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A Degeneracy in DRW Modelling of AGN Light CurvesApr 06 2016Apr 21 2016Individual light curves of active galactic nuclei (AGNs) are nowadays successfully modelled with the damped random walk (DRW) stochastic process, characterized by the power exponential covariance matrix of the signal, with the power $\beta=1$. By Monte ... More

Collapse of unit horizontal bundles equipped with a metric of Cheeger-Gromoll typeJun 14 2007We study unit horizontal bundles associated with Riemannian submersions. First we investigate metric properties of an arbitrary unit horizontal bundle equipped with a Riemannian metric of the Cheeger-Gromoll type. Next we examine it from the Gromov-Hausdorff ... More

Discovery of 5000 Active Galactic Nuclei behind the Magellanic CloudsApr 10 2009Jul 24 2009We show that using mid-IR color selection to find active galactic nuclei (AGN) is as effective in dense stellar fields such as the Magellanic Clouds as it is in extragalactic fields with low stellar densities using comparisons between the Spitzer Deep, ... More

The Magellanic Quasars Survey. I. Doubling the Number of Known AGNs Behind the Small Magellanic CloudFeb 03 2011We report the spectroscopic confirmation of 29 new, 12 plausible, and 3 previously known quasars behind the central ~1.5 deg^2 region of the Small Magellanic Cloud. These were identified in a single 2df/AAOmega observation on the Anglo-Australian Telescope ... More

Some properties of generalized higher-order convexityJul 25 2008The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

The Łojasiewicz Exponent of Semiquasihomogeneous SingularitiesMay 20 2014Let $f: (\mathbb{C}^n,0) \rightarrow (\mathbb{C},0)$ be a semiquasihomogeneous function. We give a formula for the local {\L}ojasiewicz exponent $\mathcal{L}_{0}(f)$ of $f$, in terms of weights of $f$. In particular, in the case of a quasihomogeneous ... More

A D'-type symbiotic binary in the planetary nebula SMP LMC 88Feb 08 2018SMP LMC 88 is one of the planetary nebulae (PN) in the Large Magellanic Cloud. We identify in its spectrum Raman scattered O VI lines at 6825 and 7083A. This unambiguously classifies the central object of the nebula as a symbiotic star (SySt). We identified ... More

A measurement of the intrahalo light fraction with near-infrared background anisotropiesOct 22 2012Unresolved near-infrared background anisotropies are expected to have contributions from the earliest galaxies during reionization and faint, dwarf galaxies at intermediate redshifts. Previous measurements were unable to conclusively pinpoint the dominant ... More

A note on the polynomial-like iterative equations orderApr 05 2016We discuss a new case where the order of a polynomial-like iterative equation can be lowered.

Limitations on the recovery of the true AGN variability parameters using Damped Random Walk modelingNov 24 2016Context: The damped random walk (DRW) stochastic process is nowadays frequently used to model aperiodic light curves of AGNs. A number of correlations between the DRW model parameters, the signal decorrelation timescale and amplitude, and the physical ... More

On regularization of plurisubharmonic functions near boundary pointsDec 01 2014Dec 15 2014We prove in an elementary way that for a Lipschitz domain $D\subset \cn$, all plurisubharmonic functions on $D$ can be regularized near any boundary point.

On the relative capacity on almost complex surfaceSep 28 2018Dec 19 2018We built the pluripotential theory on almost complex surfaces. Using Bedford-Taylor type relative capacities we prove among others that J-holomorphic curves as well as negligible sets are pluripolar and Josefson's type theorem on almost Stein surfaces. ... More

A note on the polynomial-like iterative equations orderApr 05 2016Nov 14 2016We show that, under reasonable assumptions, two negative roots can be eliminated from the characteristic equation of a polynomial-like iterative equation. This result gives a new case where we may lower the order of such an equation.

Justice in the Shadow of Self-Interest. An Experiment on Redistributive BehaviorAug 10 2006By means of laboratory experiment I examine the relation between fairness judgments made `behind the veil of ignorance' and actual behavior in a model situation of income inequality. As the evidence shows, when material self-interest is at stake vast ... More

Recent results from NA61/SHINEOct 27 2015The main physics goals of the NA61/SHINE programme on strong interactions are the study of the properties of the onset of deconfinement and the search for signatures of the critical point of strongly interacting matter. These goals are pursued by performing ... More

A note on the longest common substring with $k$-mismatches problemSep 25 2014Oct 14 2014The recently introduced longest common substring with $k$-mismatches ($k$-LCF) problem is to find, given two sequences $S_1$ and $S_2$ of length $n$ each, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ ... More

Local affine selections of convex multifunctionsNov 08 2016It is well known that not every convex multifunction admits an affine selection. One could ask whether there exists at least local affine selection. The answer is positive in the finite-dimensional case. The main part of this note consists of two examples ... More

On weakly locally uniformly rotund norms which are not locally uniformly rotundFeb 05 2014Jan 25 2015We show that every infinite-dimensional Banach space with separable dual admits an equivalent norm which is weakly locally uniformly rotund but not locally uniformly rotund.

On some extremalities in the approximate integrationJul 25 2008Jul 16 2012Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under suitable differentiability assumptions. In our considerations we do not ... More

New tabulation and sparse dynamic programming based techniques for sequence similarity problemsDec 08 2013May 21 2014Calculating the length of a longest common subsequence (LCS) of two strings $A$ and $B$ of length $n$ and $m$ is a classic research topic, with many worst-case oriented results known. We present two algorithms for LCS length calculation with respectively ... More

The Monge-Ampère equation on almost complex manifoldsJun 16 2011Jul 28 2012We study the Dirichlet problem for the Monge-Amp\`ere equation on almost complex manifolds. We obtain the existence of the unique smooth solution of this problem in strictly pseudoconvex domains.

Two black hole initial dataFeb 21 2005Jun 09 2005Misner initial data are a standard example of time-symmetric initial data with two apparent horizons. Compact formulae describing such data are presented in the cases of equal or non-equal masses (i.e. isometric or non-isometric horizons). The interaction ... More

Empirical Conversions of Broad-Band Optical and Infrared Magnitudes to Monochromatic Continuum Luminosities for Active Galactic NucleiApr 22 2015Oct 29 2015We use public data for 105783 quasars from The Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) that include spectral monochromatic luminosities at 5100\AA, 3000\AA, and 1350\AA, and the corresponding observed broad-band ugriz, VRI (converted), JHK ... More

Nonstandard proofs of Eggleston like theoremsApr 10 2002We prove theorems of the following form: if $A\subseteq {\mathbb R}^2$ is a big set, then there exists a big set $P\subseteq {\mathbb R}$ and a perfect set $Q\subseteq {\mathbb R}$ such that $P\times Q\subseteq A$. We discuss cases where big set means: ... More

Polynomial selections and separation by polynomialsJul 25 2008Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex functions of ... More

Monge-Ampère operator on four dimensional almost complex manifoldsMay 15 2013Jun 01 2013We define the Monge-Amp\`ere operator for continuous J-plurisubharmonic functions on four dimensional almost complex manifolds.

On regularization of $J$-plurisubharmonic functionsFeb 27 2014Mar 07 2014We show that on almost complex surfaces plurisubharmonic functions can be locally approximated by smooth plurisubharmonic functions. The main tool is the Poletsky type theorem due to U. Kuzman.

Hermite-Hadamard-type inequalities in the approximate integrationJul 25 2008Jul 16 2012We give a slight extension of the Hermite-Hadamard inequality on simplices and we use it to establish error bounds of the operators connected with the approximate integration.

Revisiting Stochastic Variability of AGNs with Structure FunctionsApr 20 2016Jul 04 2016Discrepancies between reported structure function (SF) slopes and their overall flatness as compared to expectations from the damped random walk (DRW) model, which generally well describes the variability of active galactic nuclei (AGNs), have triggered ... More

A nonlocal toy model of patterns formationMar 17 2019We study a pattern formation model described by certain nonlocal evolution equation. This evolution equation is obtained by a modification of a model introduced by Shigeru Kondo to explain colour patterns on a skin of the guppy fish. We prove the existence ... More

Support-type properties of convex functions of higher order and Hadamard-type inequalitiesJul 25 2008It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree no greater ... More

Optimal coloured perceptronsApr 11 2000Dec 13 2000Ashkin-Teller type perceptron models are introduced. Their maximal capacity per number of couplings is calculated within a first-step replica-symmetry-breaking Gardner approach. The results are compared with extensive numerical simulations using several ... More

On lacunary Toeplitz determinantsOct 09 2013By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants $\det_N\big[ c_{\ell_a-m_b}[f] \big]$ generated by holomorhpic symbols, where $\ell_a=a$ (resp. $m_b=b$) except for a finite subset ... More

Riemann--Hilbert approach to the time-dependent generalized sine kernelNov 25 2010Apr 29 2015We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models ... More

Low-$T$ asymptotic expansion of the solution to the Yang-Yang equationDec 28 2011Apr 30 2015We prove that the unique solution to the Yang-Yang equation arising in the context of the thermodynamics of the so-called non-linear Schr\"{o}dinger model admits a low-temperature expansion to all orders. Our approach provides a rigorous justification, ... More

The homotopy type of spaces of real resultants with bounded multiplicityMar 06 2018For positive integers $d,m,n\geq 1$ with $(m,n)\not= (1,1)$ and $\Bbb K=\Bbb R$ or $\Bbb C$, let $Q^{d,m}_{n}(\Bbb K)$ denote the space of $m$-tuples $(f_1(z),\cdots ,f_m(z))\in \Bbb K [z]^m$ of $\Bbb K$-coefficients monic polynomials of the same degree ... More

The homotopy type of spaces of resultants of bounded multiplicityDec 20 2016For positive integers $m,n, d\geq 1$ with $(m,n)\not= (1,1)$ and a field $\Bbb F$ with its algebraic closure $\overline{\Bbb F}$, let $\text{Poly}^{d,m}_n(\Bbb F)$ denote the space of all $m$-tuples $(f_1(z),\cdots ,f_m(z))\in \Bbb F [z]$ of monic polynomials ... More

On Form Factors of the conjugated field in the non-linear Schröodinger modelMay 05 2011Izergin-Korepin's lattice discretization of the non-linear Schr\"odinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these ... More

Spaces of algebraic maps from real projective spaces into complex projective spacesDec 20 2008Feb 08 2010We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy equivalence. In this ... More

Second sound in nuclear interactionApr 01 2008Following the method developed in monograph : From quarks to bulk matter Hadronic Press 2001the master equation for second sound in nuclear matter is obtained and solved. The velocity of second sound is calculated

On the equivalence of the Ashkin-Teller and the four-state Potts-glass models of neural networksMar 28 2001Apr 10 2001We show that for a particular choice of the coupling parameters the Ashkin-Teller spin-glass neural network model with the Hebb learning rule and one condensed pattern yields the same thermodynamic properties as the four-state anisotropic Potts-glass ... More

The Ashkin-Teller neural network near saturationJun 17 1999Jan 04 2000The thermodynamic and retrieval properties of the Ashkin-Teller neural network model storing an infinite number of patterns are examined in the replica-symmetric mean-field approximation. In particular, for linked patterns temperature-capacity phase diagrams ... More

On condensation properties of Bethe roots associated with the XXZ chainAug 24 2015I prove that the Bethe roots describing either the ground state or a certain class of "particle-hole" excited states of the XXZ spin-$1/2$ chain in any sector with magnetisation $\mathfrak{m} \in [0;1/2]$ exist and form, in the infinite volume limit, ... More

Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger modelJan 08 2011May 05 2011Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schr\"{o}dinger model. ... More

On the emptiness formation probability of the open XXZ spin-$\tf{1}{2}$ chainAug 02 2007This paper is devoted to the study of the emptiness formation probability $\tau\pa{m}$ of the open XXZ chain. We derive a closed form for $\tau\pa{m}$ at $\Delta=\tf{1}{2}$ when the boundary field vanishes. Moreover we obtain its leading asymptotics for ... More

Combinatorics of generalized Bethe equationsMay 14 2012A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result ... More

Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chainMar 01 2019Starting from the massless form factor expansion for the two-point dynamical correlation functions obtained recently, I extract the long-distance and large-time asymptotics of these correlators. The analysis yields the critical exponents and associated ... More

Statistical mechanics of the majority gameJul 08 2003The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfield ... More

Unitarity of the SoV transform for the Toda chainJun 20 2013May 04 2015The quantum separation of variables method consists in mapping the original Hilbert space where a spectral problem is formulated onto one where the spectral problem takes a simpler "separated" form. In order to realise such a program, one should construct ... More

Truncated Wiener-Hopf operators with Fisher Hartwig singularitiesMay 26 2008Jan 20 2010We derive the asymptotic behavior of determinants of truncated Wiener-Hopf operators generated by symbols having Fisher-Hartwig singularities. This task is achieved thanks to an asymptotic resolution of the Riemann-Hilbert problem associated to some generalized ... More

The homotopy type of spaces of rational curves on a toric varietyJul 09 2017Jul 25 2017Spaces of holomorphic maps from the Riemann sphere to various complex manifolds (holomorphic curves ) have played an important role in several area of mathematics. In a seminal paper G. Segal investigated the homotopy type of holomorphic curves on complex ... More

Observation of Relaxation Phenomena in Thermophysical Properties of Alloys and MetalsMay 04 2008In this paper the proposal for the study of the second sound in medium is presented. The master equation is derived and its solution is obtained, The properties of alloys with very long relaxation times, as the examples for the proposed study are discussed ... More

Simplicial resolutions and spaces of algebraic maps between real projective spacesSep 02 2011We show that the space $\tilde{A}_{d}(m,n)$ consisting of all real projective classes of $(n+1)$-tuples of real coefficients homogeneous polynomials of degree $d$ in $(m+1)$ variables, without common real roots except zero, has the same homology as the ... More

Spaces of equivariant algebraic maps from real projective spaces into complex projective spacesSep 02 2011We study the homotopy types of certain spaces closely related to the spaces of algebraic (rational) maps from the $m$ dimensional real projective space into the $n$ dimensional complex projective space for $2\leq m\leq 2n$ (we conjecture this relation ... More

Conformality of a differential with respect to Cheeger-Gromoll type metricsSep 25 2008We investigate conformality of the differential of a mapping between Riemannian manifolds if the tangent bundles are equipped with a generalized metric of Cheeger-Gromoll type.

Time delay measurement of Mg II line in CTS C30.10 with SALTJan 28 2019We report 6 yr monitoring of a distant bright quasar CTS C30.10 (z = 0.90052) with the Southern African Large Telescope (SALT). We measured the rest-frame time-lag of $562\pm 2$ days between the continuum variations and the response of the Mg II emission ... More

Discovery of Energy Dependent X-ray Microlensing in Q2237+0305Jun 29 2011We present our long term Chandra X-ray monitoring data for the gravitationally lensed quasar Q2237+0305 with 20 epochs spanning 10 years. We easily detect microlensing variability between the images in the full (0.2--8 keV), soft (0.2--2 keV), and hard ... More

Hydrodynamic Interactions in Protein FoldingDec 31 2008We incorporate hydrodynamic interactions (HI) in a coarse-grained and structure-based model of proteins by employing the Rotne-Prager hydrodynamic tensor. We study several small proteins and demonstrate that HI facilitate folding. We also study HIV-1 ... More

Inverse Systems and I-Favorable SpacesJun 26 2007Mar 03 2008A compact space X is I-favorable if, and only if X can be representing as a limit of $\sigma$-complete inverse system of compact metrizable spaces with skeletal bonding maps.

The jump of the Milnor number in the X_9 singularity classJan 07 2013The jump of the Milnor number of an isolated singularity $f_0$ is the minimal non-zero difference between the Milnor numbers of $f_0$ and one of its deformations $(f_s)).$ We prove that for the singularities in the $X_9$ singularity class their jumps ... More

Engineering Relative Compression of GenomesMar 11 2011Technology progress in DNA sequencing boosts the genomic database growth at faster and faster rate. Compression, accompanied with random access capabilities, is the key to maintain those huge amounts of data. In this paper we present an LZ77-style compression ... More

Random Graphs for Performance Evaluation of Recommender SystemsOct 28 2010The purpose of this article is to introduce a new analytical framework dedicated to measuring performance of recommender systems. The standard approach is to assess the quality of a system by means of accuracy related statistics. However, the specificity ... More

Luzin and Sierpiński sets, some nonmeasurable subsets of the plane and additive properties on the lineJun 11 2014Jun 22 2014In this paper we shall introduce some nonmeasurable and completely nonmeasurable subsets of the plane with various additional properties, e.g. being Hamel basis, intersecting each line in a strong Luzin / Sierpi\'nski set. Also some additive properties ... More

On ultralimits of sparse graph classesAug 28 2015The notion of nowhere denseness is one of the central concepts of the recently developed theory of sparse graphs. We study the properties of nowhere dense graph classes by investigating appropriate limit objects defined using the ultraproduct construction. ... More

Wei-Norman equations for classical groupsDec 18 2013We show that the non-linear autonomus Wei-Norman equations, expressing the solution of a linear system of non-autonomous equations on a Lie algebra, can be reduced to the hierarchy of matrix Riccati equations in the case of all classical simple Lie algebras. ... More

Hausdorff leaf spaces for codim-1 foliationsJan 07 2009Feb 12 2009The topology of the Hausdorff leaf spaces (HLS) for a codim-1 foliation is the main topic of this paper. At the beginning, the connection between the Hausdorff leaf space and a warped foliations is examined. Next, the author describes the HLS for all ... More

Example of an inhomogeneous cosmological model in the context of backreactionDec 12 2016In this article, we present an example of an inhomogeneous cosmological model, which is inspired by the linear perturbation theory. The metric of this model can be described as the Einstein-de Sitter background with a periodically distributed dust overdensities. ... More

Perturbatively constructed cosmological model with periodically distributed dust inhomogeneitiesNov 13 2018We constructed a simple cosmological model which approximates the Einstein-de Sitter background with periodically distributed dust inhomogeneities. By taking the metric as a power series up to the third order in some perturbative parameter $\lambda$, ... More

Selfish Attacks in Two-hop IEEE 802.11 Relay Networks: Impact and CountermeasuresOct 03 2017Jan 16 2018In IEEE 802.11 networks, selfish stations can pursue a better quality of service (QoS) through selfish MAC-layer attacks. Such attacks are easy to perform, secure routing protocols do not prevent them, and their detection may be complex. Two-hop relay ... More

Modeling a Traffic Remapping Attack Game in a Multi-hop Ad Hoc NetworkApr 13 2017Sep 05 2017In multi-hop ad hoc networks, selfish nodes may unduly acquire high quality of service (QoS) by assigning higher priority to source packets and lower priority to transit packets. Such traffic remapping attacks (TRAs) are cheap to launch, impossible to ... More

Analysis of a Traffic Remapping Attack Game in a Multi-hop Ad Hoc NetworkFeb 11 2019Multi-hop ad hoc networks are susceptible to selfish misbehavior such as traffic remapping attacks (TRAs). Selfish nodes launching such attacks acquire unduly high quality of service (QoS) by assigning higher priority to source packets and lower priority ... More

The Szlenk power type and tensor products of Banach spacesApr 12 2016We prove a formula for the Szlenk power type of the injective tensor product of Banach spaces with Szlenk index at most $\omega$. We also show that the Szlenk power type as well as summability of the Szlenk index are separably determined, and we extend ... More

On-line learning and generalisation in coupled perceptronsNov 26 2001We study supervised learning and generalisation in coupled perceptrons trained on-line using two learning scenarios. In the first scenario the teacher and the student are independent networks and both are represented by an Ashkin-Teller perceptron. In ... More

Statics and dynamics of an Ashkin-Teller neural network with low loadingJan 27 1998May 28 1998An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns built from the ... More

Aspects of the inverse problem for the Toda chainJul 15 2013May 01 2015We generalize Babelon's approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub-constituents of the model's monodromy matrix. Further, we also apply Sklyanin's recent monodromy matrix identities ... More

Fine structure of the asymptotic expansion of cyclic integralsJan 20 2010The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these functionals on ... More

Asymptotic analysis and quantum integrable modelsAug 25 2015This habilitation thesis reviews the progress made by the author respectively to studying various asymptotic regimes of correlation functions in quantum integrable models.

Form factors of bound states in the XXZ chainNov 04 2016This work focuses on the calculation of the large-volume behaviour of form factors of local operators in the XXZ spin-$1/2$ chain taken between the ground state and an excited state containing bound states. The analysis is rigorous and builds on various ... More

A Second Method to Photometrically Align Multi-Site Microlensing Light Curves: Source Color in Planetary Event MOA-2007-BLG-192Oct 12 2009At present, microlensing light curves from different telescopes and filters are photometrically aligned by fitting them to a common model. We present a second method based on photometry of common field stars. If two spectral responses are similar (or ... More

Narrow-line Seyfert 1 galaxies in the context of the Quasar Main SequenceJun 18 2018Narrow-line Seyfert 1 galaxies are defined on the basis of their line widths, and they are generally considered to be high Eddington ratio sources. But in the context of the Quasar Main Sequence, high Eddington rate sources are those which have weak [O ... More

Non-Homogenizable Classes of Finite StructuresMay 04 2016Homogenization is a powerful way of taming a class of finite structures with several interesting applications in different areas, from Ramsey theory in combinatorics to constraint satisfaction problems (CSPs) in computer science, through (finite) model ... More

The 3+1 decomposition of Conformal Yano-Killing tensors and "momentary" charges for spin-2 fieldApr 26 2014The "fully charged" spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the "non-waving" part of the spin-2 field theory. Basic facts and definitions of the spin--2 field and conformal Yano-Killing ... More

Efficient algorithms for the longest common subsequence in $k$-length substringsNov 18 2013Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences $A$ and $B$ ... More

An origin of the universe: a model alternative to Big BangApr 04 2006We propose a new approach to the model of an origin of the universe built by Oscar Klein and Hannes Alfv\'{e}n. Some modifications of assumptions underlying the model result in a possible scenario of the universe creation consistent with observations. ... More

New algorithms for binary jumbled pattern matchingOct 23 2012May 01 2013Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a string to ... More

Rank and select: Another lesson learnedMay 05 2016May 12 2016Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet in 1980s, these ... More

Generalized Luzin setsMar 03 2010In this paper we invastigate the notion of generalized (I,J) - Luzin set. This notion generalize the standard notion of Luzin set and Sierpinski set. We find set theoretical conditions which imply the existence of generalized (I,J) - Luzin set. We show ... More

On the set of limit points of conditionally convergent seriesApr 21 2016Let $\sum_{n=1}^\infty x_n$ be a conditionally convergent series in a Banach space and let $\tau$ be a permutation of natural numbers. We study the set $\operatorname{LIM}(\sum_{n=1}^\infty x_{\tau(n)})$ of all limit points of a sequence $(\sum_{n=1}^p ... More

Skeletal maps and I-favorable spacesMar 11 2010It is showed that the class of all compact Hausdorff and $I$-favorable spaces is adequate for the class of skeletal maps.

A Reputation Scheme to Discourage Selfish QoS Manipulation in Two-Hop Wireless Relay NetworksApr 27 2018Jul 31 2018In wireless networks, stations can improve their received quality of service (QoS) by handling packets of source flows with higher priority. Additionally, in cooperative relay networks, the relays can handle transit flows with lower priority. We use game ... More

The Łojasiewicz Exponent via The Valuative Hamburger-Noether ProcessMay 05 2017Let $k$ be an algebraically closed field of any characteristic. We apply the Hamburger-Noether process of successive quadratic transformations to show the equivalence of two definitions of the {\L}ojasiewicz exponent $\mathfrak{L}(\mathfrak{a})$ of an ... More

Charges of the gravitational field and (3+1) decomposition of CYK tensors part 2Mar 16 2019The work describes the method of construction of charges (conserved quantities) for the gravity field in the (3 + 1) decomposition. The presented construction uses tensors of the electrical and magnetic parts of the Weyl tensor and conformal Killing vectors. ... More

When is multiplication in a Banach algebra open?Apr 27 2017Oct 07 2017We develop the theory of Banach algebras whose multiplication (regarded as a bilinear map) is open. We demonstrate that such algebras must have topological stable rank 1, however the latter condition is strictly weaker and implies only that products of ... More

On a Zoltán Boros' problem connected with polynomial-like iterative equationsJan 26 2015We determine all continuous solutions $g\colon I\to I$ of the polynomial-like iterative equation $g^3(x)=3g(x)-2x$, where $I\subset\mathbb R$ is an interval. In particular, we obtain an answer to a problem posed by Zolt\'{a}n Boros (during the Fiftieth ... More

Entropy bounds for conjunctive queries with functional dependenciesDec 06 2015We study the problem of finding the worst-case bound for the size of the result $Q(\mathbb{ D})$ of a fixed conjunctive query $Q$ applied to a database $\mathbb{ D}$ satisfying given functional dependencies. We provide a precise characterization of this ... More

A bloated FM-index reducing the number of cache misses during the searchDec 07 2015The FM-index is a well-known compressed full-text index, based on the Burrows-Wheeler transform (BWT). During a pattern search, the BWT sequence is accessed at "random" locations, which is cache-unfriendly. In this paper, we are interested in speeding ... More

Occam's GatesJun 27 2015We present a complimentary objective for training recurrent neural networks (RNN) with gating units that helps with regularization and interpretability of the trained model. Attention-based RNN models have shown success in many difficult sequence to sequence ... More

Cardinal invariants for C-cross topologiesSep 13 2006C-cross topologies are introduced. Modifcations of the Kuratowski-Ulam Theorem are considered. Cardinal invariants add, cof, cov and non with respect to meager or nowhere dense subsets are compared. Remarks on invariants cof(nwdY) are mentioned for dense ... More

Completely nonmeasurable unionsMar 03 2010Assume that there is no quasi-measurable cardinal smaller than $2^\omega$. ($\kappa$ is quasi measurable if there exists $\kappa $-additive ideal $\ci $ of subsets of $\kappa $ such that the Boolean algebra $P(\kappa)/\ci$ satisfies c.c.c.) We show that ... More

Hausdorff gaps reconstructed from Luzin gapsMar 04 2009We consider a question: Can a given AD-family be ADR for two orthogonal uncountable towers? If $b > \omega_1$, then we rebuilt any AD-family of the cardinality $\omega_1$ onto a Hausdorff pre-gap. Moreover, if a such AD-family is a Luzin gap, then we ... More