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DGC-Net: Dense Geometric Correspondence NetworkOct 19 2018Oct 22 2018This paper addresses the challenge of dense pixel correspondence estimation between two images. This problem is closely related to optical flow estimation task where ConvNets (CNNs) have recently achieved significant progress. While optical flow methods ... More

Automatic Knee Osteoarthritis Diagnosis from Plain Radiographs: A Deep Learning-Based ApproachOct 29 2017Knee osteoarthritis (OA) is the most common musculoskeletal disorder. OA diagnosis is currently conducted by assessing symptoms and evaluating plain radiographs, but this process suffers from subjectivity. In this study, we present a new transparent computer-aided ... More

A novel method for automatic localization of joint area on knee plain radiographsJan 31 2017Apr 05 2017Osteoarthritis (OA) is a common musculoskeletal condition typically diagnosed from radiographic assessment after clinical examination. However, a visual evaluation made by a practitioner suffers from subjectivity and is highly dependent on the experience. ... More

Breast Tumor Cellularity Assessment using Deep Neural NetworksMay 05 2019Breast cancer is one of the main causes of death worldwide. Histopathological cellularity assessment of residual tumors in post-surgical tissues is used to analyze a tumor's response to a therapy. Correct cellularity assessment increases the chances of ... More

Inversion of the Spherical Mean Transform with Sources on a HyperplaneOct 08 2009The object of this study is an integral operator $\mathcal{S}$ which averages functions in the Euclidean upper half-space $\mathbb{R}_{+}^{n}$ over the half-spheres centered on the topological boundary $\partial \mathbb{R}_{+}^{n}$. By generalizing Norton's ... More

The higher order asymptotic expansion of the Krawtchouk polynomialsAug 29 2015The paper extends the classical result on the convergence of the Krawtchouk polynomials to the Hermite polynomials. We provide the uniform asymptotic expansion in terms of the Hermite polynomials. We explicitly obtain expressions for a few initial terms ... More

Descartes-Newton-Young rainbowNov 29 2018We discuss three rainbow theories created by Descartes, Newton and Young. The note is written primary for school students.

Regression modeling method of space weather predictionJun 17 2009Jan 12 2010A regression modeling method of space weather prediction is proposed. It allows forecasting Dst index up to 6 hours ahead with about 90% correlation. It can also be used for constructing phenomenological models of interaction between the solar wind and ... More

Weyl-Kac character formula for affine Lie algebra in Deligne's categoryJun 07 2019We study the characters of simple modules in the parabolic BGG category of the affine Lie algebra in Deligne's category. More specifically, we take the limit of Weyl-Kac formula to compute the character of the irreducible quotient $L(X,k)$ of the parabolic ... More

Limiting curves for the dyadic odometer and the generalized Trollope-Delange formulaJan 09 2018Aug 07 2018We study limiting curves resulting from deviations in partial sums in the ergodic theorem for the dyadic odometer and non-cylindric functions. In particular, we generalize the Trollope-Delange formula for the case of the weighted sum-of-binary-digits ... More

New series of moduli components of rank 2 semistable sheaves on $\mathbb{P}^{3}$ with singularities of mixed dimensionMar 02 2019We construct a new infinite series of irreducible components of the Gieseker-Maruyama moduli scheme $\mathcal{M}(k), ~ k \geq 3$ of coherent semistable rank 2 sheaves with Chern classes $c_1=0,~ c_2=k,~ c_3=0$ on $\mathbb{P}^3$ generic points of which ... More

Operator Lipschitz FunctionsFeb 25 2016The purpose of this survey article is a comprehensive study of operator Lipschitz functions. A continuous function $f$ on the real line ${\Bbb R}$ is called operator Lipschitz if $\|f(A)-f(B)\|\le{\rm const}\|A-B\|$ for arbitrary self-adjoint operators ... More

The effect of universe inhomogeneities on cosmological distance measurementsApr 05 2016Using the focusing equation, the equation for the cosmological angular diameter distance is derived, based on the ideas of Academician Ya.B. Zel'dovich, namely, that the distribution of matter at small angles is not homogeneous, and the light cone is ... More

Functions of perturbed unbounded self-adjoint operators. Operator Bernstein type inequalitiesMar 21 2010This is a continuation of our papers \cite{AP2} and \cite{AP3}. In those papers we obtained estimates for finite differences $(\D_Kf)(A)=f(A+K)-f(A)$ of the order 1 and $(\D_K^mf)(A)\df\sum\limits_{j=0}^m(-1)^{m-j}(m\j)f\big(A+jK\big)$ of the order $m$ ... More

For which graphs the sages can guess correctly the color of at least one hatJan 22 2019Several sages wearing colored hats occupy the vertices of a graph. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbours without exchanging any information. Each hat can have one of three colors. ... More

Functions of perturbed pairs of noncommuting contractionsAug 26 2018We consider functions $f(T,R)$ of pairs of noncommuting contractions on Hilbert space and study the problem for which functions $f$ we have Lipschitz type estimates in Schatten--von Neumann norms. We prove that if $f$ belongs to the Besov class $(B_{\infty,1}^1)_+({\Bbb ... More

Functions of noncommuting operators under perturbation of class $\boldsymbol{S}_p$Feb 17 2019In this article we prove that for $p>2$, there exist pairs of self-adjoint operators $(A_1,B_1)$ and $(A_2,B_2)$ and a function $f$ on the real line in the homogeneous Besov class $B_{\infty,1}^1({\Bbb R}^2)$ such that the differences $A_2-A_1$ and $B_2-B_1$ ... More

Large-scale collective motion of RFGC galaxies in curved space-timeApr 25 2010Jun 11 2010We consider large-scale collective motion of flat edge-on spiral galaxies from the Revised Flat Galaxy Catalogue (RFGC) taking into account the curvature of space-time in the Local Universe at the scale 100 Mpc/h. We analyse how the relativistic model ... More

Almost commuting functions of almost commuting self-adjoint operatorsDec 11 2014Let $A$ and $B$ be almost commuting (i.e, $AB-BA\in\bS_1$) self-adjoint operators. We construct a functional calculus $\f\mapsto\f(A,B)$ for $\f$ in the Besov class $B_{\be,1}^1(\R^2)$. This functional calculus is linear, the operators $\f(A,B)$ and $\psi(A,B)$ ... More

On some double sums with multiplicative charactersDec 26 2017We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.

Multimodal Machine Learning-based Knee Osteoarthritis Progression Prediction from Plain Radiographs and Clinical DataApr 12 2019Knee osteoarthritis (OA) is the most common musculoskeletal disease without a cure, and current treatment options are limited to symptomatic relief. Prediction of OA progression is a very challenging and timely issue, and it could, if resolved, accelerate ... More

Multimodal Machine Learning-based Knee Osteoarthritis Progression Prediction from Plain Radiographs and Clinical DataApr 12 2019May 06 2019Knee osteoarthritis (OA) is the most common musculoskeletal disease without a cure, and current treatment options are limited to symptomatic relief. Prediction of OA progression is a very challenging and timely issue, and it could, if resolved, accelerate ... More

Young rotation-powered pulsars as ultra-luminous X-ray sourcesFeb 25 2013The aim of the present paper is to investigate a possible contribution of the rotation-powered pulsars and pulsar wind nebulae to the population of ultraluminous X-ray sources (ULXs). We first develop an analytical model for the evolution of the distribution ... More

Clark measures on the complex sphereApr 08 2019Let $B_d$ denote the unit ball of $\mathbb{C}^d$, $d\ge 1$. Given a holomorphic function $\varphi: B_d \to B_1$, we study the corresponding family $\sigma_\alpha[\varphi]$, $\alpha\in\partial B_1$, of Clark measures on the unit sphere $\partial B_d$. ... More

Statistical criteria for possible indications of new physics in tritium $β$-decay spectrumNov 23 2014The method of quasi-optimal weights is applied to constructing (quasi-)optimal criteria for various anomalous contributions in experimental spectra. Anomalies in the spectra could indicate physics beyond the Standard Model (additional interactions and ... More

The Ranking Problem of Alternatives as a Cooperative GameNov 09 2015This paper considers the ranking problem of candidates for a certain position based on ballot papers filled by voters. We suggest a ranking procedure of alternatives using cooperative game theory methods. For this, it is necessary to construct a characteristic ... More

Functions of perturbed dissipative operatorsSep 01 2010We generalize our results of \cite{AP2} and \cite{AP3} to the case of maximal dissipative operators. We obtain sharp conditions on a function analytic in the upper half-plane to be operator Lipschitz. We also show that a H\"older function of order $\a$, ... More

Improved Parameterization of Amine-Carboxyate and Amine-Phosphate Interactions for Molecular Dynamics Simulations Using the CHARMM and AMBER Force FieldsOct 07 2015Over the past decades, molecular dynamics (MD) simulations of biomolecules have become a mainstream biophysics technique. As the length and time scales amenable to the MD method increase, shortcomings of the empirical force fields---which have been developed ... More

Operator identities relating sonar and Radon transforms in Euclidean spaceJul 18 2006We establish new relations which connect Euclidean sonar transforms (integrals taken over spheres with centers in a hyperplane) with classical Radon transforms. The relations, stated as operator identities, allow us to reduce the inversion of sonar transforms ... More

Bethe subalgebras in Yangians and the wonderful compactificationOct 16 2018Nov 12 2018We study the family of Bethe subalgebras in the Yangian $Y(\mathfrak{g})$ parameterized by the corresponding adjoint Lie group $G$. We describe their classical limits as subalgebras in the algebra of polynomial functions on the formal Lie group $G_1[[t^{-1}]]$. ... More

On Characterization of Inverse Data in the Boundary Control MethodFeb 15 2016We deal with a dynamical system \begin{align*} & u_{tt}-\Delta u+qu=0 && {\rm in}\,\,\,\Omega \times (0,T)\\ & u\big|_{t=0}=u_t\big|_{t=0}=0 && {\rm in}\,\,\,\overline \Omega\\ & \partial_\nu u = f && {\rm in}\,\,\,\partial\Omega \times [0,T]\,, \end{align*} ... More

Dissipative operators and operator Lipschitz functionsFeb 26 2018The purpose of this paper is to obtain an integral representation for the difference $f(L_1)-f(L_2)$ of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow us to establish Lipschitz type estimates ... More

Krein's trace formula for unitary operators and operator Lipschitz functions (English translation)Nov 05 2016The main result of this paper is a description of the space of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. This space coincides with the space of operator Lipschitz ... More

Operator and commutator moduli of continuity for normal operatorsAug 23 2011We study in this paper properties of functions of perturbed normal operators and develop earlier results obtained in \cite{APPS2}. We study operator Lipschitz and commutator Lipschitz functions on closed subsets of the plane. For such functions we introduce ... More

Estimates of operator moduli of continuityApr 18 2011In \cite{AP2} we obtained general estimates of the operator moduli of continuity of functions on the real line. In this paper we improve the estimates obtained in \cite{AP2} for certain special classes of functions. In particular, we improve estimates ... More

MEMOIR: Multi-class Extreme Classification with Inexact MarginNov 24 2018Multi-class classification with a very large number of classes, or extreme classification, is a challenging problem from both statistical and computational perspectives. Most of the classical approaches to multi-class classification, including one-vs-rest ... More

$s$-points in $3\rm d$ acoustical scatteringApr 14 2010The notion of $s$-points has been introduced by the authors (SIAM JMA, 39 (2008), 1821--1850) in connection with the control problem for the dynamical system governed by the $3\rm d$ acoustical equation $u_{tt}-\Delta u+qu=0$ with a real potential $q ... More

A Riemanian Approach to Blob Detection in Manifold-Valued ImagesMay 31 2019This paper is devoted to the problem of blob detection in manifold-valued images. Our solution is based on new definitions of blob response functions. We define the blob response functions by means of curvatures of an image graph, considered as a submanifold. ... More

Degeneration of Bethe subalgebras in the Yangian of $\mathfrak{gl}_n$Mar 12 2017Dec 05 2017We study degenerations of Bethe subalgebras $B(C)$ in the Yangian $Y(\mathfrak{gl}_n)$, where $C$ is a regular diagonal matrix. We show that closure of the parameter space of the family of Bethe subalgebras, which parametrizes all possible degenerations, ... More

On the electrodynamic model of ultra-relativistic laser-plasma interactions caused by radiation reaction effectsSep 23 2013{A simple electrodynamic model is developed to define plasma-field structures in self-consistent ultra-relativistic laser-plasma interactions when the radiation reaction effects come into play. An exact analysis of a circularly polarized laser interacting ... More

Recognition of stable distribution with Levy index alpha close to 2May 29 2012We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the distribution ... More

Helical bound states in the continuum of the edge states in two dimensional topological insulatorsMay 05 2015May 07 2015We study bound states embedded into the continuum of edge states in two-dimensional topological insulators. These states emerge in the presence of a short-range potential of a structural defect coupled to the boundary. In this case the edge states flow ... More

Lévy Statistics and Anomalous Transport: Lévy flights and SubdiffusionJun 25 2007Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.

Normal and Anomalous Fluctuation Relations for Gaussian Stochastic DynamicsOct 16 2012We study transient work Fluctuation Relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the Fluctuation-Dissipation ... More

Word Similarity Datasets for Thai: Construction and EvaluationApr 08 2019Distributional semantics in the form of word embeddings are an essential ingredient to many modern natural language processing systems. The quantification of semantic similarity between words can be used to evaluate the ability of a system to perform ... More

Measuring Majority Power and Veto Power of Voting RulesNov 16 2018Jun 03 2019We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful, and whether minorities can veto the candidates they do not prefer. For a given voting rule, the minimal ... More

The women day stormMar 08 2012On behalf of the International Women Day, the Sun gave a hot kiss to our mother Earth in a form of a full halo CME generated by the yesterday's double X-class flare. The resulting geomagnetic storm gives a good opportunity to compare the performance of ... More

Inverse Problem of Diffraction by an Inhomogeneous Solid with a Piecewise Hoelder Refractive IndexMar 13 2018The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz equation is reduced ... More

Measuring Majority Power and Veto Power of Voting RulesNov 16 2018Feb 21 2019We study voting rules with respect to how they allow or limit a majority to dominate minorities: whether a voting rule makes a majority powerful, and whether minorities can veto candidates that they do not prefer. For a given voting rule, the minimal ... More

Towards Large-Scale Exploratory Search over Heterogeneous SourcesNov 15 2018Nov 20 2018Since time immemorial, people have been looking for ways to organize scientific knowledge into some systems to facilitate search and discovery of new ideas. The problem was partially solved in the pre-Internet era using library classifications, but nowadays ... More

Generalised Diffusion and Wave Equations: Recent AdvancesMar 04 2019We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional, distributed ... More

On algebras of harmonic quaternion fields in ${\mathbb R}^3$Oct 02 2017Oct 11 2017Let ${\mathscr A}(D)$ be an algebra of functions continuous in the disk $D=\{z\in{\mathbb C}\,|\,\,\,|z|\leqslant 1\}$ and {\it holomorphic} into $D$. The well-known fact is that the set ${\mathscr M}$ of its characters (homomorphisms ${\mathscr A}(D)\to\mathbb ... More

Sums of multiplicative characters with additive convolutionsJun 01 2016In the paper we obtain new estimates for binary and ternary sums of multiplicative characters with additive convolutions of characteristic functions of sets, having small additive doubling. In particular, we improve a result of M.-C. Chang. The proof ... More

Optical transitions in two-dimensional topological insulators with point defectsSep 13 2016Nontrivial properties of electronic states in topological insulators are inherent not only to the surface and boundary states, but to bound states localized at structure defects as well. We clarify how the unusual properties of the defect-induced bound ... More

Constructing a Stochastic Model of Bumblebee Flights from Experimental DataFeb 11 2013The movement of organisms is subject to a multitude of influences of widely varying character: from the bio-mechanics of the individual, over the interaction with the complex environment many animals live in, to evolutionary pressure and energy constraints. ... More

Triple operator integrals in Schatten--von Neumann norms and functions of perturbed noncommuting operatorsApr 06 2015We study perturbations of functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and $B$ that can be defined in terms of double operator integrals. We prove that if $f$ belongs to the Besov class $B_{\be,1}^1(\R^2)$, then we have the following ... More

Minimal Envy and Popular MatchingsFeb 21 2019We study ex-post fairness in the object allocation problem where objects are valuable and commonly owned. A matching is fair from individual perspective if it has only inevitable envy towards agents who received most preferred objects -- minimal envy ... More

On algebraic and uniqueness properties of 3d harmonic quaternion fieldsJan 26 2019Let $\Omega$ be a smooth compact oriented 3-dimensional Riemannian manifold with boundary. A quaternion field is a pair $q=\{\alpha,u\}$ of a function $\alpha$ and a vector field $u$ on $\Omega$. A field $q$ is {\it harmonic} if $\alpha, u$ are continuous ... More

Functions of perturbed noncommuting self-adjoint operatorsNov 07 2014We consider functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and $B$ that can be defined in terms of double operator integrals. We prove that if $f$ belongs to the Besov class $B_{\be,1}^1(\R^2)$, then we have the following Lipschitz type ... More

Singlet-triplet transition in double quantum dots in two-dimensional topological insulatorsSep 14 2018We study two-electron states confined in two coupled quantum dots formed by a short-range potential in a two-dimensional topological insulator. It is shown that there is a fairly wide range of the system parameters, where the ground state is a tripletlike ... More

Geometry of Flat Directions in Scale-Invariant PotentialsApr 16 2019We observe that biquadratic potentials admit non-trivial flat directions when the determinant of the quartic coupling matrix of the scalar fields vanishes. This consideration suggests a new approach to the problem of finding flat directions in scale invariant ... More

Stationary states in single-well potentials under symmetric Levy noisesMay 05 2010We discuss the existence of stationary states for subharmonic potentials $V(x) \propto |x|^c$, $c<2$, under action of symmetric $\alpha$-stable noises. We show analytically that the necessary condition for the existence of the steady state is $c>2-\alpha$. ... More

Propagation of super high-energy cosmic rays in the GalaxySep 18 2006The propagation of high-energy cosmic rays in the Galaxy is investigated. Solutions of a diffusion model are combined with numerically calculated trajectories of particles. The resulting escape path length and interaction path length are presented and ... More

Functions of perturbed normal operatorsMar 27 2010In \cite{Pe1}, \cite{Pe2}, \cite{AP1}, \cite{AP2}, and \cite{AP3} sharp estimates for $f(A)-f(B)$ were obtained for self-adjoint operators $A$ and $B$ and for various classes of functions $f$ on the real line $\R$. In this note we extend those results ... More

Searching with and against the stream: Levy or Brown?Jun 05 2013We study the efficiency of search processes based on Levy flights (LFs) with power-law distributed jump lengths in the presence of an external drift. While LFs turn out to be efficient search processes when relative to the starting point the target is ... More

Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processesMar 22 2013We demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \simeq|x|^{\alpha}$, this process yield anomalous diffusion of the form $\ < x^2(t)\ > \simeq t^{2/(2-\alpha)}$. ... More

Barrier crossing driven by Levy noise: Universality and the Role of Noise IntensityDec 25 2006We study the barrier crossing of a particle driven by white symmetric Levy noise of index $\alpha$ and intensity $DD for three different generic types of potentials: (a) a bistable potential; (b) a metastable potential; and (c) a truncated harmonic potential. ... More

Non-renewal resetting of scaled Brownian motionDec 13 2018We investigate an intermittent stochastic process, in which the diffusive motion with time-dependent diffusion coefficient (scaled Brownian motion, SBM), is stochastically reset to its initial position and starts anew. The resetting follows a renewal ... More

Scaled Brownian motion with renewal resettingDec 13 2018May 25 2019We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient $D(t) \sim t^{\alpha -1}$ with $\alpha > 0$ (scaled Brownian motion) is stochastically reset to its initial position, and starts ... More

Non-renewal resetting of scaled Brownian motionDec 13 2018May 25 2019We investigate an intermittent stochastic process, in which the diffusive motion with time-dependent diffusion coefficient $D(t)\sim t^{\alpha-1}$, $\alpha>0$ (scaled Brownian motion), is stochastically reset to its initial position and starts anew. The ... More

Fast and Robust Algorithm for the Minimisation of the Energy of Spin SystemsApr 04 2019An optimization algorithm based on orthogonal matrix transformations is presented for the minimisation of the energy of a magnetic system with respect to spin orientations. When combined with the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) ... More

Optimization of random search processes in the presence of an external biasFeb 12 2014May 30 2014We study the efficiency of random search processes based on L{\'e}vy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher based on prior ... More

Comb model with slow and ultraslow diffusionDec 24 2015Mar 21 2016We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in $x$ and $y$ directions. Different forms of ... More

Excitation of epsilon-near-zero resonance in ultra-thin indium tin oxide shell embedded nanostructured optical fiberDec 21 2017We report a novel optical waveguide design of a hollow step index fiber modified with a thin layer of indium tin oxide (ITO). We show an excitation of highly confined waveguide mode in the proposed fiber near the wavelength where permittivity of ITO approaches ... More

A minimal model of inflation and dark radiationOct 30 2018We show that a minimal extension of the Standard Model including a new complex scalar field can explain inflation and the observed effective number of neutrinos. The real part of the singlet plays the role of the inflaton field, while the Goldstone boson ... More

Scaled Brownian motion with renewal resettingDec 13 2018Parallel to our previous work \cite{Anna0} we investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient (scaled Brownian motion, SBM) is stochastically reset to its initial position and starts ... More

Conservative random walks in confining potentialsApr 24 2018Nov 08 2018L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic systems, or even ... More

Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivityNov 12 2013We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially-varying diffusivity $D(r)$, mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion ... More

Correlated continuous-time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamicsAug 23 2013Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the generalized central ... More

Generalized diffusion-wave equation with memory kernelApr 30 2019We study generalized diffusion-wave equation in which the second order time derivative is replaced by integro-differential operator. It yields time fractional and distributed order time fractional diffusion-wave equations as particular cases. We consider ... More

On Thompson's conjecture for finite simple exceptional groups of Lie typeJul 06 2017Let $G$ be a finite group, $N(G)$ be the set of conjugacy classes of the group $G$. In the present paper it is proved $G\simeq L$ if $N(G)=N(L)$, where $G$ is a finite group with trivial center and $L$ is a finite simple group of exceptional Lie type ... More

X-ray variability of SS433: effects of the supercritical accretion discOct 30 2014We study a stochastic variability of SS433 in the $10^{-4} - 5\times 10^{-2}$ Hz frequency range based on RXTE data, and on simultaneous observations with RXTE and optical telescopes. We find that the cross-correlation functions and power spectra depend ... More

Full Downlink Channel Reconstruction using Incomplete Uplink Channel Measurements in Massive MIMO networksFeb 11 2019While more and more antennas are integrated into single mobile user equipment to increase communication quality and throughput, the number of antennas used for transmission is commonly restricted due to the concerns on hardware complexity and energy consumption, ... More

Codifference as a practical tool to measure interdependenceJul 16 2014Correlation and spectral analysis represent the standard tools to study interdependence in statistical data. However, for the stochastic processes with heavy-tailed distributions such that the variance diverges, these tools are inadequate. The heavy-tailed ... More

Nonergodic dynamics of force-free granular gasesJan 17 2015We study analytically and by event-driven molecular dynamics simulations the nonergodic and aging properties of force-free cooling granular gases with both constant and velocity-dependent (viscoelastic) restitution coefficient $\varepsilon$ for particle ... More

A minimal model of inflation and dark radiationOct 30 2018Mar 27 2019We show that a minimal extension of the Standard Model including a new complex scalar field can explain inflation and the observed effective number of neutrinos. The real part of the singlet plays the role of the inflaton field, while the Goldstone boson ... More

Lévy Ratchet in a Weak Noise Limit: Theory and SimulationAug 25 2010We study the motion of a particle embedded in a time independent periodic potential with broken mirror symmetry and subjected to a L\'evy noise possessing L\'evy stable probability law (L\'evy ratchet). We develop analytical approach to the problem based ... More

Localized heat perturbation in harmonic 1D crystals. Solutions for an equation of anomalous heat conductionFeb 25 2017In this work exact solutions for the equation that describes anomalous heat propagation in 1D harmonic lattices are obtained. Rectangular, triangular, and sawtooth initial perturbations of the temperature field are considered. The solution for an initially ... More

Ultraslow scaled Brownian motionMar 27 2015We define and study in detail \emph{utraslow scaled Brownian motion (USBM)\/} characterised by a time dependent diffusion coefficient of the form $D(t)\simeq 1/t$. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, ... More

Numerical approach to unbiased and driven generalized elastic modelAug 27 2013From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM), that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare ... More

First passage behaviour of multi-dimensional fractional Brownian motion and application to reaction phenomenaJun 07 2013Jun 13 2013Fractional Brownian motion is a generalised Gaussian diffusive process that is found to describe numerous stochastic phenomena in physics and biology. Here we introduce a multi-dimensional fractional Brownian motion (FBM) defined as a superposition of ... More

Spatio-temporal dynamics of bumblebees foraging under predation riskAug 05 2011Feb 15 2012We analyze 3D flight paths of bumblebees searching for nectar in a laboratory experiment with and without predation risk from artificial spiders. For the flight velocities we find mixed probability distributions reflecting the access to the food sources ... More

Entropy production for one-dimensional ballistic heat equation - sinusoidal initial perturbationJul 11 2018Mar 11 2019This work presents the thermodynamical analysis of the ballistic heat equation from the viewpoint of two approaches: Classical Irreversible Thermodynamics (CIT) and Extended Irreversible Thermodynamics (EIT). A formula for calculation of the entropy within ... More

Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particlesJul 20 2018Complex systems display anomalous diffusion, whose signature is a space/time scaling $x\sim t^\delta$ with $\delta \ne 1/2$ in the Probability Density Function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g., fractional Brownian ... More

Deep Multi-Agent Reinforcement Learning with Relevance GraphsNov 30 2018Over recent years, deep reinforcement learning has shown strong successes in complex single-agent tasks, and more recently this approach has also been applied to multi-agent domains. In this paper, we propose a novel approach, called MAGnet, to multi-agent ... More

Matrix approach to discrete fractional calculus II: partial fractional differential equationsNov 09 2008Jan 14 2009A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of ... More

Kramers escape driven by fractional Brownian motionFeb 09 2010We investigate the Kramers escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in ... More

Fractal Properties of Anomalous Diffusion in Intermittent MapsJul 07 2006Feb 14 2007An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous time random walk ... More

Leapover lengths and first passage time statistics for Lévy flightsJun 25 2007Exact results for the first passage time and leapover statistics of symmetric and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are shown to have leapover lengths, that are asymptotically power-law distributed with index alpha ... More

Bulk-mediated diffusion on a planar surface: full solutionMay 10 2012We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random walk approach we derive the diffusion equations for surface and bulk diffusion including the surface-bulk ... More