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.
• Representation, relaxation and convexity for variational problems in Wiener spaces
  
  • Chambolle Antonin
  • Goldman Michael
  • Novaga Matteo
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2013. We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework.
• Approximate Lipschitz stability for non-overdetermined inverse scattering at fixed energy
  
  • Novikov Roman
  Journal of Inverse and Ill-posed Problems, De Gruyter, 2013, 21 (6), pp.813–823. We prove approximate Lipschitz stability for non-overdetermined inverse scattering at fixed energy with incomplete data in dimension d ≥ 2. Our estimates are given in uniform norm for coefficient difference and related stability precision efficiently increases with increasing energy and coefficient difference regularity. In addition, our estimates are rather optimal even in the Born approximation.
• Modelling microstructure noise with mutually exciting point processes
  
  • Bacry Emmanuel
  • Delattre Sylvain
  • Hoffmann Marc
  • Muzy Jean-François
  Quantitative Finance, Taylor & Francis (Routledge), 2013, 13 (1), pp.65-77. We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point pro- cesses and relies on linear self and mutually exciting stochastic inten- sities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations. (10.1080/14697688.2011.647054)
  DOI : 10.1080/14697688.2011.647054
• Exponential instability in the inverse scattering problem on the energy interval
  
  • Isaev Mikhail
  Functional Analysis and Its Applications, Springer Verlag, 2013, 47 (3), pp.8. We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows optimality of the logarithmic stability result of [Stefanov, 1990] (up to the value of the exponent).
• State-constrained Optimal Control Problems of Impulsive Differential Equations
  
  • Forcadel Nicolas
  • Rao Zhiping
  • Zidani Hasnaa
  Applied Mathematics and Optimization, Springer Verlag (Germany), 2013, 68, pp.1--19. The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption. (10.1007/s00245-013-9193-5)
  DOI : 10.1007/s00245-013-9193-5
• Optimisation of cancer drug treatments using cell population dynamics
  
  • Billy Frédérique
  • Clairambault Jean
  • Fercoq Olivier
  , 2013, pp.265. Cancer is primarily a disease of the physiological control on cell population proliferation. Tissue proliferation relies on the cell division cycle: one cell becomes two after a sequence of molecular events that are physiologically controlled at each step of the cycle at so-called checkpoints, in particular at transitions between phases of the cycle [105]. Tissue proliferation is the main physiological process occurring in development and later in maintaining the permanence of the organism in adults, at that late stage mainly in fast renewing tissues such as bone marrow, gut and skin. (10.1007/978-1-4614-4178-6_10)
  DOI : 10.1007/978-1-4614-4178-6_10
• Central limit theorems for linear statistics of heavy tailed random matrices
  
  • Benaych-Georges Florent
  • Guionnet Alice
  • Male Camille
  , 2013. We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike to the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.