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Vertex-Fault Tolerant Complete Matching in Bipartite graphs: the Biregular CaseJul 10 2019Given a family $\mathcal{H}$ of graphs and a positive integer $k$, a graph $G$ is called vertex $k$-fault-tolerant with respect to $\mathcal{H}$, denoted by $k$-FT$(\mathcal{H})$, if $G-S$ contains some $H\in\mathcal{H}$ as a subgraph, for every $S\subset ... More

Towards optimal kernel for connected vertex cover in planar graphsOct 10 2011We study the parameterized complexity of the connected version of the vertex cover problem, where the solution set has to induce a connected subgraph. Although this problem does not admit a polynomial kernel for general graphs (unless NP is a subset of ... More

Deep Semantic Abstractions of Everyday Human Activities: On Commonsense Representations of Human InteractionsOct 10 2017We propose a deep semantic characterization of space and motion categorically from the viewpoint of grounding embodied human-object interactions. Our key focus is on an ontological model that would be adept to formalisation from the viewpoint of commonsense ... More

Commonsense Scene Semantics for Cognitive Robotics: Towards Grounding Embodied Visuo-Locomotive InteractionsSep 15 2017We present a commonsense, qualitative model for the semantic grounding of embodied visuo-spatial and locomotive interactions. The key contribution is an integrative methodology combining low-level visual processing with high-level, human-centred representations ... More

Interconnection network with a shared whiteboard: Impact of (a)synchronicity on computing powerSep 29 2011In this work we study the computational power of graph-based models of distributed computing in which each node additionally has access to a global whiteboard. A node can read the contents of the whiteboard and, when activated, can write one message of ... More

Complexity of Splits Reconstruction for Low-Degree TreesJul 10 2010Oct 18 2011Given a vertex-weighted tree T, the split of an edge xy in T is min{s_x(xy), s_y(xy)} where s_u(uv) is the sum of all weights of vertices that are closer to u than to v in T. Given a set of weighted vertices V and a multiset of splits S, we consider the ... More

ROTUNDE - A Smart Meeting Cinematography Initiative: Tools, Datasets, and Benchmarks for Cognitive Interpretation and ControlJun 05 2013We construe smart meeting cinematography with a focus on professional situations such as meetings and seminars, possibly conducted in a distributed manner across socio-spatially separated groups. The basic objective in smart meeting cinematography is ... More

Deeply Semantic Inductive Spatio-Temporal LearningAug 09 2016We present an inductive spatio-temporal learning framework rooted in inductive logic programming. With an emphasis on visuo-spatial language, logic, and cognition, the framework supports learning with relational spatio-temporal features identifiable in ... More

Robust Natural Language Processing - Combining Reasoning, Cognitive Semantics and Construction Grammar for Spatial LanguageJul 20 2016We present a system for generating and understanding of dynamic and static spatial relations in robotic interaction setups. Robots describe an environment of moving blocks using English phrases that include spatial relations such as "across" and "in front ... More

Adding a referee to an interconnection network: What can(not) be computed in one roundSep 22 2010Oct 05 2010In this paper we ask which properties of a distributed network can be computed from a little amount of local information provided by its nodes. The distributed model we consider is a restriction of the classical CONGEST (distributed) model and it is close ... More

Cognitive Interpretation of Everyday Activities: Toward Perceptual Narrative Based Visuo-Spatial Scene InterpretationJun 22 2013We position a narrative-centred computational model for high-level knowledge representation and reasoning in the context of a range of assistive technologies concerned with "visuo-spatial perception and cognition" tasks. Our proposed narrative model encompasses ... More

k-Gap Interval GraphsDec 14 2011Dec 16 2011We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated ... More

eett6f v. 1.0, A program for top quark pair production and decay into 6 fermions at linear collidersOct 14 2002The first version of a computer program "eett6f" for calculating cross sections of e+e- -> 6 fermions processes relevant for a t\bar{t}-pair production and decay at centre of mass energies typical for linear colliders is presented. "eett6f v.~1.0" allows ... More

Scattering matrices with block symmetriesFeb 28 1997Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a system with ... More

Piecewise straightening and Lipschitz simplicial volumeSep 11 2014Feb 16 2015We study the Lipschitz simplicial volume, which is a metric version of the simplicial volume. We introduce the piecewise straightening procedure for singular chains, which allows us to generalize the proportionality principle and the product inequality ... More

Critical temperature of MgB$_2$ ultrathin superconducting films: BCS model calculations in tight-binding approximationJul 14 2014We develop the multi-band BCS model of superconductivity in the ultrathin films using the orthogonal tight-binding approximation for constructing the electron wavefunctions. This allows for relatively simple determination of the band structure near the ... More

Ferrimagnetic and antiferromagnetic phase in bilayer graphene nanoflake controlled with external electric fieldsJan 31 2017May 01 2017The paper presents a computational study of the ground-state magnetic phases of a selected bilayer graphene nanoflake in external electric field and magnetic field. The electric field has parallel and perpendicular component while the magnetic field is ... More

Homological dimension of simple pro-p-Iwahori--Hecke modulesDec 01 2015Jun 27 2018Let $G$ be a split connected reductive group defined over a nonarchimedean local field of residual characteristic $p$, and let $\mathcal{H}$ be the pro-$p$-Iwahori--Hecke algebra associated to a fixed choice of pro-$p$-Iwahori subgroup. We explore projective ... More

Graphene nanoflakes in external electric and magnetic in-plane fieldsDec 14 2014Feb 12 2015The paper discusses the influence of the external in-plane electric and magnetic field on the ground state spin phase diagram of selected monolayer graphene nanostructures. The calculations are performed for triangular graphene nanoflakes with armchair ... More

Electric field control of the indirect magnetic coupling through a short graphene nanoribbonJul 23 2014Aug 19 2014In the paper we consider the system composed of two magnetic planes attached to zigzag terminations of the graphene nanostructure being an ultrashort fragment of the armchair nanoribbon. We investigate theoretically an indirect coupling between these ... More

'carlomat', version 2 of the program for automatic computation of lowest order cross sectionsMay 22 2013Aug 28 2013Version 2 of 'carlomat', a program for automatic computation of the lowest order cross sections of multiparticle reactions, is described. The substantial modifications with respect to version 1 of the program include: generation of a single phase space ... More

Pro-p-Iwahori invariants for SL_2 and L-packets of Hecke modulesAug 28 2013May 13 2015Let p be a prime number, and F a nonarchimedean local field of residual characteristic p. We explore the interaction between the pro-p-Iwahori-Hecke algebras of the group GL_n(F) and its derived subgroup SL_n(F). Using the interplay between these two ... More

ChPT calculations of pion formfactorsSep 13 2012An overview on chiral perturbation theory calculations of form factors is presented. The main focus is given on the form factors related to the lightest meson, pion, namely: pion decay constant, pion vector and scalar form factor, radiative pion decay ... More

Odd sector of QCDSep 21 2011A systematic study of the odd-intrinsic parity sector of QCD is presented. We briefly describe different applications including pi0 -> gamma gamma decay, muonic (g-2) factor and a test of the new holographic conjectures.

The RKKY Coupling between Impurity Spins in Graphene NanoflakesJun 21 2011Nov 14 2011We calculate the indirect charge carrier mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities for two selected graphene nanoflakes containing four hexagonal rings in their structure, differing by their geometry. We describe ... More

Renyi extrapolation of Shannon entropyMay 12 2003Feb 17 2005Relations between Shannon entropy and Renyi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Renyi entropies of order two and three are known, we provide an lower and an upper bound for the Shannon ... More

On the volume of the set of mixed entangled states IIFeb 12 1999Jun 07 1999The problem of of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices describing N--dimensional quantum systems ... More

The Hopf algebra isomorphism between kappa-Poincare algebra in the case g^{00}=0 and "null plane" quantum Poincare algebraNov 21 1996The Hopf algebra isomorphism between kappa-Poincare algebra defined by P.Kosinski and P.Maslanka in the case g^{00}=0 and "null plane" quantum Poincare algebra by A.Ballesteros, F.J.Herranz and M.A.del Olmo is defined.

Fundamental solution for super-critical non-symmetric Lévy-type operatorsJul 11 2018We construct the fundamental solution (the heat kernel) $p^{\kappa}$ to the equation $\partial_t =\mathcal{L}^{\kappa}$, where under certain assumptions the operator $\mathcal{L}^{\kappa}$ takes the form, $$ \mathcal{L}^{\kappa}f(x):= \int_{\mathbb{R}^d}( ... More

Monotone substochastic operators and a new Calderon coupleFeb 17 2015An important result on submajorization, which goes back to Hardy, Littlewood and P\'olya, states that $b\preceq a$ if and only if there is a doubly stochastic matrix $A$ such that $b=Aa$. We prove that under monotonicity assumptions on vectors $a$ and ... More

The Coolidge-Nagata conjecture, part IMay 22 2014Aug 27 2014Let $E\subseteq \mathbb{P}^2$ be a complex rational cuspidal curve contained in the projective plane and let $(X,D)\to (\mathbb{P}^2,E)$ be the minimal log resolution of singularities. Applying the log minimal model program to $(X,\frac{1}{2}D)$ we prove ... More

Exceptional singular Q-homology planesSep 04 2009Jan 20 2010We consider singular Q-acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is C^1- or C*-ruled or the surface is up to isomorphism one of two exceptional surfaces ... More

Lipschitz Simplicial Volume of Connected SumsApr 15 2017We prove that the locally finite simplicial volume and the Lipschitz simplicial volume are additive with respect to certain gluings of manifolds. In particular, we prove that in dimension $\geq 3$ they are additive with respect to connected sums and gluings ... More

Supersingular representations of rank 1 groupsAug 24 2018We prove that any connected reductive group of semisimple $F$-rank 1 over a $p$-adic field admits an irreducible admissible supersingular mod-$p$ representation. This establishes one of the missing cases in Vign\'eras' existence proof for general reductive ... More

Higher order weighted Sobolev spaces on the real line for strongly degenerate weights. Application to variational problems in elasticity of beamsMay 31 2019For one-dimensional interval and integrable weight function $w$ we define via completion a weighted Sobolev space $H^{m,p}_{\mu_w}$ of arbitrary integer order $m$. The weights in consideration may suffer strong degeneration so that, in general, functions ... More

Toeplitz and Hankel operators between distinct Hardy spacesAug 02 2017Feb 07 2018The paper gives the background for Toeplitz $T_a$ and Hankel $H_a$ operators acting between distinct Hardy type spaces over the unit circle $\mathbb{T}$. We characterize possible symbols of such operators and prove general versions of Brown-Halmos and ... More

Two Models for the Homotopy Theory of Cocomplete Homotopy TheoriesNov 02 2014We prove that the homotopy theory of cofibration categories is equivalent to the homotopy theory of cocomplete quasicategories. This is achieved by presenting both homotopy theories as fibration categories and constructing an explicit equivalence between ... More

The Coolidge-Nagata conjecture holds for curves with more than four cuspsFeb 16 2012Let E be a plane rational curve defined over complex numbers which has only locally irreducible singularities. The Coolidge-Nagata conjecture states that E is rectifiable, i.e. it can be transformed into a line by a birational automorphism of the plane. ... More

Recent progress in the geometry of Q-acyclic surfacesMar 11 2010Nov 09 2010We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.

Clustering genes of common evolutionary historyOct 08 2015Mar 09 2016Phylogenetic inference can potentially result in a more accurate tree using data from multiple loci. However, if the loci are incongruent--due to events such as incomplete lineage sorting or horizontal gene transfer--it can be misleading to infer a single ... More

Visual Explanation by High-Level Abduction: On Answer-Set Programming Driven Reasoning about Moving ObjectsDec 03 2017We propose a hybrid architecture for systematically computing robust visual explanation(s) encompassing hypothesis formation, belief revision, and default reasoning with video data. The architecture consists of two tightly integrated synergistic components: ... More

Homological dimension of simple pro-p-Iwahori--Hecke modulesDec 01 2015Jun 15 2016Let $G$ be a split connected reductive group defined over a nonarchimedean local field of residual characteristic $p$, and let $\mathcal{H}$ be the pro-$p$-Iwahori--Hecke algebra associated to a fixed choice of pro-$p$-Iwahori subgroup. We explore projective ... More

Critical temperature of two-dimensional hydrogenated multilayer graphene-based diluted ferromagnetMar 11 2016Jul 21 2016In the paper a theoretical study of critical (Curie) temperature of diluted ferromagnet based on multilayer graphene (or graphite) with hydrogen adatoms deposited over carbon atoms belonging to single sublattice is presented. The calculations are performed ... More

Ground-state magnetic phase diagram of bow-tie graphene nanoflakes in external magnetic fieldDec 27 2013The magnetic phase diagram of a ground state is studied theoretically for graphene nanoflakes of bow-tie shape and various size in external in-plane magnetic field. The tight-binding Hamiltonian supplemented with Hubbard term is used to model the electronic ... More

Anomalous processes and leading logarithmsFeb 28 2013Present status of odd-intrinsic sector of low energy QCD is summarized. The two-photon decay of neutral pion is shortly discussed and its connection with the pion decay constant is analysed. A theoretical tool, the leading-log calculation is also presented, ... More

On distinguishing of non-signaling boxes via completely locality preserving operationsJan 20 2014We consider discriminating between bipartite boxes with 2 binary inputs and 2 binary outputs (2x2) using the class of completely locality preserving operations i.e. those, which transform boxes with local hidden variable model (LHVM) into boxes with LHVM, ... More

Indirect coupling between localized magnetic moments in triangular graphene nanoflakesApr 08 2013Apr 24 2013The indirect, charge-carrier mediated coupling between localized magnetic moments is studied for graphene nanoflakes of triangular shape and zig-zag edge. The characteristic feature of such nanoflakes is the presence of a shell of zero-energy states in ... More

Supersingular representations of rank 1 groupsAug 24 2018May 02 2019We prove that any connected reductive group of semisimple $F$-rank 1 over a $p$-adic field admits an irreducible admissible supersingular mod-$p$ representation. This establishes one of the missing cases in Vign\'eras' existence proof for general reductive ... More

Deep Recurrent Neural Networks for ECG Signal DenoisingJul 30 2018Jan 17 2019Electrocardiographic signal is a subject to multiple noises, caused by various factors. It is therefore a standard practice to denoise such signal before further analysis. With advances of new branch of machine learning, called deep learning, new methods ... More

Chiral expansion for pi^0 decaysMay 05 2009New ongoing experimental activities that have direct reference to pi^0 decay modes call for a new theoretical study in this area. We will summarize some details and interesting facts that concern main decay modes of this lightest meson.

Semitauonic B decays at Belle/Belle IIJan 18 2019Jan 25 2019It is experimentally observed that ratios of branching fractions for semitauonic and semileptonic $B$ decays, known as the $R(D^{(*)})$, are higher than Standard Model (SM) predictions. The $B \to \bar{D}^{(*)} \tau^{+} \nu_{\tau}$ decays, except for ... More

A new proof of the theorems of Lin-Zaidenberg and Abhyankar-Moh-SuzukiMay 21 2014Feb 09 2015Using the theory of minimal models of quasi-projective surfaces we give a new proof of the theorem of Lin-Zaidenberg which says that every topologically contractible algebraic curve in the complex affine plane has equation $X^n=Y^m$ in some algebraic ... More

Cuspidal curves, minimal models and Zaidenberg's finiteness conjectureMay 21 2014Mar 11 2015Let $E\subseteq \mathbb{P}^2$ be a complex rational cuspidal curve and let $(X,D)\to (\mathbb{P}^2,E)$ be the minimal log resolution of singularities. We prove that $\bar E$ has at most six cusps and we establish an effective version of the Zaidenberg ... More

Classification of singular Q-homology planes. II. C^1- and C*-rulingsJan 12 2012A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We classify singular Q-homology planes which are C^1- or C*-ruled. We analyze their completions, the number of different rulings, the number of affine lines on ... More

Grounding Dynamic Spatial Relations for Embodied (Robot) InteractionJul 26 2016This paper presents a computational model of the processing of dynamic spatial relations occurring in an embodied robotic interaction setup. A complete system is introduced that allows autonomous robots to produce and interpret dynamic spatial phrases ... More

Irreducible admissible mod-p representations of metaplectic groupsMar 15 2016May 18 2016Let $p$ be an odd prime number, and $F$ a nonarchimedean local field of residual characteristic $p$. We classify the smooth, irreducible, admissible genuine mod-$p$ representations of the twofold metaplectic cover $\widetilde{\textrm{Sp}}_{2n}(F)$ of ... More

Contribution of dimension-six bosonic operators to Higgs decay into two photons at one-loop levelFeb 13 2004Jul 01 2004The decay of the Higgs boson into two photons is examined in a model-independent way within the effective Lagrangian approach. Contribution of one-loop diagrams including SU(2) x U(1) invariant dimension-six bosonic operators is evaluated explicitly. ... More

Top quark pair production and decay at linear colliders: signal vs. off resonance backgroundOct 29 2002Standard Model predictions for the reactions with six fermions in the final state relevant for top quark pair production and decay at linear colliders are discussed. An issue of the double resonance signal versus non doubly resonant background is addresed. ... More

Wehrl entropy, Lieb conjecture and entanglement monotonesJul 24 2003Nov 04 2003We propose to quantify the entanglement of pure states of $N \times N$ bipartite quantum system by defining its Husimi distribution with respect to $SU(N)\times SU(N)$ coherent states. The Wehrl entropy is minimal if and only if the pure state analyzed ... More

Risk-return arguments applied to options with trading costsMar 19 1998We study the problem of option pricing and hedging strategies within the frame-work of risk-return arguments. An economic agent is described by a utility function that depends on profit (an expected value) and risk (a variance). In the ideal case without ... More

A concise guide to complex Hadamard matricesDec 19 2005May 25 2006Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known ... More

Efficient Learning of Sparse Invariant RepresentationsMay 26 2011We propose a simple and efficient algorithm for learning sparse invariant representations from unlabeled data with fast inference. When trained on short movies sequences, the learned features are selective to a range of orientations and spatial frequencies, ... More

Interpolation of abstract Cesaro, Copson and Tandori spacesFeb 19 2015We study real and complex interpolation of abstract Ces\`aro, Copson and Tandori spaces, including the description of Calder\'on-Lozanovski{\v \i} construction for those spaces. The results may be regarded as generalizations of interpolation for Ces\`aro ... More

Abstract Cesàro Spaces. I. DualityJan 24 2014Mar 20 2014We study abstract Ces\`aro spaces $CX$, which may be regarded as generalizations of Ces\`aro sequence spaces $ces_p$ and Ces\`aro function spaces $Ces_p(I)$ on $I = [0,1]$ or $I = [0,\infty)$, and also as the description of optimal domain from which Ces\`aro ... More

The Jacobian Conjecture fails for pseudo-planesJan 05 2017Sep 05 2018A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its \'etale endomorphisms are proper. We study the conjecture for $\mathbb{Q}$-acyclic surfaces of negative Kodaira dimension. We show that $G$-equivariant counterexamples for ... More

Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian gridsMar 13 2018A new parametric class of semi-implicit numerical schemes for a level set advection equation on Cartesian grids is derived and analyzed. An accuracy and a stability study is provided for a linear advection equation with a variable velocity using partial ... More

Geometric and algebraic origins of additive uncertainty relationsApr 17 2018Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied to a wide ... More

Learning Efficient Algorithms with Hierarchical Attentive MemoryFeb 09 2016Feb 23 2016In this paper, we propose and investigate a novel memory architecture for neural networks called Hierarchical Attentive Memory (HAM). It is based on a binary tree with leaves corresponding to memory cells. This allows HAM to perform memory access in O(log ... More

Note on universal algorithms for learning theoryNov 23 2018We propose the general way of study the universal estimator for the regression problem in learning theory considered in "Universal algorithms for learning theory Part I: piecewise constant functions" and "Universal algorithms for learning theory Part ... More

Pointwise multipliers of Musielak--Orlicz spaces and factorizationDec 14 2018We prove that the space of pointwise multipliers between two distinct Musielak--Orlicz spaces is another Musielak-Orlicz space and the function defining it is given by an appropriately generalized Legendre transform. In particular, we obtain characterization ... More

Behavior and performance of the deep belief networks on image classificationDec 03 2009We apply deep belief networks of restricted Boltzmann machines to bags of words of sift features obtained from databases of 13 Scenes, 15 Scenes and Caltech 256 and study experimentally their behavior and performance. We find that the final performance ... More

Stationary states for underdamped anharmonic oscillators driven by Cauchy noiseMay 28 2019Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the damping is strong ... More

Abstract Cesàro spaces. II. Optimal rangeMar 25 2014Ces\`aro spaces are investigated from the optimal domain and optimal range point of view. There is a big difference between the cases on $[0, \infty)$ and on $[0, 1]$, as we can see in Theorem 1. Moreover, we present an improvement of Hardy inequality ... More

Numerical aspects of evolution of plane curves satisfying the fourth order geometric equationMay 09 2009In this review paper we present a stable Lagrangian numerical method for computing plane curves evolution driven by the fourth order geometric equation. The numerical scheme and computational examples are presented.

Probing the top-Higgs coupling through the secondary lepton distributions in the associated production of the top-quark pair and Higgs boson at the LHCJul 06 2015Sep 04 2015We complement the analysis of the anomalous top-Higgs coupling effects on the secondary lepton distributions in the associated production of the top-quark pair and Higgs boson in proton-proton collisions at the LHC of the former work by one of the present ... More

Heat kernels of non-symmetric Lévy-type operatorsApr 04 2018We construct the fundamental solution (the heat kernel) $p^{\kappa}$ to the equation $\partial_t=\mathcal{L}^{\kappa}$, where under certain assumptions the operator $\mathcal{L}^{\kappa}$ takes one of the following forms, \begin{align*} \mathcal{L}^{\kappa}f(x)&:= ... More

Classification of planar rational cuspidal curves. I. C**-fibrationsSep 13 2016To classify complex rational cuspidal curves $E\subseteq \mathbb{P}^2$ it remains to classify the ones with complement of log general type, i.e. the ones for which $\kappa(K_X+D)=2$, where $(X,D)$ is a log resolution of $(\mathbb{P}^2,E)$. It is conjectured ... More

Complex planar curves homeomorphic to a line have at most four singular pointsMay 27 2019We show that a complex planar curve homeomorphic to the projective line has at most four singular points. If it has exactly four then it has degree five and is unique up to a projective equivalence.

Singular Q-homology planes of negative Kodaira dimension have smooth locus of non-general typeJan 13 2010Feb 15 2011We continue the program of classification of normal Q-acyclic surfaces defined over the field of complex numbers, so-called 'Q-homology planes'. Here we show that if a Q-homology plane has negative Kodaira dimension then its smooth locus is not of general ... More

L{é}vy processes: concentration function and heat kernel boundsJun 28 2019We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are equivalent to the ... More

Semantic Analysis of (Reflectional) Visual Symmetry: A Human-Centred Computational Model for Declarative ExplainabilityMay 31 2018Sep 14 2018We present a computational model for the semantic interpretation of symmetry in naturalistic scenes. Key features include a human-centred representation, and a declarative, explainable interpretation model supporting deep semantic question-answering founded ... More

Binary Paragraph VectorsNov 03 2016Recently Le & Mikolov described two log-linear models, called Paragraph Vector, that can be used to learn state-of-the-art distributed representations of documents. Inspired by this work we present Binary Paragraph Vectors, simple neural networks that ... More

Improved Distance Queries and Cycle Counting by Frobenius Normal FormNov 11 2016Consider an unweighted, directed graph $G$ with the diameter $D$. In this paper, we introduce the framework for counting cycles and walks of given length in matrix multiplication time $O(n^\omega)$. The framework is based on the fast decomposition into ... More

Semi-Device Independent Quantum MoneyNov 26 2018The seminal idea of quantum money due to Stephen Wiesner, the money not forgeable due to laws of Quantum Mechanics, has laid foundations for the Quantum Information Theory in early '70s. As quantum technology develops, in parallel to crypto-currencies ... More

On discrete structures in finite Hilbert spacesJan 26 2017We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function, symmetric informationally ... More

Lipschitzian solutions to inhomogeneous linear iterative equationsJul 01 2016We study the problems of the existence, uniqueness and continuous dependence of Lipschitzian solutions $\varphi$ of equations of the form $$ \varphi(x)=\int_{\Omega}g(\omega)\varphi\big(f(x,\omega)\big)\mu(d\omega)+F(x), $$ where $\mu$ is a measure on ... More

Irreducible admissible mod-p representations of metaplectic groupsMar 15 2016Mar 18 2017Let $p$ be an odd prime number, and $F$ a nonarchimedean local field of residual characteristic $p$. We classify the smooth, irreducible, admissible genuine mod-$p$ representations of the twofold metaplectic cover $\widetilde{\textrm{Sp}}_{2n}(F)$ of ... More

Multipole matrix elements of Green function of Laplace equationJan 02 2015Multipole matrix elements of Green function of Laplace equation are calculated. The multipole matrix elements of Green function in electrostatics describe potential on a sphere which is produced by a charge distributed on the surface of a different (possibly ... More

Random unitary matrices associated to a graphNov 14 2013We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges ... 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

Superconductivity - the first 100 yearsSep 04 2011Oct 07 2011On the occasion of centenary of superconductivity discovery I remind some facts from the first period and attempts to understand the phenomenon. It turns out that most famous physicists of the first half of XX century have tried to solve the puzzle. Bardeen, ... More

Optimal cloning of qubits given by arbitrary axisymmetric distribution on Bloch sphereJul 05 2010Oct 29 2010We find an optimal quantum cloning machine, which clones qubits of arbitrary symmetrical distribution around the Bloch vector with the highest fidelity. The process is referred to as phase-independent cloning in contrast to the standard phase-covariant ... More

Neutralino annihilation to quarks with SUSY-QCD correctionsNov 10 2008The calculation of the cosmological relic density of the dark matter candidate within supersymmetric models is an interesting possibility to obtain additional constraints on the supersymmetric parameter space with respect to collider, electroweak precision, ... More

Tests of the naturalness of the coupling constants in ChPT at order p^6Apr 13 2006Jun 07 2006We derive constraints on combinations of O(p^6) chiral coupling constants by matching a recent two-loop calculation of the pi-K scattering amplitude with a set of sum rules. We examine the validity of the natural expectation that the values of the chiral ... More

Chiral expansions of the pi0 lifetimeJan 29 2009May 05 2009The corrections induced by light quark masses to the current algebra result for the $\pi^0$ lifetime are reexamined. We consider NNLO corrections and we compute all the one-loop and the two-loop diagrams which contribute to the decay amplitude at NNLO ... More

An Introduction to Quantum Entanglement: a Geometric ApproachJun 27 2006We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally entangled states. ... More

Negativity of the Wigner function as an indicator of nonclassicalityJun 02 2004A measure of nonclassicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyze this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition ... More

ee4fgamma, A program for e+e- -> 4f, 4fgamma with nonzero fermion massesAug 01 2003Apr 21 2004A computer program ee4fgamma for calculating cross sections of any four fermion final state of e+e--annihilation at high energy and the corresponding bremsstrahlung reaction that is possible in the framework of the Standard Model is presented. As the ... More

Monge Metric on the Sphere and Geometry of Quantum StatesAug 03 2000Jun 12 2001Topological and geometrical properties of the set of mixed quantum states in the N-dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphere we use the vector SU(2) coherent states and the generalised ... More

Monge Distance between Quantum StatesNov 11 1997We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q--functions). This quantity fulfills the axioms of a metric and satisfies the following semiclassical property: the distance between ... More