Results for "Bernard Julia"

total 3804took 0.22s
On covariant phase space methodsMay 08 2002It is well known that the Lagrangian and the Hamiltonian formalisms can be combined and lead to "covariant symplectic" methods. For that purpose a "pre-symplectic form" has been constructed from the Lagrangian using the so-called Noether form. However, ... More
Supergravities from fields to branesJul 02 2001The quest for unification of particles and fields and for reconciliation of Quantum Mechanics and General Relativity has led us to gauge theories, string theories, supersymmetry and higher-extended objects: membranes... Our spacetime is quantum mechanical ... More
Uniqueness of $\mathcal{N}=2$ and $3$ pure supergravities in 4DFeb 08 2018After proving the impossibility of consistent non-minimal coupling of a real Rarita-Schwinger gauge field to electromagnetism, we re-derive the necessity of introducing the graviton in order to couple a complex Rarita-Schwinger gauge field to electromagnetism, ... More
$E_{11}$, Borcherds algebras and maximal supergravityJul 29 2010Mar 22 2012The dynamical $p$-forms of torus reductions of maximal supergravity theory have been shown some time ago to possess remarkable algebraic structures. The set ("dynamical spectrum") of propagating $p$-forms has been described as a (truncation of a) real ... More
Symmetries in M-theory: Monsters, IncMar 20 2003We will review the algebras which have been conjectured as symmetries in M-theory. The Borcherds algebras, which are the most general Lie algebras under control, seem natural candidates.
Real Borcherds Superalgebras and M-theoryDec 31 2002May 02 2003The correspondence between del Pezzo surfaces and field theory models over the complex numbers or for split real forms is extended to other real forms, in particular to those compatible with supersymmetry. Specifically, all theories of the Magic triangle ... More
Superfield T-duality rules in ten dimensions with one isometryDec 28 2003Jan 07 2004In this contribution we present the superfield T-duality rules relating type IIA and type IIB supergravity potentials for the case when both type IIA and type IIB superspaces have (at least) one isometry direction. We also give a brief review of T-duality ... More
Twisted Self-Duality of Dimensionally Reduced Gravity and Vertex OperatorsDec 30 1997The Geroch group, isomorphic to the SL(2,R) affine Kac-Moody group, is an infinite dimensional solution generating group of Einstein's equations with two surface orthogonal commuting Killing vectors. We introduce another solution generating group for ... More
Hyperbolic billiards of pure D=4 supergravitiesApr 28 2003We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz (BKL) limit for all pure supergravities in D=4 spacetime dimensions, as well as for D=4, N=4 supergravities coupled to k (N=4) Maxwell supermultiplets. We find that just as for ... More
Electric-magnetic duality beyond four dimensions and in general RelativityDec 27 2005After reviewing briefly the classical examples of duality in four dimensional field theory we present a generalisation to arbitrary dimensions and to p-form fields. Then we explain how U-duality may become part of a larger non abelian V-symmetry in superstring/supergravity ... More
U-opportunities: why is ten equal to ten ?Sep 20 2002It seems to me at this time that two recent developments may permit fast progress on our way to understand the symmetry structure of toroidally (compactified and) reduced M-theory. The first indication of a (possibly) thin spot in the wall that prevents ... More
Superfield T-duality rulesMar 09 2003Jan 10 2004A geometric treatment of T-duality as an operation which acts on differential forms in superspace allows us to derive the complete set of T-duality transformation rules which relate the superfield potentials of D=10 type IIA supergravity with those of ... More
Borcherds symmetries in M-theoryMar 07 2002May 07 2002It is well known but rather mysterious that root spaces of the $E_k$ Lie groups appear in the second integral cohomology of regular, complex, compact, del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms) of toroidal compactifications ... More
Magic N=2 supergravities from hyper-free superstringsDec 18 2007Feb 14 2008We show by explicit construction the existence of various four dimensional models of type II superstrings with N=2 supersymmetry, purely vector multiplet spectrum and no hypermultiplets. Among these, two are of special interest, at the field theory level ... More
Gravitational duality near de Sitter spaceJul 27 2005Feb 19 2008Gravitational instantons ''Lambda-instantons'' are defined here for any given value Lambda of the cosmological constant. A multiple of the Euler characteristic appears as an upper bound for the de Sitter action and as a lower bound for a family of quadratic ... More
Superdualities: Below and beyond U-dualityFeb 04 2000Hidden symmetries are the backbone of Integrable two-dimensional theories. They provide classical solutions of higher dimensional models as well, they seem to survive partially quantisation and their discrete remnants in M-theory called U-dualities, would ... More
The Hasse principle for systems of quadratic and cubic diagonal equationsDec 02 2016Employing Br\"udern's and Wooley's new complification method, we establish an asymptotic Hasse principle for the number of solutions to a system of r_3 cubic and r_2 quadratic diagonal forms, when the number of cubic equations is at least double the number ... More
Orbit Approach to Separation of Variables in sl(4)-Related Integrable SystemsFeb 26 2014Aug 16 2014Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of variables. It ... More
Reconfigurable Decorated PT Nets with Inhibitor Arcs and Transition PrioritiesSep 24 2014In this paper we deal with additional control structures for decorated PT Nets. The main contribution are inhibitor arcs and priorities. The first ensure that a marking can inhibit the firing of a transition. Inhibitor arcs force that the transition may ... More
Twins of s-free numbersJul 08 2013We generalise the square sieve developed by Heath-Brown to higher powers in order to improve on the error term for the problem of counting consecutive power-free numbers.
On Vertex Sparsifiers with Steiner NodesApr 12 2012Given an undirected graph $G=(V,E)$ with edge capacities $c_e\geq 1$ for $e\in E$ and a subset $T$ of $k$ vertices called terminals, we say that a graph $H$ is a quality-$q$ cut sparsifier for $G$ iff $T\subseteq V(H)$, and for any partition $(A,B)$ of ... More
Unrestricted Consumption under a Deterministic Wealth and an Ornstein-Uhlenbeck Process as a Discount RateMar 24 2016We consider an individual or household endowed with an initial capital and an income, modeled as a linear function of time. Assuming that the discount rate evolves as an Ornstein-Uhlenbeck process, we target to find an unrestricted consumption strategy ... More
Isomorphic and Nonisomorphic, Isospectral Circulant GraphsApr 13 2009New criteria for which Cayley graphs of cyclic groups of any order can be completely determined--up to isomorphism--by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley graphs of cyclic ... More
A note on p-adic solubility for forms in many variablesNov 16 2012Feb 23 2015By adopting a new approach to the analysis of the density of p-adic solutions arising in applications of the circle method, we show that under modest conditions the existence of non-trivial p-adic solutions suffices to establish positivity of the singular ... More
Improved Bounds for the Excluded Grid TheoremFeb 08 2016We study the Excluded Grid Theorem of Robertson and Seymour. This is a fundamental result in graph theory, that states that there is some function $f: Z^+\rightarrow Z^+$, such that for all integers $g>0$, every graph of treewidth at least $f(g)$ contains ... More
Cell decompositions of quiver flag varieties for nilpotent representations of the oriented cycleSep 26 2015Feb 17 2016Generalizing Schubert cells in type A and a cell decomposition if Springer fibres in type A found by L. Fresse we prove that varieties of complete flags in nilpotent representations of an oriented cycle admit an affine cell decomposition parametrized ... More
Constant mean curvature $k$-noids in homogeneous manifoldsJun 02 2013For each $k\geq2$, we construct two families of surfaces with constant mean curvature $H$ for $H\in[0,1/2]$ in $\Sigma(\kappa)\times\R$ where $\kappa+4H^2\leq0$. The surfaces are invariant under $2\pi/k$-rotations about a vertical fiber of $\Sigma(\kappa)\times\R$, ... More
Equivariant stratifold homology theoriesJun 22 2006We define equivariant homology theories using bordism of stratifolds with a G-action, where G is a discrete group. Stratifolds are a generalization of smooth manifolds which were introduced by Kreck. He defines homology theories using bordism of suitable ... More
Euler homologyJun 22 2006We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative dimension. There ... More
Dynamics of Plant Growth; A Theory Based on Riemannian GeometryFeb 04 2016In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the growing tissue are ... More
The L^2 signature of torus knotsJan 08 2010Jun 25 2010We find a formula for the L2 signature of a (p,q) torus knot, which is the integral of the omega-signatures over the unit circle. We then apply this to a theorem of Cochran-Orr-Teichner to prove that the n-twisted doubles of the unknot, for n not 0 or ... More
Cosmological billiards and oxidationDec 22 2003Feb 06 2004We show how the properties of the cosmological billiards provide useful information (spacetime dimension and $p$-form spectrum) on the oxidation endpoint of the oxidation sequence of gravitational theories. We compare this approach to the other available ... More
Counterterms in type I SupergravitiesNov 19 1999We compute the one-loop divergences of D=10, N=1 supergravity and of its reduction to D=8. We study the tensor structure of the counterterms appearing in D=8 and D=10 and compare these to expressions previously found in the low energy expansion of string ... More
Hyperbolic Kac-Moody Algebras and Chaos in Kaluza-Klein ModelsMar 13 2001Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinsky, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike ("cosmological") singularity ... More
Polynomial-exponential decomposition from momentsSep 19 2016Oct 04 2016We analyze the decomposition problem of multivariate polynomial-exponential functions from truncated series and present new algorithms to compute their decomposition. Using the duality between polynomials and formal power series, we first show how the ... More
The Dynamics of Influence SystemsApr 17 2012Jul 24 2012Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while sometimes chaotic, influence ... More
The dynamics of pseudographs in convex Hamiltonian systemsDec 15 2004Jul 10 2008We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They emerge in a ... More
The asymptotic behaviour of solutions of forced Burgers equation on the circleMar 27 2003We describe the asymptotic behaviour of solutions of unviscid Burgers equation on the circle with time-periodic forcing. These solutions converge to periodic states, but the period of these limit states may be greater than the period of the forcing. We ... More
Results on conventional and exotic charmonium at BaBarNov 05 2013The B factories provide a unique playground for studying the properties of conventional and exotic charmonium states. We present recent results in initial state radiation and two-photon fusion, obtained using the full data set collected by the BaBar experiment. ... More
HARPO - A Gaseous TPC for High Angular Resolution Gamma-Ray Astronomy and Polarimetry from the MeV to the TeVOct 16 2012We propose a "thin" detector as a high-angular-precision telescope and polarimeter for cosmic gamma-rays above the pair-creation threshold. We have built a demonstrator based on a gaseous TPC. We are presently characterizing the detector with charged ... More
Comment on : "Neutrino Velocity Anomalies: A Resolution without a Revolution"Oct 11 2011I comment on a recent preprint "Neutrino Velocity Anomalies: A Resolution without a Revolution" that appeared recently as arXiv:1110.0989 [hep-ph]
Conformal field theories in random domains and stochastic Loewner evolutionsSep 08 2003We review the recently developed relation between the traditional algebraic approach to conformal field theories and the more recent probabilistic approach based on stochastic Loewner evolutions. It is based on implementing random conformal maps in conformal ... More
An Introduction to Yangian SymmetriesNov 30 1992Dec 01 1992We review some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories. The plan of these notes is the following: 1 - The classical Heisenberg model: Non-Abelian symmetries; The generators of the symmetries and the ... More
Living in a Low Density Black Hole, Non-Expanding Universe - Perhaps a Reflecting UniverseDec 02 2013What is the average density of a black hole, assuming its spin can prevent it from collapsing into a singularity? For stellar black holes, the average density is incredibly dense and has over a trillion G force and tidal force that will rip almost anything ... More
Letter counting: a stem cell for Cryptology, Quantitative Linguistics, and StatisticsNov 29 2012Counting letters in written texts is a very ancient practice. It has accompanied the development of Cryptology, Quantitative Linguistics, and Statistics. In Cryptology, counting frequencies of the different characters in an encrypted message is the basis ... More
Géométrie et cognition; l'exemple du continuJun 24 2008In this paper I propose the idea to establish a clear distinction between the foundations of truth and the foundations of meaning in Mathematics. I explore on the most basic example, the mathematical line, the possibility that the foundations of its meaning ... More
Some resonances of Lojasiewicz inequalitiesMar 02 2012This note presents three resonances in commutative algebra and analytic geometry of the concept of Lojasiewicz inequality. The first is the interpretation in complex analytic geometry of the best possible exponent for a function g with respect to an ideal ... More
Uniformly bounded orthonormal sections of positive line bundles on complex manifoldsApr 05 2014We show the existence of uniformly bounded sequences of increasing numbers of orthonormal sections of powers $L^k$ of a positive holomorphic line bundle $L$ on a compact K\"ahler manifold $M$. In particular, we construct for each positive integer $k$, ... More
Search for dark matter at high-power laser facilities : flawed luminosity calculations in QPS -- Quasi parallel scatteringNov 21 2013I point the erroneous use, in several papers published recently, of the well known expression for the luminosity of the head-on collision of two particle bunches, in a QPS -- Quasi parallel scattering -- configuration, in which the two beams are co-propagating, ... More
QCD and Hadronic Interactions with Initial-State-Radiation at B-FactoriesApr 09 2010The efforts to improve on the precision of the measurement and theoretical prediction of the anomalous magnetic moment of the muon a_mu have turned into a test of our understanding of the hadronic contribution to vacuum polarisation. I describe how recent ... More
Turbulence for (and by) amateursJul 06 2000Series of lectures on statistical turbulence written for amateurs but not experts. Elementary aspects and problems of turbulence in two and three dimensional Navier-Stokes equation are introduced. A few properties of scalar turbulence and transport phenomena ... More
(Perturbed) Conformal Field Theory Applied To 2D Disordered Systems: An IntroductionSep 25 1995We describe applications of (perturbed) conformal field theories to two-dimensional disordered systems. We present various methods of study~: (i) {\it A direct method} in which we compute the explicit disorder dependence of the correlation functions for ... More
Quantum Symmetries in 2D Massive Field TheoriesSep 30 1991We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions is shortly described. ... More
Derivations and Projections on Jordan Triples. An introduction to nonassociative algebra, continuous cohomology, and quantum functional analysisJun 04 2012Dec 10 2015This paper is an elaborated version of the material presented by the author in a three hour minicourse at "V International Course of Mathematical Analysis in Andalusia," Almeria, Spain, September 12-16, 2011. Part I is devoted to an exposition of the ... More
Fluctuation analysis with cell deathsJul 18 2012May 29 2013The classical Luria-Delbr\"uck model for fluctuation analysis is extended to the case where cells can either divide or die at the end of their generation time. This leads to a family of probability distributions generalizing the Luria-Delbr\"uck family, ... More
The Physics of ELFEFeb 13 1996This paper presents an overview of the physics program of the 15-30~GeV continuous beam electron facility proposed by the European community of nuclear physicists to study the quark and gluon structure of hadrons. The goal of this new facility is to explore ... More
Null Killing Vector Dimensional Reduction and Galilean GeometrodynamicsDec 01 1994The solutions of Einstein's equations admitting one non-null Killing vector field are best studied with the projection formalism of Geroch. When the Killing vector is lightlike, the projection onto the orbit space still exists and one expects a covariant ... More
Rigidification of algebras over multi-sorted theoriesAug 08 2005May 26 2009We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing that there is ... More
An overview of arithmetic motivic integrationNov 13 2008This is an attempt at an elementary exposition, with examples, of the theory of motivic integration developed by R. Cluckers and F. Loeser, with the view towards applications in representation theory of p-adic groups.
A penalized likelihood approach for robust estimation of isoform expressionOct 01 2013Ultra high-throughput sequencing of transcriptomes (RNA-Seq) has enabled the accurate estimation of gene expression at individual isoform level. However, systematic biases introduced during the sequencing and mapping processes as well as incompleteness ... More
Configurations of skew linesNov 13 2006This paper is an updated version of a survey on projective configurations of subspaces in general position. The preceding version was published in Russian in 1989 and in English in 1990 (in Leningrad Math. J.) opening a new section ``Light reading for ... More
Measuring Fairness in Ranked OutputsOct 26 2016Ranking and scoring are ubiquitous. We consider the setting in which an institution, called a ranker, evaluates a set of individuals based on demographic, behavioral or other characteristics. The final output is a ranking that represents the relative ... More
Orbit Approach to Separation of Variables in sl(3)-Related Integrable SystemsDec 06 2013Aug 16 2014Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded into a common ... More
Global solutions of functional fixed point equations via pseudo-spectral methodsFeb 26 2015Sep 02 2015We apply pseudo-spectral methods to construct global solutions of functional renormalisation group equations in field space to high accuracy. For this, we introduce a basis to resolve both finite as well as asymptotic regions of effective potentials. ... More
Positive maps, majorization, entropic inequalities, and detection of entanglementNov 21 2008Jul 09 2009In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive ... More
The Hydrodynamics of Active SystemsMar 01 2016This is a series of four lectures presented at the 2015 Enrico Fermi summer school in Varenna. The aim of the lectures is to give an introduction to the hydrodynamics of active matter concentrating on low Reynolds number examples such as cells and molecular ... More
CSCW Principles to Support Citizen ScienceFeb 28 2015Citizen science changes the way scientific research is pursued. It opens up data collection and analysis to the general public, to the wisdom of crowds. In this emerging area, there is much research to be done to better understand how we can develop citizen ... More
No Strong Parallel Repetition with Entangled and Non-signaling ProversNov 01 2009We consider one-round games between a classical verifier and two provers. One of the main questions in this area is the \emph{parallel repetition question}: If the game is played $\ell$ times in parallel, does the maximum winning probability decay exponentially ... More
On degenerate sigma-functions of genus twoSep 04 2015Oct 31 2016We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus $1$ sigma-function and elementary functions as solutions of a system of linear PDEs satisfied by the sigma-function. By way of application we derive a solution for ... More
Excited State Spectroscopy in the Lattice Gross-Neveu ModelOct 09 2007We present preliminary results of an excited state spectroscopy calculation in the 2-d lattice Gross-Neveu model. We address the construction of suitable interpolators for the variational method and their overlap with excitations. We comment on the role ... More
A note on Elkin's improvement of Behrend's constructionOct 05 2008We provide a short proof of a recent result of Elkin in which large subsets of the integers 1 up to N free of 3-term progressions are constructed.
Can the beta decay of neutral kaons be observed?Apr 25 2000The rate of the beta decay of neutral kaons is calculated within the meson dominance approach taking into account the relation between the KK\rho and \pi\pi\rho coupling constants which follows from the vector meson dominance in electromagnetic interactions ... More
New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fieldsMay 22 2013We obtain new uniform upper bounds for the (non necessarily symmetric) tensor rank of the multiplication in the extensions of the finite fields $\F_q$ for any prime or prime power $q\geq2$; moreover these uniform bounds lead to new asymptotic bounds as ... More
Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General RelativityApr 10 1998May 28 1998E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished one-dimensional ... More
Weighted uniform consistency of kernel density estimators with general bandwidth sequencesJul 09 2006Sep 29 2006We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a deterministic bandwidth ... More
Valuations and Boolean ModelsOct 27 2015Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially adapted to Boolean ... More
SU(3) magnet: finite-gap integration on the lowest genus curveDec 09 2013We consider the integrable system of isotropic SU(3) Landau-Lifshits equation as a Hamiltonian system on a coadjoint orbit of the SU(3) loop group. We connect the mentioned equation with an isotropic SU(3) magnet because it describes the mean fields of ... More
On the linearization of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement fieldNov 13 2015We consider the nonlinear,inverse problem of computing the stored energy function of a hyperelastic material from the full knowledge of the displacement field. The displacement field is described as solution of the nonlinear, dynamic, elastic wave equation, ... More
Robustness of Multi-Party EntanglementSep 20 2001How common is large-scale entanglement in nature? As a first step towards addressing this question, we study the robustness of multi-party entanglement under local decoherence, modeled by partially depolarizing channels acting independently on each subsystem. ... More
Charge diffusion and the butterfly effect in striped holographic matterAug 10 2016Oct 27 2016Recently, it has been proposed that the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals. We analytically compute the charge diffusion constant and ... More
Hochschild cohomology via incidence algebrasNov 17 2006Nov 22 2007Given an algebra A we associate an incidence algebra A(\Sigma) and compare their Hochschild cohomology groups.
Moment Approximations and Model Cascades for Shallow FlowDec 29 2017Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates depth-averaging. While ... More
The Stationary Phase Approximation, Time-Frequency Decomposition and Auditory ProcessingAug 29 2012The principle of stationary phase (PSP) is re-examined in the context of linear time-frequency (TF) decomposition using Gaussian, gammatone and gammachirp filters at uniform, logarithmic and cochlear spacings in frequency. This necessitates consideration ... More
Do Cell Phones Cause Cancer?Jul 13 2010Do cell phones, household electrical power wiring or appliance, or high voltage power lines cause cancer? Fuggedaboudit! No way! When pigs fly! When I'm the Pope! Don't text while you're driving, however, or eat your cell phone. All organisms absorb microwave ... More
Progressions arithmétiques dans les nombres premiers, d'après B. Green et T. TaoSep 28 2006B. Green and T. Tao have recently proved that 'the set of primes contains arbitrary long arithmetic progressions', answering to an old question with a remarkably simple formulation. The proof does not use any "transcendental" method and any of the deep ... More
Recognition principle for generalized Eilenberg-Mac Lane spacesOct 09 2001We give a homotopy theoretical characterization of generalized Eilenberg-Mac Lane spaces, modeled after Segal's characterization of infinite loop spaces via Gamma spaces.
From $Γ$-spaces to algebraic theoriesMay 31 2003The paper examines machines of the type of the $\Gamma$-spaces of Segal which describe homotopy structures on topological spaces. The main result of the paper shows that for any such machine one can find an algebraic theory characterizing the same structure ... More
Sparse multivariate factorization by mean of a few bivariate factorizationsNov 08 2016We describe an algorithm to factor sparse multivariate polynomials using O(d) bivariate factorizations where d is the number of variables. This algorithm is implemented in the Giac/Xcas computer algebra system.
Exploring the role of Punctuation in Parsing Natural TextMay 10 1995Few, if any, current NLP systems make any significant use of punctuation. Intuitively, a treatment of punctuation seems necessary to the analysis and production of text. Whilst this has been suggested in the fields of discourse structure, it is still ... More
A case of mathematical eponymy: the Vandermonde determinantApr 20 2012We study the historical process that led to the worldwide adoption, throughout mathematical research papers and textbooks, of the denomination "Vandermonde determinant". The mathematical object can be related to two passages in Vandermonde's writings, ... More
On the dimension of spline spaces on planar T-meshesNov 08 2010Sep 14 2015We analyze the space of bivariate functions that are piecewise polynomial of bi-degree \textless{}= (m, m') and of smoothness r along the interior edges of a planar T-mesh. We give new combinatorial lower and upper bounds for the dimension of this space ... More
A probabilistic and deterministic modular algorithm for computing Groebner basis over $\Q$Sep 16 2013Nov 18 2013Modular algorithm are widely used in computer algebra systems (CAS), for example to compute efficiently the gcd of multivariate polynomials. It is known to work to compute Groebner basis over $\Q$, but it does not seem to be popular among CAS implementers. ... More
Tiles and colorsMay 17 2000Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of two-dimensional tiling models in which the tiles are rectangles ... More
Convergence of random zeros on complex manifoldsAug 21 2007We show that the zeros of random sequences of Gaussian systems of polynomials of increasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular, the normalized distribution of zeros of systems ... More
Hadronic Contributions to R and g-2 from Initial-State-Radiation DataOct 19 2009I review the recent efforts to improve the precision of the prediction of the anomalous moment of the muon, in particular of the hadronic contribution of the vacuum polarization, which is the contribution with the largest uncertainty. Focus is given to ... More
Polarimetry of cosmic gamma-ray sources above e+e- pair creation thresholdJul 15 2013Sep 26 2013We examine the potential for gamma-ray conversion to electron-positron pairs, either in the field of a nucleus or of an electron of a detector, to measure the fraction P of linear polarization of cosmic gamma sources. For this purpose we implement, validate ... More
Some Simple (Integrable) Models of Fractional StatisticsNov 02 1994In the first part, we introduce the notion of fractional statistics in the sense of Haldane. We illustrate it on simple models related to anyon physics and to integrable models solvable by the Bethe ansatz. In the second part, we describe the properties ... More
On the scattering power of radiotherapy protonsAug 10 2009Scattering power (T = d/dx of mean squared multiple Coulomb scattering (MCS) angle), as used in proton transport theory, is properly viewed as a differential description of the Gaussian approximation to MCS theories such as Moliere's. That is, we seek ... More
Small first zeros of L-functionsApr 25 2014From a family of L-functions with unitary symmetry, Hughes and Rudnick obtained results on the height of its lowest zero. We extend their results to other families of Lfunctions according to the type of symmetry coming from statistics for low-lying zeros. ... More
Chiral Perturbation Theory and Baryon PropertiesJun 03 2007Theoretical as well as experimental progress has been made in the last decade in describing the properties of baryons. In this review I will mostly report on the theoretical issues. Two non-perturbative methods are privileged frameworks for studying these ... More