Publications

2018

• Low-cost optimization under uncertainty through box representation of robustness measures
  
  • Rivier Mickael
  • Congedo Pietro Marco
  , 2018.
• Ablative thermal protection system under uncertainties including pyrolysis gas composition
  
  • Rivier Mickael
  • Lachaud Jean
  • Congedo Pietro Marco
  , 2018, pp.1-23. Spacecrafts such as Stardust (NASA, 2006) are protected by an ablative Thermal Protection System (TPS) for their hypersonic atmospheric entry. A new generation of TPS material, called Phenolic Impregnated Carbon Ablator (PICA), has been introduced with the Stardust mission. This new generation of low density carbon-phenolic composites is now widely used in the aerospace industry. Complex heat and mass transfer phenomena coupled to phenolic pyrolysis and pyrolysis gas chemistry occur in the material during atmospheric entry. Computer programs, as the Porous material Analysis Toolbox based on OpenFoam (PATO) released open source by NASA, allow to study the material response. In this study, a non-intrusive Anchored Analysis of Variance (Anchored-ANOVA) method has been interfaced with PATO to perform low-cost sensitivity analysis on this problem featuring a large number of uncertain parameters. Then, a Polynomial-Chaos method has been employed in order to compute the statistics of some quantities of interest for the atmospheric entry of the Stardust capsule, by taking into account uncertainties on effective material properties and pyrolysis gas composition. This first study including pyrolysis gas composition uncertainties shows their key contribution to the variability of the quantities of interest.
• Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Chesnel Lucas
  • Pagneux Vincent
  Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, Royal Society, The, 2018. We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we show that such reflectionless modes can be characterized as eigenfunctions of an original non-selfadjoint spectral problem. In order to select ingoing waves on one side of the obstacle and outgoing waves on the other side, we use complex scalings (or Perfectly Matched Layers) with imaginary parts of different signs. We prove that the real eigenvalues of the obtained spectrum correspond either to trapped modes (or bound states in the continuum) or to reflectionless modes. Interestingly, complex eigenvalues also contain useful information on weak reflection cases. When the geometry has certain symmetries, the new spectral problem enters the class of PT-symmetric problems.
• Simple examples of perfectly invisible and trapped modes in waveguides
  
  • Chesnel Lucas
  • Pagneux Vincent
  Quarterly Journal of Mechanics and Applied Mathematics, Oxford University Press (OUP), 2018. We consider the propagation of waves in a waveguide with Neumann boundary conditions. We work at low wavenumber with only one propagating mode in the leads, all the other modes being evanescent. We assume that the waveguide is symmetric with respect to an axis orthogonal to the longitudinal direction and is endowed with a branch of height L whose width coincides with the wavelength of the propagating modes. In this setting, tuning the parameter L, we prove the existence of simple geometries where the transmission coefficient is equal to one (perfect invisibility). We also show that these geometries, for possibly different values of L, support so called trapped modes (non zero solutions of finite energy of the homogeneous problem) associated with eigenvalues embedded in the continuous spectrum.
• A STOCHASTIC MODEL FOR SPECIATION BY MATING PREFERENCES
  
  • Coron Camille
  • Costa Manon
  • Leman Hélène
  • Smadi Charline
  Journal of Mathematical Biology, Springer, 2018, pp.1-43. Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the carrying capacity. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations. (10.1007/s00285-017-1175-9)
  DOI : 10.1007/s00285-017-1175-9
• An example of non-uniqueness for the weighted Radon transforms along hyperplanes in multidimensions
  
  • Goncharov F G
  • Novikov Roman
  Inverse Problems, IOP Publishing, 2018, 34 (5), pp.054001. We consider the weighted Radon transforms $R_W$ along hyperplanes in $R^d , \, d ≥ 3$, with strictly positive weights $W = W (x, \theta), \, x \in R^d, \, \theta \in S^{d−1}$. We construct an example of such a transform with non-trivial kernel in the space of infinitely smooth compactly supported functions. In addition, the related weight $W$ is infinitely smooth almost everywhere and is bounded. Our construction is based on the famous example of non-uniqueness of J. Boman (1993) for the weighted Radon transforms in $R^2$ and on a recent result of F. Goncharov and R. Novikov (2016). (10.1088/1361-6420/aab24d)
  DOI : 10.1088/1361-6420/aab24d
• Guidage de personnes déficientes visuelles par audio spatialisé
  
  • Ferrand Sylvain
  • Aussal M
  • Alouges F
  , 2018. CFA 2018-Le Havre 371 Les personnes aveugles sont capables de localiser et de suivre une source sonore avec une efficacité remarquable. C'est une faculté qu'elles utilisent dans la vie de tous les jours par exemple pour suivre les pas de la personne qui les précèdent, afin de se déplacer dans la rue ou dans un bâtiment. Certaines personnes aveugles utilisent également cette faculté dans la pratique sportive, pour suivre un guide valide lors de la pratique de la course à pied ou du roller. Sur le même principe, il est possible de guider des personnes avec des sons spatialisés. Pour le montrer, nous avons développé un dispositif embarqué autonome capable de guider des personnes en utilisant des techniques de synthèse binaurale. Dans ce dispositif, nous utilisons à la fois, les informations fournies par un système de localisation temps réel (RTLS) précis et à faible latence, et les données d'orientation de la tête fournies par une centrale inertiels à bas cout (IMU). Ces données de positionnement sont utilisées pour produire des sons spatialisés par filtrage binaural afin de guider en temps réel une personne le long d'un parcours prédéfini. La personne déficiente visuelle va donc se déplacer vers le son, de la même façon qu'elle suivrait les pas d'un guide. Le système a été conçu afin de minimiser la latence globale, à la fois pour le système de localisation et le moteur de rendu audio binaural. Nous avons ainsi pu montrer qu'il était possible de guider des personnes en leur faisant suivre des sons spatialisés, de façon précise, naturelle et avec un entrainement minimum. Ce système permet déjà de guider des personnes aveugles pour pratiquer le roller dans un gymnase et ainsi leurs permettre de faire du sport de façon plus autonome.
• Novel algorithm using Active Metamodel Learning and Importance Sampling: application to multiple failure regions of low probability
  
  • Razaaly Nassim
  • Congedo Pietro Marco
  Journal of Computational Physics, Elsevier, 2018.
• Scheduling energy-consuming jobs on parallel machines with piecewise-linear costs and storage resources: A lot-sizing and scheduling perspective
  
  • Absi Nabil
  • Artigues Christian
  • Kedad-Sidhoum Safia
  • Ngueveu Sandra Ulrich
  • Rannou Janik
  • Saadi Omar
  , 2018, pp.1-4.
• Uncertainty Quantification Strategies in Systems of Solvers
  
  • Sanson Francois
  • Le Maitre Olivier
  • Congedo Pietro Marco
  , 2018.
• An Efficient Reliability Analysis Tool for the Computation of Low Tail Probabilities and Extreme Quantiles in Multiple Failure Regions: Application to Organic Rankine Cycles
  
  • Razaaly Nassim
  • Congedo Pietro Marco
  , 2018.
• How can a cause-of-death reduction be compensated for in the presence of heterogeneity? A population dynamics approach based on English data by deprivation
  
  • Kaakai Sarah
  • Labit-Hardy Héloïse
  • Arnold (-Gaille ) Séverine
  • Karoui Nicole El
  , 2018. A growing number of studies indicate a widening of socioeconomic inequalities in mortality over the past decades. It has therefore become crucially important to understand the impact of heterogeneity and its evolution on the future mortality of heterogeneous populations. In particular, recent developments in multi-population mortality have raised a number of questions, among which are the issue of consistency between subnational and national forecasts, and the evaluation of cause-of-death reduction targets set by national and international institutions. The aim of this paper is to show how the study of the population data and the population dynamics framework contribute to addressing these issues, by providing a new viewpoint on the evolution of aggregate mortality indicators in the presence of heterogeneity. Our findings rely on two unique datasets on the English population and cause-specific number of deaths by socioeconomic circumstances, over the period 1981-2015. The analysis of the data first highlights the complexity of recent demographic developments, characterized by significant composition changes in the population, with considerable variations according to the age-class or cohort, along with a widening of socioeconomic inequalities. In a second part, we introduce a dynamic framework for studying the impact of composition changes on the mortality of the global population. In particular, we are interested in quantifying the impacts of cause-of-death mortality reduction in comparison with changes of composition in a heterogeneous population. We show how a cause of death reduction could be compensated for in the presence of heterogeneity, which could lead to misinterpretations when assessing public policies impacts and/or for the forecasting of future trends. JEL: G22, J11, C60
• Highly corrupted image inpainting through hypoelliptic diffusion
  
  • Boscain Ugo
  • Chertovskih Roman
  • Gauthier Jean-Paul
  • Prandi Dario
  • Remizov Alexey
  Journal of Mathematical Imaging and Vision, Springer Verlag, 2018, pp.1–15. We present a new image inpainting algorithm, the Averaging and Hypoelliptic Evolution (AHE) algorithm, inspired by the one presented in [1] and based upon a (semi-discrete) variation of the Citti--Petitot--Sarti model of the primary visual cortex V1. In particular, we focus on reconstructing highly corrupted images (i.e. where more than the 80% of the image is missing). [1] U. Boscain, R. A. Chertovskih, J. P. Gauthier, and A. O. Remizov, Hypoelliptic diffusion and human vision: a semidiscrete new twist, SIAM J. Imaging Sci., vol. 7, no. 2, pp. 669--695, 2014. (10.1007/s10851-018-0810-4)
  DOI : 10.1007/s10851-018-0810-4
• MCMC and nested extreme risks
  
  • Fort Gersende
  • Gobet Emmanuel
  • Moulines Éric
  , 2018.
• Variational analysis for options with stochastic volatility and multiple factors
  
  • Bonnans Joseph Frédéric
  • Kröner Axel
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2018, 9 (2), pp.465-492. This paper performs a variational analysis for a class of Euro-pean or American options with stochastic volatility models, including those of Heston and Achdou-Tchou. Taking into account partial correlations and the presence of multiple factors, we obtain the well-posedness of the related partial differential equations, in some weigthed Sobolev spaces. This involves a generalization of the commutator analysis introduced by Achdou and Tchou in [2].
• Inextricable complexity of two centuries of demographic changes: A fascinating modeling challenge
  
  • El Karoui Nicole
  • Hajji Kaouther
  • Kaakai Sarah
  , 2018.
• Robust Ground footprint Estimation for Reentering Space Objects
  
  • Sanson Francois
  • Bertorello Charles
  • Finzi Celia
  • Bouilly Jean-Marc
  • Congedo Pietro Marco
  , 2018.
• Robust reconstruction of the catalytic properties of thermal protection materials from sparse high-enthalpy facility experimental data
  
  • Sanson Francois
  • Panerai Francesco
  • Magin Thierry E.
  • Congedo Pietro Marco
  Experimental Thermal and Fluid Science, Elsevier, 2018. Quantifying the catalytic properties of reusable thermal protection system materials is essential for the design of atmospheric entry vehicles. Their properties quantify the recombination of oxygen and nitrogen atoms into molecules, and allow for accurate computation of the heat flux to the spacecraft. Their rebuilding from ground test data, however, is not straightforward and subject to uncertainties. We propose a fully Bayesian approach to reconstruct the catalytic properties of ceramic matrix composites from sparse high-enthalpy facility experimental data with uncertainty estimates. The results are compared to those obtained by means of an alternative reconstruction procedure, where the experimental measurements are also treated as random variables but propagated through a deterministic solver. For the testing conditions presented in this work, the contribution to the measured heat flux of the molecular recombination is negligible. Therefore, the material catalytic property * Corresponding author. Tel.: +33(0)5 24 57 41 12 Email address: francois.sanson@inria.fr (Francois Sanson) Preprint accepted for pubblication in Elsevier cannot be estimated precisely.Moreover, epistemic uncertainties are rigorously included, such as the unknown reference calorimeter catalytic property. (10.1016/j.expthermflusci.2018.03.028)
  DOI : 10.1016/j.expthermflusci.2018.03.028
• Low-cost optimization under uncertainty through box representation of robustness measures
  
  • Rivier Mickael
  • Congedo Pietro Marco
  , 2018.
• On the two-filter approximations of marginal smoothing distributions in general state space models
  
  • Nguyen Thi Ngoc Minh
  • Le Corff Sylvain
  • Moulines Éric
  Advances in Applied Probability, Applied Probability Trust, 2018, 50 (1), pp.154-177. A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state given future observations. (10.1017/apr.2018.8)
  DOI : 10.1017/apr.2018.8
• Volatility is rough
  
  • Gatheral Jim
  • Jaisson Thibault
  • Rosenbaum Mathieu
  Quantitative Finance, Taylor & Francis (Routledge), 2018, 18 (6), pp.933-949. (10.1080/14697688.2017.1393551)
  DOI : 10.1080/14697688.2017.1393551
• Kinetic theory of two-temperature polyatomic plasmas
  
  • Orlac'H Jean-Maxime
  • Giovangigli Vincent
  • Novikova Tatiana
  • Roca Pere
  Physica A: Statistical Mechanics and its Applications, Elsevier, 2018, 494, pp.503--546. We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas. (10.1016/j.physa.2017.11.151)
  DOI : 10.1016/j.physa.2017.11.151
• PAC-Bayesian Aggregation of Affine Estimators
  
  • Montuelle L.
  • Pennec E. Le
  , 2018, pp.133-144.
• PAC-Bayesian Aggregation of Affine Estimators
  
  • Montuelle L.
  • Pennec E. Le
  Springer Proceedings in Mathematics & Statistics, Springer, 2018, 250, pp.133-144. (10.1007/978-3-319-96941-1_9)
  DOI : 10.1007/978-3-319-96941-1_9
• Robust domain decomposition methods for high performance computing in aerospace industrial context
  
  • Parret-Fréaud Augustin
  • Bovet Christophe
  • Gosselet Pierre
  • Spillane Nicole
  , 2018.