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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

No large population of unbound or wide-orbit Jupiter-mass planetsJul 24 2017Gravitational microlensing is the only method capable of exploring the entire population of free-floating planets down to Mars-mass objects, because the microlensing signal does not depend on the brightness of the lensing object. A characteristic timescale ... 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

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.

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 note on the longest common Abelian factor problemMar 03 2015Mar 11 2015Abelian string matching problems are becoming an object of considerable interest in last years. Very recently, Alatabbi et al. \cite{AILR2015} presented the first solution for the longest common Abelian factor problem for a pair of strings, reaching $O(\sigma ... 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

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

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.

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

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.

A Method to Measure the Unbiased Decorrelation Timescale of the AGN Variable Signal from Structure FunctionsDec 30 2016A simple, model-independent method to quantify the stochastic variability of active galactic nuclei (AGNs) is the structure function (SF) analysis. If the SF for the timescales shorter than the decorrelation timescale $\tau$ is a single power-law and ... More

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

The geometry of $\mathbb{C}^2$ equipped with Warren's metricJun 23 2017Aug 27 2018The aim of this note is to describe the geometry of $\mathbb{C}^2$ equipped with a K\"{a}hler metric defined by Warren. It is shown that with that metric $\mathbb{C}^2$ is a flat manifold. Explicit formulae for geodesics and volume of geodesic ball are ... 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.

On affine selections of set-valued functionsJul 25 2008The main result states that every convex set-valued function defined on a real interval with compact values in a locally convex space, admits an affine selection. In the case if the target space is a real line and the values are closed real intervals, ... 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

Recent results from the strong interactions program of NA61/SHINEMay 06 2017The NA61/SHINE experiment studies hadron production in hadron+hadron, hadron+nucleus and nucleus+nucleus collisions. The strong interactions program has two main purposes: study the properties of the onset of deconfinement and search for the signatures ... More

Life as an Explanation of the Measurement ProblemMay 13 2018May 05 2019No consensus regarding the universal validity of any particular interpretation of the measurement problem has been reached so far. The problem manifests strongly in various Wigner's-friend-type experiments where different observers experience different ... More

Making Mistakes Saves the Single World of the Extended Wigner's Friend ExperimentJan 25 2018An Extended Wigner's Friend gedankenexperiment devised by Daniela Frauchiger and Renato Renner consisting of a quantum system containing an agent who draws conclusion, upon observing the outcome of a measurement of a quantum system prepared by another ... 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

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

Evaluation of basic modules for isolated spelling error correction in Polish textsMay 26 2019Spelling error correction is an important problem in natural language processing, as a prerequisite for good performance in downstream tasks as well as an important feature in user-facing applications. For texts in Polish language, there exist works on ... More

Optimal transport on completely integrable toric manifoldsJun 17 2019We show that existence and uniqueness of solutions to transported Monge-Ampere problem on complex compact toric manifold follows easily from the real theory of optimal transportation.

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.

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.

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.

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

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

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

Assessment of continuous and discrete adjoint method for sensitivity analysis in two-phase flow simulationsMay 18 2018The efficient method for computing the sensitivities is the adjoint method. The cost of solving an adjoint equation is comparable to the cost of solving the governing equation. Once the adjoint solution is obtained, the sensitivities to any number of ... More

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

Differential as a harmonic morphism with respect to Cheeger--Gromoll type metricsAug 04 2009We investigate horizontal conformality of a differential of a map between Riemannian manifolds where the tangent bundles are equipped with Cheeger--Gromoll type metrics. As a corollary, we characterize the differential of a map as a harmonic morphism. ... 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

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

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

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.

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.

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

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

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

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

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

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

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.

Lightweight Fingerprints for Fast Approximate Keyword Matching Using Bitwise OperationsNov 22 2017We aim to speed up approximate keyword matching by storing a lightweight, fixed-size block of data for each string, called a fingerprint. These work in a similar way to hash values; however, they can be also used for matching with errors. They store information ... 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

A semantic-aided particle filter approach for AUV localizationMay 17 2019This paper presents a novel approach to AUV localization, based on a semantic-aided particle filter. Particle filters have been used successfully for robotics localization since many years. Most of the approaches are however based on geometric measurements ... 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

Wei-Norman equations for a unitary evolutionFeb 11 2013The Wei-Norman technique allows to express the solution of a system of linear non-autonomous differential equations in terms of product of exponentials. In particular it enables to find a time-ordered product of exponentials by solving a set of nonlinear ... 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

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

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

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

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

Two simple full-text indexes based on the suffix arrayMay 22 2014May 23 2016We propose two suffix array inspired full-text indexes. One, called SA-hash, augments the suffix array with a hash table to speed up pattern searches due to significantly narrowed search interval before the binary search phase. The other, called FBCSA, ... More

A practical index for approximate dictionary matching with few mismatchesJan 20 2015Feb 12 2016Approximate dictionary matching is a classic string matching problem (checking if a query string occurs in a collection of strings) with applications in, e.g., spellchecking, online catalogs, geolocation, and web searchers. We present a surprisingly simple ... More

Random Graph Generator for Bipartite Networks ModelingOct 28 2010Nov 02 2010The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of parameters.We adapt ... More

Direct sums and summability of the Szlenk indexNov 24 2015We prove that the $c_0$-sum of separable Banach spaces with uniformly summable Szlenk index has summable Szlenk index, whereas this result is no longer valid for more general direct sums. We also give a formula for the Szlenk power type of the $\mathfrak{E}$-direct ... More

The monoid consisting of Kuratowski operationsMay 15 2012Aug 30 2012The paper fills gaps in knowledge about Kuratowski operations which are already in the literature. The Cayley table for these operations has been drawn up. Techniques, using only paper and pencil, to point out all semigroups and its isomorphic types are ... More

Levy-Steinitz theorem and achievement sets of conditionally convergent series on the real planeMay 18 2017Levy-Steinitz theorem characterize sum range of conditionally convergent series, that is a set of all its convergent rearrangements; in finitely dimensional spaces -- it is an affine subspace. An achievement of a series is a set of all its subsums. We ... More

On the geometry of warped foliationsJan 19 2010We discuss the geometry of warped foliations. After examining the Levi-Civita connection, we describe the formulae for sectional, Ricci and scalar curvatures. In the final part of this note, we present some examples.

Some properties of $\mathcal{I}$-Luzin setsJan 20 2015Jan 26 2015In this paper we consider a notion of $\mathcal{I}$-Luzin set which generalizes the classical notion of Luzin set and Sierpi{\'n}ski set on Euclidean spaces. We show that there is a translation invariant $\sigma$-ideal $\mathcal{I}$ with Borel base for ... More

Inequalities between remainders of quadraturesDec 23 2016It is well-known that in the class of convex functions the (nonnegative) remainder of the Midpoint Rule of the approximate integration is majorized by the remainder of the Trapezoid Rule. Hence the approximation of the integral of the convex function ... More

On some inequality of Hermite-Hadamard typeSep 29 2011Jul 13 2012It is well-known that the left term of the classical Hermite-Hadamard inequality is closer to the integral mean value than the right one. We show that in the multivariate case it is not true. Moreover, we introduce some related inequality comparing the ... More

On the discrete boundary value problem for anisotropic equationMay 19 2011Using critical point theory methods we undertake the existence and multiplicity of solutions for discrete anisotropic two-point boundary value problems.

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

An analytic proof of the Krylov estimates for the complex Monge-Ampere equation and applicationsJun 22 2017Aug 16 2017We provide an analytic proof of a theorem of Krylov dealing with global $C^{1,1}$ estimates to solutons of degenerate complex Monge-Amp\`ere equations. As an application we show optimal regularity for various extremal functions with nonconstant boundary ... 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

copMEM: Finding maximal exact matches via sampling both genomesMay 22 2018Genome-to-genome comparisons require designating anchor points, which are given by Maximum Exact Matches (MEMs) between their sequences. For large genomes this is a challenging problem and the performance of existing solutions, even in parallel regimes, ... More

Ideals which generalize $(v^0)$Jan 29 2010We consider ideals $d^0(\mathcal{V})$ which are generalizations of the ideal $(v^0)$. We formulate couterparts of Hadamard's theorem. Then, adopting the base tree theorem and applying Kulpa-Szyma\'nski Theorem, we obtain $ cov(d^0(\mathcal{V}))\leq add(d^0(\mathcal{V}))^+$. ... 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

On regular but not completely regular spacesJan 16 2017We present how to obtain non-comparable regular but not completely regular spaces. We analyze a generalization of Mysior's example, extracting its underlying purely set-theoretic framework. This enables us to build simple counterexamples, using the Niemytzki ... 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