Publications

2017

• Benchmarking CMAES-APOP on the BBOB noiseless testbed
  
  • Nguyen Duc Manh
  • Hansen Nikolaus
  , 2017, pp.1756 - 1763. In this paper, we investigate a new approach for adapting population size in the CMA-ES. is method is based on tracking the information in each slot of S successive iterations to decide whether we should increase or decrease or keep the population size in the next slot of S iterations. e information which we collect is the non-decrease of the median of the objective function values. We will show the eeciency of our approach on some multi-modal functions with adequate global structure. (10.1145/2908812.2908864)
  DOI : 10.1145/2908812.2908864
• Simply generated non-crossing partitions
  
  • Kortchemski Igor
  • Marzouk Cyril
  Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2017, 26 (4), pp.560-592. We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing partitions with constraints on their block sizes. Our main tool is a bijection between non-crossing partitions and plane trees, which maps such simply generated non-crossing partitions into simply generated trees so that blocks of size $k$ are in correspondence with vertices of out-degree $k$. This allows us to obtain limit theorems concerning the block structure of simply generated non-crossing partitions. We apply our results in free probability by giving a simple formula relating the maximum of the support of a compactly supported probability measure on the real line in terms of its free cumulants. (10.1017/S0963548317000050)
  DOI : 10.1017/S0963548317000050
• Purcell magneto-elastic swimmer controlled by an external magnetic field
  
  • Alouges François
  • Desimone Antonio
  • Giraldi Laetitia
  • Zoppello Marta
  , 2017, 50 (1), pp.4120-4125. This paper focuses on the mechanism of propulsion of a Purcell swimmer whose segments are magnetized and react to an external magnetic field applied into the fluid. By an asymptotic analysis, we prove that it is possible to steer the swimmer along a chosen direction when the control functions are prescribed as an oscillating field. Moreover, we discuss what are the main obstructions to overcome in order to get classical controllability result for this system. (10.1016/j.ifacol.2017.08.798)
  DOI : 10.1016/j.ifacol.2017.08.798
• Clinical Identification of Geriatric Patients with Hypovitaminosis D: The ‘Vitamin D Status Predictor for Geriatrics’ Study
  
  • Annweiler Cédric
  • Riou Jeremie
  • Alessandri Axel
  • Gicquel David
  • Henni Samir
  • Feart Catherine
  • Kabeshova Anastasiia
  Nutrients, MDPI, 2017, 9 (7), pp.658. (10.3390/nu9070658)
  DOI : 10.3390/nu9070658
• Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry
  
  • Boscain Ugo
  • Neel Robert
  • Rizzi Luca
  Advances in Mathematics, Elsevier, 2017. On a sub-Riemannian manifold we define two type of Laplacians. The macroscopic Laplacian ∆ω, as the divergence of the horizontal gradient, once a volume ω is fixed, and the microscopic Laplacian, as the operator associated with a geodesic random walk. We consider a general class of random walks, where all sub-Riemannian geodesics are taken in account. This operator depends only on the choice of a complement c to the sub-Riemannian distribution, and is denoted L c. We address the problem of equivalence of the two operators. This problem is interesting since, on equiregular sub-Riemannian manifolds, there is always an intrinsic volume (e.g. Popp's one P) but not a canonical choice of complement. The result depends heavily on the type of structure under investigation: • On contact structures, for every volume ω, there exists a unique complement c such that ∆ω = L c. • On Carnot groups, if H is the Haar volume, then there always exists a complement c such that ∆H = L c. However this complement is not unique in general. • For quasi-contact structures, in general, ∆P = L c for any choice of c. In particular, L c is not symmetric w.r.t. Popp's measure. This is surprising especially in dimension 4 where, in a suitable sense, ∆P is the unique intrinsic macroscopic Laplacian. A crucial notion that we introduce here is the N-intrinsic volume, i.e. a volume that depends only on the set of parameters of the nilpotent approximation. When the nilpotent approximation does not depend on the point, a N-intrinsic volume is unique up to a scaling by a constant and the corresponding N-intrinsic sub-Laplacian is unique. This is what happens for dimension smaller or equal than 4, and in particular in the 4-dimensional quasi-contact structure mentioned above. (10.1016/j.aim.2017.04.024)
  DOI : 10.1016/j.aim.2017.04.024
• Dense flow around a sphere moving into a cloud of grains
  
  • Gondret Philippe
  • Faure Sylvain
  • Lefebvre-Lepot Aline
  • Seguin Antoine
  EPJ Web of Conferences, EDP Sciences, 2017, 140, pp.03013. A bidimensional simulation of a sphere moving at constant velocity into a cloud of smaller spherical grains without gravity is presented with a non-smooth contact dynamics method. A dense granular “cluster” zone of about constant solid fraction builds progressively around the moving sphere until a stationary regime appears with a constant upstream cluster size that increases with the initial solid fraction φ_0 of the cloud. A detailed analysis of the local strain rate and local stress fields inside the cluster reveals that, despite different spatial variations of strain and stresses, the local friction coefficient μ appears to depend only on the local inertial number I as well as the local solid fraction φ, which means that a local rheology does exist in the present non parallel flow. The key point is that the spatial variations of I inside the cluster does not depend on the sphere velocity and explore only a small range between about 10^−2 and 10−1. The influence of sidewalls is then investigated on the flow and the forces. (10.1051/epjconf/201714003013)
  DOI : 10.1051/epjconf/201714003013
• Structural optimization under overhang constraints imposed by additive manufacturing processes: an overview of some recent results
  
  • Allaire Grégoire
  • Dapogny Charles
  • Estevez Rafael
  • Faure Alexis
  • Michailidis Georgios
  , 2017. The purpose of this note is to report on the recent work [2,3], where new structural optimization strategies are proposed so that the optimized designs are free of overhang regions, which jeopardize their constructibility by additive manufacturing technologies. After showing numerical evidence that the intuitive angle-based criteria alone are insufficient to overcome this difficulty, a new constraint functional of the domain is introduced, which aggregates the self-weights of all the intermediate structures appearing in the course of the layer by layer assembly of the total structure. The mathematical analysis of this constraint is outlined and an algorithm is proposed to accelerate the significant computational effort entailed by the implementation of these ideas. Eventually, a numerical validation and several concrete examples are discussed.
• Multi-phase structural optimization of multi-layered composites and viscoelastic materials
  
  • Delgado Gabriel
  • Allaire G.
  • Hamdaoui M
  , 2017. This work is devoted to the application of the level-set method for topology optimization to multi-phase design of multi-layered composites and viscoelastic structures. In the case of composite laminates, we study their optimal design by allowing a variable stacking sequence and in-plane shape of each ply. In order to optimize both variables we rely on a decomposition technique which aggregates the constraints into one unique constraint margin function. Thanks to this approach, a rigorous equivalent bi-level optimization problem is established. On the other hand, we consider the optimal design of viscoelastic vibration damping treatments. We prove a general result describing the complex frequencies of the underlying non-linear eigenvalue problem. In both cases every layer of the structure is represented as a bi-material structure where a level set method is used to characterize the interfaces meanwhile the shape evolution is driven by a Hadamard method for boundary variations using the shape gradient. Two numerical test-cases are exhibited: In the case of multi-layered laminates, we minimize the weight of the structure subjected to a compliance and a first buckling load constraint, meanwhile for viscoelastic treatments, we maximize the the structure capacity to dissipate energy measured via the loss factor.
• Méthodes d'inversion pour la reconstruction de mines enfouies à partir de mesures d'antennes radar.
  
  • Lakhal Mohamed
  , 2017. Ce travail thèse s’inscrit dans le cadre du projet FUI Tandem portant sur l’imagerie radar de mines enfouies dans un sol sec par des antennes héliportées. Les données d’antennes correspondent à des mesures de champ électromagnétique (composante tangentielle à l’antenne) en configuration « back-scattering » : une seule antenne émettrice-réceptrice. L’objectif premier de la thèse est de valider/modifier la méthodologie SAR (Synthetic Aperture Radar) proposée par les ingénieurs pour traiter les données d’antenne et imager les mines. La difficulté essentielle réside dans le fait que la méthode SAR repose sur le principe d’un milieu de référence homogène alors que le cas d’étude ne l’est pas. Nous avons étudié l’incorporation d’une approximation bicouche du milieu de référence pour corriger l’effet du sol et obtenir des images moins sensibles à l’effet de celui-ci. La première solution consiste à mimer la technique SAR pour construire une indicatrice de la géométrie via la rétro-propagation de la donnée dans le milieu bi-couche en utilisant la formule donnée par l’approximation de Born. La deuxième option, beaucoup plus coûteuse numériquement consiste à inverser le modèle de Born avec une technique de régularisation de type variation totale. Nous nous intéressons dans une deuxième partie à l’adaptation de méthodes d’inversion de type MUSIC (MUltiple SIgnal Classification) pour retrouver l’information « profondeur » non fournie par les méthodes SAR. S’inspirant de la problématique Tandem, nous avons proposé l’extension de ces méthodes au cas de données en configuration quasi-back-scattering : une antenne émettrice couplée à un réseau 1D d’antennes réceptrices. La méthodologie est complètement nouvelle et la justification de la méthode repose sur l’analyse asymptotique du problème de diffraction dans le régime petit obstacle et champ lointain. L’étude a également été étendue à des configurations cylindriques qui pourraient être adaptées à l’imagerie bio-médicale.
• Probabilistic max-plus schemes for solving Hamilton-Jacobi-Bellman equations
  
  • Akian Marianne
  , 2017.
• Tropicalization of facets of polytopes
  
  • Allamigeon Xavier
  • Katz Ricardo D.
  Linear Algebra and its Applications, Elsevier, 2017. It is known that any tropical polytope is the image under the valuation map of ordinary polytopes over the Puiseux series field. The latter polytopes are called lifts of the tropical polytope. We prove that any pure tropical polytope is the intersection of the tropical half-spaces given by the images under the valuation map of the facet-defining half-spaces of a certain lift. We construct this lift explicitly, taking into account geometric properties of the given polytope. Moreover, when the generators of the tropical polytope are in general position, we prove that the above property is satisfied for any lift. This solves a conjecture of Develin and Yu. (10.1016/j.laa.2017.02.011)
  DOI : 10.1016/j.laa.2017.02.011
• Empirical Bayes approaches to PageRank type algorithms for rating scientific journals
  
  • Foulley Jean-Louis
  • Celeux Gilles
  • Josse Julie
  , 2017. Following criticisms against the journal Impact Factor, new journal influence scores have been developed such as the Eigenfactor or the Prestige Scimago Journal Rank. They are based on PageR-ank type algorithms on the cross-citations transition matrix of the citing-cited network. The PageR-ank algorithm performs a smoothing of the transition matrix combining a random walk on the data network and a teleportation to all possible nodes with fixed probabilities (the damping factor being α = 0.85). We reinterpret this smoothing matrix as the mean of a posterior distribution of a Dirichlet-multinomial model in an empirical Bayes perspective. We suggest a simple yet efficient way to make a clear distinction between structural and sampling zeroes. This allows us to contrast cases with self-citations are included or excluded to avoid overvalued journal bias. We estimate the model parameters by maximizing the marginal likelihood with a Majorize-Minimize algorithm. The procedure ends up with a score similar to the PageRank ones but with a damping factor depending on the journal at hand. The procedures are illustrated with an example about cross-citations among 47 statistical journals studied by Varin et al. (2016).
• Computation study of aluminum droplet combustion in two atmospheres
  
  • Muller Mathieu
  • Davidenko Dmitry
  • Giovangigli Vincent
  , 2017.
• Optimization of oriented and parametric cellular structures by the homogenization method
  
  • Geoffroy-Donders Perle
  • Allaire Grégoire
  • Cortial Julien
  • Pantz Olivier
  , 2017. We present here a topology optimization method based on a homogenization approach to design oriented and parametrized cellular structures. The present work deals with 2-D square cells featuring a rectangular hole, because their structure is close to that of rank-2 sequential laminates, which are optimal for compliance optimization. For several cells, the value and the parametric sensitivities of their effective elastic tensor can easily be computed, by the resolution of a cell problem. The obtained results can be used to build a surrogate model for the homogenized constitutive law. Moreover, we add the local orientation of the cells to our problem. Then, an optimal composite shape is computed thanks to an alternate directions algorithm. The crucial ingredient of the methodology is the extraction of a quasi-periodic and additive manufacturable structure from the previously obtained composite shape, based on the introduction of a space transformation.
• Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion
  
  • Boscain Ugo
  • Chertovskih Roman
  • Gauthier Jean-Paul
  • Prandi Dario
  • Remizov Alexey
  , 2018 (64), pp.37 - 53. In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit the information of where the image is corrupted, and others that do it. While the first algorithm is able to reconstruct only images that our visual system is still capable of recognize, we show that those of the second type completely transcend such limitation providing reconstructions at the state-of-the-art in image inpainting. This can be interpreted as a validation of the fact that our visual cortex actually encodes the first type of algorithm. (10.1051/proc/201864037)
  DOI : 10.1051/proc/201864037
• A model of layer by layer mechanical constraint for additive manufacturing in shape and topology optimization
  
  • Allaire Grégoire
  • Dapogny Charles
  • Faure Alexis
  • Michailidis Georgios
  , 2017. We propose a new functional of the domain, to be used in shape and topology optimization problems as a means to enforce the manufacturability of structures by additive manufacturing processes. Instead of considering merely the final shape, it aggregates objective functions (like compliance) for all the intermediate structures of the shape appearing in the course of its layer by layer assembly and subject to their self-weights. We compute its shape derivative and implement it into a shape and topology optimization algorithm based on the level set method. It turns out that this class of constraint functional is very costly to evaluate, due to the large number of successive layers required to build the final shape (each of them requiring a finite element analysis). Therefore, we introduce an interpolation algorithm which significantly accelerates the computational effort. The main idea is to build a piecewise affine approximation of the cost function and of its shape derivative by using the derivative of the elastic displacement with respect to the height of the intermediate structure (this is another application of the concept of shape derivative). Eventually, a numerical validation and some concrete examples are discussed.
• River Optimisation : short-term hydro-bidding under uncertainty
  
  • Wahid Faisal
  , 2017. The hydro-bidding problem is about computing optimal offer policies in order to maximize the expected profit of a hydroelectric producer participating in an electricity market. It combines the decision making process of both the trader and the hydro-dispatcher into one stochastic optimization problem. It is a sequential decision making problem, and can be formulated as a multistage stochastic program.These models can be difficult to solve when the value function is not concave. In this thesis, we study some of the limitations of the hydro-bidding problem, and propose a new stochastic optimization method called the Mixed-Integer Dynamic Approximation Scheme (MIDAS). MIDAS solves nonconvex, stochastic programs with monotonic value functions. It works in similar fashion to the Stochastic Dual Dynamic Programming (SDDP), but instead of using cutting planes, it uses step functions to create an outer approximation of the value function. MIDAS will converge almost surely to (T+1)ε optimal policies for continuous state variables, and to the exact optimum policy for integer state variables.We use MIDAS to solve three types of nonconvex hydro-bidding problem. The first hydro-bidding model we solve has integer state variables due to discrete production states. In this model we demonstrate that MIDAS constructs offer policies which are better than SDDP. The next hydro-bidding model has a mean reverting autoregressive price processs instead of a Markov chain. The last hydro-bidding incorporates headwater effects, where the power generation function is dependent on both the reservoir storage level and the turbine waterflow. In all of these models, we demonstrate convergence of MIDAS in finite iterations.MIDAS takes significantly longer to converge than SDDP due to its mixed-integer program (MIP) sub-problems. For hydro-bidding models with continuous state variables, its computation time depends on the value of δ. A larger δ reduces the computation time for convergence but also increases optimality error ε.In order to speed up MIDAS, we introduced two heuristics. The first heuristic is a step function selection heuristic, which is similar to the cut selection scheme in SDDP. This heuristic improves the solution time by up to 64%. The second heuristic iteratively solves the MIP sub-problems in MIDAS using smaller MIPs, rather than as one large MIP. This heuristic improves the solution time up to 60%. Applying both of the heuristics, we were able to use MIDAS to solve a hydro-bidding problem, consisting of a 4 reservoir, 4 station hydro scheme with integer state variables.
• Ambient noise correlation-based imaging with moving sensors
  
  • Garnier Josselin
  • Fink Mathias
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2017, 11 (3), pp.477 - 500. (10.3934/ipi.2017022)
  DOI : 10.3934/ipi.2017022
• Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
  
  • Durmus Alain
  • Moulines Éric
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2017, 27 (3), pp.1551 - 1587. In this paper, we study a method to sample from a target distribution π over Rd having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with π. For both constant and decreasing step sizes in the Euler discretization, we obtain nonasymptotic bounds for the convergence to the target distribution π in total variation distance. A particular attention is paid to the dependency on the dimension d, to demonstrate the applicability of this method in the high-dimensional setting. These bounds improve and extend the results of Dalalyan [J. R. Stat. Soc. Ser. B. Stat. Methodol. (2017) 79 651–676]. (10.1214/16-AAP1238)
  DOI : 10.1214/16-AAP1238
• Geometric constraints for shape and topology optimization in architectural design
  
  • Dapogny Charles
  • Faure Alexis
  • Michailidis Georgios
  • Allaire Grégoire
  • Couvelas Agnes
  • Estevez Rafael
  Computational Mechanics, Springer Verlag, 2017, 59 (6), pp.933–965. This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions. (10.1007/s00466-017-1383-6)
  DOI : 10.1007/s00466-017-1383-6
• Persistently damped transport on a network of circles
  
  • Chitour Yacine
  • Mazanti Guilherme
  • Sigalotti Mario
  Transactions of the American Mathematical Society, American Mathematical Society, 2017, 369 (6), pp.3841-3881. In this paper we address the exponential stability of a system of transport equations with intermittent damping on a network of $N \geq 2$ circles intersecting at a single point $O$. The $N$ equations are coupled through a linear mixing of their values at $O$, described by a matrix $M$. The activity of the intermittent damping is determined by persistently exciting signals, all belonging to a fixed class. The main result is that, under suitable hypotheses on $M$ and on the rationality of the ratios between the lengths of the circles, such a system is exponentially stable, uniformly with respect to the persistently exciting signals. The proof relies on an explicit formula for the solutions of this system, which allows one to track down the effects of the intermittent damping. (10.1090/tran/6778)
  DOI : 10.1090/tran/6778
• Shape optimization of a layer by layer mechanical constraint for additive manufacturing
  
  • Allaire Grégoire
  • Dapogny Charles
  • Faure Alexis
  • Michailidis Georgios
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2017, 355 (6), pp.699-717. The purpose of this note is to introduce a new functional of the domain, to be used in shape optimization problems as a means to enforce the constructibility of shapes by additive manufacturing processes. This functional aggregates the self-weights of all the intermediate structures of the shape appearing in the course of its layer by layer assembly. Its mathematical analysis is outlined and an algorithm is proposed to accelerate the significant computational effort entailed by the implementation of these ideas. Eventually, a numerical validation and a concrete example are discussed. (10.1016/j.crma.2017.04.008)
  DOI : 10.1016/j.crma.2017.04.008
• Eigenvalue problems with sign-changing coefficients
  
  • Carvalho Camille
  • Chesnel Lucas
  • Ciarlet Patrick
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2017, 355 (6), pp.671 - 675. We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We describe the main spectral properties of these problems according to the features of the coefficients. Then, under some assumptions on the mesh, we explain how one can use classical finite element methods to approximate the spectrum as well as the eigenfunctions while avoiding spurious modes. We also prove localisation results of the eigenfunctions for certain sets of coefficients. (10.1016/j.crma.2017.05.002)
  DOI : 10.1016/j.crma.2017.05.002
• Emergence of long-range phase coherence in nonlocal fluids of light
  
  • Garnier Josselin
  • Fusaro Adrien
  • Xu G.
  • Conti C.
  • Faccio D.
  • Trillo Stefano
  • Picozzi A.
  Physical Review A : Atomic, molecular, and optical physics [1990-2015], American Physical Society, 2017, 95 (6). The emergence of long-range phase coherence among random nonlinear waves is a fascinating effect that characterizes fundamental phenomena such as the condensation of nonlinear waves and the related manifestation of superfluidity of certain turbulent flows. Here we report a previously unrecognized phenomenon of spontaneous emergence of long-range phase coherence among incoherent waves interacting through a nonlocal nonlinearity. The theory reveals that the establishment of long-range phase coherence constitutes a generic property of a conservative (Hamiltonian) system of highly nonlocal random waves that evolve in the strongly nonlinear regime. Aside from phase coherence, the field exhibits intensity fluctuations whose coherence length is shown to increase in a dramatic way during the evolution of the system. The analysis can be transposed to the temporal domain, revealing the emergence of temporal phase coherence among incoherent waves propagating in nonlinear materials featured by a noninstantaneous nonlinear response (10.1103/PhysRevA.95.063818)
  DOI : 10.1103/PhysRevA.95.063818
• A risk analysis for a system stabilized by a central agent
  
  • Garnier Josselin
  • Papanicolaou George
  • Yang Tzu-Wei
  Risk and Decision Analysis, IOS, 2017, 6 (2), pp.97 - 120. (10.3233/RDA-160117)
  DOI : 10.3233/RDA-160117