Publications

2020

• 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
• 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
• Orlicz Random Fourier Features
  
  • Chamakh Linda
  • Gobet Emmanuel
  • Szabó Zoltán
  Journal of Machine Learning Research, Microtome Publishing, 2020, 21 (145), pp.1−37. Kernel techniques are among the most widely-applied and influential tools in machine learning with applications at virtually all areas of the field. To combine this expressive power with computational efficiency numerous randomized schemes have been proposed in the literature, among which probably random Fourier features (RFF) are the simplest and most popular. While RFFs were originally designed for the approximation of kernel values, recently they have been adapted to kernel derivatives, and hence to the solution of large-scale tasks involving function derivatives. Unfortunately, the understanding of the RFF scheme for the approximation of higher-order kernel derivatives is quite limited due to the challenging polynomial growing nature of the underlying function class in the empirical process. To tackle this difficulty, we establish a finite-sample deviation bound for a general class of polynomial-growth functions under α-exponential Orlicz condition on the distribution of the sample. Instantiating this result for RFFs, our finite-sample uniform guarantee implies a.s. convergence with tight rate for arbitrary kernel with α-exponential Orlicz spectrum and any order of derivative.
• Avis en réponse à la saisine du 2 juillet 2020 relative au projet de décret modifiant l’article D.531-2 du code de l'environnement
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • 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.44 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.
• 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
• 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.
• 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
• 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.
• 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
• 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.
• 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
• 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
• 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
• 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
• 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.
• 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.
• 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
• Problem and Non-Problem Gamblers: A Cross-Sectional Clustering Study by Gambling Characteristics
  
  • Guillou-Landréat Morgane
  • Chereau Boudet Isabelle
  • Perrot Bastien
  • Romo Lucia
  • Codina Irene
  • Magalon David
  • Fatseas Melina
  • Luquiens Amandine
  • Brousse Georges
  • Challet-Bouju Gaëlle
  • Grall-Bronnec Marie
  BMJ Open, BMJ Publishing Group, 2020, 10 (2), pp.e030424. OBJECTIVES: Gambling characteristics are factors that could influence problem gambling development. The aim of this study was to identify a typology of gamblers to frame risky behaviour based on gambling characteristics (age of initiation/of problem gambling, type of gambling: pure chance/chance with pseudoskills/chance with elements of skill, gambling online/offline, amount wagered monthly) and to investigate clinical factors associated with these different profiles in a large representative sample of gamblers. DESIGN AND SETTING: The study is a cross-sectional analysis to the baseline data of the french JEU cohort study (study protocol : Challet-Bouju et al, 2014). Recruitment (April 2009 to September 2011) involved clinicians and researchers from seven institutions that offer care for or conduct research on problem gamblers (PG). Participants were recruited in gambling places, and in care centres. Only participants who reported gambling in the previous year between 18 and 65 years old were included.Participants gave their written informed consent, it was approved by the French Research Ethics Committee. PARTICIPANTS: The participants were 628 gamblers : 256 non-problem gamblers (NPG), 169 problem gamblers without treatment (PGWT) and 203 problem gamblers seeking treatment (PGST). RESULTS: Six clustering models were tested, the one with three clusters displayed a lower classification error rate (7.92%) and was better suited to clinical interpretation : 'Early Onset and Short Course' (47.5%), 'Early Onset and Long Course' (35%) and 'Late Onset and Short Course' (17.5%). Gambling characteristics differed significantly between the three clusters. CONCLUSIONS: We defined clusters through the analysis of gambling variables, easy to identify, by psychiatrists or by physicians in primary care. Simple screening concerning these gambling characteristics could be constructed to prevent and to help PG identification. It is important to consider gambling characteristics : policy measures targeting gambling characteristics may reduce the risk of PG or minimise harm from gambling. TRIAL REGISTRATION NUMBER: NCT01207674 (ClinicalTrials.gov); Results. (10.1136/bmjopen-2019-030424)
  DOI : 10.1136/bmjopen-2019-030424
• Model Reduction for Large-Scale Earthquake Simulation in an Uncertain 3D Medium
  
  • Sochala Pierre
  • de Martin Florent
  • Le Maitre Olivier
  International Journal for Uncertainty Quantification, Begell House Publishers, 2020, 10 (2), pp.101-127. In this paper, we are interested in the seismic wave propagation into an uncertain medium. To this end, we performed an ensemble of 400 large-scale simulations that requires 4 million core-hours of CPU time. In addition to the large computational load of these simulations, solving the uncertainty propagation problem requires dedicated procedures to handle the complexities inherent to large data set size and the low number of samples. We focus on the peak ground motion at the free surface of the 3D domain, and our analysis utilizes a surrogate model combining two key ingredients for complexity mitigation: i) a dimension reduction technique using empirical orthogonal basis functions and ii) a functional approximation of the uncertain reduced coordinates by polynomial chaos expansions. We carefully validate the resulting surrogate model by estimating its predictive error using bootstrap, truncation, and cross-validation procedures. The surrogate model allows us to compute various statistical information of the uncertain prediction, including marginal and joint probability distributions, interval probability maps, and 2D fields of global sensitivity indices. (10.1615/Int.J.UncertaintyQuantification.2020031165)
  DOI : 10.1615/Int.J.UncertaintyQuantification.2020031165
• A MOMENT CLOSURE BASED ON A PROJECTION ON THE BOUNDARY OF THE REALIZABILITY DOMAIN: 1D CASE
  
  • Pichard Teddy
  Kinetic and Related Models, AIMS, 2020, 13 (6), pp.1243-1280. This work aims to develop and test a projection technique for the construction of closing equations of moment systems. One possibility to define such a closure consists in reconstructing an underlying kinetic distribution from a vector of moments, then expressing the closure based on this reconstructed function. Exploiting the geometry of the realizability domain, i.e. the set of moments of positive distribution function, we decompose any realizable vectors into two parts, one corresponding to the moments of a chosen equilibrium function, and one obtain by a projection onto the boundary of the realizability domain in the direction of equilibrium function. A realizable closure of both of these parts are computed with standard techniques providing a realizable closure for the full system. This technique is tested for the reduction of a radiative transfer equation in slab geometry. (10.3934/xx.xx.xx.xx)
  DOI : 10.3934/xx.xx.xx.xx
• Intensity fluctuations in random waveguides
  
  • Garnier Josselin
  Communications in Mathematical Sciences, International Press, 2020, 18 (4), pp.947-971. (10.4310/CMS.2020.v18.n4.a3)
  DOI : 10.4310/CMS.2020.v18.n4.a3
• High-Resolution Interferometric Synthetic Aperture Imaging in Scattering Media
  
  • Borcea Liliana
  • Garnier Josselin
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2020, 13 (1), pp.291-316. The goal of synthetic aperture imaging is to estimate the reflectivity of a remoteregion of interest by processing data gathered with a moving sensor which emits periodically a signaland records the backscattered wave. We introduce and analyze a high-resolution interferometric method for synthetic aperture imaging through an unknown scattering medium which distorts thewave. The method builds on the coherent interferometric (CINT) approach which uses empiricalcross-correlations of the measurements to mitigate the distortion, at the expense of a loss of resolutionof the image. The new method shows that, while mitigating the wave distortion, it is possible toobtain a robust and sharp estimate of the modulus of the Fourier transform of the reflectivity function.A high-resolution image can then be obtained by a phase retrieval algorithm. (10.1137/19M1272470)
  DOI : 10.1137/19M1272470