Publications

2014

• Vue artistique de Monument Valley au lever du Soleil avec la Grande Ourse
  
  • Colonna Jean-Francois
  , 2014. Artistic view of Monument Valley at sunrise with the Great Bear (Vue artistique de Monument Valley au lever du Soleil avec la Grande Ourse)
• Fixed point of payment-free Shapley operators and structural properties of mean payoff games
  
  • Akian Marianne
  • Gaubert Stéphane
  • Hochart Antoine
  , 2014.
• On The Sample Complexity Of Sparse Dictionary Learning
  
  • Seibert Matthias
  • Kleinsteuber Martin
  • Gribonval Rémi
  • Jenatton Rodolphe
  • Bach Francis
  , 2014. In the synthesis model signals are represented as a sparse combinations of atoms from a dictionary. Dictionary learning describes the acquisition process of the underlying dictionary for a given set of training samples. While ideally this would be achieved by optimizing the expectation of the factors over the underlying distribution of the training data, in practice the necessary information about the distribution is not available. Therefore, in real world applications it is achieved by minimizing an empirical average over the available samples. The main goal of this paper is to provide a sample complexity estimate that controls to what extent the empirical average deviates from the cost function. This estimate then provides a suitable estimate to the accuracy of the representation of the learned dictionary. The presented approach exemplifies the general results proposed by the authors in [1] and gives more concrete bounds of the sample complexity of dictionary learning. We cover a variety of sparsity measures employed in the learning procedure. (10.1109/SSP.2014.6884621)
  DOI : 10.1109/SSP.2014.6884621
• Monument Valley au lever du Soleil
  
  • Colonna Jean-Francois
  , 2014. Monument Valley at sunrise (Monument Valley au lever du Soleil)
• Monument Valley au lever du Soleil
  
  • Colonna Jean-Francois
  , 2014. Monument Valley at sunrise (Monument Valley au lever du Soleil)
• Policy iteration for stochastic zero-sum games
  
  • Akian Marianne
  • Gaubert Stéphane
  , 2014.
• Fixed point of payment-free Shapley operators and structural properties of mean payoff games
  
  • Akian Marianne
  • Gaubert Stéphane
  • Hochart Antoine
  , 2014.
• Spectral conditions for the controllability of the Schroedinger equation
  
  • Boscain Ugo
  , 2014. Spectral conditions for the controllability of the Schroedinger equation
• Optimization of running strategies based on anaerobic energy and variations of velocity
  
  • Bonnans J. Frederic
  , 2014. 1 Keller's model 2 Variable energy recreation 3 Bounding the derivative of f
• L’art de couper les têtes sans faire mal
  
  • Le Pennec Erwan
  Interstices, INRIA, 2014. Retrouver un objet à partir d’une collection de radiographies de cet objet : on appelle cela, en mathématiques, un problème inverse.
• Hilbert isometries
  
  • Walsh Cormac
  , 2014.
• Volume Viscosity and Internal Energy Relaxation : Symmetrization and Chapman-Enskog Expansion
  
  • Giovangigli Vincent
  • Yong Wen-An
  , 2014. We analyze a mathematical model for the relaxation of translational and internal temperatures in a nonequilibrium gas. The system of partial differential equations---derived from the kinetic theory of gases---is recast in its natural entropic symmetric form as well as in a convenient hyperbolic-parabolic symmetric form. We investigate the Chapman-Enskog expansion in the fast relaxation limit and establish that the temperature difference become asymptotically proportional to the divergence of the velocity field. This asymptotic behavior yields the volume viscosity term of the limiting one-temperature fluid model.
• Optimization of composite structures: A shape and topology sensitivity analysis
  
  • Delgado Gabriel
  , 2014. This thesis is devoted to the study of two main problems, namely the optimal design of multi-layered composite laminates and the topological sensitivity analysis in anisotropic elastostatics. Concerning the composite design, we consider minimal weight structures subjected to stiffness and buckling constraints, where the design variables are the shape/topology of each ply and the stacking sequence. Indeed, the composite laminate is made up of a collection of fiber reinforced orthotropic plies whose main axes can take four different orientations: 0º,90º,45º,-45º. The way these orientations are arranged within the composite defines the stacking sequence. The physical behavior of the multi-layered laminate is governed by the system of linearized von Kármán equations for plates. In order to optimize both design variables, we rely on a decomposition technique which aggregates the constraints into one unique constraint called margin function. Thanks to this approach, a rigorous equivalent bi-level optimization problem is established. The latter problem is made up of a lower level represented by the combinatorial optimization of the stacking sequence and a higher level represented by the shape/topology optimization of each ply. We propose for the stacking sequence optimization an outer approximation method which iteratively solves a set of mixed integer linear problems associated to the evaluation of the constraint margin function. For the shape/topology optimization of each ply, we lean on the level set method for the description of the interfaces and the Hadamard method for boundary variations by means of the computation of the shape gradient. An aeronautic test case is exhibited for different constraints, namely compliance, reserve factor and first buckling load. The second main problem of this thesis deals with the topological derivative of cost functionals that depend on the stress and the displacement (assuming a linearly elastic material behavior) in a general 2D and 3D anisotropic setting, where both the background and the inhomogeneity may have arbitrary anisotropic elastic properties. A small-inhomogeneity expansion of the cost function is mathematically justified for a wide class of displacement and stress-based cost functionals having smooth densities and computational procedures are then discussed. Several 2D and 3D numerical examples are presented, in particular demonstrating the proposed formulation of the topological derivative on practical cases involving anisotropic elasticity and non-quadratic cost functionals. Independently of the foregoing subjects, we treat additionally two optimal design problems. First we consider the optimal distribution of several elastic materials in a fixed working domain with either a sharp or a smooth interface. In order to optimize both the geometry and topology of the mixture, we rely on the level set method and the signed distance function for the description of the interfaces between the different phases. Secondly, in the framework of efficient power complements to aircraft engines, we seek to come up with the optimal micro-structure of micro-tubular fuel cells via an inverse homogenization technique which maximizes the contact surface subjected to a pressure drop and a permeability constraint. The optimal periodic design (fluid/solid) emerges from the application of a shape gradient algorithm coupled to a level-set method for the geometrical description of the corresponding cell problem.
• Settling down of seasonal migrants promotes bird diversification
  
  • Rolland Jonathan
  • Jiguet Frédéric
  • Jønsson Knud Andreas
  • Condamine Fabien
  • Morlon Hélène
  Proceedings of the Royal Society B: Biological Sciences, Royal Society, The, 2014, 281 (1784), pp.20140473. How seasonal migration originated and impacted diversification in birds remains largely unknown. Although migratory behaviour is likely to affect bird diversification, previous studies have not detected any effect. Here, we infer ancestral migratory behaviour and the effect of seasonal migration on speciation and extinction dynamics using a complete bird tree of life. Our analyses infer that sedentary behaviour is ancestral, and that migratory behaviour evolved independently multiple times during the evolutionary history of birds. Speciation of a sedentary species into two sedentary daughter species is more frequent than speciation of a migratory species into two migratory daughter species. However,migratory species often diversify by generating a sedentary daughter species in addition to the ancestral migratory one. This leads to an overall higher migratory speciation rate. Migratory species also experience lower extinction rates. Hence, although migratory species represent a minority (18.5%) of all extant birds, they have a higher net diversification rate than sedentary species. These results suggest that the evolution of seasonal migration in birds has facilitated diversification through the divergence of migratory subpopulations that become sedentary, and illustrate asymmetrical diversification as a mechanism by which diversification rates are decoupled from species richness. (10.1098/rspb.2014.0473)
  DOI : 10.1098/rspb.2014.0473
• Montagnes et brouillard
  
  • Colonna Jean-Francois
  , 2014. Mountains and fog (Montagnes et brouillard)
• Apprentissage de dictionnaire pour les représentations parcimonieuses
  
  • Gribonval Rémi
  • Jenatton Rodolphe
  • Bach Francis
  • Kleinsteuber Martin
  • Seibert Matthias
  , 2014. A popular approach within the signal processing and machine learning communities consists in modelling high-dimensional data as sparse linear combinations of atoms selected from a dictionary. Given the importance of the choice of the dictionary for the operational deployment of these tools, a growing interest for \emph{learned} dictionaries has emerged. The most popular dictionary learning techniques, which are expressed as large-scale matrix factorization through the optimization of a non convex cost function, have been widely disseminated thanks to extensive empirical evidence of their success and steady algorithmic progress. Yet, until recently they remained essentially heuristic. We will present recent work on statistical aspects of sparse dictionary learning, contributing to the characterization of the excess risk as a function of the number of training samples. The results cover non only sparse dictionary learning but also a much larger class of constrained matrix factorization problems.
• Agrégation PAC-bayésienne d'estimateurs par projection
  
  • Montuelle Lucie
  • Le Pennec Erwan
  , 2014. L'agrégation d'estimateur a l'aide de poids exponentiels dépendant de leur risque offre de bonnes performances en moyenne. Malheureusement, il est impossible d'obtenir un aussi bon contrôle du risque de l'estimateur agrégé en probabilité. Pour contourner ce problème, nous considérons des poids exponentiels du risque pénalisé. Cette technique permet d'obtenir une inégalité oracle inexacte en probabilité. En surpénalisant, avec une prise en compte de la norme de la fonction estimée, une inégalité exacte est accessible.
• Adaptation in a stochastic multi-resources chemostat model
  
  • Champagnat Nicolas
  • Jabin Pierre-Emmanuel
  • Méléard Sylvie
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2014, 101 (6), pp.755–788. We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics. Adaptive dynamics so far has been put on a rigorous footing only for direct competition models (Lotka-Volterra models) involving a competition kernel which describes the competition pressure from one individual to another one. We extend this to a multi-resources chemostat model, where the competition between individuals results from the sharing of several resources which have their own dynamics. Starting from a stochastic birth and death process model, we prove that, when advantageous mutations are rare, the population behaves on the mutational time scale as a jump process moving between equilibrium states (the polymorphic evolution sequence of the adaptive dynamics literature). An essential technical ingredient is the study of the long time behavior of a chemostat multi-resources dynamical system. In the small mutational steps limit this process in turn gives rise to a differential equation in phenotype space called canonical equation of adaptive dynamics. From this canonical equation and still assuming small mutation steps, we prove a rigorous characterization of the evolutionary branching points. (10.1016/j.matpur.2013.10.003)
  DOI : 10.1016/j.matpur.2013.10.003
• Minimal time trajectories for two-level quantum systems with two bounded controls
  
  • Boscain Ugo
  • Grönberg Fredrik
  • Long Ruixing
  • Rabitz Herschel
  Journal of Mathematical Physics, American Institute of Physics (AIP), 2014, 55 (6), pp.062106. In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we treat the time-optimal control problem with techniques of optimal synthesis on 2D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the initial condition. (10.1063/1.4882158)
  DOI : 10.1063/1.4882158
• A new proof for the convergence of an individual based model to the Trait substitution sequence
  
  • Gupta Ankit
  • Metz J.A.J.
  • Tran Viet Chi
  Acta Applicandae Mathematicae, Springer Verlag, 2014, 131, pp.1-27. We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and we view the process in the timescale of mutations. Using averaging techniques due to Kurtz (1992), we give a new proof of the convergence of the individual based model to the trait substitution sequence of Metz et al. (1992) first worked out by Dieckman and Law (1996) and rigorously proved by Champagnat (2006): rigging the model such that ''invasion implies substitution'', we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population. (10.1007/s10440-013-9847-y)
  DOI : 10.1007/s10440-013-9847-y
• Multi-input Schrödinger equation: controllability, tracking, and application to the quantum angular momentum
  
  • Boscain Ugo
  • Caponigro Marco
  • Sigalotti Mario
  Journal of Differential Equations, Elsevier, 2014, 256 (11), pp.3524-3551. We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schrödinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability, approximate controllability in $H^s$, and tracking in modulus. The result is more general than those present in the literature even in the case of one control and permits to treat situations in which the spectrum of the uncontrolled operator is very degenerate (e.g. it has multiple eigenvalues or equal gaps among different pairs of eigenvalues). We apply the general result to a rotating polar linear molecule, driven by three orthogonal external fields. A remarkable property of this model is the presence of infinitely many degeneracies and resonances in the spectrum preventing the application of the results in the literature. (10.1016/j.jde.2014.02.004)
  DOI : 10.1016/j.jde.2014.02.004
• On the Complexity of Strongly Connected Components in Directed Hypergraphs
  
  • Allamigeon Xavier
  Algorithmica, Springer Verlag, 2014, 69 (2), pp.335–369. (10.1007/s00453-012-9729-0)
  DOI : 10.1007/s00453-012-9729-0
• Sensitivity analysis for the outages of nuclear power plants
  
  • Barty Kengy
  • Bonnans J. Frederic
  • Pfeiffer Laurent
  Energy Systems, Springer, 2014, 5 (2), pp.371-406. Nuclear power plants must be regularly shut down in order to perform refueling and maintenance operations. The scheduling of the outages is the first problem to be solved in electricity production management. It is a hard combinatorial problem for which an exact solving is impossible. Our approach consists in modelling the problem by a two-level problem. First, we fix a feasible schedule of the dates of the outages. Then, we solve a low-level problem of optimization of elecricity production, by respecting the initial planning. In our model, the low-level problem is a deterministic convex optimal control problem. Given the set of solutions and Lagrange multipliers of the low-level problem, we can perform a sensitivity analysis with respect to dates of the outages. The approximation of the value function which is obtained could be used for the optimization of the schedule with a local search algorithm. (10.1007/s12667-013-0096-y)
  DOI : 10.1007/s12667-013-0096-y
• Stabilization of Persistently Excited Linear Systems by Delayed Feedback Laws
  
  • Mazanti Guilherme
  Systems and Control Letters, Elsevier, 2014, 68, pp.57-67. This paper considers the stabilization to the origin of a persistently excited linear system by means of a linear state feedback, where we suppose that the feedback law is not applied instantaneously, but after a certain positive delay (not necessarily constant). The main result is that, under certain spectral hypotheses on the linear system, stabilization by means of a linear delayed feedback is indeed possible, generalizing a previous result already known for non-delayed feedback laws. (10.1016/j.sysconle.2014.03.006)
  DOI : 10.1016/j.sysconle.2014.03.006
• Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2)
  
  • Duits Remco
  • Boscain U.
  • Rossi F.
  • Sachkov Y.
  Journal of Mathematical Imaging and Vision, Springer Verlag, 2014, 49 (2), pp.384-417. (10.1007/s10851-013-0475-y)
  DOI : 10.1007/s10851-013-0475-y