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Bs Physics at LEP, SLD, and CDF: Delta m_s and Delta Gamma_sApr 27 2001The current status of the experimental knowledge of $\Bs$ meson physics is reviewed. Results from LEP and CDF on the width difference $\dgs$ are presented, the corresponding average is found to be in good agreement with the present theoretical estimation. ... More

Random Binary Mappings for Kernel Learning and Efficient SVMJul 19 2013Mar 28 2014Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image descriptors, as well ... More

Comment on "Ensemble Projection for Semi-supervised Image Classification"Aug 29 2014In a series of papers by Dai and colleagues [1,2], a feature map (or kernel) was introduced for semi- and unsupervised learning. This feature map is build from the output of an ensemble of classifiers trained without using the ground-truth class labels. ... More

Minimal Images in Deep Neural Networks: Fragile Object Recognition in Natural ImagesFeb 08 2019The human ability to recognize objects is impaired when the object is not shown in full. "Minimal images" are the smallest regions of an image that remain recognizable for humans. Ullman et al. 2016 show that a slight modification of the location and ... More

Herding Generalizes Diverse M -Best SolutionsNov 14 2016We show that the algorithm to extract diverse M -solutions from a Conditional Random Field (called divMbest [1]) takes exactly the form of a Herding procedure [2], i.e. a deterministic dynamical system that produces a sequence of hypotheses that respect ... More

Herding Generalizes Diverse M -Best SolutionsNov 14 2016Jan 30 2017We show that the algorithm to extract diverse M -solutions from a Conditional Random Field (called divMbest [1]) takes exactly the form of a Herding procedure [2], i.e. a deterministic dynamical system that produces a sequence of hypotheses that respect ... More

Foveation-based Mechanisms Alleviate Adversarial ExamplesNov 19 2015Jan 19 2016We show that adversarial examples, i.e., the visually imperceptible perturbations that result in Convolutional Neural Networks (CNNs) fail, can be alleviated with a mechanism based on foveations---applying the CNN in different image regions. To see this, ... More

Frobenius and Cartier algebras of Stanley-Reisner rings (II)Aug 26 2016Sep 29 2016It is known that the Frobenius algebra of the injective hull of the residue field of a complete Stanley-Reisner ring (i.e. a formal power series ring modulo a squarefree monomial ideal) can be only principally generated or infinitely generated as algebra ... More

Approximation results of Artin-Tougeron-type for general filtrations and for $C^r$-equationsJul 23 2019Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals, $\{I^j\}$, and to Noetherian rings. In this short note we extend several ... More

Revisiting the determinacy on New Keynesian ModelsDec 11 2017May 17 2018The goal of this paper is to shed light on the determinacy question that arises in New Keynesian models as result of a combination of several monetary policy rules; in these models, we provide conditions to guarantee existence and uniqueness of equilibrium ... More

Theory IIIb: Generalization in Deep NetworksJun 29 2018A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient descent. This ... More

SEEDS: Superpixels Extracted via Energy-Driven SamplingSep 16 2013Superpixel algorithms aim to over-segment the image by grouping pixels that belong to the same object. Many state-of-the-art superpixel algorithms rely on minimizing objective functions to enforce color ho- mogeneity. The optimization is accomplished ... More

Theory of Deep Learning III: explaining the non-overfitting puzzleDec 30 2017Jan 16 2018A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics associated ... More

On some local cohomology spectral sequencesFeb 06 2018Jul 17 2018We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived functors of ... More

Multi Web Audio Sequencer: Collaborative Music MakingMay 16 2019Recent advancements in web-based audio systems have enabled sufficiently accurate timing control and real-time sound processing capabilities. Numerous specialized music tools, as well as digital audio workstations, are now accessible from browsers. Features ... More

Issues in Electric-Magnetic DualitySep 20 2002Chapters : 1. Introduction to electric-magnetic duality 2. Classical duality in bosonic brane electrodynamics 3. Massless spin two gauge theory 4. Duality-symmetric actions and chiral forms 5. BRST quantization of duality-symmetric Maxwell's theory 6. ... More

A matrix phase for the phi^4 scalar field on the fuzzy sphereFeb 27 2004May 13 2004The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is also one of ... More

Grand Unification on Noncommutative SpacetimeMay 12 2006Mar 22 2007We compute the beta-functions of the standard model formulated on a noncommutative spacetime. If we assume that the scale for spacetime noncommutativity is of the order of 2.2 \times 10^{15} GeV we find that the three gauge couplings of the standard model ... More

Quantum Electrodynamics on Noncommutative SpacetimeApr 05 2006Mar 22 2007We propose a new method to quantize gauge theories formulated on a canonical noncommutative spacetime with fields and gauge transformations taken in the enveloping algebra. We show that the theory is renormalizable at one loop and compute the beta function ... More

Symmetries, Microcausality and Physics on Canonical Noncommutative SpacetimeMay 03 2006May 09 2006In this paper we describe how to implement symmetries on a canonical noncommutative spacetime. We focus on noncommutative Lorentz transformations. We then discuss the structure of the light cone on a canonical noncommutative spacetime and show that field ... More

What are the Bounds on Space-Time Noncommutativity?Jan 14 2004In this article we consider the bounds on the noncommutative nature of space-time. We argue that these bounds are extremely model dependent. In the only phenomenologically viable framework, i.e. when the fields are taken to be in the enveloping of the ... More

Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: a surveyJul 16 2015Oct 19 2015We present the proof of several inequalities using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP estimate. First, we give a new and simple proof of a lower bound of Berestycki, Nirenberg, and Varadhan concerning the ... More

Characterization of $n$-rectifiability in terms of Jones' square function: Part IJan 07 2015Jan 19 2015In this paper it is shown that if $\mu$ is a finite Radon measure in $\mathbb R^d$ which is $n$-rectifiable and $1\leq p\leq 2$, then $$\int_0^\infty \beta_{\mu,p}^n(x,r)^2\,\frac{dr}r<\infty \quad {for $\mu$-a.e. $x\in\mathbb R^d$,}$$ where $$\beta_{\mu,p}^n(x,r) ... More

Diffractive Rho Meson Electroproduction at High Q^2 and High |t|Jul 02 2002The electroproduction of rho mesons is studied at HERA with the H1 detector at high Q^2 and high |t|. Cross sections are measured as a function of Q^2, W and t. The W dependence of the gamma*-p cross section is observed to increase with Q^2 from values ... More

Canonical bases of higher-level q-deformed Fock spacesJun 09 2006We show that the transition matrices between the standard and the canonical bases of infinitely many weight subspaces of the higher-level q-deformed Fock spaces are equal.

Hadronic and rare B decays with the BaBar and Belle experimentsMay 16 2012We review recent experimental results on Bd and Bs mesons decays by the BaBar and Belle experiments. These include measurements of the color-suppressed decays B0bar to D(*)0h0, h0=pi0, eta, etaprime, omega, observation of the baryonic decay B0bar to Lambdac+ ... More

The mutual singularity of harmonic measure and Hausdorff measure of codimension smaller than oneJan 23 2019Jan 26 2019Let $\Omega\subset\mathbb R^{n+1}$ be open and let $E\subset \partial\Omega$ with $0<H^s(E)<\infty$, for some $s\in(n,n+1)$, satisfy a local capacity density condition. In this paper it is shown that the harmonic measure cannot be mutually absolutely ... More

A conjecture for q-decomposition matrices of cyclotomic v-Schur algebrasMay 18 2005Apr 27 2006The Jantzen sum formula for cyclotomic v-Schur algebras yields an identity for some q-analogues of the decomposition matrices of these algebras. We prove a similar identity for matrices of canonical bases of higher-level Fock spaces. We conjecture then ... More

Natural generalized inverse and core of an element in semigroups, rings and Banach and Operator AlgebrasMar 16 2012Using the recent notion of inverse along an element in a semigroup, and the natural partial order on idempotents, we study bicommuting generalized inverses and define a new inverse called natural inverse, that generalizes the Drazin inverse in a semigroup, ... More

Dualité de Cartier et modules de BreuilNov 16 2005Let O\_K be a complete discrete valuation ring. Denote by K its fractions field and by k its residue field. Assume that k is of characteristic p>0 and perfect. Breuil gives an anti-equivalence between the category of finite flat O\_K-group schemes killed ... More

Sur la classification de quelques phi-modules simplesJul 10 2008This note is an appendix to a preprint by E. Hellmann. We give a complete classification of simple objects of the category of vector spaces D over K = Fpbar((u)) equipped with an endomorphism phi whose image generates D and that are semi-linear with respect ... More

Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indicesJul 31 2003We prove that, the initial value problem associated to u_{t} + i\alphau_{xx} + \beta u_{xxx} + i\gamma |u|^{2}u = 0, x,t \in R, is locally well-posed in Sobolev spaces H^{s} for s>-1/4.

Uniform measures and uniform rectifiabilityOct 02 2013Dec 16 2014In this paper it is shown that if $\mu$ is an n-dimensional Ahlfors-David regular measure in $R^d$ which satisfies the so-called weak constant density condition, then $\mu$ is uniformly rectifiable. This had already been proved by David and Semmes in ... More

The Fano surface of the Klein cubic threefoldJan 27 2010We prove that the Klein cubic threefold $F$ is the only smooth cubic threefold which has an automorphism of order 11. We compute the period lattice of the intermediate Jacobian of $F$ and study its Fano surface $S$. We compute also the set of fibrations ... More

Elliptic curve configurations on Fano surfacesApr 11 2008Jan 27 2010The elliptic curves on a surface of general type constitute an obstruction for the cotangent sheaf to be ample. In this paper, we give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic threefold. That ... More

Characterization of $n$-rectifiability in terms of Jones' square function: Part IJan 07 2015Nov 12 2017In this paper it is shown that if $\mu$ is a finite Radon measure in $\mathbb R^d$ which is $n$-rectifiable and $1\leq p\leq 2$, then $$\int_0^\infty \beta_{\mu,p}^n(x,r)^2\,\frac{dr}r<\infty \quad {for $\mu$-a.e. $x\in\mathbb R^d$,}$$ where $$\beta_{\mu,p}^n(x,r) ... More

Fibre derivatives: some applications to singular lagrangiansJul 27 2000The fibre derivative of a bundle map is studied in detail. In the particular case of a real function, several constructions useful to study singular lagrangians are presented. Some applications are given; in particular, a geometric construction useful ... More

Higher spin algebras as higher symmetriesApr 06 2007Aug 23 2007The exhaustive study of the rigid symmetries of arbitrary free field theories is motivated, along several lines, as a preliminary step in the completion of the higher-spin interaction problem in full generality. Some results for the simplest example (a ... More

Clusters, Graphs, and Networks for Analysing Internet-Web-Supported Communication within a Virtual CommunityJul 10 2007The proposal is to use clusters, graphs and networks as models in order to analyse the Web structure. Clusters, graphs and networks provide knowledge representation and organization. Clusters were generated by co-site analysis. The sample is a set of ... More

Geometry of the Feigenbaum mapNov 15 1997Aug 11 1998We show that the Feigenbaum-Cvitanovic equation can be interpreted as a linearizing equation, and the domain of analyticity of the Feigenbaum fixed point of renormalization as a basin of attraction. There is a natural decomposition of this basin which ... More

Asymptotically safe weak interactionsDec 26 2010We emphasize that the electroweak interactions without a Higgs boson are very similar to quantum general relativity. The Higgs field could just be a dressing field and might not exist as a propagating particle. In that interpretation, the electroweak ... More

Very Light Cosmological Scalar Fields from a Tiny Cosmological ConstantMay 03 2007Jun 28 2007We discuss a mechanism which generates a mass term for a scalar field in an expanding universe. The mass of this field turns out to be generated by the cosmological constant and can be naturally small if protected by a conformal symmetry which is however ... More

Softening the Naturalness ProblemFeb 07 2003Mar 17 2003It was observed by Veltman a long time ago that a special value for the Higgs boson mass could lead to a cancellation of the quadratically divergent corrections to the Higgs boson's squared mass which appear at one loop. We present a class of low energy ... More

Essential spectrum of local multi-trace boundary integral operatorsAug 03 2015Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does ... More

Quantum Mechanics, Gravity and Modified Quantization RelationsApr 29 2015In this paper we investigate a possible energy scale dependence of the quantization rules and in particular, from a phenomenological point of view, an energy scale dependence of an effective $\hbar$. We set a bound on the deviation from the value of $\hbar$ ... More

A new light on the breaking of uniaxial symmetry in nematicsJul 01 2013Sep 18 2013Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. For an arbitrary form of the bulk energy density, we show that energy minimizers among uniaxially symmetric configurations ... More

Random matrix over a DVR and LU factorizationDec 03 2012Let R be a discrete valuation ring (DVR) and K be its fraction field. If M is a matrix over R admitting a LU decomposition, it could happen that the entries of the factors L and U do not lie in R, but just in K. Having a good control on the valuations ... More

Hadronic B Decays to Charm and Charmonium With the BaBar ExperimentSep 17 2008Oct 17 2008The {\it BaBar} experiment has recorded the decays of more than 465$\times 10^6 B\bar{B}$ pairs since 1999, and is reaching an unprecedented precision in the measurement of hadronic B decays. The following results are presented: tests of QCD factorization ... More

Renormalized stress tensor in one-bubble spacetimesApr 08 1999We compute the two-point function and the renormalized expectation value of the stress tensor of a quantum field interacting with a nucleating bubble. Two simple models are considered. One is the massless field in the Vilenkin-Ipser-Sikivie spacetime ... More

Painleve's problem and the semiadditivity of analytic capacityApr 02 2002Let $\gamma(E)$ be the analytic capacity of a compact set $E$ and let $\gamma_+(E)$ be the capacity of $E$ originated by Cauchy transforms of positive measures. In this paper we prove that $\gamma(E)\approx\gamma_+(E)$ with estimates independent of $E$. ... More

A new proof of the boundedness results for stable solutions to semilinear elliptic equationsJul 11 2019We consider the class of stable solutions to semilinear equations $-\Delta u=f(u)$ in a bounded smooth domain of $\mathbb{R}^n$. In dimensions $n\le 4$, an interior a priori $L^\infty$ bound for stable solutions is known to hold for all $C^1$ nonlinearities ... More

Requirements Management for Service Providers: the Case of Services for CitizensJan 19 2013Take the Internet of Things, a piece of cloud computing, a handful of smart cities, don't forget social platforms, flavour it with mobile technologies and ever-changing environments, shake it up and... voila! What a wonderful service! Oops! Wait a minute, ... More

Representations semi-stables de torsion dans le cas peu ramifieJul 17 2004Oct 24 2004Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laffaille theory gives a description of the torsion crystalline Z_p-representations of the absolute Galois group of K (p denotes the characteristic of the residual field). ... More

On concrete models for local operator spacesOct 28 2008In this short note, we propose a concrete analogue of the space $\cL(H)$ for local operator spaces, the multinormed $C^*$-algebra $\displaystyle\prod_{\alpha} \cL(H_{\alpha})$.

Courants dynamiques pluripolairesMar 08 2010We show the existence of birational self-maps f of P^k which are algebraically stable with algebraic degree d, for which there is a unique positive closed (1,1) current T satisfying f^*T=d T and ||T||=1 and for which the current T gives total mass to ... More

On the bit-size of non-radical triangular setsOct 17 2017We present upper bounds on the bit-size of coefficients of non-radical lexicographical Groebner bases in purely triangular form (triangular sets) of dimension zero. This extends a previous work [Dahan-Schost, Issac'2004], constrained to radical triangular ... More

Cosmological Evolution of the Higgs Boson's Vacuum Expectation ValueJul 21 2017We point out that the expansion of the universe leads to a cosmological time evolution of the vacuum expectation of the Higgs boson. Within the standard model of particle physics, the cosmological time evolution of the vacuum expectation of the Higgs ... More

Improved Low-qubit Hidden Shift AlgorithmsJan 31 2019Hidden shift problems are relevant to assess the quantum security of various cryptographic constructs. Multiple quantum subexponential time algorithms have been proposed. In this paper, we propose some improvements on a polynomial quantum memory algorithm ... More

Rigid covariance, equivalence principle and Fermi rigid coordinates:gravitational wavesJul 17 2018Jan 21 2019For a given space-time and for an arbitrary time-like geodesic, we analyze the conditions for the construction of Fermi coordinates so that they are also rigid covariant. We then apply these conditions to linear plane gravitational waves.

Computations with p-adic numbersJan 24 2017This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts: first, we ... More

The Dual Standard Model and the 750 GeV Events at the LHCApr 21 2016The aim of this short paper is to discuss the recently observed excess at 750 GeV by both CMS and ATLAS in the light of the dual standard model. Within this framework it is natural to introduce neutral spin 0 and/or spin 2 $SU(2)$ glue mesons which could ... More

Principal values for Riesz transforms and rectifiabilityAug 01 2007Let $E\subset R^d$ with $H^n(E)<\infty$, where H^n stands for the $n$-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit $$\lim_{\ve\to0}\int_{y\in E:|x-y|>\ve} \frac{x-y}{|x-y|^{n+1}} dH^n(y)$$ exists ... More

A new proof of the boundedness results for stable solutions to semilinear elliptic equationsJul 11 2019Jul 12 2019We consider the class of stable solutions to semilinear equations $-\Delta u=f(u)$ in a bounded smooth domain of $\mathbb{R}^n$. Since 2010 an interior a priori $L^\infty$ bound for stable solutions is known to hold in dimensions $n \leq 4$ for all $C^1$ ... More

Rectifiability of measures and the $β_p$ coefficientsAug 07 2017Jan 19 2018In some former works of Azzam and Tolsa it was shown that $n$-rectifiability can be characterized in terms of a square function involving the David-Semmes $\beta_2$ coefficients. In the present paper we construct some counterexamples which show that a ... More

A priori estimates for solutions of a nonlinear dispersive equationAug 24 2005Mar 19 2010This paper has been withdrawn by the author due to a crucial error.

Sharp global well-posedness for a higher order Schrödinger equationApr 28 2005Apr 30 2005Using the theory of almost conserved energies and the ``I-method'' developed by Colliander, Keel, Staffilani, Takaoka and Tao, we prove that the initial value problem for a higher order Schr\"odinger equation is globally well-posed in Sobolev spaces of ... More

Residues of skew rational functions and linearized Goppa codesAug 22 2019This paper constitutes a first attempt to do analysis with skew polynomials. Precisely, our main objective is to develop a theory of residues for skew rational functions (which are, by definition, the quotients of two skew polynomials). We prove in particular ... More

Sobolev and isoperimetric inequalities with monomial weightsOct 16 2012Apr 20 2015We consider the monomial weight $|x_1|^{A_1}...|x_n|^{A_n}$ in $\mathbb R^n$, where $A_i\geq0$ is a real number for each $i=1,...,n$, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight. They are the analogue ... More

Regularity of stable solutions up to dimension 7 in domains of double revolutionFeb 06 2012We consider the class of semi-stable positive solutions to semilinear equations $-\Delta u=f(u)$ in a bounded domain $\Omega\subset\mathbb R^n$ of double revolution, that is, a domain invariant under rotations of the first $m$ variables and of the last ... More

Virial expansion with Feynman diagramsSep 22 2011We present a field theoretic method for the calculation of the second and third virial coefficients b2 and b3 of 2-species fermions interacting via a contact interaction. The method is mostly analytic. We find a closed expression for b3 in terms of the ... More

Estimation des dimensions de certaines variétés de KisinMay 13 2010Jan 30 2011In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the dimension we ... More

The Transverse SpinJul 25 2002Sep 30 2002Contents : 1. Pre-history 2. Transversity versus helicity 3. The massless limit. "Cardan" and "see-saw" transformations 4. Transversity distribution delta q(x). The diquark spectator model 5. Soffer inequality 6. Tensor charge sum rule 7. t-channel analysis ... More

Construction optimale d'images bolometriques - Contribution a l'etude du milieu interstellaire et du rayonnement fossileOct 02 2002This work takes part of the development of far-infrared and millimeter astrophysics. We have worked on the data processing and analysis in the fields of the Galactic interstellar medium, through the dust thermal emission, and cosmology through the observation ... More

Iterative map-making methods for Cosmic Microwave Background data analysisSep 27 2001The map-making process of Cosmic Microwave Background data involves linear inversion problems which cannot be performed by a brute force approach for the large timelines of most modern experiments. We present optimal iterative map-making methods, both ... More

Planck Length and CosmologyApr 11 2007We show that an unification of quantum mechanics and general relativity implies that there is a fundamental length in Nature in the sense that no operational procedure would be able to measure distances shorter than the Planck length. Furthermore we give ... More

Radiative Lepton Decays and the Substructure of LeptonsAug 08 2001The leptons are viewed as composite objects, exhibiting anomalous magnetic moments and anomalous flavor-changing transition moments. The decay \mu \to e \gamma is expected to occur with a branching ratio of the same order as the present experimental limit. ... More

Equivalence Principle and the Gauge Hierarchy ProblemAug 21 2007Mar 19 2008We show that the gauge hierarchy problem can be solved in the framework of scalar-tensor theories of gravity very much in the same way as it is solved in the Randall-Sundrum scenario. Our solution involves a fine-tuning of the gravitational sector. However ... More

On the Precision of a Length MeasurementJan 09 2007We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the discreteness of spacetime ... More

Space-Time Symmetries of Noncommutative SpacesNov 15 2004Apr 13 2005We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under noncommutative Lorentz ... More

Hyperelliptic curves covering an elliptic curve twiceMar 18 2013We show that for any elliptic curve (with j invariant not 0 or 1728) over any field of characteristic different from 2 and 3, there exists an hyperelliptic curve H of genus 5 with two independent maps to the given elliptic curve. We also show that, if ... More

Handel's fixed point theorem revisitedAug 10 2012Michael Handel proved in [7] the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. ... More

BMO, H^1, and Calderon-Zygmund operators for non doubling measuresFeb 18 2000Given a Radon measure $\mu$ on $R^d$, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when $\mu$ is doubling remain valid for the space BMO introduced in this paper, ... More

Polynomial parametrizations of length $4$ Büchi sequencesAug 18 2010B\"uchi's problem asks whether there exists a positive integer $M$ such that any sequence $(x_n)$ of at least $M$ integers, whose second difference of squares is the constant sequence $(2)$, satisifies $x_n^2=(x+n)^2$ for some $x\in\Z$. A positive answer ... More

Classes of semigroups modulo Green's relation HMar 16 2012Inverses semigroups and orthodox semigroups are either defined in terms of inverses, or in terms of the set of idempotents E(S). In this article, we study analogs of these semigroups defined in terms of inverses modulo Green's relation H, or in terms ... More

Simultaneous estimation of the mean and the variance in heteroscedastic Gaussian regressionJul 16 2008Dec 30 2008Let $Y$ be a Gaussian vector of $\mathbb{R}^n$ of mean $s$ and diagonal covariance matrix $\Gamma$. Our aim is to estimate both $s$ and the entries $\sigma_i=\Gamma_{i,i}$, for $i=1,...,n$, on the basis of the observation of two independent copies of ... More

Bounded negativity, Miyaoka-Sakai inequality and elliptic curve configurationsNov 25 2014Mar 14 2015Similarly to the linear Harbourne constant recently defined, we study the elliptic $H$-constants of $\mathbb{P}^{2}$ and Abelian surfaces. We exhibit configurations of smooth plane cubic curves whose Harbourne index is arbitrarily close to $-4$. As a ... More

Squares in arithmetic progression over number fieldsSep 09 2009We show that there exists an upper bound for the number of squares in arithmetic progression over a number field that depends only on the degree of the field. We show that this bound is 5 for quadratic fields, and also that the result generalizes to $k$-powers ... More

Abelian varieties with many endomorphisms and their absolutely simple factorsFeb 04 2011We characterize the abelian varieties arising as absolutely simple factors of GL2-type varieties over a number field k. In order to obtain this result, we study a wider class of abelian varieties: the k-varieties A/k satisfying that $\End_k^0(A)$ is a ... More

$n+1$ formalism of $f($Lovelock$)$ gravityDec 09 2017May 02 2018In this note we perform the $n+1$ decomposition, or Arnowitt Deser Misner (ADM) formulation of $f($Lovelock$)$ gravity theory. The hamiltonian form of Lovelock gravity was known since the work of C. Teitelboim and J. Zanelli in 1987, but this result had ... More

Fano surfaces with 12 or 30 elliptic curvesJan 27 2010Feb 05 2010Curves of low genus on a surface carry important informations on that surface. We study the Fano surfaces of lines of cubic threefolds that contain 12 or 30 elliptic curves. We determine their Picard number and compute a basis of the N\'eron-Severi group ... More

Calderon-Zygmund capacities and Wolff potentials on Cantor setsJan 18 2010Jan 31 2013We show that, for some Cantor sets in R^d, the capacity g_s associated to the s-dimensional Riesz kernel x/|x|^{s+1} is comparable to the capacity C_{2(d-s)/3,3/2} from non linear potential theory. It is an open problem to show that, when s is positive ... More

Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonalityMay 07 2008In this paper we study some questions in connection with uniform rectifiability and the $L^2$ boundedness of Calderon-Zygmund operators. We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients which are ... More

On generalized Kummer surfaces and the orbifold Bogomolov-Miyaoka-Yau inequalityAug 30 2017Dec 29 2017A generalized Kummer surface $X=Km(T,G)$ is the resolution of a quotient of a torus $T$ by a finite group of symplectic automorphisms $G$. We complete the classification of generalized Kummer surfaces by studying the two last groups which have not been ... More

Bifurcation analysis in a frustrated nematic cellOct 25 2013Nov 13 2013Using Landau-de Gennes theory to describe nematic order, we study a frustrated cell consisting of nematic liquid crystal confined between two parallel plates. We prove the uniqueness of equilibrium states for a small cell width. Letting the cell width ... More

An alternative view on the electroweak interactionsAug 23 2010We discuss an alternative to the Higgs mechanism which leads to gauge invariant masses for the electroweak bosons. The key idea is to reformulate the gauge invariance principle which, instead of being applied as usual at the level of the action, is applied ... More

Yang-Mills Theories on Noncommutative Space-TimeJan 27 2004We describe some recent progress in our understanding of Yang-Mills theories formulated on noncommutative spaces and in particular how to formulate the standard model on such spaces.

A review of Quantum Gravity at the Large Hadron ColliderMay 11 2010The aim of this article is to review the recent developments in the phenomenology of quantum gravity at the Large Hadron Collider. We shall pay special attention to four-dimensional models which are able to lower the reduced Planck mass to the TeV region ... More

Minimal Grand Unification Model in an Anthropic LandscapeJun 28 2004It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification ... More

Virtual Black Holes, Remnants and the Information ParadoxDec 19 2014We revisit the question of the contributions of Planckian quantum black holes in general and of remnants in particular to low energy physics observables. As long as quantum gravity preserves the symmetries of the low energy effective field theory, we ... More

On the 1+3 Formalism in General RelativityMay 24 2014We present in this paper the formalism for the splitting of a four-dimensional Lorentzian manifold by a set of time-like integral curves. Introducing the geometrical tensors characterizing the local spatial frames induced by the congruence (namely, the ... More