMay 13 2019May 19 2019The unitarity corrections to the propagator of reggeized gluons calculated in the framework of QCD RFT require a knowledge of the expressions for Reggeon propagator and vertices of interaction of three reggeized gluons (Reggeons) to one QCD loop precision, ... More

Increasing the efficiency of quantum walk with entangled qubitsMay 27 2019We investigate how arbitrary number of entangled qubits affects properties of quantum walk. We consider variance, positions with non-zero probability density and entropy as criteria to determine the optimal number of entangled qubits in quantum walk. ... More

Studying the Feasibility and Importance of Software Testing: An AnalysisJan 23 2010Software testing is a critical element of software quality assurance and represents the ultimate review of specification, design and coding. Software testing is the process of testing the functionality and correctness of software by running it. Software ... More

Optimization of fuzzy analogy in software cost estimation using linguistic variablesSep 12 2012One of the most important objectives of software engineering community has been the increase of useful models that beneficially explain the development of life cycle and precisely calculate the effort of software cost estimation. In analogy concept, there ... More

Direct photon radiation from a rich baryon Quark-Gluon Plasma systemOct 07 2006Feb 21 2007The direct photon radiation from a hot and slightly strong interacting fireball system of a rich baryon quark-gluon plasma, using the Boltzmann distribution function for the incoming particles and Bose-Einstein distribution for gluon and Fermi-Dirac distribution ... More

AdS/QCD without Kaluza-Klein modes: Radial spectrum from higher dimensional QCD operatorsMay 30 2019Within the framework of AdS/QCD models, the spectrum of radially excited hadrons is identified with a tower of Kaluza-Klein (KK) states in dual theory. We discuss some theoretical pitfalls with such a modeling of hadron spectrum and propose an alternative ... More

Cluster Growth in two- and three-dimensional Granular GasesApr 28 2003Dec 11 2003Dissipation in granular media leads to interesting phenomena as there are cluster formation and crystallization in non-equilibrium dynamical states. The freely cooling system is examined concerning the energy decay and the cluster evolution in time, both ... More

Plasmon band gap generated by intense ion acoustic wavesOct 12 2009Apr 26 2010In the presence of an intense ion acoustic wave, the energy-momentum dispersion relation of plasmons is strongly modified to exhibit a band gap structure. The intensity of an ion acoustic wave might be measured from the band gap width. The plasmon band ... More

Symmetry analysis and exact solutions of one class of (1+3)-dimensional boundary-value problems of the Stefan typeJul 31 2014We present the group classification of one class of (1+3)-dimensional nonlinear boundary-value problems of the Stefan type that simulate the processes of melting and evaporation of metals. The results obtained are used for the construction of the exact ... More

About the fastest growth of Order Parameter in Models of PercolationJun 14 2011Can there be a `Litmus test' for determining the nature of transition in models of percolation? In this paper we argue that the answer is in the affirmative. All one needs to do is to measure the `growth exponent' $\chi$ of the largest component at the ... More

Branching Process in a Stochastic Extremal ModelApr 27 2009Sep 16 2009We considered a stochastic version of the Bak-Sneppen model (SBSM) of ecological evolution where the the number $M$ of sites mutated in a mutation event is restricted to only two. Here the mutation zone consists of only one site and this site is randomly ... More

Self-Organization in a Granular Medium by Internal AvalanchesSep 12 2000Internal avalanches of grain displacements can be created inside a granular material kept in a bin in two ways: (i) By removing a radomly selected grain at the bottom of the bin (ii) By breaking a stable arch of grains clogging a hole at the bottom of ... More

Minimally almost periodic group topology on infinite countable Abelian groups: A solution to Comfort's questionFeb 07 2010Oct 07 2011For any countable subgroup $H$ of an unbounded Abelian group $G$ there is a complete Hausdorff group topology $\tau$ such that $H$ is the von Neumann radical of $(G,\tau)$. In particular, we obtain the positive answer to Comfort's question: any unbounded ... More

The explanation of unexpected temperature dependence of the muon catalysis in solid deuteriumApr 30 2001It is shown that due to the smallness of the inelastic cross-section of the $d\mu$-atoms scattering in the crystal lattice at sufficiently low temperatures the $dd\mu$-mesomolecules formation from the upper state of the hyperfine structure $d\mu (F=3/2)$ ... More

Nonperturbative calculations in light-front QEDOct 01 2010The methods of light-front quantization and Pauli-Villars regularization are applied to a nonperturbative calculation of the dressed-electron state in quantum electrodynamics. This is intended as a test of the methods in a gauge theory, as a precursor ... More

Simultaneous Linear Inequalities: Yesterday and TodayJul 13 2010Jul 14 2010This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.

Mathematics and Economics of Leonid KantorovichJan 02 2011This is a short overview of the contribution of Leonid Kantorovich into the formation of the modern outlook on the interaction between mathematics and economics.

A computation of an universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)Nov 18 2007Nov 20 2007We compute an universal weight function (off-shell Bethe vectors) in any representation with a weight singular vector of the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_N)$ applying the method of projections of Drinfeld currents developed in arXiv:math/0610398. ... More

The Szego class with a polynomial weightMar 26 2004Let p be a trigonometric polynomial, nonnegative on the unit circle $\mathbb{T}$. We say that a measure $\sigma$ on $\mathbb{T}$ belongs to the polynomial Szego class, if $d\sigma=sigma'_{ac}d\theta+d\sigma_s$, $\sigma_s$ is singular, and $p\ln \sigma'_{ac}$ ... More

Submodular spectral functions of principal submatrices of a hermitian matrix, extensions and applicationsJul 20 2010Jun 19 2012We extend the multiplicative submodularity of the principal determinants of a nonnegative definite hermitian matrix to other spectral functions. We show that if $f$ is the primitive of a function that is operator monotone on an interval containing the ... More

Comparing the Ag-content of poltinniks using X-ray fluorescenceFeb 12 2013X-ray fluorescence experiments have been performed in order to analyze the elemental composition of four Russian 50-kopek coins ("poltinniks") minted during 1913, 1921, and 1924. By comparing the intensities of the Ag K{\alpha} X-rays emitted by the poltinniks, ... More

Nonstandard Tools for Nonsmooth AnalysisJun 11 2012This is an overview of the basic tools of nonsmooth analysis which are grounded on nonstandard models of set theory. By way of illustration we give a criterion for an infinitesimally optimal path of a general discrete dynamic system.