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Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybridsMar 06 2009Sep 25 2009A controlled hybridization between full quantum dynamics and semiclassical approaches (mean-field and truncated Wigner) is implemented for interacting many-boson systems. It is then demonstrated how simulating the resulting hybrid evolution equations ... More

First-principles quantum simulations of many-mode open interacting Bose gases using stochastic gauge methodsJul 01 2005Many-mode interacting Bose gases (1D,2D,3D) are simulated from first principles. The model uses a second-quantized Hamiltonian with two-particle interactions (possibly ranged), external potential, and interactions with an environment, with no further ... More

A tractable prescription for large-scale free flight expansion of wavefunctionsFeb 10 2016Mar 06 2016A numerical recipe is given for obtaining the density image of an initially compact quantum mechanical wavefunction that has expanded by a large but finite factor under free flight. The recipe given avoids the memory storage problems that plague this ... More

Classical field records of a quantum system: their internal consistency and accuracyApr 23 2015Nov 25 2015We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in 1d, 2d, and 3d by a careful study of the ideal gas limit. Numerical benchmarking in 1d shows that the ideal gas results carry ... More

Correlation waves after quantum quenches in one- to three-dimensional BECsOct 04 2013We obtain the universal form of spatial density and phase correlations after a quantum quench in dilute ultracold Bose gases, and give compact time-dependent expressions for the most visible effects. A Bogoliubov description in a local density approximation ... More

Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solutionJul 31 2017Number fluctuations in a one-dimensional Bose gas consist of contributions from many smaller independent localized fluctuations, the density grains. We have derived a set of extended integral equations from the Yang-Yang solution for finite temperature ... More

Quantum fluctuation effects on the quench dynamics of thermal quasicondensatesAug 30 2014Feb 12 2016We study the influence of quantum fluctuations on the phase, density, and pair correlations in a trapped quasicondensate after a quench of the interaction strength. To do so, we derive a description similar to the stochastic Gross-Pitaevskii equation ... More

A semiclassical field theory that is freed of the ultraviolet catastropheApr 12 2019A more accurate semiclassical theory for ultracold gases is derived, in which the occupation of high energy modes is dynamically constrained to the Bose-Einstein distribution. This regularized version of the SGPE model preserves the proper nonlinear energy ... More

Correlation evolution in dilute Bose-Einstein condensates after quantum quenchesOct 04 2013Feb 19 2019The universal forms of quantum density and phase correlations after an interaction quench are found for dilute 1d, 2d, and 3d condensates. A Bogoliubov approach in a local density aproximation is used. We obtain compact expressions for the most visible ... More

Comment on "Quantum entangled dark solitons formed by ultracold atoms in optical lattices"Jan 07 2010We demonstrate that knowledge of two body correlation functions like g2(x) is insufficient to draw conclusions about whether solitons fill in or not in individual experimental runs. In our example, g2 is filled in, while the soliton is not.

Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space TechniquesJul 14 2013We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. The new representation ... More

Concurrence in arbitrary dimensionsJul 30 2001We argue that a complete characterisation of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multi-dimensional generalizations ... More

The time-reversal test for stochastic quantum dynamicsNov 26 2004The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultra-cold atomic Bose-Einstein condensates (BEC) to condensed matter, biology, and even astrophysics. Here we demonstrate ... More

Anisotropy in s-wave Bose-Einstein condensate collisions and its relationship to superradianceJun 05 2014Aug 30 2014We report the experimental realization of a single-species atomic four-wave mixing process with BEC collisions for which the angular distribution of scattered atom pairs is not isotropic, despite the collisions being in the $s$-wave regime. Theoretical ... More

BPS counting for knots and combinatorics on wordsAug 23 2016We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded ... More

On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditionsMay 24 2018Jan 10 2019We study the non-autonomously forced Burgers equation $$ u_t(x,t) + u(x,t)u_x(x,t) - u_{xx}(x,t) = f(x,t) $$ on the space interval $(0,1)$ with two sets of the boundary conditions: the Dirichlet and periodic ones. For both situations we prove that there ... More

Hyperbolic geometry for non-differential topologistsJan 22 2018A soft presentation of hyperbolic spaces, free of differential apparatus, is offered. Fifth Euclid's postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and hyperbolic and Euclidean ... More

Spontaneous Four-Wave Mixing of de Broglie Waves: Beyond OpticsNov 24 2009May 27 2010We investigate the atom-optical analog of degenerate four-wave mixing of photons by colliding two Bose-Einstein condensates (BECs) of metastable helium and measuring the resulting momentum distribution of the scattered atoms with a time and space resolved ... More

A note on symmetries in the path integral formulation of the Langevin dynamicsMar 23 2017Dec 30 2018We study a dissipative Langevin dynamics in the path integral formulation using the Martin-Siggia-Rose formalism. The effective action is supersymmetric and we identify the supercharges. In addition we study the transformations generated by superderivatives, ... More

Sub-Poissonian number differences in four-wave mixing of matter wavesAug 04 2010Nov 03 2010We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, ... More

Information transfer and fidelity in quantum copiersMar 15 2000Apr 12 2000We find that very different quantum copying machines are optimal depending on the indicator used to assess their performance. Several quantum copying machine models acting on non-orthogonal input states are investigated, and assessed according to two ... More

Maxwell-like picture of General Relativity and its Planck limitJan 13 2013Nov 29 2013We show that Geroch decomposition leads us to Maxwell-like representation of gravity in $(3+1)$ metrics decomposition that may be perceived as Lorentz invariant version of GEM. For such decomposition we derive four-potential $V^\mu$ and gravitational ... More

Saddle point solutions in Yang-Mills-dilaton theorySep 26 1992The coupling of a dilaton to the $SU(2)$-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analitical and numerical methods. In the abelian sector of the theory there are finite-energy ... More

Geometria nieortodoksyjnaJun 18 2001This is an introductory text to differential geometry (written in Polish) aimed for high-school students.

Cauchy flights in confining potentialsJul 05 2009Oct 24 2009We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process whose target ... More

Entropy and time: Thermodynamics of diffusion processesApr 24 2006Apr 29 2008We give meaning to the first and second laws of thermodynamics in case of mesoscopic out-of-equilibrium systems which are driven by diffusion processes. The notion of the entropy production is analyzed. The role of the Helmholtz extremum principle is ... More

Comment on ``Connection between the Burgers equation with an elastic forcing term and a stochastic process''May 21 2006In the above mentioned paper by E. Moreau and O. Vall\'{e}e [Phys. Rev. {\bf E 73}, 016112, (2006)], the one-dimensional Burgers equation with an elastic (attractive) forcing term has been claimed to be connected with the Ornstein-Uhlenbeck process. We ... More

Random Dynamics, Entropy Production and Fisher InformationNov 18 2002Jul 01 2003We analyze a specific role of probability density gradients in the theory of irreversible transport processes. The classic Fisher information and information entropy production concepts are found to be intrinsically entangled with the very notion of the ... More

Noise perturbations in the Brownian motion and quantum dynamicsApr 23 1999The third Newton law for mean velocity fields is utilised to generate anomalous (enhanced) or non-dispersive diffusion-type processes which, in particular, can be interpreted as a probabilistic counterpart of the Schr\"{o}dinger picture quantum dynamics. ... More

Interstellar H2 toward HD 37903Feb 26 2010Mar 14 2011We present an analysis of interstellar H2 toward HD 37903, which is a hot, B 1.5 V star located in the NGC 2023 reflection nebula. Meyer et al. (2001) have used a rich spectrum of vibrationally excited H2 observed by the HST to calculate a model of the ... More

On Value at Risk for foreign exchange rates - the copula approachAug 18 2006The aim of this paper is to determine the Value at Risk (VaR) of the portfolio consisting of long positions in foreign currencies on an emerging market. Basing on empirical data we restrict ourselves to the case when the tail parts of distributions of ... More

The Distance to the Large Magellanic CloudJan 31 2000I demonstrate that the two unexpected results in the local Universe: anomalous intrinsic (V-I)_0 colors of RR Lyrae stars and clump giants in the Galactic center, and very short distances to Magellanic Clouds inferred from clump giants, can be at least ... More

Harmonizing the RR Lyrae and Clump Distance Scales - Stretching the Short Distance Scale to Intermediate Ranges?Jan 26 2000Sep 26 2000I explore the consequences of making the RR Lyrae and clump giant distance scales consistent in the solar neighborhood, Galactic bulge and Large Magellanic Cloud (LMC). I employ two major assumptions: 1) that the absolute magnitude - metallicity, M_V(RR) ... More

Weak convergence of the sequences of homogeneous Young measures associated with a class of oscillating functionsJul 11 2018Feb 12 2019We consider the sequences of oscillating functions which are sums of the functions having continuously differentiable inverses. We show that if the total slopes of the elements of these sequences form monotonic sequence then the sequence of the respective ... More

On a certain family of U(b)-modulesMar 01 2016Oct 08 2016We report on results of Kra\'skiewicz and the author, and Watanabe on KP modules materializing Schubert polynomials, and filtrations having KP modules as their subquotients. We discuss applications of KP filtrations and ample KP bundles to positivity, ... More

Generic identities for finite group actionsApr 16 2019Let $G$ be a finite group of order $n$, and $Z_G=\mathbb{Z}\langle\zeta_{i,g}\mid g\in G,\ i=1,2,\dots,n\rangle$ be the free generic algebra, with canonical action of $G$ according to $(\zeta_{i,g})^x=\zeta_{i,x^{-1}g}$. It is proved that there exists ... More

Bounded convergence theoremsSep 10 2013There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such ... More

Spatial CLT for the supercritical Ornstein-Uhlenbeck superprocessMar 29 2012In this paper we consider a superprocess being a measure-valued diffusion corresponding to the equation $u_{t}=Lu+\alpha u-\beta u^{2}$, where $L$ is the infinitesimal operator of the \emph{Ornstein-Uhlenbeck process} and $\beta>0,\:\alpha>0$. The latter ... More

Quantum information approach to normal representation of extensive gamesJul 16 2011Jul 19 2011We modify the concept of quantum strategic game to make it useful for extensive form games. We prove that our modification allows to consider the normal representation of any finite extensive game using the fundamental concepts of quantum information. ... More

$K(π, 1)$-neighborhoods and comparison theoremsJul 01 2014A technical ingredient in Faltings' original approach to p-adic comparison theorems involves the construction of $K(\pi, 1)$-neighborhoods for a smooth scheme X over a mixed characteristic dvr with a perfect residue field: every point of X has an open ... More

Consistency of modified versions of Bayesian Information Criterion in sparse linear regression with subgaussian errorsNov 15 2014May 29 2018We consider a sparse linear regression model, when the number of available predictors, $p$, is much larger than the sample size, $n$, and the number of non-zero coefficients, $p_0$, is small. To choose the regression model in this situation, we cannot ... More

Occupation time fluctuations of Poisson and equilibrium finite variance branching systemsDec 17 2005May 12 2006Functional limit theorems are presented for the rescaled occupation time fluctuations process of a critical finite variance branching particle system in $R^d$ with symmetric a-stable motion starting off from either a standard Poisson random field or from ... More

Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spacesMay 28 2011An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with respect to ideals) ... More

Primes of the form x^2+n*y^2 in function fieldsNov 15 2009Mar 17 2011Let n be a square-free polynomial over F_q, where q is an odd prime power. In this paper, we determine which irreducible polynomials p in F_q[x] can be represented in the form X^2+nY^2 with X, Y in F_q[x]. We restrict ourselves to the case where X^2+nY^2 ... More

A characterization of Keller mapsSep 09 2011Dec 09 2011Let k be a field of characteristic zero. Let phi be a k-endomorphism of the polynomial algebra k[x_1,...,x_n]. It is known that phi is an automorphism if and only if it maps irreducible polynomials to irreducible polynomials. In this paper we show that ... More

On normal, formally normal and quasinormal composition operators in $\ell^2$-spacesAug 14 2014Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.

Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the targetFeb 01 2006We study a question of density of Lipschitz mappings in the Sobolev class of mappings from a closed manifold into a singular space. The main result of the paper shows that if we change the metric in the target space to a bi-Lipschitz equivalent one, than ... More

Hyperbolicity and Averaging for the Srzednicki-Wójcik equationJul 09 2016For the Srzednicki-W\'ojcik equation, the planar nonautonomous ODE parameterized by $\kappa \in \mathbb{R}$, $$ z'=\overline{z}(1+ |z|^2 \exp(i \kappa t)), \qquad z(t) \in \mathbb{C} $$ using averaging we show how the region of hyperbolicty grows with ... More

Weak convergence of the sequences of homogeneous Young measures associated with a class of oscillating functionsJul 11 2018Mar 09 2019We take under consideration Young measures with densities. The notion of density of a Young measure is introduced and illustrated with examples. It is proved that the density of a Young measure is weakly sequentially closed set. In the case when density ... More

Seshadri constants and special configurations of points in the projective planeNov 26 2017Oct 07 2018In the present note, we focus on certain properties of special curves that might be used in the theory of multi-point Seshadri constants for ample line bundles on the complex projective plane. In particular, we provide three Ein-Lazarsfeld-Xu-type lemmas ... More

Permutations without long decreasing subsequences and random matricesMar 16 2006Dec 31 2006We study the shape of the Young diagram \lambda associated via the Robinson-Schensted-Knuth algorithm to a random permutation in S_n such that the length of the longest decreasing subsequence is not bigger than a fixed number d; in other words we study ... More

A Purely Algebraic Proof of the Fundamental Theorem of AlgebraApr 21 2015Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the fact that odd-degree ... More

Thom polynomials and Schur functions ISep 10 2005May 15 2006We give the Thom polynomials for the singularities I_2,2 and A_3 associated with maps (C^n,0) -> (C^{n+k},0) with parameter k>=0. We give the Schur function expansions of these Thom polynomials. Moreover, for the singularities A_i (with any parameter ... More

Small growth vectors of the compactifications of the contact systems on $J^{\,r}(1,1)$Feb 23 2011It is well known that the compactifications of the canonical contact systems living on real jet spaces $J^{\,r}(1,1)$, $r \ge 2$, are locally universal Goursat distributions, $\Delta^r$, living on compact manifolds (called Goursat monsters) having open ... More

$\hat{Z}$ invariants at rational $τ$Jun 24 2019$\hat{Z}$ invariants of 3-manifolds were introduced as series in $q=e^{2\pi i\tau}$ in order to categorify Witten-Reshetikhin-Turaev invariants corresponding to $\tau=1/k$. However modularity properties suggest that all roots of unity are on the same ... More

Problem with almost everywhere equalityJul 07 2011A topological space $Y$ is said to have (AEEP) if the following condition is fulfilled. Whenever $(X,\mathfrak{M})$ is a measurable space and $f, g: X \to Y$ are two measurable functions, then the set $\Delta(f,g) = \{x \in X:\ f(x) = g(x)\}$ is a member ... More

Generic identities for finite group actionsApr 16 2019May 20 2019Let $G$ be a finite group of order $n$, and $Z_G=\mathbb{Z}\langle\zeta_{i,g}\mid g\in G,\ i=1,2,\dots,n\rangle$ be the free generic algebra, with canonical action of $G$ according to $(\zeta_{i,g})^x=\zeta_{i,x^{-1}g}$. It is proved that there exists ... More

Convergence of Rothe scheme for hemivariational inequalities of parabolic typeAug 27 2011Mar 08 2012This article presents the convergence analysis of a sequence of piecewise constant and piecewise linear functions obtained by the Rothe method to the solution of the first order evolution partial differential inclusion $u'(t)+Au(t)+\iota^*\partial J(\iota ... More

A characterization of toric varieties in characteristic pMar 24 2013If $X$ is a smooth toric variety over an algebraically closed field of positive characteristic and $L$ is an invertible sheaf on $X$, it is known that $F_* L$, the push-forward of $L$ along the Frobenius morphism of $X$, is a direct sum of invertible ... More

Symmetric polynomials and divided differences in formulas of intersection theoryMay 28 1996The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci; some explicit ... More

Hirzebruch-type inequalities viewed as tools in combinatoricsAug 28 2018Sep 28 2018The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest in many combinatorial ... More

On CR (Cauchy-Riemann) almost cosymplectic manifoldsSep 09 2012Oct 05 2012In the paper we develop a framework for the alternative way of the study of a local geometry of almost cosymplectic manifolds with Kahlerian leaves. The main idea is to apply the concept of a geometry and analysis of CR manifolds. Locally the almost cosymplectic ... More

Simple error bounds for the multivariate Laplace approximation under weak local assumptionsNov 01 2015Apr 11 2016The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is presented. ... More

Asymptotics of Jack charactersJun 21 2015May 16 2018Jack characters are a one-parameter deformation of the characters of the symmetric groups; a deformation given by the coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions. We study Jack characters from ... More

Blowup of solutions for nonlinear nonlocal heat equationsJul 10 2018Blowup analysis for solutions of a general evolution equation with nonlocal diffusion and localized source is performed. By comparison with recent results on global-in-time solutions, a dichotomy result is obtained.

A caricature of a singular curvature flow in the planeMar 25 2008We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak solutions to the semi-discretization ... More

Nonuniform BriberyNov 30 2007We study the concept of bribery in the situation where voters are willing to change their votes as we ask them, but where their prices depend on the nature of the change we request. Our model is an extension of the one of Faliszewski et al. [FHH06], where ... More

Equivariant self-similar wave maps from Minkowski spacetime into 3-sphereOct 17 1999May 25 2000We prove existence of a countable family of spherically symmetric self-similar wave maps from 3+1 Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state wave map found previously by Shatah. The first excitation ... More

Pseudoscalar Meson Temporal Correlation Function in HTL approachAug 11 2006The temporal pseudoscalar meson correlation function in a QCD plasma is investigated in a range of temperatures exceeding $T_c$ and first time for a finite momenta which is of the experimental interest. The imaginary time formalism is employed for the ... More

Low-energy amplitudes in the non-local chiral quark modelNov 11 2009Jan 19 2010We apply chiral quark model with momentum dependent quark mass to two kinds of non-perturbative objects. These are: photon Distribution Amplitudes which we calculate up to twist-4 in tensor, vector and axial channels and pion-photon Transition Distribution ... More

In-medium ion mass renormalization and lattice vibrations in the neutron star crustDec 30 2003The inner crust of a neutron star consists of nuclei immersed in a superfluid neutron liquid. As these nuclei move through the fermionic medium they bring it into motion as well. As a result their mass is strongly renormalized and the spectrum of the ... More

Deuterium depletion and magnesium enhancement in the local discJul 19 2005Oct 12 2005The local disc deuter is known to be depleted in comparison to the local bubble. We show, that the same lines of sight that are depleted in deuter, are enhanced in magnesium. Heavier elements - Si and Fe do not show any difference in the abundance between ... More

Some topological invariants and biorthogonal systems in Banach spacesSep 19 2012We consider topological invariants on compact spaces related to the sizes of discrete subspaces (spread), densities of subspaces, Lindelof degree of subspaces, irredundant families of clopen sets and others and look at the following associations between ... More

Homotopy Decompositions of Looped Stiefel manifolds, and their ExponentsFeb 20 2010Let $p$ be an odd prime, and fix integers $m$ and $n$ such that $0<m<n\leq (p-1)(p-2)$. We give a $p$-local homotopy decomposition for the loop space of the complex Stiefel manifold $W_{n,m}$. Similar decompositions are given for the loop space of the ... More

Evading network-level emulationJun 10 2009Recently more and more attention has been paid to the intrusion detection systems (IDS) which don't rely on signature based detection approach. Such solutions try to increase their defense level by using heuristics detection methods like network-level ... More

Dynamic Data Flow Analysis via Virtual Code Integration (aka The SpiderPig case)Jun 03 2009Paper addresses the process of dynamic data flow analysis using virtual code integration (VCI), often refered to as dynamic binary rewriting. This article will try to demonstrate all of the techniques that were applied in the SpiderPig project. It will ... More

Clump Distance to the Magellanic Clouds and Anomalous Colors in the Galactic BulgeOct 11 1999Nov 13 1999I demonstrate that the two unexpected results in the local Universe: 1) anomalous intrinsic (V-I)_0 colors of the clump giants and RR Lyrae stars in the Galactic center, and 2) very short distances to the Magellanic Clouds (LMC, SMC) as inferred from ... More

A Complexity of double dummy bridgeSep 23 2013This paper presents an analysis of complexity of double dummy bridge. Values of both, a state-space (search-space) complexity and a game tree complexity have been estimated. ----- Oszacowanie z{\l}o\.zono\'sci problemu rozgrywki w otwarte karty w bryd\.zu ... More

Femtoscopy analysis of d-Au interactions at $\sqrt{s}=200$GeVAug 06 2014The femtoscopy correlation radii for d-Au collisions at $200$GeV are calculated in the hydrodynamic model and compared to PHENIX collaboration data. For asymmetric systems, such as d-Au or p-Pb collisions, the correlation radius $R_{out-long}$ is estimated ... More

Wilson lines and gauge invariant off-shell amplitudesMar 19 2014Apr 24 2014We study matrix elements of Fourier-transformed straight infinite Wilson lines as a way to calculate gauge invariant tree-level amplitudes with off-shell gluons. The off-shell gluons are assigned "polarization vectors" which (in the Feynman gauge) are ... More

Arcs intersecting at most onceFeb 07 2014Aug 26 2014We prove that on a punctured oriented surface with Euler characteristic chi < 0, the maximal cardinality of a set of essential simple arcs that are pairwise non-homotopic and intersecting at most once is 2|chi|(|chi|+1). This gives a cubic estimate in ... More

On one-loop corrections to matching conditions of Lattice HQET including 1/m_b termsDec 09 2013HQET is an effective theory for QCD with N_f light quarks and a massive valence quark if the mass of the latter is much bigger than Lambda_QCD. As any effective theory, HQET is predictive only when a set of parameters has been determined through a process ... More

Top degree of Jack characters and enumeration of mapsJun 21 2015Mar 16 2016Jack characters are (suitably normalized) coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions. These quantities have been introduced recently by Lassalle who formulated some challenging conjectures about ... More

Wild binary segmentation for multiple change-point detectionNov 04 2014We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to ... More

Combining Fuzzy Cognitive Maps and Discrete Random VariablesDec 29 2015In this paper we propose an extension to the Fuzzy Cognitive Maps (FCMs) that aims at aggregating a number of reasoning tasks into a one parallel run. The described approach consists in replacing real-valued activation levels of concepts (and further ... More

Connecting orbits for nonlinear differential equations at resonanceMay 01 2015Nov 02 2015We study the existence of orbits connecting stationary points for the first order differential equations being at resonance at infinity, where the right hand side is the perturbations of a sectorial operator. Our aim is to prove an index formula expressing ... More

The CLS 2+1 flavor simulationsDec 31 2014We report on the status of large volume simulations with 2+1 dynamical fermions which are being performed by the CLS initiative. The algorithmic details include: open boundary conditions, twisted mass reweighting and RHMC, whereas the main feature of ... More

Weak consistency of modified versions of Bayesian Information Criterion in a sparse linear regression with non-normal error termNov 15 2014We consider a sparse linear regression model, when the number of available predictors $p$ is much bigger than the sample size $n$ and the number of non-zero coefficients $p_0$ is small. To choose the regression model in this situation, we cannot use classical ... More

Generic identities for finite group actionsApr 16 2019Apr 24 2019Let $G$ be a finite group of order $n$, and $Z_G=\mathbb{Z}\langle\zeta_{i,g}\mid g\in G,\ i=1,2,\dots,n\rangle$ be the free generic algebra, with canonical action of $G$ according to $(\zeta_{i,g})^x=\zeta_{i,x^{-1}g}$. It is proved that there exists ... More

Some properties of the moment estimator of shape parameter for the gamma distributionAug 17 2011Exact distribution of the moment estimator of shape parameter for the gamma distribution for small samples is derived. Order preserving properties of this estimator are presented.

Occupation time fluctuation limits of infinite variance equilibrium branching systemsFeb 01 2008We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The branching law is ... More

Functional calculus for diagonalizable matricesNov 30 2012For an arbitrary function f:\Omega \rightarrow C (where \Omega is a subset of the field C) and a positive integer k let f act on all diagonalizable complex matrices whose all eigenvalues lie in Omega in the following way: f[P Diag(z1,...,zk) P-1] = P ... More

Quadratic bosonic and free white noisesMar 20 2003We discuss the meaning of renormalization used for deriving quadratic bosonic commutation relations introduced by Accardi and find a representation of these relations on an interacting Fock space. Also, we investigate classical stochastic processes which ... More

Effect of resonance on the existence of periodic solutions for strongly damped wave equationOct 25 2013Oct 30 2015We are interested in the differential equation $\ddot u(t) = -A u(t) - c A \dot u(t) + \lambda u(t) + F(t,u(t))$, where $c > 0$ is a damping factor, $A$ is a sectorial operator and $F$ is a continuous map. We consider the situation where the equation ... More

Strong isomorphism in Eisert-Wilkens-Lewenstein type quantum gamesJan 19 2017The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate ... More

On fast bounded locality sensitive hashingApr 19 2017In this paper, we examine the hash functions expressed as scalar products, i.e., $f(x)=<v,x>$, for some bounded random vector $v$. Such hash functions have numerous applications, but often there is a need to optimize the choice of the distribution of ... More

Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisionsNov 21 2017The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear ... More

Moduli of $Π$-algebrasMay 16 2017We describe a homotopy-theoretic approach to the moduli of $\Pi$-algebras of Blanc-Dwyer-Goerss using the $\infty$-category $P_{\Sigma}(Sph)$ of product-preserving presheaves on finite-wedges of positive-dimensional spheres, reproving all of their results ... More

On three dimensional conformally flat almost cosymplectic manifoldsOct 04 2007In the paper there are described new examples of conformally flat three dimensional almost cosymplectic manifolds. All these manifolds form a class which was completely characterized.

Multinomial identities arising from the free probability theoryFeb 08 2002Feb 24 2003We prove a family of new identities fulfilled by multinomial coefficients, which were conjectured by Dykema and Haagerup. Our method bases on a study of the, so-called, triangular operator T by the means of the free probability theory.