Results for "Karol Gregor"

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Deep AutoRegressive NetworksOct 31 2013May 20 2014We introduce a deep, generative autoencoder capable of learning hierarchies of distributed representations from data. Successive deep stochastic hidden layers are equipped with autoregressive connections, which enable the model to be sampled from quickly ... More
Neural Variational Inference and Learning in Belief NetworksJan 31 2014Jun 04 2014Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied to them scale ... More
Learning Representations by Maximizing CompressionAug 04 2011We give an algorithm that learns a representation of data through compression. The algorithm 1) predicts bits sequentially from those previously seen and 2) has a structure and a number of computations similar to an autoencoder. The likelihood under the ... 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
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
Spin solid phases of spin 1 and spin 3/2 antiferromagnets on a cubic latticeApr 06 2007We study spin S=1 and S=3/2 Heisenberg antiferromagnets on a cubic lattice focusing on spin solid states. Using Schwinger boson formulation for spins, we start in a U(1) spin liquid phase proximate to Neel phase and explore possible confining paramagnetic ... More
Impurities in triangular lattice spin 1/2 antiferromagnetMay 09 2008We study effects of nonmagnetic impurities in a spin-1/2 frustrated triangular antiferromagnet with the aim of understanding the observed broadening of $^{13}$C NMR lines in the organic spin liquid material $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$. For high temperatures ... More
Studies of non-magnetic impurities in the spin-1/2 Kagome AntiferromagnetFeb 03 2008Motivated by recent experiments on ZnCu$_3$(OH)$_6$Cl$_2$, we study the inhomogeneous Knight shifts (local susceptibilities) of spin 1/2 Kagome antiferromagnet in the presence of nonmagnetic impurities. Using high temperature series expansion, we calculate ... More
Fast approximations to structured sparse coding and applications to object classificationFeb 28 2012We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We store a lookup ... More
Families of line-graphs and their quantizationOct 23 2001Jul 15 2002Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L^n(G). We give ... More
Learning and Querying Fast Generative Models for Reinforcement LearningFeb 08 2018A key challenge in model-based reinforcement learning (RL) is to synthesize computationally efficient and accurate environment models. We show that carefully designed generative models that learn and operate on compact state representations, so-called ... More
Variational Intrinsic ControlNov 22 2016In this paper we introduce a new unsupervised reinforcement learning method for discovering the set of intrinsic options available to an agent. This set is learned by maximizing the number of different states an agent can reliably reach, as measured by ... 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
'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
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.
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
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
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
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
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
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
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.
Generalization of Clausius-Mossotti approximation in application to short-time transport properties of suspensionsJul 21 2015Sep 29 2015In 1983 Felderhof, Ford and Cohen gave microscopic explanation of the famous Clausius-Mossotti formula for the dielectric constant of nonpolar dielectric. They based their considerations on the cluster expansion of the dielectric constant, which relates ... More
Credit acceptance process strategy case studies - the power of Credit ScoringMar 25 2014The paper is aware of the importance of certain figures that are essential to an understanding of Credit Scoring models in credit acceptance process optimization, namely if the power of discrimination measured by Gini value is increased by 5% then the ... More
A classification of the irreducible mod-p representations of U(1,1)(Q_p^2/Q_p)Oct 02 2012Dec 09 2015Let p be a prime number. We classify all smooth irreducible mod-p representations of the unramified unitary group U(1,1)(Q_p^2/Q_p) in two variables. We then investigate Langlands parameters in characteristic p associated to U(1,1)(Q_p^2/Q_p), and propose ... More
Scattering series in mobility problem for suspensionsAug 21 2012Oct 09 2012The mobility problem for suspension of spherical particles immersed in an arbitrary flow of a viscous, incompressible fluid is considered in the regime of low Reynolds numbers. The scattering series which appears in the mobility problem is simplified. ... More
Current status of CARLOMAT, a program for automatic computation of lowest order cross sectionsJun 30 2008The current status of CARLOMAT, a program for automatic computation of the lowest order cross sections of multiparticle reactions is described, the results of comparisons with other multipurpose Monte Carlo programs are shown and some new results on e+e- ... More
PDFs for nuclear targetsJun 25 2010Understanding nuclear effects in parton distribution functions (PDF) is an essential component needed to determine the strange and anti-strange quark contributions in the proton. In addition Nuclear Parton Distribution Functions (NPDF) are critically ... More
Top quark pair production and decay into 6 fermions at linear collidersOct 04 2001Jan 03 2002The production of a t\bar{t}-pair and its decay into a 6 fermion final state of different flavours in e+e- annihilation at centre of mass energies typical for linear colliders is analyzed in the framework of the Standard Model. The results of calculation ... More
The infinitesimal form of induced representation of the kappa-Poincare groupOct 15 1996The infinitesimal form of the induced representation of the kappa-Poincare group is constructed. The infinitesimal action of the kappa-Poincare group on the kappa-Minkowski space is described. The actions of these two infinitesimal forms on the solution ... More
Citation graph, weighted impact factors and performance indicesApr 14 2009Mar 11 2010A scheme of evaluating an impact of a given scientific paper based on importance of papers quoting it is investigated. Introducing a weight of a given citation, dependent on the previous scientific achievements of the author of the citing paper, we define ... 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
Indirect RKKY interaction in armchair graphene nanoribbonsNov 03 2012A form of an indirect Ruderman-Kittel-Kasuya-Yosida (RKKY)-like coupling between magnetic on-site impurities in armchair graphene nanoribbons is studied theoretically. The calculations are based on a tight-binding model for a finite nanoribbon system ... 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.
LHCb VELO UpgradeApr 18 2016The upgrade of the LHCb experiment, scheduled for LHC Run-III, scheduled to start in 2021, will transform the experiment to a trigger-less system reading out the full detector at 40 MHz event rate. All data reduction algorithms will be executed in a high-level ... More
Widths of KL$_{2,3}$ atomic level for Ca, Fe, ZnApr 05 2014Widths of $KL_{2,3}$ atomic levels for Ca, Fe, Zn has been calculated in a fully-relativistic way using the extensive multiconfiguration Dirac-Fock and modified Dirac-Hartree-Slater calculations. The study of de-excitation of the $K^{-1}L_{2,3}^{-1}$ ... More
Banking retail consumer finance data generator - credit scoring data repositoryMay 15 2011This paper presents two cases of random banking data generators based on migration matrices and scoring rules. The banking data generator is a new hope in researches of finding the proving method of comparisons of various credit scoring techniques. There ... 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
Classification of singular Q-homology planes. I. Structure and singularitiesJun 19 2008Jan 13 2012A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient singularity ... 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
MCDF-RCI predictions for structure and width of $Kα_{1,2}$ x-ray line of Al and SiAug 20 2014Multiconfiguration Dirac-Fock and Relativistic Configuration Interaction methods have been employed to predict the structure and the width of $K\alpha_{1,2}$ x-ray lines of Al and Si. The influences of electron correlation and inclusion of possible satellite ... More
Improving legibility of natural deduction proofs is not trivialJul 04 2014Sep 16 2014In formal proof checking environments such as Mizar it is not merely the validity of mathematical formulas that is evaluated in the process of adoption to the body of accepted formalizations, but also the readability of the proofs that witness validity. ... More
New applications of CARLOMATJun 02 2014Jul 30 2014Modifications of CARLOMAT, a program for automatic computation of the lowest order cross sections of multiparticle reactions, that include an abridgement of the phase space integration routine, an interface to parton density functions, improvement of ... More
The top--Higgs coupling at the LHCOct 09 2013The factorization scale dependence of the anomalous top-Higgs coupling effects in the leading order differential cross sections and distributions of the secondary lepton in the process of associated production of the top quark pair and the Higgs boson ... More
Secondary lepton distributions as a probe of the top--higgs coupling at the LHCMar 20 2013Jul 11 2013The differential distributions in rapidity and angles of the secondary lepton in the associated production of the top quark pair and higgs boson in proton-proton collisions at the LHC are quite sensitive to the top-higgs coupling. However, the effects ... More
CARLOMAT_3.0, an automatic tool for the electron-positron annihilation into hadrons at low energiesApr 22 2015Jul 01 2015A new version of CARLOMAT that allows to generate automatically the Monte Carlo programs dedicated to the description of the processes e+e- -> hadrons at low center-of-mass energies is presented. The program has been substantially modified in order to ... More
'carlomat', A program for automatic computation of lowest order cross sectionsMar 19 2009The current version of 'carlomat', a program for automatic computation of the lowest order cross sections of multiparticle reactions, is described. The program can be used as the Monte Carlo generator of unweighted events as well.
The bicovariant differential calculus on the kappa-Poincare and kappa-Weyl groupsJun 26 1996The bicovariant differential calculus on fourdimensional kappa-Poincare group and corresponding Lie-algebra like structure for any metric tensor are described. The bicovariant differential calculus on four-dimensional kappa-Weyl group and corresponding ... More
Studying top quark pair production at a linear collider with a program 'eett6f'May 09 2003Some features of a program 'eett6f' for top quark pair production and decay into six fermions at linear colliders are discussed. Lowest order standard model predictions for cross sections of some six fermion channels and for the top quark decay width ... More
Quartic quantum theory: an extension of the standard quantum mechanicsApr 08 2008Jun 30 2008We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be ... More
Localization of Eigenstates & Mean Wehrl EntropyOct 21 1999Dynamics of a periodically time dependent quantum system is reflected in the features of the eigenstates of the Floquet operator. Of the special importance are their localization properties quantitatively characterized by the eigenvector entropy, the ... 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
Indirect coupling between localized magnetic moments in zero-dimensional graphene nanostructures (quantum dots)Sep 25 2013Oct 24 2013The indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling between on-site magnetic impurities is studied for two kinds of graphene nanoflakes consisting of approximately 100 carbon atoms, posessing either zigzag or armchair edge. The tight-binding Hamiltonian ... 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
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
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
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
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
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
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.
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
Product of Ginibre matrices: Fuss-Catalan and Raney distributionsMar 17 2011May 05 2011Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distribution P_s(x), such that their moments are equal to the Fuss-Catalan numbers or order s. We find a representation of the Fuss--Catalan ... More
On powers of half-twists in M(0,2n)Aug 30 2016We use elementary skein theory to prove a version of a result of Stylianakis who showed that under mild restrictions on m and n, the normal closure of the m-th power of a half-twist has infinite index in the mapping class group of a sphere with 2n punctures. ... More
Report from the IUPAP Commission on Particles and Fields (C11)Oct 18 2008Oct 21 2008The Commission 11 (C11) on Particles and Fields of the International Union of Pure and Applied Physics (IUPAP) supervises the organization of the main conferences in particle physics. In the period 2007-2008 it has been active in the oversight and venue ... More
Improving the Success Probability for Shor's Factoring AlgorithmAug 29 2002Given n=p*q with p and q prim and y in Z_{p*q}^*. Shor's Algorithm computes the order r of y, i.e. y^r=1 (mod n). If r=2k is even and y^k \ne -1 (mod n) we can easily compute a non trivial factor of n: gcd(y^k-1,n). In the original paper it is shown that ... More
Sparse Bayesian time-varying covariance estimation in many dimensionsAug 30 2016Dynamic covariance estimation for multivariate time series suffers from the curse of dimensionality. This renders parsimonious estimation methods essential for conducting reliable statistical inference. In this paper, the issue is addressed by modeling ... More
Spin-nematic order in the frustrated pyrochlore-lattice quantum rotor modelNov 23 2005As an example of ordering due to quantum fluctuations, we examine the nearest-neighbor antiferromagnetic quantum O(n) rotor model on the pyrochlore lattice. Classically, this system remains disordered even at zero temperature; we find that adding quantum ... More
MADE: Masked Autoencoder for Distribution EstimationFeb 12 2015Jun 05 2015There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our method masks the ... More
What is the Best Feature Learning Procedure in Hierarchical Recognition Architectures?Jun 05 2016(This paper was written in November 2011 and never published. It is posted on arXiv.org in its original form in June 2016). Many recent object recognition systems have proposed using a two phase training procedure to learn sparse convolutional feature ... More
Bottom-Up Earley DeductionFeb 05 1995We propose a bottom-up variant of Earley deduction. Bottom-up deduction is preferable to top-down deduction because it allows incremental processing (even for head-driven grammars), it is data-driven, no subsumption check is needed, and preference values ... More
Isocurvature Perturbations in Quintessence CosmologiesOct 09 2003We present a systematic treatment of the initial conditions and evolution of cosmological perturbations in a universe containing photons, baryons, neutrinos, cold dark matter, and a scalar quintessence field. By formulating the evolution in terms of a ... More
On powers of half-twists in M(0,2n)Aug 30 2016Oct 14 2016We use elementary skein theory to prove a version of a result of Stylianakis who showed that under mild restrictions on m and n, the normal closure of the m-th power of a half-twist has infinite index in the mapping class group of a sphere with 2n punctures. ... More
Time-dependent optical linewidth in fluctuating environments: Stochastic modelsAug 31 2001Time-resolved optical lineshapes are calculated using a second-order inhomogeneous cumulant expansion. The calculation shows that in the inhomogeneous limit the optical spectra are determined solely by two-time correlation functions. Therefore, measurements ... More
Using Extended Derksen Ideals in Computational Invariant TheoryOct 25 2013Mar 31 2014The main purpose of this paper is to develop new algorithms for computing invariant rings in a general setting. This includes invariants of nonreductive groups but also of groups acting on algebras over certain rings. In particular, we present an algorithm ... More
Nonlinear response functions in an exponential trap modelJul 16 2014The nonlinear response to an oscillating field is calculated for a kinetic trap model with an exponential density of states and the results are compared to those for the model with a Gaussian density of states. The calculations are limited to the high ... More
Fluctuation-dissipation relations for a general class of master equationsSep 04 2003The fluctuation-dissipation relation is calculated for a class of stochastic models obeying a master equation. The transition rates are assumed to obey detailed balance also in the presence of a field. It is shown that in general the linear response cannot ... More
Dynamic heterogeneities in the out-of-equilibrium dynamics of simple spherical spin modelsApr 17 2003Aug 04 2003The response of spherical two-spin interaction models, the spherical ferromagnet (s-FM) and the spherical Sherrington-Kirkpatrick (s-SK) model, is calculated for the protocol of the so-called nonresonant hole burning experiment (NHB) for temperatures ... More
$\overline{\mathcal{R}}_{15}$ is of general typeNov 26 2015Nov 29 2016We prove that the moduli space $\overline{\mathcal{R}}_{15}$ of Prym curves of genus $15$ is of general type. To this end we exhibit a virtual divisor $\overline{\mathcal{D}}_{15}$ on $\overline{\mathcal{R}}_{15}$ as the degeneracy locus of a globalized ... More
Derivation of the Inverse Schulze-Hardy RuleJan 13 2016Mar 18 2016The inverse Schulze-Hardy rule was recently proposed based on experimental observations (Cao et al., Langmuir, 2015, 31, 6610-6614). This rule describes an interesting new situation of the aggregation of charged colloidal particles in the presence of ... More
The Transcendence Degree over a RingSep 07 2011For a finitely generated algebra over a field, the transcendence degree is known to be equal to the Krull dimension. The aim of this paper is to generalize this result to algebras over rings. A new definition of the transcendence degree of an algebra ... More
Nonlinear response theory for Markov processes: Simple models for glassy relaxationMar 08 2012The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external ... More
Multi-Dimensional InheritanceNov 17 1994In this paper, we present an alternative approach to multiple inheritance for typed feature structures. In our approach, a feature structure can be associated with several types coming from different hierarchies (dimensions). In case of multiple inheritance, ... More
Densities of the Raney distributionsNov 30 2012We prove that if $p\ge 1$ and $0< r\le p$ then the sequence $\binom{mp+r}{m}\frac{r}{mp+r}$, $m=0,1,2,...$, is positive definite, more precisely, is the moment sequence of a probability measure $\mu(p,r)$ with compact support contained in $[0,+\infty)$. ... 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
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
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
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
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
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
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
The Coolidge-Nagata conjectureFeb 25 2015Let $E\subseteq \mathbb{P}^2$ be a complex rational cuspidal curve contained in the projective plane. The Coolidge-Nagata conjecture asserts that $E$ is Cremona equivalent to a line, i.e. it is mapped onto a line by some birational transformation of $\mathbb{P}^2$. ... 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