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Uncertainty in Neural Networks: Bayesian EnsemblingOct 12 2018Jan 27 2019Understanding the uncertainty of a neural network's (NN) predictions is essential for many applications. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to the large number of parameters and ... More

Learning through Probing: a decentralized reinforcement learning architecture for social dilemmasSep 26 2018Dec 22 2018Multi-agent reinforcement learning has received significant interest in recent years notably due to the advancements made in deep reinforcement learning which have allowed for the developments of new architectures and learning algorithms. Using social ... More

Understanding The Impact of Partner Choice on Cooperation and Social Norms by means of Multi-agent Reinforcement LearningFeb 08 2019The human ability to coordinate and cooperate has been vital to the development of societies for thousands of years. While it is not fully clear how this behavior arises, social norms are thought to be a key factor in this development. In contrast to ... More

Understanding The Impact of Partner Choice on Cooperation and Social Norms by means of Multi-agent Reinforcement LearningFeb 08 2019Feb 13 2019The human ability to coordinate and cooperate has been vital to the development of societies for thousands of years. While it is not fully clear how this behavior arises, social norms are thought to be a key factor in this development. In contrast to ... More

Bayesian Inference with Anchored Ensembles of Neural Networks, and Application to Exploration in Reinforcement LearningMay 29 2018Jul 02 2018The use of ensembles of neural networks (NNs) for the quantification of predictive uncertainty is widespread. However, the current justification is intuitive rather than analytical. This work proposes one minor modification to the normal ensembling methodology, ... More

High-accuracy first-principles determination of the structural, vibrational and thermodynamical properties of diamond, graphite, and derivativesDec 22 2004The structural, dynamical, and thermodynamical properties of diamond, graphite and layered derivatives (graphene, rhombohedral graphite) are computed using a combination of density-functional theory (DFT) total-energy calculations and density-functional ... More

Quantum cryptography with and without entanglementDec 01 2003Quantum cryptography is reviewed, first using entanglement both for the intuition and for the experimental realizations. Next, the implementation is simplified in several steps until it becomes practical. At this point entanglement has disappeared. This ... More

Dark soliton past a finite-size obstacleJan 04 2005Sep 05 2005We consider the collision of a dark soliton with an obstacle in a quasi-one-dimensional Bose condensate. We show that in many respects the soliton behaves as an effective classical particle of mass twice the mass of a bare particle, evolving in an effective ... More

Compact Extra Dimensions in Quantum MechanicsNov 01 2016Extra-dimensions are a common topic in popular descriptions of theoretical physics with which undergraduate student most often have no contact in physics courses. This paper shows how students could be introduced to this topic by presenting an approach ... More

The class of the affine line is a zero divisor in the Grothendieck ring: an improvementApr 22 2016Jul 21 2016Lev A. Borisov has shown that the class of the affine line is a zero divisor in the Grothendieck ring of algebraic varieties over complex numbers. We improve the final formula by removing a factor.

Finite-Type Invariants of order one for long virtual knotsFeb 25 2016Oct 11 2016We extend to the long virtual knot case the constructions first presented by A. Henrich and later generalized by the author to the framed virtual knot case. These consist of three Vassiliev invariants of order one, including a universal one, as well as ... More

Is Einstein Still Right?Oct 13 2015This is an article commissioned by the Spanish Physics Magazine ("Revista Espa\~nola de F\'isica") for the Centennial Anniversary of the discovery of General Relativity. The article reviews experimental and observational efforts to test Einstein's theory ... More

De finetti theorems, mean-field limits and bose-Einstein condensationJun 17 2015These notes deal with the mean-field approximation for equilibrium states of N-body systems in classical and quantum statistical mechanics. A general strategy for the justification of effective models based on statistical independence assumptions is presented ... More

Extreme points in non-positive curvatureFeb 22 2016Jun 06 2016A natural analogue of the Krein--Milman theorem is shown to fail for CAT(0) spaces.

Lipschitz-Killing curvatures and polar imagesDec 09 2015We relate the Lipschitz-Killing measures of a definable set $X \subset \mathbb{R}^n$ in an o-minimal structure to the volumes of generic polar images. For smooth submanifolds of $\mathbb{R}^n$, such results were established by Langevin and Shifrin.Then ... More

The Expected Codimension of a Matroid VarietySep 02 2013Matroid varieties are the closures in the Grassmannian of sets of points defined by specifying which Pl\"ucker coordinates vanish and which don't. In general these varieties are very ill-behaved, but in many cases one can estimate their codimension by ... More

Quantum entanglement in condensed matter systemsDec 10 2015Jun 30 2016This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, ... More

Observable properties of strong gravitational lensesNov 16 2016It is shown which properties of a strong gravitational lens can in principle be recovered from observations of multiple extended images when no assumptions are made about the deflector or sources. The mapping between individual multiple images is identified ... More

The Why and How of Nonnegative Matrix FactorizationJan 21 2014Mar 07 2014Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this property of NMF ... More

Fantappiè's final relativity and Lie algebra deformationsNov 01 2012Jun 01 2014The purpose of this note is to discuss a few lines appearing in the work of late Fantappi\`e. They concern the proof of rigidity of a specific real semisimple Lie algebra: ${\mathfrak O}(4,1)$. Our intention is to discuss to what extent such proof constitutes ... More

AMS-02 in Space: Physics ResultsNov 18 2015The Alpha Magnetic Spectrometer (AMS-02) is a particle physics experiment designed to study origin and nature of Galactic Cosmic Rays (CRs) up to TeV energies from space. With its high sensitivity, long exposure and excellent identification capabilities, ... More

Multiplicity distributions inside parton cascades developing in a mediumAug 01 2006The explanation of the suppression of high-pT hadron yields at RHIC in terms of jet-quenching implies that the multiplicity distributions of particles inside a jet and jet-like particle correlations differ strongly in nucleus-nucleus collisions at RHIC ... More

Low-energy excitations of a linearly Jahn-Teller coupled orbital quintetOct 05 2004The low-energy spectra of the single-mode h x (G+H) linear Jahn-Teller model is studied by means of exact diagonalization. Both eigenenergies and photoemission spectral intensities are computed. These spectra are useful to understand the vibronic dynamics ... More

Multiple sources or late injection of short-lived r-nuclides in the early solar system?Feb 24 2005Comparisons between the predicted abundances of short-lived r-nuclides (107Pd, 129I, 182Hf, and 244Pu) in the interstellar medium (ISM) and the observed abundances in the early solar system (ESS) conclusively showed that these nuclides cannot simply be ... More

Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatoricsOct 15 2014Mar 28 2015In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model {\it via} the so-called ... More

GIT-cones and quiversMar 06 2009In this work, we improve results about GIT-cones associated to the action of any reductive group $G$ on a projective variety $X$. These results are applied to give a short proof of a Derksen-Weyman's Theorem which parametrizes bijectively the faces of ... More

Geometric Invariant Theory and Generalized Eigenvalue Problem IIMar 06 2009Let $G$ be a connected reductive subgroup of a complex connected reductive group $\hat{G}$. Fix maximal tori and Borel subgroups of $G$ and $\hat{G}$. Consider the cone $LR^\circ(\hat{G},G)$ generated by the pairs $(\nu,\hat{\nu})$ of strictly dominant ... More

A short geometric proof of a conjecture of FultonJan 23 2009We give a new geometric proof of a conjecture of Fulton on the Littlewood-Richardson coefficients. This conjecture was firstly proved by Knutson, Tao and Woodward using the Honeycomb theory. A geometric proof was given by Belkale. Our proof is based on ... More

Multiplicative formulas in Cohomology of $G/P$ and in quiver representationsDec 11 2008Consider a partial flag variety $X$ which is not a grassmaninan. Consider also its cohomology ring ${\rm H}^*(X,\ZZ)$ endowed with the base formed by the Poincar\'e dual classes of the Schubert varieties. In \cite{Richmond:recursion}, E. Richmond showed ... More

Direct demonstration of the completeness of the eigenstates of the Schrodinger equation with local and non-local potentials bearing a Coulomb tailDec 17 2007Feb 12 2008Demonstrating the completeness of wave functions solutions of the radial Schrodinger equation is a very difficult task. Existing proofs, relying on operator theory, are often very abstract and far from intuitive comprehension. However, it is possible ... More

In-Place Longest Common ExtensionsAug 17 2016Oct 11 2016Longest Common Extension (LCE) queries are a fundamental sub-routine in many string-processing algorithms, including (but not limited to) suffix-sorting, string matching, compression, and identification of repeats and palindrome factors. A LCE query takes ... More

Bridging knowing and proving in mathematics An essay from a didactical perspectiveMar 27 2014The learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which they can apply ... More

Global Eikonal Condition for Lorentzian Distance Function in Noncommutative GeometryMar 29 2010Aug 17 2010Connes' noncommutative Riemannian distance formula is constructed in two steps, the first one being the construction of a path-independent geometrical functional using a global constraint on continuous functions. This paper generalizes this first step ... More

In-Place Longest Common ExtensionsAug 17 2016Oct 19 2016Longest Common Extension (LCE) queries are a fundamental sub-routine in many string-processing algorithms, including (but not limited to) suffix-sorting, string matching, compression, and identification of repeats and palindrome factors. A LCE query takes ... More

Duplicate Detection with Efficient Language Models for Automatic Bibliographic Heterogeneous Data IntegrationApr 27 2015We present a new method to detect duplicates used to merge different bibliographic record corpora with the help of lexical and social information. As we show, a trivial key is not available to delete useless documents. Merging heteregeneous document databases ... More

Conformal generally covariant quantum field theory: The scalar field and its Wick productsJun 04 2008Feb 03 2009In this paper we generalize the construction of generally covariant quantum theories given in the work of Brunetti, Fredenhagen and Verch to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally ... More

On localization and position operators in Moebius-covariant theoriesOct 25 2006Mar 27 2007Some years ago it was shown that, in some cases, a notion of locality can arise from the group of symmetry enjoyed by the theory, thus in an intrinsic way. In particular, when Moebius covariance is present, it is possible to associate some particular ... More

The Lent Particle Method, Application to Multiple Poisson IntegralsApr 16 2010We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for thelaws of random functionals of L\'evy processes or solutions of stochastic differential ... More

Stochastic approach for the subordination in Bochner senseFeb 12 2009It is possible to construct a double indexed process with sample paths a surface of a family of subordinators obtained by subordination. We study here a branch of this subordination process. This opens martingale methods on symbolic calculus questions. ... More

On error operators related to the arbitrary functions principleJan 27 2013The error on a real quantity Y due to the graduation of the measuring instrument may be asymptotically represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator does not depend on the probability ... More

The crust of neutron starsNov 13 2006The structure of the crust of a neutron star is completely determined by the experimentally measured nuclear masses up to a density of the order of 10^11 g.cm^{-3}. At higher densities, the composition of the crust still remains uncertain, mainly due ... More

Band structure effects for dripped neutrons in neutron star crustMay 03 2004Dec 01 2004The outer layers of a neutron star are supposed to be formed of a solid Coulomb lattice of neutron rich nuclei. At densities above neutron drip density (about one thousandth of nuclear saturation density), this lattice is immersed in a neutron fluid. ... More

Consistent description of leptonic and hadroninc spectra in cosmic raysOct 30 2015The AMS Collaboration has recently released data on cosmic ray (CR) leptons and hadrons that can shed light on two exciting problems in CR physics: on one side, the origin of the rise of the CR positron fraction above ~10 GeV of energy, on the other side, ... More

Cosmic-ray protons, nuclei, electrons, and antiparticles under a two-halo scenario of diffusive propagationSep 18 2015Oct 19 2015We report calculations of cosmic-ray proton, nuclei, antiproton, electron and positron energy spectra within a "two-halo model" of diffusive transport. The two halos represent a simple, physically consistent generalization of the standard diffusion models, ... More

AMS-02 in space: physics results, overview, and challengesOct 31 2015The Alpha Magnetic Spectrometer (AMS-02) is a state of the art particle detector measuring cosmic rays (CRs) on the International Space Station (ISS) since May 19th 2011. AMS-02 identifies CR leptons and nuclei in the energy range from hundreds MeV to ... More

Ecological Succession ModelJun 06 2003We introduce a new interacting particle system intended to model an example of ecological succession involving two species: the bracken and the european beech. The objective is to exhibit phase transitions by proving that there exist three possible evolutions ... More

Symbolic dynamics: from the $N$-centre to the $(N+1)$-body problem, a preliminary studyNov 01 2012Sep 16 2013We consider a restricted $(N+1)$-body problem, with $N \geq 3$ and homogeneous potentials of degree $-\a<0$, $\a \in [1,2)$. We prove the existence of infinitely many collision-free periodic solutions with negative and small Jacobi constant and small ... More

Heegner points and Eisenstein seriesAug 11 2008We give an alternative computation of the twisted second moment of critival values of class group $L$-functions attached to an imaginary quadratic field. The method avoids long calculations and yields the expected polynomial growth in the $s$-parameter ... More

An overview on the proof of the splitting theorem in non-smooth contextMay 21 2013We give a quite detailed overview on the proof of the Cheeger-Colding-Gromoll splitting theorem in the abstract framework of spaces with Riemannian Ricci curvature bounded from below.

Stratified critical points one the real Milnor fibre and integral-geometric formulasJul 29 2013Let $(X,0) \subset (\mathbb{R}^n,0)$ be the germ of a closed subanalytic set and let $f$ and $g : (X,0) \rightarrow (\mathbb{R},0)$ be two subanalytic functions. Under some conditions, we relate the critical points of $g$ on the real Milnor fibre $X \cap ... More

An alternative scenario for the formation of specialized protein nano-domains (cluster phases) in biomembranesSep 24 2009Sep 28 2010We discuss a realistic scenario, accounting for the existence of sub-micrometric protein domains in cell membranes. At the biological level, such membrane domains have been shown to be specialized, in order to perform a determined biological task, in ... More

Theory of fluorescence correlation spectroscopy at variable observation area for two-dimensional diffusion on a meshgridNov 29 2007It has recently been proposed, with the help of numerical investigations, that fluorescence correlation spectroscopy at variable observation area can reveal the existence of a meshgrid of semi-permeable barriers hindering the two-dimensional diffusion ... More

Decoding color codes by projection onto surface codesAug 28 2013We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. Applying this ... More

Studies of e+e- Collisions with a Hard Initial-State Photon at BaBarOct 15 2005Oct 28 2005We present preliminary BaBar measurements of hadronic cross sections in $e^+e^-$ annihilation using the radiative return technique. The cross sections for $e^+e^- \to p\bar{p} $, $ 3(\pi^+\pi^-)$, $ 2(\pi^+\pi^-)2\pi^0$, and $ K^+K^-2(\pi^+\pi^-)$ are ... More

On the algebraic structure of isotropic generalized elasticity theoriesSep 16 2013In this paper the algebraic structure of the isotropic nth-order gradient elasticity is investigated. In the classical isotropic elasticity it is well-known that the constitutive relation can be broken down into two uncoupled relations between elementary ... More

Optical Communication Without PhotonsApr 30 2013I analyse a recent quantum communication protocol by Salih et al. that allows one to communicate without any particle carrying the information from the sender to the receiver. I show how this can equally be achieved using classical communication.

Bell inequalities: many questions, a few answersFeb 02 2007May 13 2007What can be more fascinating than {\it experimental metaphysics}, to quote one of Abner Shimony's enlightening expressions? Bell inequalities are at the heart of the study of nonlocality. I present a list of open questions, organised in three categories: ... More

Quantum cloning without signalingJan 06 1998Perfect Quantum Cloning Machines (QCM) would allow to use quantum nonlocality for arbitrary fast signaling. However perfect QCM cannot exist. We derive a bound on the fidelity of QCM compatible with the no-signaling constraint. This bound equals the fidelity ... More

Discussion on the spectral coherence between planetary, solar and climate oscillations: a reply to some critiquesNov 30 2014During the last few years a number of works have proposed that planetary harmonics regulate solar oscillations and the Earth climate. Herein I address some critiques. Detailed analysis of the data do support the planetary theory of solar and climate variation. ... More

Empirical analysis of the solar contribution to global mean air surface temperature changeDec 22 2009The solar contribution to global mean air surface temperature change is analyzed by using an empirical bi-scale climate model characterized by both fast and slow characteristic time responses to solar forcing: $\tau_1 =0.4 \pm 0.1$ yr, and $\tau_2= 8 ... More

Discussion on climate oscillations: CMIP5 general circulation models versus a semi empirical harmonic model based on astronomical cyclesOct 05 2013Power spectra of global surface temperature (GST) records reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC (2013), are ... More

Multi-scale harmonic model for solar and climate cyclical variation throughout the Holocene based on Jupiter-Saturn tidal frequencies plus the 11-year solar dynamo cycleMar 19 2012The sunspot record since 1749 is made of three major cycles (9.98, 10.9 and 11.86 yr). The side frequencies are related to the spring tidal period of Jupiter and Saturn (9.93 yr) and to the tidal sidereal period of Jupiter (11.86 yr). A simplified harmonic ... More

Testing an astronomically-based decadal-scale empirical harmonic climate model versus the IPCC (2007) general circulation climate modelsJan 06 2012We compare the performance of a recently proposed empirical climate model based on astronomical harmonics against all available general circulation climate models (GCM) used by the IPCC (2007) to interpret the 20th century global surface temperature. ... More

Applications of correlation inequalities to low density graphical codesSep 30 2005This contribution is based on the contents of a talk delivered at the Next-SigmaPhi conference held in Crete in August 2005. It is adressed to an audience of physicists with diverse horizons and does not assume any background in communications theory. ... More

Discussion on common errors in analyzing sea level accelerations, solar trends and global warmingMay 13 2013Errors in applying regression models and wavelet filters used to analyze geophysical signals are discussed: (1) multidecadal natural oscillations (e.g. the quasi 60-year Atlantic Multidecadal Oscillation (AMO), North Atlantic Oscillation (NAO) and Pacific ... More

Theoretical determination of etab's electromagnetic decay widthMay 28 2003We discuss the theoretical predictions for the two photon decay width of the pseudoscalar etab meson. Predictions from potential models are examined. It is found that various models are in good agreement with each other. Results for etab are also compared ... More

Stochastic spatial model of producer-consumer systems on the latticeJan 01 2013The objective of this paper is to give a rigorous analysis of a stochastic spatial model of producer-consumer systems that has been recently introduced by Kang and the author to understand the role of space in ecological communities in which individuals ... More

The naming game in language dynamics revisitedJan 01 2013This article studies a biased version of the naming game in which players located on a connected graph interact through successive conversations to bootstrap a common name for a given object. Initially, all the players use the same word B except for one ... More

On some errors related to the graduation of measuring instrumentsOct 11 2006Oct 31 2006The error on a real quantity Y due to the graduation of the measuring instrument may be represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator do not depend on the probability law of Y as soon ... More

Learning audio and image representations with bio-inspired trainable feature extractorsJan 02 2018Recent advancements in pattern recognition and signal processing concern the automatic learning of data representations from labeled training samples. Typical approaches are based on deep learning and convolutional neural networks, which require large ... More

Valeurs multiples de fonctions L de formes modulairesApr 07 2016This doctoral thesis studies the overlap between two well-known collections of results in number theory: the theory of periods and period polynomials of modular forms as developed by Eichler, Shimura and Manin and its extensions by K\"ohnen and Zagier, ... More

Conserved chiral currents on the boundary of 3D Maxwell theoryFeb 05 2019In this paper the 3D Maxwell theory with single-sided planar boundary is studied. As a consequence of the existence, on the boundary, of two Ward identities, we find two chiral conserved edge currents satisfying a Ka\c{c}-Moody algebra with central charge ... More

Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluidMar 29 2019We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized ... More

A new regularization possibility for the Boltzmann equation with soft potentialsDec 20 2007We consider a simplified Boltzmann equation: spatially homogeneous, two-dimensional, radially symmetric, with Grad's angular cutoff, and linearized around its initial condition. We prove that for a sufficiently singular velocity cross section, the solution ... More

Linear Algebra in the vector space of intervalsJun 28 2010In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with respect to the ... More

Gelfand pairs admit parabolic subgroupsFeb 25 2019Feb 28 2019Every Gelfand pair (G,K) admits a decomposition G=KP, where P<G is an amenable subgroup. In particular, the Furstenberg boundary of G is homogeneous. By parabolic induction, this also yields canonical pure spherical functions on G.

Translation of Dolbeault representations on reductive homogeneous spacesJan 02 2015Mar 07 2016We adapt techniques used in the study of the cubic Dirac operator on homogeneous reductive spaces to the Dolbeault operator on elliptic coadjoint orbits to prove that cohomologically induced representations have an infinitesimal character, that cohomological ... More

On the structure of self-complementary graphsAug 28 2013A \emph{self-complementary} graph is a graph isomorphic to its complement. An isomorphism between $G$ and its complement, viewed as a permutation of $V(G)$, is then called an \emph{antimorphism}. A \emph{skew partition} of $G$ is a partition of $V(G)$ ... More

On the coarsest topology preserving continuityOct 11 2006We study a topology on a space of functions, called sticking topology, with the property to be the weakest among the topologies preserving continuity. In suitable frameworks, this topology preserves borelianity, local integrability, right continuity and ... More

Connecting discrete and continuum dislocation mechanics: a non-singular spectral frameworkApr 03 2018In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To this end, an ... More

Least Squares Two-Point Function EstimationAug 16 2018The standard estimator for the two-point function of a homogeneous and isotropic random field is a special case of a larger class of least squares estimators that interpolate the function values. Using a different interpolation scheme, two-point function ... More

Entropy of Hilbert metrics and length spectrum of Hitchin representations in $\mathrm{PSL}(3,\mathbb{R})$Jun 15 2015Jul 28 2015We prove a sharp inequality between the Blaschke and Hilbert distance on a proper convex domain: for any two points $x$ and $y$, \[d^B(x,y) < d^H(x,y) +1.\] We obtain two interesting consequences: the first one is the volume entropy rigidity for Hilbert ... More

About Knop's action of the Weyl group on the set of the set of orbits of a spherical subgroup in the flag manifoldFeb 24 2004Let $G$ be a complex connected reductive algebraic group. Let $G/B$ denote the flag variety of $G$. Let $H$ be an algebraic subgroup of $G$ such that the set ${\bf H}(G/B)$ of the $H$-orbits in $G/B$ is finite ; $H$ is said to be {\it spherical}. These ... More

Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrationsMay 27 2008We carry on the study of Fourier integral operators of H{\"o}rmander's type acting on the spaces $(\mathcal{F}L^p)_{comp}$, $1\leq p\leq\infty$, of compactly supported distributions whose Fourier transform is in $L^p$. We show that the sharp loss of derivatives ... More

The Shift, properties and recommendations for practical useOct 24 2006Because the stochastic calculus yields rarely random variables with laws defined by explicit closed formulas, probabilistic numerical computations are done most often by simulation. The simulation by the shift, whose field of application is as wide as ... More

Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.MJul 08 2003We obtain a lower bound for the normalised height of a non-torsion hypersurface $V$ of a C.M. abelian variety $A$ which is a refinement of a precedent result. This lower bound is optimal in terms of the geometric degree of $V$, up to an absolute power ... More

Small resolutions of minuscule Schubert varietiesJan 06 2006Jan 31 2006In this paper, we describe on the one hand, all relative minimal models Y of a minuscule Schubert variety X using some combinatorics on quivers and we prove that the morphism from Y to X is small (in the sense of intersection cohomology). On the other ... More

Computing modular Galois representationsNov 07 2012Jun 12 2013We compute modular Galois representations associated with a newform $f$, and study the related problem of computing the coefficients of $f$ modulo a small prime $\ell$. To this end, we design a practical variant of the complex approximations method presented ... More

An $\varepsilon$-regularity result with mean curvature control for Willmore immersions and application to minimal bubblingApr 10 2019In this paper we prove a convergence result for sequences of Willmore immersions with simple minimal bubbles. To this end we replace the total curvature control in T. Rivi\`ere's proof of the $\varepsilon$-regularity for Willmore immersions by a control ... More

On the first Stiefel-Whitney class of moduli space for real rational stable curves in the projective spaceJul 18 2008Apr 21 2009Moduli space of genus zero stable maps to the projective three-space naturally carries a real structure such that the fixed locus is a moduli space for real rational spatial curves with real marked points. The latter is a normal projective real variety. ... More

Universally defining finitely generated subrings of global fieldsDec 11 2018It is a problem of general interest when a domain $R$ is first-order-definable within its field of fractions $K$ via a universal first-order formula. We show that this is the case when $K$ is a global field and $R$ is finitely generated. Hereby we recover ... More

A classification theorem for boundary 2-transitive automorphism groups of treesSep 16 2015Nov 30 2016Let $T$ be a locally finite tree all of whose vertices have valency at least $6$. We classify, up to isomorphism, the closed subgroups of $\mathrm{Aut}(T)$ acting $2$-transitively on the set of ends of $T$ and whose local action at each vertex contains ... More

Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebrasApr 13 2005Mar 13 2006We show that the different labelings of the crystal graph for irreducible highest weight $\mathcal{U}\_q (\hat{\mathfrak{sl}}\_e)$-modules lead to different labelings of the simple modules for non semisimple Ariki-Koike algebras by using Lusztig $a$-values. ... More

JMMO Fock space and Geck-Rouquier classification of simple modules for Hecke algebrasJan 18 2005This paper is a survey on the representation theory of Hecke algebras, Ariki-Koike algebras and connections with quantum group.

Crystal graphs of irreducible $U_v(\hat{sl}_e)$-modules of level two and Uglov bipartitionsJul 11 2006We give a simple description of the natural bijection between the set of FLOTW bipartitions and the set of Uglov bipartitions (which generalizes the set of Kleshchev bipartitions). These bipartitions, which label the crystal graphs of irreducible $\mathcal{U}\_v({\hat{\mathfrak{sl}}\_e})$-modules ... More

On the parametrization of the simple modules for Ariki-Koike algebras at roots of unityNov 03 2003Oct 14 2004Following ideas of Geck and Rouquier, we show that there exists a ``canonical basic set'' of Specht modules in bijection with the simple modules of Ariki-Koike algebras at roots of unity. Moreover, we determine the parametrization of this set and we give ... More

Derrida's random energy models. From spin glasses to the extremes of correlated random fieldsDec 02 2014These are notes for a mini-course on the extremes of correlated random fields which I gave in the spring 2013 in Marseille. The first chapter recalls the paradigmatic random energy models with finitely many scales introduced by B. Derrida in the context ... More

Differential calculus for Dirichlet forms : the measure-valued gradient preserved by imageOct 16 2006In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $\Gamma$ -- i.e. error structures -- and we are looking for an object related to $\Gamma$ which is linear ... More

Stochastic analysis of Bernoulli processesSep 18 2008Jun 01 2018These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable representation, anticipating ... More

An algorithm for the computation of the decomposition matrices for Ariki-Koike algebrasSep 16 2004We give a purely combinatorial algorithm for the computation of the decomposition matrices for Ariki-Koike algebras when the parameters are powers of the same root of unity. It generalizes the LLT algorithm.