Publications

2013

• La conjecture de Syracuse -visualisation bidimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -bidimensional display- (La conjecture de Syracuse -visualisation bidimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-Francois
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-Francois
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• Les deux premières itérations de la construction de la courbe de von Koch
  
  • Colonna Jean-Francois
  , 2013. The first two iterations of the construction of the von Koch curve (Les deux premières itérations de la construction de la courbe de von Koch)
• Un cylindre défini à l'aide de trois champs bidimensionnels
  
  • Colonna Jean-Francois
  , 2013. A cylinder defined by means of three bidimensional fields (Un cylindre défini à l'aide de trois champs bidimensionnels)
• Une surface intermédiaire entre une 'double sphère' et un cylindre
  
  • Colonna Jean-Francois
  , 2013. A surface between a 'double sphere' and a cylinder (Une surface intermédiaire entre une 'double sphère' et un cylindre)
• Une surface intermédiaire entre une 'double sphère' et un cylindre
  
  • Colonna Jean-Francois
  , 2013. A surface between a 'double sphere' and a cylinder (Une surface intermédiaire entre une 'double sphère' et un cylindre)
• La conjecture de Goldbach
  
  • Colonna Jean-Francois
  , 2013. The Goldbach conjecture (La conjecture de Goldbach)
• L’opérateur de Laplace-Beltrami en Géométrie presque-Riemannienne
  
  • Boscain Ugo
  • Laurent Camille
  Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2013, 63 (5), pp.1739 - 1770. Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. Generically, the singular set is an embedded one dimensional manifold and there are three type of points: Riemannian points where the two vector fields are linearly independent, Grushin points where the two vector fields are collinear but their Lie bracket is not and tangency points where the two vector fields and their Lie bracket are collinear and the missing direction is obtained with one more bracket. Generically tangency points are isolated. In this paper we study the Laplace-Beltrami operator on such a structure. In the case of a compact orientable surface without tangency points, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence a quantum particle in such a structure cannot cross the singular set and the heat cannot flow through the singularity. This is an interesting phenomenon since when approaching the singular set (i.e. where the vector fields become collinear), all Riemannian quantities explode, but geodesics are still well defined and can cross the singular set without singularities. This phenomenon appears also in sub-Riemannian structure which are not equiregular i.e. in which the grow vector depends on the point. We show this fact by analyzing the Martinet case. (10.5802/aif.2813)
  DOI : 10.5802/aif.2813
• Un 'double sphere' défini à l'aide de trois champs bidimensionnels
  
  • Colonna Jean-Francois
  , 2013. A 'double sphere' defined by means of three bidimensional fields (Un 'double sphere' défini à l'aide de trois champs bidimensionnels)
• La conjecture de Goldbach
  
  • Colonna Jean-Francois
  , 2013. The Goldbach conjecture (La conjecture de Goldbach)
• Une surface intermédiaire entre une 'double sphère' et un cylindre
  
  • Colonna Jean-Francois
  , 2013. A surface between a 'double sphere' and a cylinder (Une surface intermédiaire entre une 'double sphère' et un cylindre)
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') pour seize éclairages différents -section tridimensionnelle
  
  • Colonna Jean-François
  , 2013. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') for sixteen different lightings -tridimensional cross-section- (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') pour seize éclairages différents -section tridimensionnelle-)
• An Optimal Affine Invariant Smooth Minimization Algorithm
  
  • d'Aspremont Alexandre
  • Guzmán Cristóbal
  • Jaggi Martin
  , 2013. We formulate an affine invariant implementation of the algorithm in Nesterov (1983). We show that the complexity bound is then proportional to an affine invariant regularity constant defined with respect to the Minkowski gauge of the feasible set. We also detail matching lower bounds when the feasible set is an ℓp ball. In this setting, our bounds on iteration complexity for the algorithm in Nesterov (1983) are thus optimal in terms of target precision, smoothness and problem dimension.
• On the extinction of Continuous State Branching Processes with catastrophes
  
  • Bansaye Vincent
  • Pardo Millan Juan Carlos
  • Smadi Charline
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2013, 18, pp.1-31. We consider continuous state branching processes (CSBP) with additional multiplicative jumps modeling dramatic events in a random environment. These jumps are described by a Lévy process with bounded variation paths. We construct a process of this class as the unique solution of a stochastic differential equation. The quenched branching property of the process allows us to derive quenched and annealed results and to observe new asymptotic behaviors. We characterize the Laplace exponent of the process as the solution of a backward ordinary differential equation and establish the probability of extinction. Restricting our attention to the critical and subcritical cases, we show that four regimes arise for the speed of extinction, as in the case of branching processes in random environment in discrete time and space. The proofs are based on the precise asymptotic behavior of exponential functionals of Lévy processes. Finally, we apply these results to a cell infection model and determine the mean speed of propagation of the infection. (10.1214/EJP.v18-2774)
  DOI : 10.1214/EJP.v18-2774
• On the robust superhedging of measurable claims
  
  • Possamaï Dylan
  • Royer Guillaume
  • Touzi Nizar
  Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2013, 18 (95), pp.1-13. The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by van Handel, Neufeld, and Nutz. We show that the dual formulation of this problem is valid in a context suitable for martingale optimal transportation or, more generally, for optimal transportation under controlled stochastic dynamics (10.1214/ECP.v18-2739)
  DOI : 10.1214/ECP.v18-2739
• A Hamilton-Jacobi approach to junction problems and application to traffic flows
  
  • Imbert Cyril
  • Monneau Régis
  • Zidani Hasnaa
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2013, 19 (01), pp.pp 129-166. This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a ''junction'', that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to be new. They are applied to the study of some models arising in traffic flows. The techniques developed in the present article provide new powerful tools for the analysis of such problems. (10.1051/cocv/2012002)
  DOI : 10.1051/cocv/2012002
• Energy and regularity dependent stability estimates for near-field inverse scattering in multidimensions
  
  • Isaev Mikhail
  Journal of Mathematics, Hindawi Publishing Corp., 2013, pp.DOI:10.1155/2013/318154. We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimension $d\geq 3$. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimension $d=2$ is also given. (10.1155/2013/318154)
  DOI : 10.1155/2013/318154
• On the asymptotics of a Robin eigenvalue problem
  
  • Cakoni Fioralba
  • Chaulet Nicolas
  • Haddar Houssem
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2013, 351, pp.517-521. The considered Robin problem can formally be seen as a small perturbation of a Dirichlet problem. However, due to the sign of the impedance value, its associated eigenvalues converge point-wise to −∞ as the perturbation goes to zero. We prove in this case that Dirichlet eigenpairs are the only accumulation points of the Robin eigenpairs with normalized eigenvectors. We then provide a criterion to select accumulating sequences of eigenvalues and eigenvectors and exhibit their full asymptotic with respect to the small parameter. (10.1016/j.crma.2013.07.022)
  DOI : 10.1016/j.crma.2013.07.022
• Semi-infinite paths of the two dimensional radial spanning tree
  
  • Baccelli François
  • Coupier David
  • Tran Viet Chi
  Advances in Applied Probability, Applied Probability Trust, 2013, 45 (4), pp.895-916. We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite paths and the sphere with radius $r$ grows sublinearly with $r$. Then, we prove that in each (deterministic) direction, there exists with probability one a unique semi-infinite path, framed by an infinite number of other semi-infinite paths of close asymptotic directions. The set of (random) directions in which there are more than one semi-infinite paths is dense in $[0,2\pi)$. It corresponds to possible asymptotic directions of competition interfaces. We show that the RST can be decomposed in at most five infinite subtrees directly connected to the root. The interfaces separating these subtrees are studied and simulations are provided. (10.1239/aap/1386857849)
  DOI : 10.1239/aap/1386857849
• A homogenization approach for the motion of motor proteins
  
  • Mirrahimi Sepideh
  • Souganidis Panagiotis E.
  Nonlinear Differential Equations and Applications, Springer Verlag, 2013, 20, pp.129-147. We consider the asymptotic behavior of an evolving weakly coupled Fokker-Planck system of two equations set in a periodic environment. The magnitudes of the diffusion and the coupling are respectively proportional and inversely proportional to the size of the period. We prove that, as the period tends to zero, the solutions of the system either propagate (concentrate) with a fixed constant velocity (determined by the data) or do not move at all. The system arises in the modeling of motor proteins which can take two different states. Our result implies that, in the limit, the molecules either move along a filament with a fixed direction and constant speed or remain immobile. (10.1007/s00030-012-0156-3)
  DOI : 10.1007/s00030-012-0156-3