Publications

2020

• Quantitative modeling links in vivo microstructural and macrofunctional organization of human and macaque insular cortex, and predicts cognitive control abilities
  
  • Menon Vinod
  • Gallardo Guillermo
  • Pinsk Mark
  • Nguyen Van-Dang
  • Li Jing-Rebecca
  • Cai Weidong
  • Wassermann Demian
  , 2020. (10.1101/662601)
  DOI : 10.1101/662601
• Adaptive Bayesian SLOPE—High-dimensional Model Selection with Missing Values
  
  • Jiang Wei
  • Bogdan Malgorzata
  • Josse Julie
  • Miasojedow Blazej
  • Rockova Veronika
  , 2020. We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure -- adaptive Bayesian SLOPE -- which effectively combines the SLOPE method (sorted l1 regularization) together with the Spike-and-Slab LASSO method. We position our approach within a Bayesian framework which allows for simultaneous variable selection and parameter estimation, despite the missing values. As with the Spike-and-Slab LASSO, the coefficients are regarded as arising from a hierarchical model consisting of two groups: (1) the spike for the inactive and (2) the slab for the active. However, instead of assigning independent spike priors for each covariate, here we deploy a joint "SLOPE" spike prior which takes into account the ordering of coefficient magnitudes in order to control for false discoveries. Through extensive simulations, we demonstrate satisfactory performance in terms of power, FDR and estimation bias under a wide range of scenarios. Finally, we analyze a real dataset consisting of patients from Paris hospitals who underwent a severe trauma, where we show excellent performance in predicting platelet levels. Our methodology has been implemented in C++ and wrapped into an R package ABSLOPE for public use.
• Computing bi-tangents for transmission belts
  
  • Chouly Franz
  • Loubani Jinan
  • Lozinski Alexei
  • Méjri Bochra
  • Merito Kamil
  • Passos Sébastien
  • Pineda Angie
  , 2020. In this note, we determine the bi-tangents of two rotated ellipses, and we compute the coordinates of their points of tangency. For these purposes, we develop two approaches. The first one is an analytical approach in which we compute analytically the equations of the bi-tangents. This approach is valid only for some cases. The second one is geometrical and is based on the determination of the normal vector to the tangent line. This approach turns out to be more robust than the first one and is valid for any configuration of ellipses.
• Nonparametric imputation by data depth
  
  • Mozharovskyi Pavlo
  • Josse Julie
  • Husson François
  Journal of the American Statistical Association, Taylor & Francis, 2020, 115 (529), pp.241-253. The presented methodology for single imputation of missing values borrows the idea from data depth --- a measure of centrality defined for an arbitrary point of the space with respect to a probability distribution or a data cloud. This consists in iterative maximization of the depth of each observation with missing values, and can be employed with any properly defined statistical depth function. On each single iteration, imputation is narrowed down to optimization of quadratic, linear, or quasiconcave function being solved analytically, by linear programming, or the Nelder-Mead method, respectively. Being able to grasp the underlying data topology, the procedure is distribution free, allows to impute close to the data, preserves prediction possibilities different to local imputation methods (k-nearest neighbors, random forest), and has attractive robustness and asymptotic properties under elliptical symmetry. It is shown that its particular case --- when using Mahalanobis depth --- has direct connection to well known treatments for multivariate normal model, such as iterated regression or regularized PCA. The methodology is extended to the multiple imputation for data stemming from an elliptically symmetric distribution. Simulation and real data studies positively contrast the procedure with existing popular alternatives. The method has been implemented as an R-package. (10.1080/01621459.2018.1543123)
  DOI : 10.1080/01621459.2018.1543123
• The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
  
  • Backhoff Julio
  • Conforti Giovanni
  • Gentil Ivan
  • Léonard Christian
  Probability Theory and Related Fields, Springer Verlag, 2020, 178, pp.475-530. (10.1007/s00440-020-00977-8)
  DOI : 10.1007/s00440-020-00977-8
• Kinetic derivation of diffuse-interface fluid models
  
  • Giovangigli Vincent
  Physical Review E, American Physical Society (APS), 2020, 102. We present a full derivation of capillary fluid equations from the kinetic theory of dense gases. These equations involve van der Waals' gradient energy, Korteweg's tensor, and Dunn and Serrin's heat flux as well as viscous and heat dissipative fluxes. Starting from macroscopic equations obtained from the kinetic theory of dense gases, we use a second-order expansion of the pair distribution function in order to derive the diffuse interface model. The capillary extra terms and the capillarity coefficient are then associated with intermolecular forces and the pair interaction potential. (10.1103/physreve.102.012110)
  DOI : 10.1103/physreve.102.012110
• Commentaires sur le rapport de surveillance de culture du MON 810 en 2018. Paris, le 25 février 2020
  
  • Du Haut Conseil Des Biotechnologies Comité Scientifique
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • 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
  • de Verneuil Hubert
  • Vilotte Jean-Luc
  , 2020, pp.35 p.. Les analyses contenues dans le rapport de surveillance de Bayer Agriculture BVBA ne font apparaître aucun problème majeur associé à la culture de maïs MON 810 en 2018. Toutefois, le CS du HCB identifie encore certaines faiblesses et limites méthodologiques concernant la surveillance de la sensibilité des ravageurs ciblés à la toxine Cry1Ab, remettant en question les conclusions du rapport. Le HCB estime notamment que l’utilisation d’une dose diagnostic présente certaines limites pour la détection précoce de l’évolution de la résistance, tant dans son principe intrinsèque que dans sa mise en oeuvre par Bayer, et recommande une méthode alternative de type F2 screen permettant de déterminer la fréquence des allèles de résistance au sein d’une population de ravageurs cibles. Par ailleurs, le HCB formule des recommandations destinées à renforcer la mise en oeuvre des zones refuges pour prévenir ou retarder le développement de résistance à la toxine Cry1Ab chez les ravageurs ciblés. Concernant la surveillance générale, le CS du HCB relève un problème de pertinence méthodologique quant aux questions étudiées, avec des règles de décision arbitraires, des conclusions incorrectement justifiées et un possible biais associé au format d’enquête auprès du panel d’agriculteurs qui ont accepté de répondre au questionnaire. Enfin, le CS du HCB recommande que le rapport de surveillance considère la présence de téosinte dans des zones de culture du maïs MON 810 en Espagne et les risques potentiels associés à une éventuelle introgression de gènes de maïs MON 810 chez le téosinte.
• Optimal Hedging Under Fast-Varying Stochastic Volatility
  
  • Garnier Josselin
  • Sølna Knut
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2020, 11 (1), pp.274-325. In a market with a rough or Markovian mean-reverting stochastic volatility thereis no perfect hedge. Here it is shown how various delta-type hedging strategies perform and canbe evaluated in such markets in the case of European options.A precise characterization of thehedging cost, the replication cost caused by the volatilityfluctuations, is presented in an asymptoticregime of rapid mean reversion for the volatility fluctuations. The optimal dynamic asset basedhedging strategy in the considered regime is identified as the so-called “practitioners” delta hedgingscheme. It is moreover shown that the performances of the delta-type hedging schemes are essentiallyindependent of the regularity of the volatility paths in theconsidered regime and that the hedgingcosts are related to a Vega risk martingale whose magnitude is proportional to a new market riskparameter. It is also shown via numerical simulations that the proposed hedging schemes whichderive from option price approximations in the regime of rapid mean reversion, are robust: the“practitioners” delta hedging scheme that is identified as being optimal by our asymptotic analysiswhen the mean reversion time is small seems to be optimal witharbitrary mean reversion times. (10.1137/18M1221655)
  DOI : 10.1137/18M1221655
• Regression Monte Carlo methods for HJB-type equations: which approximation space?
  
  • Barrera David
  • Gobet Emmanuel
  • Lopez-Salas Jose
  • Turkedjiev Plamen
  • Vasquez Carlos
  • Zubelli Jorge
  , 2020.
• Tropical planar networks
  
  • Gaubert Stéphane
  • Niv Adi
  Linear Algebra and its Applications, Elsevier, 2020, 595, pp.123-144. We show that every tropical totally positive matrix can be uniquely represented as the transfer matrix of a canonical totally connected weighted planar network. We deduce a uniqueness theorem for the factorization of a tropical totally positive in terms of elementary Jacobi matrices. (10.1016/j.laa.2020.02.019)
  DOI : 10.1016/j.laa.2020.02.019
• A quantitative McDiarmid’s inequality for geometrically ergodic Markov chains
  
  • Havet Antoine
  • Lerasle Matthieu
  • Moulines Éric
  • Vernet Elodie
  Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2020, 25. (10.1214/20-ECP286)
  DOI : 10.1214/20-ECP286
• Error estimates for phase recovering from phaseless scattering data
  
  • Novikov Roman
  • Sivkin Vladimir
  Eurasian Journal of Mathematical and Computer Applications, Eurasian National University, Kazakhstan (Nur-Sultan), 2020, 8 (1), pp.44-61. We study the simplest explicit formulas for approximate finding the complex scattering amplitude from modulus of the scattering wave function. We obtain detailed error estimates for these formulas in dimensions d = 3 and d = 2.
• ADDITIVE MANUFACTURING SCANNING PATHS OPTIMIZATION USING SHAPE OPTIMIZATION TOOLS
  
  • Boissier M
  • Allaire G.
  • Tournier Christophe
  Structural and Multidisciplinary Optimization, Springer Verlag, 2020, 61, pp.2437–2466. This paper investigates path planning strategies for additive manufacturing processes such as powder bed fusion. The state of the art mainly studies trajectories based on existing patterns. Parametric optimization on these patterns or allocating them to the object areas are the main strategies. We propose in this work a more systematic optimization approach without any a priori restriction on the trajectories. The typical optimization problem is to melt the desired structure, without overheating (to avoid thermally induced residual stresses) and possibly with a minimal path length. The state equation is the heat equation with a source term depending on the scanning path. First, in a steady-state context, shape optimization tools are applied to trajec-tories. Second, for time-dependent problems, an optimal control method is considered instead. In both cases, gradient type algorithms are deduced and tested on 2-d examples. Numerical results are discussed, leading to a better understanding of the problem and thus to short-and long-term perspectives. (10.1007/s00158-020-02614-3)
  DOI : 10.1007/s00158-020-02614-3
• State-constrained control-affine parabolic problems I: First and Second order necessary optimality conditions
  
  • Aronna M Soledad
  • Bonnans J. Frederic
  • Kröner Axel
  Set-Valued and Variational Analysis, Springer, 2020. In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimen-sional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions. The appendix provides an example illustrating the applicability of our results.
• Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions
  
  • Bansaye Vincent
  • Cloez Bertrand
  • Gabriel Pierre
  Acta Applicandae Mathematicae, Springer Verlag, 2020, 166 (1), pp.29-72. We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and Doeblin's type conditions for coupling the associated process. Our aim is to provide quantitative estimates for linear partial differential equations and we develop several applications for population dynamics in varying environment. We start with the asymptotic profile for a growth diffusion model with time and space non-homogeneity. Moreover we provide general estimates for semigroups which become asymptotically homogeneous, which are applied to an age-structured population model. Finally, we obtain a speed of convergence for periodic semi-groups and new bounds in the homogeneous setting. They are are illustrated on the renewal equation. (10.1007/s10440-019-00253-5)
  DOI : 10.1007/s10440-019-00253-5
• SCALPEL3: a scalable open-source library for healthcare claims databases
  
  • Bacry Emmanuel
  • Gaiffas Stéphane
  • Leroy Fanny
  • Morel Maryan
  • Nguyen D.P.
  • Sebiat Youcef
  • Sun Dian
  International Journal of Medical Informatics, Elsevier, 2020.
• Variance Reduction Methods and Multilevel Monte Carlo Strategy for Estimating Densities of Solutions to Random Second-Order Linear Differential Equations
  
  • Jornet Marc
  • Calatayud Julia
  • Le Maitre Olivier
  • Cortés Juan Carlos
  International Journal for Uncertainty Quantification, Begell House Publishers, 2020, 10 (5), pp.467-497. This paper concerns the estimation of the density function of the solution to a random nonautonomous second-order linear differential equation with analytic data processes. In a recent contribution, we proposed to express the density function as an expectation, and we used a standard Monte Carlo algorithm to approximate the expectation. Although the algorithms worked satisfactorily for most test problems, some numerical challenges emerged for others, due to large statistical errors. In these situations, the convergence of the Monte Carlo simulation slows down severely, and noisy features plague the estimates. In this paper, we focus on computational aspects and propose several variance reduction methods to remedy these issues and speed up the convergence. First, we introduce a pathwise selection of the approximating processes which aims at controlling the variance of the estimator. Second, we propose a hybrid method, combining Monte Carlo and deterministic quadrature rules, to estimate the expectation. Third, we exploit the series expansions of the solutions to design a multilevel Monte Carlo estimator. The proposed methods are implemented and tested on several numerical examples to highlight the theoretical discussions and demonstrate the significant improvements achieved.
• Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions
  
  • Akimoto Youhei
  • Auger Anne
  • Hansen Nikolaus
  Theoretical Computer Science, Elsevier, 2020, 832, pp.42-67. Quality gain is the expected relative improvement of the function value in a single step of a search algorithm. Quality gain analysis reveals the dependencies of the quality gain on the parameters of a search algorithm, based on which one can derive the optimal values for the parameters. In this paper, we investigate evolution strategies with weighted recombination on general convex quadratic functions. We derive a bound for the quality gain and two limit expressions of the quality gain. From the limit expressions, we derive the optimal recombination weights and the optimal step-size, and find that the optimal recombination weights are independent of the Hessian of the objective function. Moreover, the dependencies of the optimal parameters on the dimension and the population size are revealed. Differently from previous works where the population size is implicitly assumed to be smaller than the dimension, our results cover the population size proportional to or greater than the dimension. Simulation results show the optimal parameters derived in the limit approximates the optimal values in non-asymptotic scenarios. (10.1016/j.tcs.2018.05.015)
  DOI : 10.1016/j.tcs.2018.05.015
• An Eco-Routing Algorithm for HEVs Under Traffic Conditions
  
  • Rhun Arthur Le
  • Bonnans Frédéric
  • Nunzio Giovanni De
  • Leroy Thomas
  • Martinon Pierre
  IFAC-PapersOnLine, Elsevier, 2020, 53 (2), pp.14242 - 14247. In a previous work, a bi-level optimization approach was presented for the energy management of Hybrid Electric Vehicles (HEVs), using a statistical model for traffic conditions. The present work is an extension of this framework to the eco-routing problem. The optimal trajectory is computed as the shortest path on a weighted graph whose nodes are (position, state of charge) pairs for the vehicle. The edge costs are provided by cost maps from an offline optimization at the lower level of small road segments. The error due to the discretization of the state of charge is proven to be linear if the cost maps are Lipschitz. The classical A * algorithm is used to solve the problem, with a heuristic based on a lower bound of the energy needed to complete the travel. The eco-routing method is compared to the fastest-path strategy by numerical simulations on a simple synthetic road network. (10.1016/j.ifacol.2020.12.1158)
  DOI : 10.1016/j.ifacol.2020.12.1158
• Hölder-logarithmic stability in Fourier synthesis
  
  • Isaev Mikhail
  • Novikov Roman G
  Inverse Problems, IOP Publishing, 2020, 36 (12), pp.125003(17 pp.). We prove a Hölder-logarithmic stability estimate for the problem of finding a sufficiently regular compactly supported function v on R^d from its Fourier transform Fv given on [−r, r]^d. This estimate relies on a Hölder stable continuation of Fv from [−r, r]^d to a larger domain. The related reconstruction procedures are based on truncated series of Chebyshev polynomials. We also give an explicit example showing optimality of our stability estimates. (10.1088/1361-6420/abb5df)
  DOI : 10.1088/1361-6420/abb5df
• Universal limits of substitution-closed permutation classes
  
  • Bassino Frédérique
  • Bouvel Mathilde
  • Féray Valentin
  • Gerin Lucas
  • Maazoun Mickaël
  • Pierrot Adeline
  Journal of the European Mathematical Society, European Mathematical Society, 2020, 22 (11), pp.3565-3639. We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating series of the simple permutations in the class. Under a mild sufficient condition, the limit is an elementary one-parameter deformation of the limit of uniform separable permutations, previously identified as the Brownian separable permuton. This limiting object is therefore in some sense universal. We identify two other regimes with different limiting objects. The first one is degenerate; the second one is nontrivial and related to stable trees. These results are obtained thanks to a characterization of the convergence of random permutons through the convergence of their expected pattern densities. The limit of expected pattern densities is then computed by using the substitution tree encoding of permutations and performing singularity analysis on the tree series. (10.4171/JEMS/993)
  DOI : 10.4171/JEMS/993
• Computing invariant sets of random differential equations using polynomial chaos
  
  • Breden Maxime
  • Kuehn Christian
  SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2020, 19 (1), pp.577–618. Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are studied by using Monte-Carlo methods or by direct numerical simulation techniques using polynomial chaos (PC), i.e., by a series expansion of the random parameters in combination with forward integration. Here we take a dynamical systems viewpoint and focus on the invariant sets of differential equations such as steady states, stable/unstable manifolds, periodic orbits, and heteroclinic orbits. We employ PC to compute representations of all these different types of invariant sets for RODEs. This allows us to obtain fast sampling, geometric visualization of distributional properties of invariants sets, and uncertainty quantification of dynamical output such as periods or locations of orbits. We apply our techniques to a predator-prey model, where we compute steady states and stable/unstable manifolds. We also include several benchmarks to illustrate the numerical efficiency of adaptively chosen PC depending upon the random input. Then we employ the methods for the Lorenz system, obtaining computational PC representations of periodic orbits, stable/unstable manifolds and heteroclinic orbits. (10.1137/18M1235818)
  DOI : 10.1137/18M1235818
• Null space gradient flows for constrained optimization with applications to shape optimization
  
  • Feppon Florian
  • Allaire Grégoire
  • Dapogny Charles
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2020, 26, pp.90. The purpose of this article is to introduce a gradient-flow algorithm for solving equality and inequality constrained optimization problems, which is particularly suited for shape optimization applications. We rely on a variant of the Ordinary Differential Equation (ODE) approach proposed by Yamashita (Math. Program. 18 (1980) 155–168) for equality constrained problems: the search direction is a combination of a null space step and a range space step, aiming to decrease the value of the minimized objective function and the violation of the constraints, respectively. Our first contribution is to propose an extension of this ODE approach to optimization problems featuring both equality and inequality constraints. In the literature, a common practice consists in reducing inequality constraints to equality constraints by the introduction of additional slack variables. Here, we rather solve their local combinatorial character by computing the projection of the gradient of the objective function onto the cone of feasible directions. This is achieved by solving a dual quadratic programming subproblem whose size equals the number of active or violated constraints. The solution to this problem allows to identify the inequality constraints to which the optimization trajectory should remain tangent. Our second contribution is a formulation of our gradient flow in the context of – infinite-dimensional – Hilbert spaces, and of even more general optimization sets such as sets of shapes, as it occurs in shape optimization within the framework of Hadamard’s boundary variation method. The cornerstone of this formulation is the classical operation of extension and regularization of shape derivatives. The numerical efficiency and ease of implementation of our algorithm are demonstrated on realistic shape optimization problems. (10.1051/cocv/2020015)
  DOI : 10.1051/cocv/2020015
• Fluctuation theory in the Boltzmann--Grad limit
  
  • Bodineau Thierry
  • Gallagher Isabelle
  • Saint-Raymond Laure
  • Simonella Sergio
  Journal of Statistical Physics, Springer Verlag, 2020, 180, pp.873–895. We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation. Deviations from this behaviour are described by dynamical correlations, which can be fully characterized for short times. This provides both a fluctuating Boltzmann equation and large deviation asymptotics.
• Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies
  
  • Akimoto Youhei
  • Hansen Nikolaus
  Evolutionary Computation, Massachusetts Institute of Technology Press (MIT Press), 2020, 28 (3), pp.405-435. We introduce an acceleration for covariance matrix adaptation evolution strategies (CMA-ES) by means of adaptive diagonal decoding (dd-CMA). This diagonal acceleration endows the default CMA-ES with the advantages of separable CMA-ES without inheriting its drawbacks. Technically, we introduce a diagonal matrix $D$ that expresses coordinate-wise variances of the sampling distribution in $DCD$ form. The diagonal matrix can learn a rescaling of the problem in the coordinates within linear number of function evaluations. Diagonal decoding can also exploit separability of the problem, but, crucially, does not compromise the performance on non-separable problems. The latter is accomplished by modulating the learning rate for the diagonal matrix based on the condition number of the underlying correlation matrix. dd-CMA-ES not only combines the advantages of default and separable CMA-ES, but may achieve overadditive speedup: it improves the performance, and even the scaling, of the better of default and separable CMA-ES on classes of non-separable test functions that reflect, arguably, a landscape feature commonly observed in practice. The paper makes two further secondary contributions: we introduce two different approaches to guarantee positive definiteness of the covariance matrix with active CMA, which is valuable in particular with large population size; we revise the default parameter setting in CMA-ES, proposing accelerated settings in particular for large dimension. All our contributions can be viewed as independent improvements of CMA-ES, yet they are also complementary and can be seamlessly combined. In numerical experiments with dd-CMA-ES up to dimension 5120, we observe remarkable improvements over the original covariance matrix adaptation on functions with coordinate-wise ill-conditioning. The improvement is observed also for large population sizes up to about dimension squared. (10.1162/evco_a_00260)
  DOI : 10.1162/evco_a_00260