Results for "Karol Gregor"

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Learning Attractor Dynamics for Generative MemoryNov 23 2018A central challenge faced by memory systems is the robust retrieval of a stored pattern in the presence of interference due to other stored patterns and noise. A theoretically well-founded solution to robust retrieval is given by attractor dynamics, which ... 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
$\overline{R}_{15}$ is of general typeNov 26 2015In [FL10], Farkas and Ludwig calculated the Kodaira dimension of the moduli space $\overline{R}_g$ of Prym curves for various $g$. In particular, for $g \geq 14$, $g \not= 15$, the space is of general type. The aim of this paper is to close the gap at ... More
Traces on Module Categories over Fusion CategoriesJun 25 2012Jan 27 2015We consider traces on module categories over pivotal fusion categories which are compatible with the module structure. It is shown that such module traces characterise the Morita classes of special haploid symmetric Frobenius algebras. Moreover, they ... 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
Temporal Difference Variational Auto-EncoderJun 08 2018Jan 02 2019To act and plan in complex environments, we posit that agents should have a mental simulator of the world with three characteristics: (a) it should build an abstract state representing the condition of the world; (b) it should form a belief which represents ... More
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
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
Sequences of Orthogonal Polynomials related to Isotropy Orbits of Symmetric SpacesAug 07 2017Studying the isotropy orbits of compact symmetric spaces Reiswich introduced a family of explicit polynomials in one variable in order to describe the unique minimal isotropy orbit of compact symmetric spaces with Dynkin diagram of type $D_m$. Based on ... 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
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
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
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 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
Nonlinear response theory for Markov processes III: Stochastic models for dipole reorientationsAug 09 2018Oct 09 2018The nonlinear response of molecular systems undergoing Markovian stochastic reorientations is calculated up to fifth order in the amplitude of the external field. Time-dependent perturbation theory is used to compute the relevant response functions as ... More
Pivotal tricategories and a categorification of inner-product modulesMay 22 2014This article investigates duals for bimodule categories over finite tensor categories. We show that finite bimodule categories form a tricategory and discuss the dualities in this tricategory using inner homs. We consider inner-product bimodule categories ... More
Statistics of reversible transitions in two-state trajectories in force-ramp spectroscopyJan 16 2014Apr 23 2014A possible way to extract information about the reversible dissociation of a molecular adhesion bond from force fluctuations observed in force ramp experiments is discussed. For small loading rates the system undergoes a limited number of unbinding and ... More
Records in stochastic processes -- Theory and applicationsNov 26 2012Jul 16 2013In recent years there has been a surge of interest in the statistics of record-breaking events in stochastic processes. Along with that, many new and interesting applications of the theory of records were discovered and explored. The record statistics ... More
The First Year of the Large Hadron Collider: A Brief ReviewApr 21 2011The first year of LHC data taking provided an integrated luminosity of about 35/pb in proton-proton collisions at sqrt(s)=7 TeV. The accelerator and the experiments have demonstrated an excellent performance. The experiments have obtained important physics ... More
A multi-epoch XMM-Newton campaign on the core of the massive Cyg OB2 associationOct 19 2011Cyg OB2 is one of the most massive associations of O-type stars in our Galaxy. Despite the large interstellar reddening towards Cyg OB2, many studies, spanning a wide range of wavelengths, have been conducted to more clearly understand this association. ... More
Parametric down-conversion in photonic crystal waveguidesAug 24 2005Sep 13 2006Photonic crystals create dramatic new possibilities for nonlinear optics. Line defects are shown to support modes suitable for the production of pairs of photons by the material's second order nonlinearity even if the phase-matching conditions cannot ... More
Aging in a free-energy landscape model for glassy relaxationAug 19 2005The aging properties of a simple free-energy landscape model for the primary relaxation in supercooled liquids are investigated. The intermediate scattering function and the rotational correlation functions are calculated for the generic situation of ... More
Aging effects in simple models for glassy relaxationJan 17 2006Apr 13 2006Aging effects in the two-time correlation function and the response function after a quench from a high temperature to some low temperature are considered for a simple kinetic random energy model exhibiting stretched exponential relaxation. Because the ... 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
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
Twists of Mukai bundles and the geometry of the level $3$ modular variety over $\overline{\mathcal{M}}_8$Jun 22 2016We study divisors on the moduli spaces $\overline{\mathcal{R}}_{g,\ell}$ of level curves in genus $6$ and $8$ which we obtain by imposing conditions on the Mukai bundle of such curves. These bundles were used in a well-known construction of Mukai which ... More
Perspectives for observing hot massive stars with XMM-Newton in the years 2017 -- 2027Jan 17 2017XMM-Newton has deeply changed our picture of X-ray emission of hot, massive stars. High-resolution X-ray spectroscopy as well as monitoring of these objects helped us gain a deeper insight into the physics of single massive stars with or without magnetic ... More
Twists of Mukai bundles and the geometry of the level $3$ modular variety over $\overline{\mathcal{M}}_8$Jun 22 2016Mar 18 2017For a curve $C$ of genus $6$ or $8$ and a torsion bundle $\eta$ of order $\ell$ we study the vanishing of the space of global sections of the twist $E_C \otimes \eta$ of the rank two Mukai bundle $E_C$ of $C$. The bundle $E_C$ was used in a well-known ... 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
Modeling record-breaking stock pricesJul 08 2013We study the statistics of record-breaking events in daily stock prices of 366 stocks from the Standard and Poors 500 stock index. Both the record events in the daily stock prices themselves and the records in the daily returns are discussed. In both ... More
Dynamical Energy Analysis - determining wave energy distributions in complex vibro-acoustical structuresMar 12 2008We propose a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures. The technique interpolates between standard Statistical Energy Analysis (SEA) and full ray tracing containing both these ... 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
Periodic orbit action correlations in the Baker mapJan 13 2000Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the existence of universal ... More
ProFIT: Prolog with Features, Inheritance and TemplatesFeb 05 1995ProFIT is an extension of Standard Prolog with Features, Inheritance and Templates. ProFIT allows the programmer or grammar developer to declare an inheritance hierarchy, features and templates. Sorted feature terms can be used in ProFIT programs together ... 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
Skein-theoretical derivation of some formulas of HabiroJun 24 2003We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of sl_2 invariants of integral homology 3-spheres. Habiro originally derived these formulas using the quantum group U_q sl_2. As an application, ... More
Moments of Sectional CurvatureJul 20 2017The sectional curvature of a compact Riemannian manifold M can be seen as a random variable on the Grassmann bundle of 2-planes in TM endowed with the Fubini-Study volume density. In this article we calculate the moments of this random variable by integrating ... 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
Matrix-tree theorems and the Alexander-Conway polynomialNov 04 2002This talk is a report on joint work with A. Vaintrob [arXiv:math.CO/0109104 and math.GT/0111102]. It is organised as follows. We begin by recalling how the classical Matrix-Tree Theorem relates two different expressions for the lowest degree coefficient ... 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
Semi-Device Independent Quantum MoneyNov 26 2018Mar 19 2019The seminal idea of quantum money not forgeable due to laws of Quantum Mechanics proposed by Stephen Wiesner, has laid foundations for the Quantum Information Theory in early '70s. Recently, several other schemes for quantum currencies have been proposed, ... More
Internal Language of Finitely Complete $(\infty, 1)$-categoriesSep 27 2017We prove that the homotopy theory of Joyal's tribes is equivalent to that of fibration categories. As a consequence, we deduce a variant of the conjecture asserting that Martin-L\"of Type Theory with dependent sums and intensional identity types is the ... More
Improved Distance Queries and Cycle Counting by Frobenius Normal FormNov 11 2016Jan 10 2017Consider 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 $\widetilde{O}(n^\omega)$. The framework is based on the fast decomposition ... More
Form factors of bound states in the XXZ chainNov 04 2016This work focuses on the calculation of the large-volume behaviour of form factors of local operators in the XXZ spin-$1/2$ chain taken between the ground state and an excited state containing bound states. The analysis is rigorous and builds on various ... More
Green's function coupled cluster formulations utilizing extended inner excitationsSep 18 2018Nov 16 2018In this paper we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as ... More
Kato classes for Lévy processesMar 19 2015Jul 11 2016We prove that the definitions of the Kato class by the semigroup and by the resolvent of the L\'{e}vy process on $\mathbb{R}^d$ coincide if and only if 0 is not regular for {0}. If 0 is regular for {0} then we describe both classes in detail. We also ... More
Higher order semi-implicit schemes for linear advection equation on Cartesian grids with numerical stability analysisNov 13 2016A new class of semi-implicit numerical schemes for linear advection equation on Cartesian grids is derived that is inspired by so-called $\kappa$-schemes used with fully explicit discretizations for this type of problems. Opposite to fully explicit $\kappa$-scheme ... More
Introducing shrinkage in heavy-tailed state space models to predict equity excess returnsMay 30 2018We forecast S&P 500 excess returns using a flexible econometric state space model with non-Gaussian features at several levels. Estimation and prediction are conducted using fully-fledged Bayesian techniques. More precisely, we control for overparameterization ... More
Page Stream Segmentation with Convolutional Neural Nets Combining Textual and Visual FeaturesOct 09 2017Mar 25 2019In recent years, (retro-)digitizing paper-based files became a major undertaking for private and public archives as well as an important task in electronic mailroom applications. As a first step, the workflow involves scanning and Optical Character Recognition ... More
Drift Estimation for Stochastic Reaction-Diffusion SystemsApr 09 2019A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part. Emphasis is put on ... More
A drone can hear the shape of a roomJan 29 2019We show that one can reconstruct the shape of a room with planar walls from the first-order echoes received by four non-planar microphones placed on a drone with generic position and orientation. Both the cases where the source is located in the room ... More
Smooth Nonparametric Bernstein Vine CopulasOct 07 2012We propose to use nonparametric Bernstein copulas as bivariate pair-copulas in high-dimensional vine models. The resulting smooth and nonparametric vine copulas completely obviate the error-prone need for choosing the pair-copulas from parametric copula ... More
Riemannian and Kählerian Normal CoordinatesJul 20 2017In every point of a K\"ahler manifold there exist special holomorphic coordinates well adapted to the underlying geometry. Comparing these K\"ahler normal coordinates with the Riemannian normal coordinates defined via the exponential map we prove that ... More
Towards Conceptual CompressionApr 29 2016We introduce a simple recurrent variational auto-encoder architecture that significantly improves image modeling. The system represents the state-of-the-art in latent variable models for both the ImageNet and Omniglot datasets. We show that it naturally ... More
Sparse Bayesian vector autoregressions in huge dimensionsApr 11 2017We develop a Bayesian vector autoregressive (VAR) model that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature ... More
Classification of Levi degenerate homogeneous CR-manifolds in dimension 5Oct 11 2006In this paper we present new examples of homogeneous 2-nondegenerate CR-manifolds of dimension 5 and give, up to local CR-equivalence, a full classification of all CR-manifolds of this type.
Arcfinder: An algorithm for the automatic detection of gravitational arcsJul 24 2006Jul 25 2006We present an efficient algorithm designed for and capable of detecting elongated, thin features such as lines and curves in astronomical images, and its application to the automatic detection of gravitational arcs. The algorithm is sufficiently robust ... More
Local tube realizations of CR-manifolds and maximal abelian subalgebrasOct 11 2008Aug 21 2009For every CR-manifold germ (M,a) local tube realizations are characterized by certain abelian subalgebras of the real Lie algebra hol(M,a) of all germs of (real-analytic) infinitesimal transformations. For instance, if M is holomorphically non-degenerate, ... More
Characterization of cycle domains via Kobayashi hyperbolicityApr 29 2002A real form $G$ of a complex semisimple Lie group $G^C$ has only finitely many orbits in any given $G^C$-flag manifold $Z=G^C/Q$. The complex geometry of these orbits is of interest, e.g., for the associated representation theory. The open orbits $D$ ... More
Notes on Evanescent Wave Bragg-Reflection WaveguidesSep 02 2013We investigate an extended version of the Bragg reflection waveguide (BRW) with air gaps as one of the layers. This design has the potential of drastically simplifying the epitaxial structure for integrated nonlinear optical elements at the expense of ... More
Nucleation and growth of thin films of rod--like conjugated moleculesJan 18 2013Feb 15 2013Thin films formed from small molecules rapidly gain importance in different technological fields. To explain their growth, methods developed for zero--dimensional atoms as the film forming particles are applied. However, in organic thin film growth the ... More
Fully covariant radiation force on a polarizable particleSep 28 2012The electromagnetic force on a polarizable particle is calculated in a covariant framework. Local equilibrium temperatures for the electromagnetic field and the particle's dipole moment are assumed, using a relativistic formulation of the fluctuation-dissipation ... More
A New Matrix-Tree TheoremSep 17 2001Feb 28 2002The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in the expansion of the determinant of a certain matrix. We prove that in the case of three-graphs (that is, hypergraphs whose edges have exactly three vertices) ... More
On reconstructing n-point configurations from the distribution of distances or areasApr 15 2003One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this distribution. After ... More
Computing invariants of algebraic group actions in arbitrary characteristicApr 19 2007Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring K[X]^G in the case where G is reductive. Furthermore, we address the case where G is connected and unipotent, so the ... More
Neural Autoregressive Distribution EstimationMay 07 2016May 27 2016We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a weight sharing ... More
Towards Principled Unsupervised LearningNov 19 2015Dec 03 2015General unsupervised learning is a long-standing conceptual problem in machine learning. Supervised learning is successful because it can be solved by the minimization of the training error cost function. Unsupervised learning is not as successful, because ... More
DRAW: A Recurrent Neural Network For Image GenerationFeb 16 2015May 20 2015This paper introduces the Deep Recurrent Attentive Writer (DRAW) neural network architecture for image generation. DRAW networks combine a novel spatial attention mechanism that mimics the foveation of the human eye, with a sequential variational auto-encoding ... More
Binary Paragraph VectorsNov 03 2016Nov 14 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
Geometric and algebraic origins of additive uncertainty relationsApr 17 2018Apr 25 2019Constructive 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
One-Shot Generalization in Deep Generative ModelsMar 16 2016May 25 2016Humans have an impressive ability to reason about new concepts and experiences from just a single example. In particular, humans have an ability for one-shot generalization: an ability to encounter a new concept, understand its structure, and then be ... More
Sparse Bayesian vector autoregressions in huge dimensionsApr 11 2017Jun 27 2018We develop a Bayesian vector autoregressive (VAR) model that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature ... More
A "Muon Mass Tree" with alpha-quantized Lepton, Quark and Hadron MassesJul 20 2006A "muon mass tree" is displayed that contains the excitation systematics for accurately reproducing the masses of the six Standard Model quarks (u,d,s,c,b,t); the heavy leptons; the proton; the phi, J/Psi and Upsilon vector meson thrshold states; the ... More
The top quark to electron mass ratio m(t) = 18*m(e)/alpha^2 where alpha = e^2/hslash*cMar 24 2006Threshold-state elementary particle lifetimes exhibit a scaling in powers of alpha = e^2/hslash*c, and a reciprocal electron-based 1/alpha scaling in particle masses that extends over two powers of 1/alpha. The m(e)/alpha coupling generates accurate q ... More
On the iterated Crank-Nicolson for hyperbolic and parabolic equations in numerical relativityJan 31 2006The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this scheme for hyperbolic ... More
Bounds on the degree of APN polynomials The Case of $x^{-1}+g(x)$Jan 27 2009We prove that functions $f:\f{2^m} \to \f{2^m}$ of the form $f(x)=x^{-1}+g(x)$ where $g$ is any non-affine polynomial are APN on at most a finite number of fields $\f{2^m}$. Furthermore we prove that when the degree of $g$ is less then 7 such functions ... More
Comment on "Hole-Burning Experiments within Glassy Models with Infinite Range Interactions"Dec 08 2000Comment on: L.F. Cugliandolo and J.L. Iguain; Phys. Rev. Lett. {\bf 85} 3448 (2000)
Vanshing Theorems for Quaternionic Kaehler ManifoldsJan 11 2000We discuss a peculiar interplay between the representation theory of the holonomy group of a Riemannian manifold, the Weitzenboeck formula for the Hodge-Laplace operator on forms and the Lichnerowicz formula for twisted Dirac operators. For quaternionic ... More
On Reconstructing Configurations of Points in ${\mathbb P}^2$ from a Joint Distribution of InvariantsMay 16 2004Consider the diagonal action of the projective group $\PGL_3$ on $n$ copies of ${\mathbb P}^2$. In addition, consider the action of the symmetric group $\Sigma_n$ by permuting the copies. In this paper we find a set of generators for the invariant field ... More
Faster than Lyapunov decays of classical Loshcmidt echoSep 19 2003Dec 16 2003We show that in the classical interaction picture the echo-dynamics, namely the composition of perturbed forward and unperturbed backward hamiltonian evolution, can be treated as a time-dependent hamiltonian system. For strongly chaotic (Anosov) systems ... More
Study of Spectral Statistics of Classically Integrable SystemsMar 24 2000In this work we present the results of a study of spectral statistics for a classically integrable system, namely the rectangle billiard. We show that the spectral statistics are indeed Poissonian in the semiclassical limit for almost all such systems, ... More
The Weitzenböck MachineFeb 01 2007In this article we give a unified treatment of the construction of all possible Weitzenb\"ock formulas for all irreducible, non--symmetric holonomy groups. The resulting classification is two--fold, we construct explicitly a basis of the space of Weitzenb\"ock ... More
A Factor-Augmented Markov Switching (FAMS) ModelApr 30 2019This paper investigates the role of high-dimensional information sets in the context of Markov switching models with time varying transition probabilities. Markov switching models are commonly employed in empirical macroeconomic research and policy work. ... More