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LASER: Lightweight And SEcure Remote keyless entry protocol (Extended version)May 14 2019Since Remote Keyless Entry (RKE) systems started to be widely used, several vulnerabilities in their protocols have been found. Attacks such as jamming-and-replay attacks and relay attacks are still effective against most recent RKE systems, even when ... More

LASER: Lightweight And SEcure Remote keyless entry protocol (Extended version)May 14 2019May 15 2019Since Remote Keyless Entry (RKE) systems started to be widely used, several vulnerabilities in their protocols have been found. Attacks such as jamming-and-replay attacks and relay attacks are still effective against most recent RKE systems, even when ... 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

Weighted norm inequalities for Calderon-Zygmund operators without doubling conditionsJan 23 2001Oct 17 2011In this paper we develop a kind of A_p theory for Calderon-Zygmund operators in a non-homogeneous setting. Let \mu be a Borel measure on \R^d which may be non doubling. The only condition that \mu must satisfy is \mu(B(x,r))\leq Cr^n for all x\in\R^d, ... More

Littlewood-Paley theory and the T(1) theorem with non doubling measuresJun 05 2000Let $\mu$ be a Borel measure on $R^d$ which may be non doubling. The only condition that $\mu$ must satisfy is $\mu(B(x,r))\leq C r^n$ for all $x\in R^d$, $r>0$, and for some fixed $0<n\leq d$. In this paper, we develop Littlewood-Paley theory for functions ... 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

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

Boundedness of stable solutions to semilinear elliptic equations: a surveyApr 20 2017This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known $L^{\infty}$ estimates that hold for all nonlinearities. Such estimates are known to hold up to dimension ... More

What determines the ultimate precision of a quantum computer?Feb 24 2017Apr 12 2019A quantum error correction (QEC) code uses $N_{\rm c}$ quantum bits to construct one "logical" quantum bits of better quality than the original "physical" ones. QEC theory predicts that the failure probability $p_L$ of logical qubits decreases exponentially ... More

Barycentric Subspace Analysis on ManifoldsJul 11 2016Oct 04 2017This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the ... More

Expected number of critical points of random holomorphic sections over complex projective spaceJan 24 2017Jan 25 2017We study the high dimensional asymptotics of the expected number of critical points of a given Morse index of Gaussian random holomorphic sections over complex projective space. We explicitly compute the exponential growth rate of the expected number ... More

Phragmén's sequential method with a variance criterionNov 18 2016A variant of Phragm\'en's method for proportional representation via approval voting is briefly explored. Instead of D'Hondt's rule, this variant generalizes Sainte-Lagu\"e's rule.

On the number of terms in the Lovelock productsNov 23 2018Mar 22 2019In this short note we wonder about the explicit expression of the expanding of the $p$-th Lovelock product. We use the 1990's works of S. A. Fulling et al. on the symmetries of the Riemann tensor, and we show that the number of independent scalars appearing ... More

Measuring precise radial velocities on individual spectral lines. I. Validation of the method and application to mitigate stellar activitySep 05 2018Oct 22 2018Stellar activity is the main limitation to the detection of Earth-twins using the RV technique. Despite many efforts in trying to mitigate the effect of stellar activity using empirical and statistical techniques, it seems that we are facing an obstacle ... More

Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theoryMay 26 2019For nonnegative even kernels $K$, we consider the $K$-nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated $K$-nonlocal mean curvature equation in an open set $\Omega\subset\mathbb{R}^n$, ... More

On Searches for Gravitational Dark Matter with Quantum SensorsJul 12 2019The possibility of searching for dark matter with quantum sensors has recently received a lot of attention. In this short paper, we discuss the possibility of searching for gravitational dark matter with quantum sensors and identify a very narrow window ... More

Curvature effects on the empirical mean in Riemannian and affine Manifolds: a non-asymptotic high concentration expansion in the small-sample regimeJun 18 2019The asymptotic concentration of the Fr{\'e}chet mean of IID random variables on a Rieman-nian manifold was established with a central limit theorem by Bhattacharya \& Patrangenaru (BP-CLT) [6]. This asymptotic result shows that the Fr{\'e}chet mean behaves ... 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

Variance optimal hedging with application to Electricity marketsNov 10 2017Aug 28 2018In Electricity markets, illiquidity, transaction costs and market price characteristics prevent managers to replicate exactly contracts. A residual risk is always present and the hedging strategy depends on a risk criterion chosen. We present an algorithm ... 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

Primordial Black Holes and a Large Hidden SectorJul 17 2010Nov 01 2010In this note we point out that primordial black holes could be much shorter lived than usually assumed if there is a large hidden sector of particles that only interacts gravitationally with the particles of the standard model. The observation of the ... More

Cosmological Constant and Noncommutative SpacetimeOct 19 2005We show that the cosmological constant appears as a Lagrange multiplier if nature is described by a canonical noncommutative spacetime. It is thus an arbitrary parameter unrelated to the action and thus to vacuum fluctuations. The noncommutative algebra ... More

An algorithm for computing the canonical bases of higher-level q-deformed Fock spacesSep 14 2006Dec 12 2006We derive a straightening-free algorithm that computes the canonical bases of any higher-level q-deformed Fock space.

Barycentric Subspace Analysis on ManifoldsJul 11 2016This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and more general type of family of subspaces in manifolds that we call barycen-tric subspaces. They are implicitly defined ... More

Determination of the best optimal estimation parameters for validation of infrared hyperspectral sounding retrievalsMay 14 2012The availability of hyperspectral infrared remote sensing instruments, like AIRS and IASI, on board of Earth observing satellites opens the possibility of obtaining high vertical resolution atmospheric profiles. We present an objective and simple technique ... More

Uniaxial symmetry in nematic liquid crystalsFeb 05 2014Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. We show that the uniaxial symmetry constraint is very restrictive and can in general not be satisfied, except in very ... More

Quantum black holes and effective quantum gravity approachesDec 21 2014This is the text of the invited talk I have given at the Karl Schwarzschild Meeting in Frankfurt in 2013.

Dispersive and dissipative effects in quantum field theory in curved space-time to model condensed matter systemsNov 06 2014The two main predictions of quantum field theory in curved space-time, namely Hawking radiation and cosmological pair production, have not been directly tested and involve ultra high energy configurations. As a consequence, they should be considered with ... More

The Lightest of Black HolesOct 10 2014In this paper we consider general relativity in the large $N$ limit, where $N$ stands for the number of particles in the model. Studying the resummed graviton propagator, we propose to interpret its complex poles as black hole precursors. Our main result ... More

On lexicographic Groebner bases of radical ideals in dimension zero: interpolation and structureJul 17 2012Oct 01 2012Due to the elimination property held by the lexicographic monomial order, the corresponding Groebner bases display strong structural properties from which meaningful informations can easily be extracted. We study these properties for radical ideals of ... More

Comments on higher-spin symmetriesJul 28 2008Nov 14 2010The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the torsion constraints, ... More

Représentations galoisiennes p-adiques et (phi,tau)-modulesOct 23 2010Oct 01 2012Let p be an odd prime number and K be a p-adic field. In this paper, we develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the p-cyclotomic extension by the extension K_infty obtained by adding to K a compatible system of p^n-th ... More

Conjecture de l'inertie modérée de SerreSep 29 2005Let K be a local field of mixte characteristics. We assume that the residue field is perfect. Let X\_K be a proper smooth scheme over K admitting an integer model X which is proper and semi-stable. In this article, we prove a period isomorphism linking ... More

About Inverse 3-SATMar 18 2013Aug 26 2013The Inverse 3-SAT problem is known to be coNP Complete. This article shows a new interesting way to solve directly the problem by using closure under resolution and partial assignment properties. An algorithm is proposed which lets solve the (co)Inverse ... More

Genus 2 curve configurations on Fano surfacesFeb 24 2010We study the configurations of genus 2 curves on the Fano surfaces of cubic threefolds. We establish a link between some involutive automorphisms acting on such a surface S and genus 2 curves on S. We give a partial classification of the Fano surfaces ... More

Schémas en groupes et poids de Diamond-SerreMay 09 2007This note is a correction of (statement and proof of) proposition 3.3.1 of Toby Gee's preprint intitled *On the weights of mod p Hilbert modular forms*. The aim is to compare Galois representations arising from extensions of some group schemes (over the ... More

Adaptive sparse grids for time dependent Hamilton-Jacobi-Bellman equations in stochastic controlAug 19 2014We introduce some sparse grids interpolations used in Semi-Lagrangian schemes for linear and fully non-linear diffusion Hamilton Jacobi Bellman equations arising in stochastic control. We prove that the method introduced converges toward the viscosity ... More

Monte Carlo for high-dimensional degenerated Semi Linear and Full Non Linear PDEsMay 14 2018We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not suffer from the so called curse of dimensionality and it can be used to solve problems that were out of ... More

Trivial points on towers of curvesJan 12 2012We define and study trivial points on towers of curves over number fields, and we show their finiteness in some cases. We relate these to the unboundeness of the gonality of the curves, which we show under some hypothesis. The problem is related to recent ... More

An introduction to p-adic period ringsAug 22 2019This paper is the augmented notes of a course I gave jointly with Laurent Berger in Rennes in 2014. Its aim was to introduce the periods rings B crys and B dR and state several comparison theorems between{\'e}tale and crystalline or de Rham cohomologies ... More

Rectifiable measures, square functions involving densities, and the Cauchy transformAug 29 2014Jan 31 2015This paper is devoted to the proof of two related results. The first one asserts that if $\mu$ is a Radon measure in $\mathbb R^d$ satisfying $$\limsup_{r\to 0} \frac{\mu(B(x,r))}{r}>0\quad \text{ and }\quad \int_0^1\left|\frac{\mu(B(x,r))}{r} - \frac{\mu(B(x,2r))}{2r}\right|^2\,\frac{dr}r< ... 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

A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decompositionFeb 25 2000Given a doubling measure $\mu$ on $R^d$, it is a classical result of harmonic analysis that Calderon-Zygmund operators which are bounded in $L^2(\mu)$ are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes ... 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

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

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

The Asset Liability Management problem of a nuclear operator : a numerical stochastic optimization approachNov 15 2016We numerically study an Asset Liability Management problem linked to the decommissioning of French nuclear power plants. We link the risk aversion of practitioners to an optimization problem. Using different price models we show that the optimal solution ... 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

Jump formulas for singular integrals and layer potentials on rectifiable setsNov 19 2018Nov 28 2018In this paper the jump formulas for the double layer potential and other singular integrals are proved for arbitrary rectifiable sets, by defining suitable non-tangential limits. The arguments are quite straightforward and only require some Calder\'on-Zygmund ... 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

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