Publications

2020

• Variance reduction for Markov chains with application to MCMC
  
  • Belomestny D
  • Iosipoi L
  • Moulines E
  • Naumov A
  • Samsonov S
  Statistics and Computing, Springer Verlag (Germany), 2020. In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A distinctive feature of the proposed approach is its ability to significantly reduce the overall finite sample variance. This feature is theoretically demonstrated by means of a deep non asymptotic analysis of a variance reduced functional as well as by a thorough simulation study. In particular we apply our method to various MCMC Bayesian estimation problems where it favourably compares to the existing variance reduction approaches.
• Parametric inference for diffusions observed at stopping times
  
  • Gobet Emmanuel
  • Stazhynski Uladzislau
  Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2020, 14 (1). In this paper we study the problem of parametric inference for multidimensional diffusions based on observations at random stopping times. We work in the asymptotic framework of high frequency data over a fixed horizon. Previous works on the subject (such as [Doh87, GJ93, Gob01, AM04] among others) consider only deterministic, strongly predictable or random, independent of the process, observation times, and do not cover our setting. Under mild assumptions we construct a consistent sequence of estimators, for a large class of stopping time observation grids (studied in [GL14, GS18]). Further we carry out the asymptotic analysis of the estimation error and establish a Central Limit Theorem (CLT) with a mixed Gaussian limit. In addition, in the case of a 1-dimensional parameter, for any sequence of estimators verifying CLT conditions without bias, we prove a uniform a.s. lower bound on the asymptotic variance, and show that this bound is sharp. (10.1214/20-EJS1708)
  DOI : 10.1214/20-EJS1708
• A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: The one-dimensional case
  
  • Tomasevic Milica
  • Talay Denis
  Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2020, 26 (2), pp.1323-1353. In this paper we analyze a stochastic interpretation of the one-dimensional parabolic-parabolic Keller-Segel system without cut-off. It involves an original type of McKean-Vlasov interaction kernel. At the particle level, each particle interacts with all the past of each other particle by means of a time integrated functional involving a singular kernel. At the mean-field level studied here, the McKean-Vlasov limit process interacts with all the past time marginals of its probability distribution in a similarly singular way. We prove that the parabolic-parabolic Keller-Segel system in the whole Euclidean space and the corresponding McKean-Vlasov stochastic differential equation are well-posed for any values of the parameters of the model. (10.3150/19-BEJ1158)
  DOI : 10.3150/19-BEJ1158
• A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors
  
  • Akian Marianne
  • Gaubert Stéphane
  • Hochart Antoine
  Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2020, 40, pp.207--231. We establish a generalized Perron-Frobenius theorem, based on a combinatorial criterion which entails the existence of an eigenvector for any nonlinear order-preserving and positively homogeneous map $f$ acting on the open orthant $\mathbb{R}_{\scriptscriptstyle >0}^n$. This criterion involves dominions, i.e., sets of states that can be made invariant by one player in a two-person game that only depends on the behavior of $f$ "at infinity". In this way, we characterize the situation in which for all $\alpha, \beta > 0$, the "slice space" $\mathcal{S}_\alpha^\beta := \{ x \in \mathbb{R}_{\scriptscriptstyle >0}^n \mid \alpha x \leq f(x) \leq \beta x \}$ is bounded in Hilbert's projective metric, or, equivalently, for all uniform perturbations $g$ of $f$, all the orbits of $g$ are bounded in Hilbert's projective metric. This solves a problem raised by Gaubert and Gunawardena (Trans. AMS, 2004). We also show that the uniqueness of an eigenvector is characterized by a dominion condition, involving a different game depending now on the local behavior of $f$ near an eigenvector. We show that the dominion conditions can be verified by directed hypergraph methods. We finally illustrate these results by considering specific classes of nonlinear maps, including Shapley operators, generalized means and nonnegative tensors. (10.3934/dcds.2020009)
  DOI : 10.3934/dcds.2020009
• Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models
  
  • Bonnet Celine
  • Chahour Keltoum
  • Clément Frédérique
  • Postel Marie
  • Yvinec Romain
  ESAIM: Proceedings and Surveys, EDP Sciences, 2020, 67, pp.72-99. In this study, we describe different modeling approaches for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or stochastic (SDE) differential equations, and accounting for interactions between follicles. We put a special focus on representing the populationlevel feedback exerted by growing ovarian follicles onto the activation of quiescent follicles. We take advantage of the timescale difference existing between the growth and activation processes to apply model reduction techniques in the framework of singular perturbations. We first study the linear versions of the models to derive theoretical results on the convergence to the limit models. In the nonlinear cases, we provide detailed numerical evidence of convergence to the limit behavior. We reproduce the main semi-quantitative features characterizing the ovarian follicle pool, namely a bimodal distribution of the whole population, and a slope break in the decay of the quiescent pool with aging. (10.1051/proc/202067006)
  DOI : 10.1051/proc/202067006
• On the Turnpike Property and the Receding-Horizon Method for Linear-Quadratic Optimal Control Problems
  
  • Breiten Tobias
  • Pfeiffer Laurent
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2020, 58 (2), pp.26. Optimal control problems with a very large time horizon can be tackled with the Receding Horizon Control (RHC) method, which consists in solving a sequence of optimal control problems with small prediction horizon. The main result of this article is the proof of the exponential convergence (with respect to the prediction horizon) of the control generated by the RHC method towards the exact solution of the problem. The result is established for a class of infinite-dimensional linear-quadratic optimal control problems with time-independent dynamics and integral cost. Such problems satisfy the turnpike property: the optimal trajectory remains most of the time very close to the solution to the associated static optimization problem. Specific terminal cost functions, derived from the Lagrange multiplier associated with the static optimization problem, are employed in the implementation of the RHC method. (10.1137/18M1225811)
  DOI : 10.1137/18M1225811
• 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
• 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
• 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.
• 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
• 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.
• 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
• 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.
• 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