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Effects of high vs moderate-intensity training on neuroplasticity and functional recovery after focal ischemiaFeb 08 2018Background and Purpose: This study was designed to compare the effects of high-intensity interval training (HIT) and moderate-intensity continuous training (MOD) on functional recovery and cerebral plasticity during the first 2 weeks following cerebral ... More

Normal numbers from Steinhaus viewpointJun 22 2008In this paper we recall a non-standard construction of the Borel sigma-algebra B in [0,1] and construct a family of measures (in particular, Lebesgue measure) in B by a completely non-topological method. This approach, that goes back to Steinhaus, in ... More

First-order expansion for the Dirichlet eigenvalues of an elliptic system with oscillating coefficientsNov 10 2011This paper is concerned with the homogenization of the Dirichlet eigenvalue problem, posed in a bounded domain $\Omega\subset\mathbb R^2$, for a vectorial elliptic operator $-\nabla\cdot A^\epsilon(\cdot)\nabla$ with $\epsilon$-periodic coefficients. ... More

Properties of the Solomon homomorphismFeb 25 2003Let W be a finite Coxeter group. In this paper, we show that the properties of the Solomon algebra homomorphism Phi (from the Solomom descent algebra to the algebra of class functions) are strongly related to enumerative results: certain joint statistics ... More

Maximal f-vectors of Minkowski sums of large numbers of polytopesJan 31 2010It is known that in the Minkowski sum of $r$ polytopes in dimension $d$, with $r<d$, the number of vertices of the sum can potentially be as high as the product of the number of vertices in each summand. However, the number of vertices for sums of more ... More

Temperature-extended Jarzynski relation: Application to the numerical calculation of the surface tensionFeb 02 2007Apr 05 2007We consider a generalization of the Jarzynski relation to the case where the system interacts with a bath for which the temperature is not kept constant but can vary during the transformation. We suggest to use this relation as a replacement to the thermodynamic ... More

On universality in aging ferromagnetsApr 01 2004Jun 17 2004This work is a contribution to the study of universality in out-of-equilibrium lattice models undergoing a second-order phase transition at equilibrium. The experimental protocol that we have chosen is the following: the system is prepared in its high-temperature ... More

Bernoulli coding map and almost sure invariance principle for endomorphisms of $\mathbb{P}^k$Dec 04 2007Dec 06 2008Let $f$ be an holomorphic endomorphism of $\mathbb{P}^k$ and $\mu$ be its measure of maximal entropy. We prove an Almost Sure Invariance Principle for the systems $(\mathbb{P}^k,f,\mu)$. Our class $\cal{U}$ of observables includes the H\"older functions ... More

Fermi liquid theory for SU(N) Kondo modelMay 25 2009Sep 23 2009We extend the Fermi liquid theory of Nozi\`eres by introducing the next-to-leading order corrections to the Fermi liquid fixed point. For a general SU(N) Kondo impurity away from half-filling, this extension is necessary to compute observables (resistivity, ... More

$ζ$-regularised spectral determinants on metric graphsJun 10 2010Several general results for the spectral determinant of the Schr\"odinger operator on metric graphs are reviewed. Then, a simple derivation for the $\zeta$-regularised spectral determinant is proposed, based on the Roth trace formula. Two types of boundary ... More

Wigner time delay and related concepts -- Application to transport in coherent conductorsJul 01 2015Feb 19 2016The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems; the case of disorder in 1D ... More

Dirac-Born-Infeld and k-inflation: the CMB anisotropies from string theoryOct 12 2009Inflationary models within string theory exhibit unusual scalar field dynamics involving non-minimal kinetic terms and generically referred to as k-inflation. In this situation, the standard slow-roll approach used to determine the behavior of the primordial ... More

Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorderAug 03 2013Feb 23 2014The $q$-state Potts model with a long-range correlated disorder is studied by means of large-scale Monte Carlo simulations for $q=2,4,8$ and 16. Evidence is given of the existence of a Griffiths phase, where the thermodynamic quantities display an algebraic ... More

Phase Reduction in the Noise Induced Escape Problem for Systems close to ReversibilityJul 04 2013We consider n-dimensional deterministic flows obtained by perturbing a gradient flow. We assume that the gradient flow admits a stable curve of stationary points, and thus if the perturbation is not too large the perturbed flow also admits an attracting ... More

Controling the number of focal elementsMar 14 2013A basic belief assignment can have up to 2^n focal elements, and combining them with a simple conjunctive operator will need O(2^2n) operations. This article proposes some techniques to limit the size of the focal sets of the bbas to be combined while ... More

Matters of time directionality in gravitation theoryJun 17 2016Sep 06 2016Several issues related to time directionality as they arise from a semi-classical perspective are discussed which are all directly or indirectly relevant to gravitation theory. Important clarifications are achieved regarding in particular the concept ... More

Analytic torsion of Hirzebruch surfacesJan 05 2004Using different forms of the arithmetic Riemann-Roch theorem and the computations of Bott-Chern secondary classes, we compute the analytic torsion and the height of Hirzebruch surfaces.

Radiative Transport Limit for the Random Schrödinger Equation with Long-Range CorrelationsOct 14 2011In this paper we study the asymptotic phase space energy distribution of solution of the Schr\"{o}dinger equation with a time-dependent random potential. The random potential is assumed to be with slowly decaying correlations. We show that the Wigner ... More

Pointwise ergodic theorems with rate and application to limit theorems for stationary processesApr 01 2009We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale approximation, we obtain ... More

Fluctuation-dissipation relation for the Ising-Glauber model with arbitrary exchange couplingsDec 04 2002We derive an exact expression of the response function to an infinitesimal magnetic field for the Ising-Glauber model with arbitrary exchange couplings.nThe result is expressed in terms of thermodynamic averages and does not depend on initial conditions ... More

Spectral properties of self-similar lattices and iteration of rational mapsJan 18 2002Mar 19 2003In this text we consider discrete Laplace operators defined on lattices based on finitely-ramified self-similar sets, and their continuous analogous defined on the self-similar sets themselves. We are interested in the spectral properties of these operators. ... More

3D viscous incompressible fluid around one thin obstacleDec 18 2011Jun 20 2013In this article, we consider Leray solutions of the Navier-Stokes equations in the exterior of one obstacle in 3D and we study the asymptotic behavior of these solutions when the obstacle shrinks to a curve or to a surface. In particular, we will prove ... More

On last passage times of linear diffusions to curved boundariesApr 25 2012The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following Robbins & Siegmund, ... More

Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbersMay 01 2012Oct 22 2012Some results on the ordered statistics of eigenvalues for one-dimensional random Schr\"odinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces eigenvalue ... More

On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approachJun 01 2007Feb 19 2008We consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$ and $\mathcal{G}_2$ attached at one point. We derive a formula relating the spectral determinant of the Laplace operator $S_\mathcal{G}(\gamma)=\det(\gamma-\Delta)$ in terms of ... More

Mixing Least-Squares Estimators when the Variance is UnknownNov 02 2007We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some cases the ... More

The ATLAS Forward Physics ProjectFeb 04 2013We describe the main components of the ATLAS Forward Physics project, namely the movable beam pipe, the tracking and timing detectors which allow to detect intact protons in the final state at the LHC. The position detector is composed on 6 layers of ... More

Hyperscaling violation in the 2D 8-state Potts model with long-range correlated disorderMar 08 2013Jul 12 2013The first-order phase transition of the two-dimensional eight-state Potts model is shown to be rounded when long-range correlated disorder is coupled to energy density. Critical exponents are estimated by means of large-scale Monte Carlo simulations. ... More

The exact numerical treatment of inflationary modelsMar 19 2007Oct 07 2015The precision reached by the recent CMB measurements gives new insights into the shape of the primordial power spectra of the cosmological perturbations. In the context of inflationary cosmology, this implies that the CMB data are now sensitive to the ... More

Fermionic currents flowing along extended objectsNov 09 2002This PhD thesis discusses the internal structure of topological defects, and branes in extra-dimensions, carrying fermionic currents. The general framework in which these objects may appear is presented in the first part while the second part is devoted ... More

Estimation of Gaussian graphs by model selectionOct 10 2007Jul 16 2008We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To estimate the ... More

Cavitation induced by explosion in a model of ideal fluidDec 07 1998We discuss the problem of an explosion in the cubic-quintic superfluid model, in relation to some experimental observations. We show numerically that an explosion in such a model might induce a cavitation bubble for large enough energy. This gives a consistent ... More

Minimal and maximal elements in Kazhdan-Lusztig double sided cells of $S_n$ and Robinson-Schensted correspondanceApr 04 2003Nov 17 2005In symmetric groups, a two-sided cell is the set of all permutations which are mapped by the Robinson-Schensted correspondence on a pair of tableaux of the same shape. In this article, we show that the set of permutations in a two-sided cell which have ... More

Schrödinger operators on fractal lattices with random blow-upsJan 18 2002Starting from a finitely ramified self-similar set $X$ we can construct an unbounded set $X_{<\infty>}$ by blowing-up the initial set $X$. We consider random blow-ups and prove elementary properties of the spectrum of the natural Laplace operator on $X_{<\infty>}$ ... More

Explicit computations of Serre's obstruction for genus 3 curves and application to optimal curvesJan 19 2009Feb 19 2009Let k be a field of characteristic different from 2. There can be an obstruction for an indecomposable principally polarized abelian threefold (A,a) over k to be a Jacobian over k. It can be computed in terms of the rationality of the square root of the ... More

Loss of Resolution for the Time Reversal of Waves in Random Underwater Acoustic ChannelsJan 24 2012In this paper we analyze a time-reversal experiment in a random underwater acoustic channel. In this kind of waveguide with semi-infinite cross section a propagating field can be decomposed over three kinds of modes: the propagating modes, the radiating ... More

Wave Decoherence for the Random Schroedinger Equation with Long-Range CorrelationsDec 07 2011Jun 22 2012In this paper, we study the decoherence of a wave described by the solution to a Schroedinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze the decoherence ... More

Uniqueness for two dimensional incompressible ideal flow on singular domainsSep 06 2011Oct 19 2013The existence of a solution to the two dimensional incompressible Euler equations in singular domains was established in [G\'erard-Varet and Lacave, The 2D Euler equation on singular domains, submitted]. The present work is about the uniqueness of such ... More

Electrical Networks, Symplectic Reductions, and Application to the Renormalization Map of Self-Similar LatticesApr 10 2003Jan 30 2004The first part of this paper deals with electrical networks and symplectic reductions. We consider two operations on electrical networks (the "trace map" and the "gluing map") and show that they correspond to symplectic reductions. We also give several ... More

Singular integrals meet modulation invarianceApr 22 2003Many concepts of Fourier analysis on Euclidean spaces rely on the specification of a frequency point. For example classical Littlewood Paley theory decomposes the spectrum of functions into annuli centered at the origin. In the presence of structures ... More

Asymptotic analysis of boundary layer correctors in periodic homogenizationMay 07 2012This paper is devoted to the asymptotic analysis of boundary layers in periodic homogenization. We investigate the behaviour of the boundary layer corrector, defined in the half-space $\Omega_{n,a}:=\{y\cdot n-a>0\}$, far away from the boundary and prove ... More

Numerical study of Schramm-Loewner Evolution in the random 3-state Potts modelJun 18 2010We have numerically studied the properties of the interface induced in the ferromagnetic random-bond three-state Potts model by symmetry-breaking boundary conditions. The fractal dimension $d_f$ of the interface was determined. The corresponding SLE parameter ... More

Wavelet block thresholding for samples with random design: a minimax approach under the $L^p$ riskAug 30 2007We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the $\mathbb{L}^p$ risk with $p\ge 2$ over Besov balls. We prove that it is near optimal and ... More

Numerical study of the critical phases of the frustrated Z(5) modelFeb 25 2016Jun 03 2016The phase diagram of the $\mathbb{Z}(5)$ spin model is studied numerically on the square lattice by means of the {\sl Density Matrix Renormalization Group}. In the regime where the two nearest-neighbor couplings have opposite signs, a critical phase, ... More

Wave-induced motion of magnetic spheresJan 06 2016We report an experimental study of the motion of magnetized beads driven by a travelling wave magnetic field. For sufficiently large wave speed, we report the existence of a backward motion, in which the sphere can move in the direction opposite to the ... More

Filtrations and BuildingsNov 20 2014Mar 09 2015We construct and study a scheme theoretical version of the Tits vectorial building, relate it to filtrations on fiber functors, and use them to clarify various constructions pertaining to Bruhat-Tits buildings, for which we also provide a Tannakian description. ... More

DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock modelJul 22 2014Oct 12 2014The two Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus $\Upsilon_2$ is computed by imposing ... More

Mixing time of A + B -> 0 in 1DAug 18 2014Aug 17 2015A mixing time density of $A + B \to 0$ on a finite one dimensional domain is defined for general initial and boundary conditions in which $A$ and $B$ diffuse at the same rate. The density is a measure of the number of $A$ and $B$ particles that mix through ... More

Some limiting laws associated with the integrated Brownian motionJul 04 2013We study some limit theorems for the normalized law of integrated Brownian motion perturbed by several examples of functionals: the first passage time, the nth passage time, the last passage time up to a finite horizon and the supremum. We show that the ... More

Topologically equisingular deformations of homogeneous hypersurfaces with line singularities are equimultipleJun 26 2015We prove that if $\{f_t\}$ is a family of line singularities with constant L\^e numbers and such that $f_0$ is a homogeneous polynomial, then $\{f_t\}$ is equimultiple. This extends to line singularities a well known theorem of A. M. Gabri\`elov and A. ... More

A compact LIL for martingales in $2$-smooth Banach spaces with applicationsSep 17 2012Apr 13 2015We prove the compact law of the iterated logarithm for stationary and ergodic differences of (reverse or not) martingales taking values in a separable $2$-smooth Banach space (for instance a Hilbert space). Then, in the martingale case, the almost sure ... More

Beyond two criteria for supersingularity: coefficients of division polynomialsMar 20 2013Let E: y^2 = x^3 + Ax + B be an elliptic curve defined over a finite field of characteristic p\geq 3. In this paper we prove that the coefficient at x^{p(p-1)/2} in the p-th division polynomial \psi_p(x) of E equals the coefficient at x^{p-1} in (x^3 ... More

Tomorrow's Metamaterials: Manipulation of Electromagnetic Waves in Space, Time and SpacetimeFeb 13 2016Metamaterials represent one of the most vibrant fields of modern science and technology. They are generally dispersive structures in the direct and reciprocal space and time domains. Upon this consideration, I overview here a number of metamaterial innovations ... More

Fast Bayesian inference for slow-roll inflationDec 09 2013Jun 02 2014We present and discuss a new approach increasing by orders of magnitude the speed of performing Bayesian inference and parameter estimation within the framework of slow-roll inflation. The method relies on the determination of an effective likelihood ... More

Cosmic strings and their induced non-Gaussianities in the cosmic microwave backgroundMay 26 2010Aug 11 2010Motivated by the fact that cosmological perturbations of inflationary quantum origin were born Gaussian, the search for non-Gaussianities in the cosmic microwave background (CMB) anisotropies is considered as the privileged probe of non-linear physics ... More

Equation of state of cosmic strings with fermionic current-carriersJul 03 2000Dec 14 2000The relevant characteristic features, including energy per unit length and tension, of a cosmic string carrying massless fermionic currents in the framework of the Witten model in the neutral limit are derived through quantization of the spinor fields ... More

Preliminary BABAR results on B0 mixing with dileptons and on lifetime with partially reconstructed B0 decaysNov 03 2000With an integrated luminosity of 7.7 fb-1 collected on resonance by BABAR at the PEP-II asymmetric B Factory, we measure the difference in mass between the neutral B eigenstates, Delta(m_d), to be (0.507+/-0.015+/-0.022)x 10^{12} hbar s^{-1} with dileptons ... More

Spectral Analysis of a Self-Similar Sturm-Liouville OperatorJan 30 2004In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace operators on unbounded ... More

A quasi-potential for conservation laws with boundary conditionsOct 18 2010We compute the quasi-potential and determine minimizing paths for an action functional related to scalar conservation laws on an interval with boundary conditions in the sense of Bardos et al. (1979). Taking as input an exclusion-like flux function, a ... More

Theoretical Basis for a Solution to the Cosmic Coincidence ProblemMar 03 2006May 31 2010Following a short discussion of some unresolved issues in the standard model of cosmology (considered to be a generic $\Lambda$CDM model with flat geometry and an early period of inflation), we describe the current state of research on the problem of ... More

Two Dimensional Incompressible Ideal Flow Around a Small CurveFeb 04 2011We study the asymptotic behavior of solutions of the two dimensional incompressible Euler equations in the exterior of a curve when the curve shrinks to a point. This work links two previous results: [Iftimie, Lopes Filho and Nussenzveig Lopes, Two Dimensional ... More

Two Dimensional Incompressible Viscous Flow Around a Thin Obstacle Tending to a CurveJul 10 2008Feb 13 2009In [Lacave, IHP, ana, to appear (2008)] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem in the viscous ... More

Christoffel words and Markoff triplesSep 19 2008Markoff triples are parametrized uniquely by Christoffel words.

A pseudo-RIP for multivariate regressionJun 28 2011We give a suitable RI-Property under which recent results for trace regression translate into strong risk bounds for multivariate regression. This pseudo-RIP is compatible with the setting $n < p$.

A far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like modelMar 26 2003Jul 21 2003We derive an exact expression of the response function to an infinitesimal magnetic field for an Ising-Glauber-like model with arbitrary exchange couplings. The result is expressed in terms of thermodynamic averages and does not depend on the initial ... More

Individual energy level distributions for one-dimensional diagonal and off-diagonal disorderApr 17 2000Jun 28 2000We study the distribution of the $n$-th energy level for two different one-dimensional random potentials. This distribution is shown to be related to the distribution of the distance between two consecutive nodes of the wave function. We first consider ... More

On the dimension of invariant measures of endomorphisms of $\mathbb{CP}^k$Sep 16 2008Apr 13 2010Let $f$ be an endomorphism of $\mathbb{CP}^k$ and $\nu$ be an $f$-invariant measure with positive Lyapunov exponents $(\lambda_1,\...,\lambda_k)$. We prove a lower bound for the pointwise dimension of $\nu$ in terms of the degree of $f$, the exponents ... More

On the Ritt property and weak type maximal inequalities for convolution powers on $\ell^1(\Z)$Jan 21 2016In this paper we study the behaviour of convolution powers of probability measures $\mu$ on $\Z$, such that $(\mu(n))_{n\in \N}$ is completely monotone or such that $\nu$ is centered with a second moment. In particular we exhibit many new examples of ... More

Mazur's inequality and laffaille's theoremSep 02 2015We look at various questions related to filtrations in $p$-adic Hodgetheory, using a blend of building and Tannakian tools. Specifically,Fontaine and Rapoport used a theorem of Laffaille on filtered isocrystalsto establish a converse of Mazur's inequality ... More

Stability of the Griffiths phase in the 2D Potts model with correlated disorderApr 25 2014A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D $q$-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice ... More

Hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundariesDec 04 2006Sep 02 2011We consider attractive particle systems in $\Z^d$ with product invariant measures. We prove that when particles are restricted to a subset of $\Z^d$, with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the unique entropy ... More

Fermionic massive modes along cosmic stringsJun 15 2001Nov 05 2001The influence on cosmic string dynamics of fermionic massive bound states propagating in the vortex, and getting their mass only from coupling to the string forming Higgs field, is studied. Such massive fermionic currents are numerically found to exist ... More

Tevatron Top ResultsMay 28 2006I present the latest results from the CDF and D0 collaborations on top quark production (single top and top quark pair production) at the Tevatron proton-antiproton collider at sqrt(s) =1.96 TeV, measurements of the top quark decay properties such as ... More

Expectation of Stratonovich iterated integrals of Wiener processesAug 24 2010The solution of a (stochastic) differential equation (SDE) can be locally approximated by a stochastic expansion, a linear combination of iterated integrals. Quantities of interest, like moments, can then be approximated with the expansion. We present ... More

Groupes p-divisibles, groupes finis et modules filtrésSep 01 2000Let k be a perfect field of characteristic p>0. When p>2, Fontaine and Laffaille have classified p-divisibles groups and finite flat p-groups over the Witt vectors W(k) in terms of filtered modules. Still assuming p>2, we extend these classifications ... More

Constructions of minimal periodic surfaces and minimal annuli in Sol3Nov 20 2013We construct two one-parameter families of minimal properly embedded surfaces in the Lie group Sol3 using a Weierstrass-type representation. These surfaces are not invariant by a one-parameter group of ambient isometries. The first one can be viewed as ... More

Permutahedra and Associahedra: Generalized associahedra from the geometry of finite reflection groupsDec 14 2011This is a chapter in an upcoming Tamari Festscrift. Permutahedra are a class of convex polytopes arising naturally from the study of finite reflection groups, while generalized associahedra are a class of polytopes indexed by finite reflection groups. ... More

Wave Propagation in Shallow-Water Acoustic Random WaveguidesNov 30 2009In shallow-water waveguides a propagating field can be decomposed over three kinds of modes: the propagating modes, the radiating modes and the evanescent modes. In this paper we consider the propagation of a wave in a randomly perturbed waveguide and ... More

Local model of semi-toric integrable systems: theory and applicationsAug 06 2014Oct 05 2015In this article we show how one can use the local models of integrable Hamiltonian systems near critical points to prove a localization theorem for certain singular loci of integrables semi-toric systems for dimension greater than 4.

Two Dimensional Incompressible Ideal Flow Around a Thin Obstacle Tending to a CurveApr 17 2008May 07 2008In this work we study the asymptotic behavior of solutions of the incompressible two-dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by Iftimie, Lopes Filho ... More

Families of hypersurfaces of large degreeOct 08 2009We show that general moving enough families of high enough degree hypersurfaces in a complex projective space do not have a dominant set of sections.

Low rank Multivariate regressionSep 27 2010Jun 22 2011We consider in this paper the multivariate regression problem, when the target regression matrix $A$ is close to a low rank matrix. Our primary interest in on the practical case where the variance of the noise is unknown. Our main contribution is to propose ... More

Penalizing null recurrent diffusionsNov 14 2011We present some limit theorems for the normalized laws (with respect to functionals involving last passage times at a given level up to time t) of a large class of null recurrent diffusions. Our results rely on hypotheses on the L\'evy measure of the ... More

Leonardo's rule, self-similarity and wind-induced stresses in treesMay 13 2011Nov 15 2011Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the ... More

Optimal Strouhal number for swimming animalsFeb 01 2011To evaluate the swimming performances of aquatic animals, an important dimensionless quantity is the Strouhal number, St = fA/U, with f the tail-beat frequency, A the peak-to-peak tail amplitude, and U the swimming velocity. Experiments with flapping ... More

Secant varieties and successive minimaOct 23 2001Given an arithmetic surface and a positive hermitian line bundle over it, we bound the successive minima of the lattice of global sections of this line bundle. Our method combines a result of C.Voisin on secant varieties of projective curves with previous ... More

Effect of connecting wires on the decoherence due to electron-electron interaction in a metallic ringJul 19 2007We consider the weak localization in a ring connected to reservoirs through leads of finite length and submitted to a magnetic field. The effect of decoherence due to electron-electron interaction on the harmonics of AAS oscillations is studied, and more ... More

Scattering theory on graphs (2): the Friedel sum ruleDec 12 2001Mar 01 2002We consider the Friedel sum rule in the context of the scattering theory for the Schr\"odinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples ... More

Large entropy measures for endomorphisms of CP(k)Nov 24 2009Let $f$ be an holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$. We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large metric entropy, ... More

Stability of giant vortices in quantum liquidsFeb 03 2004We show how giant vortices can be stabilized in strong external potential Bose-Einstein condensates. We illustrate the formation of these vortices thanks to the relaxation Ginzburg-Landau dynamics for two typical potentials in two spatial dimensions. ... More

Wave turbulence and Bose-Einstein condensatesJan 09 2004Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability density of ... More

Les variétés sur le corps à un élémentApr 28 2003We propose a definition of varieties over the field with one element. These have extensions of scalars to the ring of integers which are varieties in the usual sense. We show that toric varieties can be defined over the field with one element. We also ... More

Existence d'une courbe de genre 5 sur F_3 avec 13 points rationnelsFeb 12 2003Let N_q(g) the maximal number of points on a genus g curve over F_q. We prove that N_3(5)=13.

Un processus ponctuel associé aux maxima locaux du mouvement brownienApr 30 2010Let $B = (B_t)_{t \in {\bf R}}$ be a symmetric Brownian motion, i.e. $(B_t)_{t \in {\bf R}_+}$ and $(B_{-t})_{t \in {\bf R}_+}$ are independent Brownian motions starting at $0$. Given $a \ge b>0$, we describe the law of the random set $${\cal M}_{a,b} ... More

Algebraic homotopy classes of rational functionsDec 11 2009Dec 23 2009We compute the set of naive pointed homotopy classes of endomorphisms of the projective line P^1 over the spectrum of a field. Our computation compares well with Fabien Morel's one of the motivic pointed homotopy classes of endomorphisms of P^1: there ... More

Linearly recursive sequences and Dynkin diagramsApr 23 2012Motivated by a construction in the theory of cluster algebras (Fomin and Zelevinsky), one associates to each acyclic directed graph a family of sequences of natural integers, one for each vertex; this construction is called a {\em frieze}; these sequences ... More

Bifurcation into spectral gaps for a noncompact semilinear Schrödinger equation with nonconvex potentialJul 04 2012This paper shows that the nonlinear periodic eigenvalue problem $${cases} -\Delta u + V(x) u - f(x,u) = \lambda u, u \in H^1(\IR^N), {cases}$$ has a nontrivial branch of solutions emanating from the upper bound of every spectral gap of $-\Delta + V$. ... More

A Gale-Berlekamp permutation-switching problem in higher dimensionsJan 28 2018Let an $n\times n$ array $\left( a_{ij}\right) $ of lights be given, each either on (when $a_{ij}=1$) or off (when $a_{ij}=-1$). For each row and each column there is a switch so that if the switch is pulled ($x_{i}=-1$ for row $i$ and $y_{j}=-1$ for ... More

Ontology-based Recommender System of Economic ArticlesJan 21 2013Decision makers need economical information to drive their decisions. The Company Actualis SARL is specialized in the production and distribution of a press review about French regional economic actors. This economic review represents for a client a prospecting ... More

The invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3DJul 09 2009Mar 30 2010The full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian is presented in 2 and 3D. It allows for explicit expression for the Euler characteristic in ND and computation of ... More