Publications

2017

• Online Learning and Blackwell Approachability with Partial Monitoring: Optimal Convergence Rates
  
  • Kwon Joon
  • Perchet Vianney
  JMLR Papers, 2017, 54, pp.604-613. Blackwell approachability is an online learning setup generalizing the classical problem of regret minimization by allowing for instance multi-criteria optimization, global (online) optimization of a convex loss, or online linear optimization under some cumulative constraint. We consider partial monitoring where the decision maker does not necessarily observe the outcomes of his decision (unlike the traditional regret/bandit literature). Instead, he receives a random signal correlated to the decision-outcome pair, or only to the outcome. We construct, for the first time, approachability algorithms with convergence rate of order O(T −1/2) when the signal is independent of the decision and of order O(T −1/3) in the case of general signals. Those rates are optimal in the sense that they cannot be improved without further assumption on the structure of the objectives and/or the signals.
• EFSA-GMO-DE-2017-141 1
  
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2017.
• Instability of dielectrics and conductors in electrostatic fields
  
  • Allaire Grégoire
  • Rauch Jeffrey
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2017, 124, pp.233-268. This article proves most of the assertion in §116 of Maxwell's treatise on electromagnetism. The results go under the name Earnshaw's Theorem and assert the absence of stable equilibrium configurations of conductors and dielectrics in an external electrostatic field.
• Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
  
  • Garcke Jochen
  • Kröner Axel
  Journal of Scientific Computing, Springer Verlag, 2017, 70 (1), pp.1-28. An approach to solve finite time horizon suboptimal feedback control problems for partial differential equations is proposed by solving dynamic programming equations on adaptive sparse grids. The approach is illustrated for the wave equation and an extension to equations of Schrödinger type is indicated. A semi-discrete optimal control problem is introduced and the feedback control is derived from the corresponding value function. The value function can be characterized as the solution of an evolutionary Hamilton-Jacobi Bellman (HJB) equation which is defined over a state space whose dimension is equal to the dimension of the underlying semi-discrete system. Besides a low dimensional semi-discretization it is important to solve the HJB equation efficiently to address the curse of dimensionality. We propose to apply a semi-Lagrangian scheme using spatially adaptive sparse grids. Sparse grids allow the discretization of the value functions in (higher) space dimensions since the curse of dimensionality of full grid methods arises to a much smaller extent. For additional efficiency an adaptive grid refinement procedure is explored. We present several numerical examples studying the effect the parameters characterizing the sparse grid have on the accuracy of the value function and the optimal trajectory.
• Moral hazard in dynamic risk management
  
  • Cvitanić Jakša
  • Possamaï Dylan
  • Touzi Nizar
  Management Science, INFORMS, 2017, 63 (10), pp.3328-3346. We consider a contracting problem in which a principal hires an agent to manage a risky project. When the agent chooses volatility components of the output process and the principal observes the output continuously, the principal can compute the quadratic variation of the output, but not the individual components. This leads to moral hazard with respect to the risk choices of the agent. We identify a family of admissible contracts for which the optimal agent's action is explicitly characterized, and, using the recent theory of singular changes of measures for Itô processes, we study how restrictive this family is. In particular, in the special case of the standard Homlstrom-Milgrom model with fixed volatility, the family includes all possible contracts. We solve the principal-agent problem in the case of CARA preferences, and show that the optimal contract is linear in these factors: the contractible sources of risk, including the output, the quadratic variation of the output and the cross-variations between the output and the contractible risk sources. Thus, like sample Sharpe ratios used in practice, path-dependent contracts naturally arise when there is moral hazard with respect to risk management. In a numerical example, we show that the loss of efficiency can be significant if the principal does not use the quadratic variation component of the optimal contract. (10.1287/mnsc.2016.2493)
  DOI : 10.1287/mnsc.2016.2493
• Self-administered vitamin D status predictor : older adults are able to use a self-questionnaire for evaluating their vitamin D status
  
  • Annweiler Cédric
  • Kabeshova Anastasiia
  • Callens Alix
  • Paty Marie-Liesse
  • Holick Michael F.
  • Duval Guillaume T.
  PLoS ONE, Public Library of Science, 2017, 12 (11). The 16-item Vitamin D Status Predictor (VDSP) questionnaire helps to identify, without resorting to a blood test, older adults with low vitamin D concentrations. Our objective was to determine whether a self-administered VDSP was concordant with the VDSP administered by a physician, and to examine the concordance of every single item of the VDSP. Methods A total of 349 older in- and outpatients (mean, 83.2±7.2years; 59% female) were consecutively recruited in the geriatric ward of the University Hospital of Angers, France. All participants completed a self-administered VDSP questionnaire (self-VDSP) in paper format composed of 17 items exploring age, gender, general condition, nutrition, vision, mood, cognition, gait and falls, and osteoporosis. All participants underwent subsequently a full clinical examination by a physician exploring the same areas (rater-VDSP). Results The agreement between the self-VDSP and the rater-VDSP was almost perfect for the probability of having low vitamin D concentrations, regardless of the definition used (i.e., ≤25, ≤50 or ≤75 nmol/L). The agreements between physicians’ and patients’ responses were significant for every single VDSP item. The agreement was fair to perfect for all items, except for cognitive disorders, undernutrition and polymorbidity (poor agreement). Conclusions Older adults are able to evaluate their own probabilities of severe vitamin D deficiency, deficiency and insufficiency. A self-questionnaire may promote the use of the VDSP tool in this population, and help clinicians in decisions to supplement their patients in a reasoned way. (10.1371/journal.pone.0186578)
  DOI : 10.1371/journal.pone.0186578
• Correction to Black--Scholes Formula Due to Fractional Stochastic Volatility
  
  • Garnier Josselin
  • Sølna Knut
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2017, 8 (1), pp.560 - 588. (10.1137/15M1036749)
  DOI : 10.1137/15M1036749
• Consistent functional cross field design for mesh quadrangulation
  
  • Azencot Omri
  • Corman Etienne
  • Ben-Chen Mirela
  • Ovsjanikov Maks
  ACM Transactions on Graphics, Association for Computing Machinery, 2017, 36 (4), pp.92. We propose a novel technique for computing consistent cross fields on a pair of triangle meshes given an input correspondence, which we use as guiding fields for approximately consistent quadrangulations. Unlike the majority of existing methods our approach does not assume that the meshes share the same connectivity or even have the same number of vertices, and furthermore does not place any restrictions on the topology (genus) of the shapes. Importantly, our method is robust with respect to small perturbations of the given correspondence, as it only relies on the transportation of real-valued functions and thus avoids the costly and error-prone estimation of the map differential. Key to this robustness is a novel formulation, which relies on the previously-proposed notion of power vectors, and we show how consistency can be enforced without pre-alignment of local basis frames, in which these power vectors are computed. We demonstrate that using the same formulation we can both compute a quadrangulation that would respect a given symmetry on the same shape or a map across a pair of shapes. We provide quantitative and qualitative comparison of our method with several baselines and show that it both provides more accurate results and allows to handle more general cases than existing techniques. (10.1145/3072959.3073696)
  DOI : 10.1145/3072959.3073696
• Cell Averaging Two-Scale Convergence: Applications to Periodic Homogenization
  
  • Alouges François
  • Di Fratta Giovanni
  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2017, 15 (4), pp.1651-1671. (10.1137/16M1085309)
  DOI : 10.1137/16M1085309
• Understanding the Time-Dependent Effective Diffusion Coefficient Measured by Diffusion MRI: the Intra-Cellular Case
  
  • Haddar Houssem
  • Li Jing-Rebecca
  • Schiavi Simona
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2017. Diffusion Magnetic Resonance Imaging (dMRI) can be used to measure a time-dependent effective diffusion coefficient that can in turn reveal information about the tissue geometry. Recently a mathematical model for the time-dependent effective diffusion coefficient was obtained using homogenization techniques after imposing a certain scaling relationship for the time, the biological cell membrane permeability, the diffusion-encoding magnetic field gradient strength, and a periodicity length of the cellular geometry. With this choice of the scaling of the physical parameters, the effective diffusion coefficient of the medium can be computed after solving a diffusion equation subject to a time-dependent Neumann boundary condition, independently in the biological cells and in the extra-cellular space. In this paper, we analyze this new model, which we call the H-ADC model, in the case of finite domains, which is relevant to diffusion inside biological cells. We use both the eigenfunction expansion and the single layer potential representation for the solution of the above mentioned diffusion equation to obtain analytical expressions for the effective diffusion coefficient in different diffusion time regimes. These expressions are validated using numerical simulations in two dimensions.
• An approximation of the M 2 closure: application to radiotherapy dose simulation
  
  • Pichard T
  • Alldredge G W
  • Brull Stéphane
  • Dubroca B
  • Frank M
  Journal of Scientific Computing, Springer Verlag, 2017. Particle transport in radiation therapy can be modelled by a kinetic equation which must be solved numerically. Unfortunately, the numerical solution of such equations is generally too expensive for applications in medical centers. Moment methods provide a hierarchy of models used to reduce the numerical cost of these simulations while preserving basic properties of the solutions. Moment models require a closure because they have more unknowns than equations. The entropy-based closure is based on the physical description of the particle interactions and provides desirable properties. However, computing this closure is expensive. We propose an approximation of the closure for the first two models in the hierarchy, the M 1 and M 2 models valid in one, two or three dimensions of space. Compared to other approximate closures, our method works in multiple dimensions. We obtain the approximation by a careful study of the domain of realizability and by invariance properties of the entropy minimizer. The M 2 model is shown to provide significantly better accuracy than the M 1 model for the numerical simulation of a dose computation in radiotherapy. We propose a numerical solver using those approximated closures. Numerical experiments in dose computation test cases show that the new method is more efficient compared to numerical solution of the minimum entropy problem using standard software tools.
• HOMOGENIZATION OF STOKES SYSTEM USING BLOCH WAVES
  
  • Allaire Grégoire
  • Ghosh Tuhin
  • Vanninathan Muthusamy
  Networks and Heterogeneous Media, American Institute of Mathematical Sciences, 2017, 12 (4), pp.525-550. In this work, we study the Bloch wave homogenization for the Stokes system with periodic viscosity coefficient. In particular, we obtain the spectral interpretation of the homogenized tensor. The presence of the incompressibility constraint in the model raises new issues linking the homogenized tensor and the Bloch spectral data. The main difficulty is a lack of smoothness for the bottom of the Bloch spectrum, a phenomenon which is not present in the case of the elasticity system. This issue is solved in the present work, completing the homogenization process of the Stokes system via the Bloch wave method.
• A numerical approach to determine mutant invasion fitness and evolutionary singular strategies
  
  • Fritsch Coralie
  • Campillo Fabien
  • Ovaskainen Otso
  Theoretical Population Biology, Elsevier, 2017, 115, pp.89-99. We propose a numerical approach to study the invasion fitness of a mutant and to determine evolutionary singular strategies in evolutionary structured models in which the competitive exclusion principle holds. Our approach is based on a dual representation, which consists of the modelling of the small size mutant population by a stochastic model and the computation of its corresponding deterministic model. The use of the deterministic model greatly facilitates the numerical determination of the feasibility of invasion as well as the convergence-stability of the evolutionary singular strategy. Our approach combines standard adaptive dynamics with the link between the mutant survival criterion in the stochastic model and the sign of the eigenvalue in the corresponding deterministic model. We present our method in the context of a mass-structured individual-based chemostat model. We exploit a previously derived mathematical relationship between stochastic and deterministic representations of the mutant population in the chemostat model to derive a general numerical method for analyzing the invasion fitness in the stochastic models. Our method can be applied to the broad class of evolutionary models for which a link between the stochastic and deterministic invasion fitnesses can be established. (10.1016/j.tpb.2017.05.001)
  DOI : 10.1016/j.tpb.2017.05.001
• Sampling method for sign changing contrast
  
  • Audibert Lorenzo
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2017. We extend the applicability of the Generalized Linear Sampling Method (GLSM) [2] and the Factorization Method (FM)[14] to the case of inhomogeneities where the contrast change sign strictly inside the obstacle. Both methods give an exact characterization of the target shapes in term of the fareld operator (at a xed frequency). One of the key ingredient to prove this exact characterization is based on a factorization of the fareld operator. This factorization involves three operators which should exhibit specic properties. This paper is concerned with the extension of the coercivity property required on one of them to the case of sign changing contrast both for isotropic and anisotropic scatters with possibly dierent supports for the isotropic and anisotropic parts. We fnally validate the method through some numerical tests in two dimensions.
• Parameter Estimation in Nonlinear Mixed Effect Models Using saemix, an R Implementation of the SAEM Algorithm
  
  • Comets Emmanuelle
  • Lavenu Audrey Paris
  • Lavielle Marc
  Journal of Statistical Software, University of California, Los Angeles, 2017, 80 (3), pp.i03. The saemix package for R provides maximum likelihood estimates of parameters in nonlinear mixed effect models, using a modern and efficient estimation algorithm, the stochastic approximation expectation-maximisation (SAEM) algorithm. In the present paper we describe the main features of the package, and apply it to several examples to illustrate its use. Making use of S4 classes and methods to provide user-friendly interaction, this package provides a new estimation tool to the R community. (10.18637/jss.v080.i03)
  DOI : 10.18637/jss.v080.i03
• On perturbed proximal gradient algorithms
  
  • Atchadé Yves
  • Fort Gersende
  • Moulines Éric
  Journal of Machine Learning Research, Microtome Publishing, 2017, 18 (10), pp.1-33.
• The infinitesimal model: definition, derivation, and implications
  
  • Barton Nick
  • Etheridge Alison M
  • Véber Amandine
  Theoretical Population Biology, Elsevier, 2017. Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation , population structure, ... We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1/\sqrt{M}. Simulations suggest that in some cases the convergence may be as fast as 1/\sqrt{M} .
• Adaptive multipreconditioned FETI: scalability results and robustness assessment
  
  • Bovet Christophe
  • Parret-Fréaud Augustin
  • Spillane Nicole
  • Gosselet Pierre
  Computers & Structures, Elsevier, 2017, 193, pp.1-20. The purpose of this article is to assess the adaptive multipreconditioned FETI solvers (AMPFETI) on realistic industrial problems and hardware. The multi-preconditioned FETI algorithm (first introduced as Simultaneous FETI [1]) is a non-overlapping domain decomposition method which exhibits good robust-ness properties without requiring the explicit knowledge of the original partial differential equation, or any a priori analysis of the algebraic system through eigenvalues problems. Multipreconditioned FETI solves critical problems in significantly fewer iterations than classical FETI but each iteration involves a larger computational effort. An adaptive strategy (known as the adaptive mul-tipreconditioned conjugate gradient algorithm [2]) has been proposed to achieve balance between robustness and efficiency and we will observe that it provides an efficient solver for the problems considered here. (10.1016/j.compstruc.2017.07.010)
  DOI : 10.1016/j.compstruc.2017.07.010
• Optimal control of slender microswimmers
  
  • Zoppello Marta
  • Desimone Antonio
  • Alouges François
  • Giraldi Laetitia
  • Martinon Pierre
  , 2017, pp.21. We discuss a reduced model to compute the motion of slender swimmers which propel themselves by changing the curvature of their body. Our approach is based on the use of Resistive Force Theory for the evaluation of the viscous forces and torques exerted by the surrounding fluid, and on discretizing the kinematics of the swimmer by representing its body through an articulated chain of N rigid links capable of planar deformations. The resulting system of ODEs governing the motion of the swimmer is easy to assemble and to solve, making our reduced model a valuable tool in the design and optimization of bio-inspired artificial microdevices. We prove that the swimmer is controllable in the whole plane for N is greater of equal to 3 and for almost every set of stick lengths. As a direct result, there exists an optimal swimming strategy to reach a desired configuration in minimum time. Numerical experiments for N = 3 (Purcell swimmer) suggest that the optimal strategy is periodic, namely a sequence of identical strokes. Our results indicate that this candidate for an optimal stroke indeed gives a better displacement speed than the classical Purcell stroke. (10.1007/978-3-319-73371-5_8)
  DOI : 10.1007/978-3-319-73371-5_8
• Dependence of tropical eigenspaces
  
  • Niv Adi
  • Rowen Louis
  Communications in Algebra, Taylor & Francis, 2017, 45 (3), pp.924-942. We study the pathology that causes tropical eigenspaces of distinct su-pertropical eigenvalues of a non-singular matrix A, to be dependent. We show that in lower dimensions the eigenvectors of distinct eigenvalues are independent, as desired. The index set that differentiates between subsequent essential monomials of the characteristic polynomial, yields an eigenvalue λ, and corresponds to the columns of adj(A + λI) from which the eigenvectors are taken. We ascertain the cause for failure in higher dimensions, and prove that independence of the eigenvectors is recovered in case the " difference criterion " holds, defined in terms of disjoint differences between index sets of subsequent coefficients. We conclude by considering the eigenvectors of the matrix A ∇ := 1 det(A) adj(A) and the connection of the independence question to generalized eigenvectors. (10.1080/00927872.2016.1172603)
  DOI : 10.1080/00927872.2016.1172603
• A characterization of switched linear control systems with finite L 2 -gain
  
  • Chitour Yacine
  • Mason Paolo
  • Sigalotti Mario
  IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 62, pp.1825-1837. Motivated by an open problem posed by J.P. Hespanha, we extend the notion of Barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation. We use these tools to prove that the finiteness of the L2-gain is equivalent, for a large set of switched linear control systems, to the condition that the generalized spectral radius associated with any minimal realization of the original switched system is smaller than one. (10.1109/tac.2016.2593678)
  DOI : 10.1109/tac.2016.2593678
• Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots
  
  • Akian Marianne
  • Gaubert Stéphane
  • Sharify Meisam
  Linear Algebra and its Applications, Elsevier, 2017, 528, pp.394--435. We show that the sequence of moduli of the eigenvalues of a matrix polynomial is log-majorized, up to universal constants, by a sequence of "tropical roots" depending only on the norms of the matrix coefficients. These tropical roots are the non-differentiability points of an auxiliary tropical polynomial, or equivalently, the opposites of the slopes of its Newton polygon. This extends to the case of matrix polynomials some bounds obtained by Hadamard, Ostrowski and Pólya for the roots of scalar polynomials. We also obtain new bounds in the scalar case, which are accurate for "fewnomials" or when the tropical roots are well separated. (10.1016/j.laa.2016.11.004)
  DOI : 10.1016/j.laa.2016.11.004
• Multipoint scatterers with zero-energy bound states
  
  • Grinevich Piotr
  • Novikov Roman
  Theoretical and Mathematical Physics, Consultants bureau, 2017, 193 (2), pp.1675-1679. We study multipoint scatterers with zero-energy bound states in three dimensions. We present examples of such scatterers with multiple zero eigenvalue or with strong multipole localization of zero-energy bound states.
• Regularity for the optimal compliance problem with length penalization
  
  • Chambolle Antonin
  • Lamboley Jimmy
  • Lemenant Antoine
  • Stepanov Eugene
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2017. We prove some regularity results for a connected set S in the planar domain O, which minimizes the compliance of its complement O\S, plus its length. This problem, interpreted as to find the best location for attaching a membrane subject to a given external force f so as to minimize the compliance, can be seen as an elliptic PDE version of the average distance problem/irrigation problem (in a penalized version rather than a constrained one), which has been extensively studied in the literature. We prove that minimizers consist of a finite number of smooth curves meeting only by three at 120 degree angles, containing no loop, and possibly touching the boundary of the domain only tangentially. Several new technical tools together with the classical ones are developed for this purpose.
• Certified Descent Algorithm for shape optimization driven by fully-computable a posteriori error estimators
  
  • Giacomini Matteo
  • Pantz Olivier
  • Trabelsi Karim
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2017, 23 (3), pp.977-1001. In this paper we introduce a novel certified shape optimization strategy-named Certified Descent Algorithm (CDA)-to account for the numerical error introduced by the Finite Element approximation of the shape gradient. We present a goal-oriented procedure to derive a certified upper bound of the error in the shape gradient and we construct a fully-computable, constant-free a posteriori error estimator inspired by the complementary energy principle. The resulting CDA is able to identify a genuine descent direction at each iteration and features a reliable stopping criterion. After validating the error estimator, some numerical simulations of the resulting certified shape optimization strategy are presented for the well-known inverse identification problem of Electrical Impedance Tomography. (10.1051/cocv/2016021)
  DOI : 10.1051/cocv/2016021