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Quadratic harnesses from generalized beta integralsSep 24 2010We use generalized beta integrals to construct examples of Markov processes with linear regressions, and quadratic second conditional moments.

Compound real Wishart and q-Wishart matricesJun 25 2008We introduce a family of matrices with non-commutative entries that generalize the classical real Wishart matrices. With the help of the Brauer product, we derive a non-asymptotic expression for the moments of traces of monomials in such matrices; the ... More

Markov processes with free Meixner lawsOct 06 2009Mar 01 2010We study a time-non-homogeneous Markov process which arose from free probability, and which also appeared in the study of stochastic processes with linear regressions and quadratic conditional variances. Our main result is the explicit expression for ... More

Wilson's 6-j laws and stitched Markov processesSep 12 2011We show how to insert time into the parameters of the Wilson's 6-j laws to construct discrete Markov chains with these laws. By a quadratic transformation we convert them into Markov processes with linear regressions and quadratic conditional variances. ... More

Asymmetric Simple Exclusion Process with open boundaries and Quadratic HarnessesNov 03 2015Jul 14 2016We show that the joint moment generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of a Markov processes called quadratic harness. We use our representation ... More

On integrability of quadratic harnessesOct 06 2011We investigate integrability properties of processes with linear regressions and quadratic conditional variances. We establish the right order of dependence of which moments are finite on the parameter defined below, raising the question of determining ... More

Asymptotic normality for traces of polynomials in independent complex Wishart matricesJan 11 2007We derive a non-asymptotic expression for the moments of traces of monomials in several independent complex Wishart matrices, extending some explicit formulas available in the literature. We then deduce the explicit expression for the cumulants. From ... More

On integration with respect to the q-Brownian motionJul 26 2014For a parameter 0<q<1, we use the Jackson q-integral to define integration with respect to the so called q-Brownian motion. Our main results are the q-analogs of the L_2-isometry and of the Ito formula for polynomial integrands. We also indicate how the ... More

Large deviations of empirical measures under symmetric interactionMar 17 2002Dec 02 2003In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product measures and hence ... More

Meixner matrix ensemblesSep 23 2010May 03 2011We construct a family of matrix ensembles that fits Anshelevich's regression postulates for "Meixner laws on matrices". We show that the Laplace transform of a general n by n Meixner matrix ensemble satisfies a system of partial differential equations ... More

Stitching pairs of Levy processes into harnessesOct 08 2011We consider natural exponential families of Levy processes with randomized parameter. Such processes are Markov, and under suitable assumptions, pairs of such processes with shared randomization can be stitched together into a single harness. The stitching ... More

Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulationsJan 18 2013We present a mathematical model, and the corresponding mathematical analysis, that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of subpopulations represented ... More

Singular values of large non-central random matricesFeb 08 2018We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It provides a decomposition ... More

Infinitesimal generators of q-Meixner processesSep 13 2013We show that the weak infinitesimal generator of a class of Markov processes acts on bounded continuous functions with bounded continuous second derivative as a singular integral with respect to the orthogonality measure of the explicit family of polynomials. ... More

On Cauchy-Stieltjes Kernel FamiliesOct 09 2012We explore properties of Cauchy-Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy-Stieltjes family to the pseudo-variance function of the initial Cauchy-Stieltjes family. We also ... More

Free Exponential Families as Kernel FamiliesJan 12 2006Apr 28 2009Free exponential families have been previously introduced as a special case of the q-exponential family. We show that free exponential families arise also from a procedure analogous to the definition of exponential families by using the Cauchy-Stieltjes ... More

Context and ontology in understanding of dialogsMay 15 1995We present a model of NLP in which ontology and context are directly included in a grammar. The model is based on the concept of {\em construction}, consisting of a set of features of form, a set of semantic and pragmatic conditions describing its application ... More

Natural Language Processing: Structure and ComplexityJul 13 1996We introduce a method for analyzing the complexity of natural language processing tasks, and for predicting the difficulty new NLP tasks. Our complexity measures are derived from the Kolmogorov complexity of a class of automata --- {\it meaning automata}, ... More

Cascades in the Earth's magnetosphere initiated by photons with the parameters of the highest energy AGASA eventsSep 03 2001Jun 27 2002We investigate the cascading effects of extremely high energy (EHE) photons in the Earth's magnetosphere assuming that these photons arrive with the parameters of the highest energy AGASA events (energies, arrival directions). For the location of the ... More

Nonexistence of "Spin Transverse Force" for a Relativistic ElectronJan 16 2007Using the complete Dirac Hamiltonian for a relativistic electron it is shown that the spin transverse force derived by S.Q. Shen, Phys. Rev. Lett. 95, 187203 (2005) does not exist. This force is an artefact resulting from an approximate form of the employed ... More

One-dimensional semirelativity for electrons in carbon nanotubesOct 07 2005It is shown that the band structure of single-wall semiconducting carbon nanotubes (CNT) is analogous to relativistic description of electrons in vacuum, with the maximum velocity $u$= $10^8$cm/s replacing the light velocity. One-dimensional semirelativistic ... More

Zitterbewegung and its effects on electrons in semiconductorsNov 18 2004An analogy between the band structure of narrow gap semiconductors and the Dirac equation for relativistic electrons in vacuum is used to demonstrate that semiconductor electrons experience a Zitterbewegung (trembling motion). Its frequency is $\omega_Z ... More

Measuring semantic complexityMay 08 1995We define {\em semantic complexity} using a new concept of {\em meaning automata}. We measure the semantic complexity of understanding of prepositional phrases, of an "in depth understanding system", and of a natural language interface to an on-line calendar. ... More

From compositional to systematic semanticsMar 24 1995We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is required to be ... More

Stationary Markov chains with linear regressionsJul 05 2000In a previous paper we determined one dimensional distributions of a stationary field with linear regressions and quadratic conditional variances under a linear constraint on the coefficients of the quadratic expression. In this paper we show that for ... More

The Compactness of Construction GrammarsMay 15 1995We present an argument for {\em construction grammars} based on the minimum description length (MDL) principle (a formal version of the Ockham Razor). The argument consists in using linguistic and computational evidence in setting up a formal model, and ... More

Electron dynamics in crystalline semiconductorsSep 14 2012Electron dynamics in crystalline semiconductors is described by distinguishing between an instantaneous velocity related to electron's momentum and an average velocity related to its quasi-momentum in a periodic potential. It is shown that the electron ... More

On v^2/c^2 expansion of the Dirac equation with external potentialsAug 10 2004The v^2/c^2 expansion of the Dirac equation with external potentials is reexamined. A complete, gauge invariant form of the expansion to order (1/c)^2 is established which contains two additional terms, as compared to various versions existing in the ... More

TeV neutrinos from accreting X-ray pulsarsMay 30 2009Pulsars inside binary systems can accrete matter that arrives up to the pulsar surface provided that its period is long enough. During the accretion process, matter has to be accelerated to the rotational velocity of the pulsar magnetosphere at the distance ... More

Conditional moments of q-Meixner processesFeb 29 2004Dec 13 2004We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-parameter family of orthogonal polynomials which generalize the Meixner polynomials. ... More

Classical bi-Poisson process: an invertible quadratic harnessAug 20 2005We give an elementary construction of a time-invertible Markov process which is discrete except at one instance. The process is one of the quadratic harnesses studied in our previous papers and can be regarded as a random joint of two independent Poisson ... More

Asymptotic results for empirical measures of weighted sums of independent random variablesJul 26 2006We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting partial sums ... More

Bi-Poisson processApr 13 2004We study a two parameter family of processes with linear regressions and linear conditional variances. We give conditions for the unique solution of this problem, and point out the connection between the resulting Markov processes and the generalized ... More

On a class of free Levy laws related to a regression problemOct 28 2004Jan 11 2006The free Meixner laws arise as the distributions of orthogonal polynomials with constant-coefficient recursions. We show that these are the laws of the free pairs of random variables which have linear regressions and quadratic conditional variances when ... More

Askey--Wilson polynomials, quadratic harnesses and martingalesDec 03 2008Jan 07 2011We use orthogonality measures of Askey--Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey--Wilson polynomials are orthogonal martingale polynomials for these processes.

Spatial control of electron spins by electric and magnetic fields in double quantum wellsJun 20 2012A system of two quantum wells (QW), one made of HgCdTe and the other of HgCdMnTe, subjected to electric and magnetic fields $F$ and $B$ parallel to the growth direction, is proposed and described theoretically. It is shown that in such a system the spin ... More

Internal absorption of gamma-rays in relativistic blobs of active galactic nucleiOct 11 2006We investigate the production of gamma-rays in the inverse Compton (IC) scattering process by leptons accelerated inside relativistic blobs in jets of active galactic nuclei. Leptons are injected homogeneously inside the spherical blob and initiate IC ... More

Temperature dependence of the electron spin $\textbf{g}$ factor in CdTe and InPSep 06 2011Temperature dependence of the electron spin $g$ factors in bulk CdTe and InP are calculated and compared with experiment. It is assumed that the only modification of the band structure related to temperature is a dilatation change in the fundamental energy ... More

Variational representations of Varadhan FunctionalsSep 01 2000Motivated by the theory of large deviations, we introduce a class of non-negative non-linear functionals that have a variational "rate function" representation.

One-sided Cauchy-Stieltjes Kernel FamiliesJun 22 2009Jul 29 2010This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded ... More

Infinitesimal generators for a class of polynomial processesNov 23 2014Nov 19 2015We study the infinitesimal generators of evolutions of linear mappings on the space of polynomials, which correspond to a special class of Markov processes with polynomial regressions called quadratic harnesses. We relate the infinitesimal generator to ... More

Bridges of quadratic harnessesMar 01 2009Feb 07 2012Quadratic harnesses are typically non-homogeneous Markov processes with time-dependent state space. Using an appropriately defined affine transformation we show that all bridges of a given quadratic harness can be transformed into other standard quadratic ... More

A quadratic regression problem for two-state algebras with application to the Central Limit TheoremFeb 02 2008Jan 26 2009We extend a free version of the Laha-Lukacs theorem to probability spaces with two-states. We then use this result to generalize a noncommutative CLT of Kargin to the two-state setting.

Oblique spin-flip reflection of relativistic electrons from a potential barrierOct 15 2013Mar 27 2014The Dirac equation is used to describe oblique spin-conserving and spin-flip reflections of relativistic electrons from a one-dimensional potential barrier in a vacuum. When an electron hits the barrier from an oblique direction, its spin-up and spin-down ... More

Numerical simulations of thin accretion discs with PLUTODec 27 2014Our goal is to perform global simulations of thin accretion discs around compact bodies like neutron stars with dipolar magnetic profile and black holes by exploiting the facilities provided by state-of-the-art grid-based, high resolution shock capturing ... More

A Sheaf Model of Contradictions and Disagreements. Preliminary Report and DiscussionJan 27 2018We introduce a new formal model -- based on the mathematical construct of sheaves -- for representing contradictory information in textual sources. This model has the advantage of letting us (a) identify the causes of the inconsistency; (b) measure how ... More

Central Production with Tagged Forward Protons and the Star Detector at RHICAug 28 2008We describe a setup which will allow extend the physics reach of the STAR detector at RHIC to include the measurement of very forward protons. Tagging on very forward protons, detected by the Roman Pots at RHIC energies, selects processes, in which the ... More

Spin-flip reflection of electrons from a potential barrier in heterostructuresMar 27 2014Spin-conserving and spin-flip opaque reflections of electrons from a potential barrier in heterostructures are described. An electric field of the barrier is considered to be the only source of energy spin splitting in the presence of spin-orbit interaction ... More

Influence of clouds on the parameters of images measured by IACT at very high energiesSep 29 2014Observations with the Cherenkov telescopes are in principle limited to the clear sky conditions due to significant absorption of Cherenkov light by clouds. If the cloud level is high enough or the atmospheric transmission of the cloud is high, then high ... More

Variability of GeV gamma-ray emission in QSO B0218+357 due to microlensing on intermediate size structuresApr 04 2016Strong gravitational lensing leads to an occurrence of multiple images, with different magnifications, of a lensed source. Those magnifications can in turn be modified by microlensing on smaller mass scales within the lens. Recently, measurements of the ... More

An ultraluminous nascent millisecond pulsarNov 04 2014Jan 30 2015If the ultraluminous source (ULX) M82 X-2 sustains its measured spin-up value of $\dot \nu= 10^{-10}\,{\rm s^{-2}}$, it will become a millisecond pulsar in less than $10^5\,$ years. The observed (isotropic) luminosity of $10^{40}\,$ erg/s also supports ... More

Theory of symmetric screening for solids and plasmasDec 08 2004Apr 18 2007This paper has been withdrawn due to errors found by authors. A correct version of this paper is published in: Tomasz M. Rusin, Wlodek Zawadzki, "Quantum theory of symmetric screening in the Hartree approximation", Phys. stat. sol. (b) 243, 1286-1295 ... More

Two-photon echo method for observing electron Zitterbewegung in carbon nanotubesApr 24 2014The phenomenon of Zitterbewegung (ZB, trembling motion) of electrons is described in zigzag carbon nanotubes (CNT) excited by laser pulses. The tight binding approach is used for the band structure of CNT and the effect of light is introduced by the vector ... More

New theory of screening for 3D and 2D electron gasesSep 28 2004Apr 18 2007This paper has been withdrawn due to errors found by authors. A correct version of this paper is published in: Tomasz M. Rusin, Wlodek Zawadzki, "Quantum theory of symmetric screening in the Hartree approximation" Phys. stat. sol. (b) 243, 1286-1295 (2006) ... More

Theory of electron Zitterbewegung in graphene probed by femtosecond laser pulsesDec 27 2008Jul 30 2009We propose an experiment allowing an observation of Zitterbewegung (ZB, trembling motion) of electrons in graphene in the presence of a magnetic field. In contrast to the existing theoretical work we make no assumptions concerning shape of the electron ... More

Multi-mode behavior of electron Zitterbewegung induced by an electromagnetic wave in grapheneAug 03 2013Dec 09 2013Electrons in monolayer graphene in the presence of an electromagnetic (or electric) wave are considered theoretically. It is shown that the electron motion is a nonlinear combination of Zitterbewegung (ZB, trembling motion) resulting from the periodic ... More

The physics of kHz QPOs---strong gravity's coupled anharmonic oscillatorsMay 03 2001We explain the origin of the puzzling high frequency peaks (QPOs) in the variability power spectra of accreting neutron stars and black holes as a non-linear 1:2 or 1:3 resonance between orbital and radial epicyclic motion. These resonances are present ... More

Gamma-rays from binary system with energetic pulsar and Be star with aspherical wind: PSR B1259-63/SS2883Jan 23 2008At least one massive binary system containing an energetic pulsar, PSR B1259-63/SS2883, has been recently detected in the TeV gamma-rays by the HESS telescopes. These gamma-rays are likely produced by particles accelerated in the vicinity of the pulsar ... More

Zitterbewegung (trembling motion) of electrons in semiconductors: a ReviewJan 03 2011We review recent research on Zitterbewegung (ZB, trembling motion) of electrons in semiconductors. A brief history of the subject is presented, the trembling motion in semirelativistic and spin systems is considered and its main features are emphasized. ... More

Trembling motion of relativistic electrons in a magnetic fieldMar 29 2010Dec 30 2010Zitterbewegung (ZB, the trembling motion) of free relativistic electrons in a vacuum in the presence of an external magnetic field is calculated. It is shown that the motion of an electron wave packet has intraband frequency components, corresponding ... More

Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ionsAug 08 2010Dec 30 2010One-electron 3+1 and 2+1 Dirac equations are used to calculate the motion of a relativistic electron in a vacuum in the presence of an external magnetic field. First, calculations are carried on an operator level and exact analytical results are obtained ... More

Zitterbewegung of electrons in carbon nanotubes created by laser pulsesDec 17 2013May 03 2014We describe a possibility of creating non-stationary electron wave packets in zigzag carbon nanotubes (CNT) illuminated by short laser pulses. After disappearance of the pulse the packet experiences the trembling motion (Zitterbewegung, ZB). The band ... More

Epicyclic orbital oscillations in Newton's and Einstein's dynamicsJun 20 2002We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical geometry of Schwarzschild's ... More

Zitterbewegung of electrons in graphene in a magnetic fieldDec 21 2007Jul 07 2008Electric current and spacial displacement due to trembling motion [Zitterbewegung (ZB)] of electrons in graphene in the presence of an external magnetic field are described. Contributions of both inequivalent $K$ points in the Brillouin zone of graphene ... More

Non-locality of Foldy-Wouthuysen and related transformations for the Dirac equationAug 20 2011Non-localities of Foldy-Wouthuysen and related transformations, which are used to separate positive and negative energy states in the Dirac equation, are investigated. Second moments of functional kernels generated by the transformations are calculated, ... More

Nature of electron Zitterbewegung in crystalline solidsSep 02 2009We demonstrate both classically and quantum mechanically that the Zitterbewegung (ZB, the trembling motion) of electrons in crystalline solids is nothing else, but oscillations of velocity assuring the energy conservation when the electron moves in a ... More

Transient Zitterbewegung of charge carriers in graphene and carbon nanotubesFeb 19 2007Apr 24 2007Observable effects due to trembling motion (Zitterbewegung, ZB) of charge carriers in bilayer graphene, monolayer graphene and carbon nanotubes are calculated. It is shown that, when the charge carriers are prepared in the form of gaussian wave packets, ... More

A precise determination of angular momentum in the black hole candidate GRO J1655-40May 04 2001We note that the recently discovered 450 Hz frequency in the X-ray flux of the black hole candidate GRO J1655-40 is in a 3:2 ratio to the previously known 300 Hz frequency of quasi-periodic oscillations (QPO) in the same source. If the origin of high ... More

Damping of electron Zitterbewegung in carbon nanotubesFeb 21 2014Zitterbewegung (ZB, trembling motion) of electrons in semiconductor carbon nanotubes is described taking into account dephasing processes. The density matrix formalism is used for the theory. Differences between decay of ZB oscillations due to electron ... More

Green functions of electrons in monolayer and bilayer graphene in a magnetic fieldOct 20 2010Feb 16 2011Closed expressions for the Green functions of the stationary two-dimensional two-component Schrodinger equation for an electron moving in monolayer and bilayer graphene in the presence of a magnetic field are obtained in terms of the Whittaker functions. ... More

Non-locality of energy separating transformations for Dirac electrons in a magnetic fieldOct 12 2011Aug 18 2012We investigate a non-locality of Moss-Okninski transformation (MOT) used to separate positive and negative energy states in the 3+1 Dirac equation for relativistic electrons in the presence of a magnetic field. Properties of functional kernels generated ... More

Zitterbewegung of Klein-Gordon particles and its simulation by classical systemsMay 21 2012The Klein-Gordon equation is used to calculate the Zitterbewegung (ZB, trembling motion) of spin-zero particles in absence of fields and in the presence of an external magnetic field. Both Hamiltonian and wave formalisms are employed to describe ZB and ... More

Free Quadratic HarnessMar 24 2010Nov 18 2010Free quadratic harness is a Markov process from the class of quadratic harnesses, i.e. processes with linear regressions and quadratic conditional variances. The process has recently been constructed for a restricted range of parameters in the paper "Askey-Wilson ... More

Estimating heterozygosity from a low-coverage genome sequence, leveraging data from other individuals sequenced at the same sitesDec 17 2012High-throughput shotgun sequence data makes it possible in principle to accurately estimate population genetic parameters without confounding by SNP ascertainment bias. One such statistic of interest is the proportion of heterozygous sites within an individual's ... More

Probabilistic aspects of Al-Salam-Chihara polynomialsApr 14 2003Dec 02 2003We solve the connection coefficient problem between the Al-Salam-Chihara polynomials and the q-Hermite polynomials, and we use the resulting identity to answer a question from probability theory. We also derive the distribution of some Al-Salam-Chihara ... More

Quasi-periodic oscillations of perturbed toriNov 09 2015Feb 08 2016We performed axisymmetric hydrodynamical simulations of oscillating tori orbiting a non-rotating black hole. The tori in equilibrium were constructed with a constant distribution of angular momentum in a pseudo-Newtonian potential (Klu{\'z}niak-Lee). ... More

Large deviations for the leaves in some random treesSep 27 2008Large deviation principles and related results are given for a class of Markov chains associated to the "leaves" in random recursive trees and preferential attachment random graphs, as well as the "cherries" in Yule trees. In particular, the method of ... More

Spectral measure of large random Hankel, Markov and Toeplitz matricesJul 25 2003Feb 27 2006We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables $\{X_k\}$ of unit variance, and for symmetric Markov matrices generated by i.i.d. ... More

The bi-Poisson process: a quadratic harnessOct 11 2005Apr 21 2008This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. ... More

Quadratic Harnesses, q-commutations, and orthogonal martingale polynomialsApr 10 2005We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a q-commutation relation. This implies that quadratic harnesses are essentially ... More

The twin paradox on the photon sphereDec 11 2006We consider a new version of the twin paradox. The twins move along the same circular free photon path around the Schwarzschild center. In this case, despite their different velocities, all twins have the same non-zero acceleration. On the circular photon ... More

A Model for Grid User ManagementJun 13 2003Registration and management of users in a large scale Grid computing environment presents new challenges that are not well addressed by existing protocols. Within a single Virtual Organization (VO), thousands of users will potentially need access to hundreds ... More

Conduction electrons in acceptor-doped GaAs/GaAlAs heterostructures: a reviewApr 24 2016We review magneto-optical and magneto-transport effects in GaAs/GaAlAs heterostructures doped in GaAlAs barriers with donors, providing two-dimensional electron gas in GaAs quantum wells, and additionally doped with smaller amounts of acceptors (mostly ... More

Numerical simulations of oscillating tori in a pseudo-Newtonian potentialJan 25 2016We have modeled hydrodynamical tori in the Klu{\'z}niak-Lee pseudo-Newtonian potential. The tori in equilibrium were perturbed with uniform sub-sonic velocity fields: vertical, radial and diagonal respectively, and allowed to evolve in time. We identify ... More

Towards Semantic Modeling of Contradictions and Disagreements: A Case Study of Medical GuidelinesAug 02 2017We introduce a formal distinction between contradictions and disagreements in natural language texts, motivated by the need to formally reason about contradictory medical guidelines. This is a novel and potentially very useful distinction, and has not ... More

Stationary random fields with linear regressionsAug 05 2000We analyze certain stationary fields with linear regressions and quadratic conditional variances. This classic probabilistic problem leads somewhat unexpectedly to stationary Markov processes closely tied to non-commutative probability through the q-Hermite ... More

On slow-fading non-separable correlation MIMO systemsJul 12 2007In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. We propose a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. ... More

Classical versions of q-Gaussian processes: conditional moments and Bell's inequalitySep 02 2000Feb 29 2004We show that classical processes corresponding to operators what satisfy a q-commutative relation have linear regressions and quadratic conditional variances. From this we deduce that Bell's inequality for their covariances can be extended from q=-1 to ... More

Projection formulas for orthogonal polynomialsJun 04 2006Dec 12 2007We prove a projection formula for the four-parameter family of orthogonal polynomials that are a reparameterization of the polynomials in the Askey-Wilson class. By carefully analyzing the recurrence relations we manage to avoid using the explicit expression ... More

The orbital resonance model for twin peak kHz QPOsJan 22 2004Many Galactic black hole and neutron star sources in low X-ray mass binaries show QPOs (quasi periodic oscillations) in their observed X-ray fluxes, i.e. peaks in the Fourier variability power spectra. Pairs of twin peaks are observed, and in black-hole ... More

Global transient dynamics of three-dimensional hydrodynamical disturbances in a thin viscous accretion diskJun 01 2009Jun 11 2009Thin viscous Keplerian accretion disks are considered asymptotically stable, even though they can show significant dynamic activity on short timescales. In this paper the dynamics of non-axisymmetric hydrodynamical disturbances of disks are investigated ... More

No observational proof of the black-hole event-horizonJul 12 2002Recently, several ways of obtaining observational proof of the existence of black-hole horizons have been proposed. We argue here that such proof is fundamentally impossible: observations can provide arguments, sometimes very strong ones, in favour of ... More

Watsonsim: Overview of a Question Answering EngineDec 02 2014The objective of the project is to design and run a system similar to Watson, designed to answer Jeopardy questions. In the course of a semester, we developed an open source question answering system using the Indri, Lucene, Bing and Google search engines, ... More

Levitating atmospheres of Eddington-luminosity neutron starsNov 30 2015Apr 02 2016We construct models of static, spherically symmetric shells supported by the radiation flux of a luminous neutron star in the Schwarzschild metric. The atmospheres are disconnected from the star and levitate above its surface. Gas pressure and density ... More

High-frequency QPOs as a problem in physics: non-linear resonanceFeb 01 2004The presence of a kHz frequency in LMXBs has been expected from scaling laws, by analogy with the QPO phenomenon in HMXB X-ray pulsars. Interpretation of the two kHz frequencies, observed in accreting neutron stars, in terms of non-linear resonance in ... More

QPOs in Cataclysmic Variables and in X-ray BinariesMar 07 2005Jul 29 2005Recent observations, reported by Warner and Woudt, of Dwarf Nova Oscillations (DNOs) exhibiting frequency drift, period doubling, and 1:2:3 harmonic structure, can be understood as disc oscillations that are excited by perturbations at the spin frequency ... More

Spectra of large block matricesOct 09 2006In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. This paper proposes a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to ... More

Epicyclic frequencies for rotating strange quark stars: the importance of stellar oblatenessMar 05 2014Kilohertz QPOs can be used as a probe of the inner regions of accretion disks in compact stars and hence also of the properties of the central object. Most models of kHz QPOs involve epicyclic frequencies to explain their origin. We compute the epicyclic ... More

Resonance in Forced Oscillations of an Accretion Disk and Kilohertz Quasi Periodic OscillationsFeb 03 2004Feb 27 2004We have performed numerical simulations of a radially perturbed "accretion" torus around a black hole or neutron star and find that the torus performs radial and vertical motions at the appropriate epicyclic frequencies. We find clear evidence that vertical ... More

A non-linear resonance model for the black hole and neutron star QPOs: theory supported by observationsMar 31 2006Kilohertz Quasi-Periodic Oscillations (QPOs) have been detected in many accreting X-ray binaries. It has been suggested that the highest QPO frequencies observed in the modulation of the X-ray flux reflect a non-linear resonance between two modes of accreting ... More