Publications

2018

• First steps in the formalization of convex polyhedra in Coq
  
  • Allamigeon Xavier
  , 2018.
• Coupling a hierarchy of diffuse interface models with kinetic-based moment methods for spray atomization simulations in cryogenic rocket engines
  
  • Cordesse Pierre
  • Murrone Angelo
  • Massot Marc
  , 2018. Jet atomizations play a crucial role in many applications such as in cryogenic combustion chambers, thus must be thoroughly studied to understand their impact on high-frequency instabilities. Since direct numerical simulations of these two-phase flows in a real configuration of an engine are still out of reach, predictive numerical tools must be developed using reduced-order models. However great care must be taken on the choices of these models in order to both have sound mathematics properties and lead to predictive simulations. The contribution of this work is three-fold. First, we present an original fully Eulerian modelling strategy. It relies on the coupling of a hierarchy of diffuse interface models with a Eulerian kinetic-based moment method (KBMM). Special attention will be given to the description of various disequilibrium levels for the diffuse interface model, which describes the separated and mixed zones. A member of the KBMM hierarchy will accurately describe the polydisperse evaporating spray generated through atomization. Second, to cope with the strong discontinuities encountered in jet atomization, a robust and accurate numerical method using multi-slope MUSCL technique will be applied. The extension of the proposed strategy to the various levels of the diffuse interface models will be discussed. Third, relying on the previous two points, large eddy simulations of a jet atomization in a cryogenic combustion chamber in subcritical conditions are presented using various levels of modelling.
• Condition numbers of stochastic mean payoff games and what they say about nonarchimedean semidefinite programming
  
  • Allamigeon Xavier
  • Gaubert Stephane
  • Katz Ricardo
  • Skomra Mateusz
  , 2018. Semidefinite programming can be considered over any real closed field, including fields of Puiseux series equipped with their nonarchimedean valuation. Nonarchimedean semidefinite programs encode parametric families of classical semidefinite programs, for sufficiently large values of the parameter. Recently, a correspondence has been established between nonarchimedean semidefinite programs and stochastic mean payoff games with perfect information. This correspondence relies on tropical geometry. It allows one to solve generic nonarchimedean semidefinite feasibility problems, of large scale, by means of stochastic game algorithms. In this paper, we show that the mean payoff of these games can be interpreted as a condition number for the corresponding nonarchimedean feasibility problems. This number measures how close a feasible instance is from being infeasible, and vice versa. We show that it coincides with the maximal radius of a ball in Hilbert's projective metric, that is included in the feasible set. The geometric interpretation of the condition number relies in particular on a duality theorem for tropical semidefinite feasibility programs. Then, we bound the complexity of the feasibility problem in terms of the condition number. We finally give explicit bounds for this condition number, in terms of the characteristics of the stochastic game. As a consequence, we show that the simplest algorithm to decide whether a stochastic mean payoff game is winning, namely value iteration, has a pseudopolynomial complexity when the number of random positions is fixed.
• Diffusion processes in discontinuous media: numerical algorithms and benchmark tests
  
  • Lejay Antoine
  • Pichot Géraldine
  • Lenôtre Lionel
  , 2018.
• Supplement to "High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm
  
  • Durmus Alain
  • Moulines Éric
  , 2018. Supplementary material to the paper available at https://arxiv.org/abs/1605.01559
• Stopping Criteria, Initialization, and Implementations of BFGS and their Effect on the BBOB Test Suite
  
  • Blelly Aurore
  • Felipe-Gomes Matheus
  • Auger Anne
  • Brockhoff Dimo
  , 2018. Benchmarking algorithms is a crucial task to understand them and to make recommendations for which algorithms to use in practice. However, one has to keep in mind that we typically compare only algorithm implementations and that care must be taken when making general statements about an algorithm while implementation details and parameter settings might have a strong impact on the performance. In this paper, we investigate those impacts of initialization, internal parameter setting, and algorithm implementation over different languages for the well-known BFGS algorithm. We must conclude that even in the default setting, the BFGS algorithms in Python's scipy library and in Matlab's fminunc differ widely—with the latter even changing significantly over time. (10.1145/3205651.3208303)
  DOI : 10.1145/3205651.3208303
• GECCO 2018 tutorial on evolutionary multiobjective optimization
  
  • Brockhoff Dimo
  , 2018.
• Algorithms for the resolution of stochastic control problems in high dimension by using probabilistic and max-plus methods
  
  • Fodjo Eric
  , 2018. Stochastic optimal control problems with finite horizon are a class of optimal control problems where intervene stochastic processes in a bounded time. As many optimal control problems, they are often solved using a dynamic programming approach which results in a second order Partial Differential Equation (PDE) called the Hamilton-Jacobi-Bellman equation. Grid-based methods, probabilistic methods or more recently max-plus methods can be used then to solve this PDE. However, the first type of methods default in a space of high dimension because of the curse of dimensionality while the second type of methods allowed till now to solve only problems where the nonlinearity of the PDE with respect to the second order derivatives is not very high. As for the third type of method, it results in an explosion of the complexity of the value function. We introduce two new probabilistic schemes in order to enlarge the class of problems that can be solved with probabilistic methods. One is adapted to PDE with bounded coefficients while the other can be applied to PDE with bounded or unbounded coefficients. We prove the convergence of the two probabilistic scheme and obtain error estimates in the case of a PDE with bounded coefficients. We also give some results about the behavior of the second probabilistic scheme in the case of a PDE with unbounded coefficients. After that, we introduce a completely new type of method to solve stochastic optimal control problems with finite horizon that we call the max-plus probabilistic method. It allows to add the non linearity feature of max-plus methods to a probabilistic method while controlling the complexity of the value function. An application to the computation of the optimal super replication price of an option in an uncertain correlation model is given in a 5 dimensional space.
• FATIGUE EFFECTS IN ELASTIC MATERIALS WITH VARIATIONAL DAMAGE MODELS: A VANISHING VISCOSITY APPROACH
  
  • Alessi Roberto
  • Crismale Vito
  • Orlando Gianluca
  , 2018. We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the fact that damage is favoured in regions where the cumulation of the elastic strain (or other relevant variables, depend on the model) is higher. To prove the existence of a quasistatic evolution, we follow a vanishing viscosity approach based on two steps: we first let the time-step τ of the time-discretisation and later the viscosity parameter ε go to zero. As τ → 0 , we find ε-approximate viscous evolutions; then, as ε → 0 , we find a rescaled approximate evolution satisfying an energy-dissipation balance.
• Analysis and Implementation of a Hourly Billing Mechanism for Demand Response Management
  
  • Jacquot Paulin
  • Beaude Olivier
  • Gaubert Stéphane
  • Oudjane Nadia
  IEEE Transactions on Smart Grid, Institute of Electrical and Electronics Engineers, 2018. An important part of the Smart Grid literature on residential Demand Response deals with game-theoretic consumption models. Among those papers, the hourly billing model is of special interest as an intuitive and fair mechanism. We focus on this model and answer to several theoretical and practical questions. First, we prove the uniqueness of the consumption profile corresponding to the Nash equilibrium, and we analyze its efficiency by providing a bound on the Price of Anarchy. Next, we address the computational issue of the equilibrium profile by providing two algorithms: the cycling best response dynamics and a projected gradient descent method, and by giving an upper bound on their convergence rate to the equilibrium. Last, we simulate this demand response framework in a stochastic environment where the parameters depend on forecasts. We show numerically the relevance of an online demand response procedure, which reduces the impact of inaccurate forecasts. (10.1109/TSG.2018.2855041)
  DOI : 10.1109/TSG.2018.2855041
• On the role of bulk viscosity in compressible reactive shear layer developments
  
  • Boukharfane Radouan
  • Martínez Ferrer Pedro José Martinez Ferrer
  • Mura Arnaud
  • Giovangigli Vincent
  , 2018.
• Discriminative and Quantitative Analysis of Antineoplastic Taxane Drugs Using a Handheld Raman Spectrometer
  
  • Lê Laetitia
  • Tfayli Ali
  • Prognon Patrice
  • Caudron Eric
  BioMed Research International, Hindawi Publishing Corporation, 2018, 2018, pp.1-7. (10.1155/2018/8746729)
  DOI : 10.1155/2018/8746729
• Optimal Affine-Invariant Smooth Minimization Algorithms
  
  • d'Aspremont Alexandre
  • Guzman Cristobal
  • Jaggi Martin
  SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2018, 28 (3), pp.2384 - 2405. (10.1137/17M1116842)
  DOI : 10.1137/17M1116842
• Efficient Metropolis-Hastings sampling for nonlinear mixed effects models
  
  • Karimi Belhal
  • Lavielle Marc
  , 2019. The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge slowly for high dimension problems, or when the joint structure of the distributions to sample is complex. We propose a Metropolis-Hastings (MH) algorithm based on a multidimensional Gaussian proposal that takes into account the joint conditional distribution of the random effects and does not require any tuning, in contrast with more sophisticated samplers such as the Metropolis Adjusted Langevin Algorithm or the No-U-Turn Sampler that involve costly tuning runs or intensive computation. Indeed, this distribution is automatically obtained thanks to a Laplace approximation of the original model. We show that such approximation is equivalent to linearizing the model in the case of continuous data. Numerical experiments based on real data highlight the very good performances of the proposed method for continuous data models.
• Percolation, permutations, particules en interaction
  
  • Gerin Lucas
  , 2018. Ce mémoire est consacré à la présentation d’une grande partie de mes travaux de recherche depuis mon recrutement comme maître de conférences en 2009. Ces travaux se situent à l’interface entre probabilités discrètes, combinatoire et optimisation combinatoire, et physique statistique.
• Analytical approximations of local-Heston volatility model and error analysis
  
  • Bompis Romain
  • Gobet Emmanuel
  Mathematical Finance, Wiley, 2018, 28 (3), pp.920-961. This paper consists in providing and mathematically analyzing the expansion of an option price (with bounded Lipschitz payoff) for model combining local and stochastic volatility. The local volatility part has a general form, with appropriate growth and boundedness assumptions. For the stochastic part, we choose a square root process, which is widely used for modeling the behavior of the variance process (Heston model). We rigorously establish tight error estimates of our expansions, using Malliavin calculus, which requires a careful treatment because of the lack of weak differentiability of the model; this error analysis is interesting on its own. Moreover, in the particular case of Call-Put options, we also provide expansions of the Black-Scholes implied volatility which allows to obtain very simple and rapid formulas in comparison to the Monte Carlo approach while maintaining a very competitive accuracy. (10.1111/mafi.12154)
  DOI : 10.1111/mafi.12154
• The Brownian limit of separable permutations
  
  • Bassino Frédérique
  • Bouvel Mathilde
  • Féray Valentin
  • Gerin Lucas
  • Pierrot Adeline
  The Annals of Probability, Institute of Mathematical Statistics, 2018, 46 (4), pp.2134 - 2189. We study random uniform permutations in an important class of pattern-avoiding permutations:the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given patternin such a random permutation in terms of the Brownian excursion. In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a "Brownian separable permuton". (10.1214/17-AOP1223)
  DOI : 10.1214/17-AOP1223
• A Practical Guide to Experimentation (and Benchmarking)
  
  • Hansen Nikolaus
  , 2018.
• CMA-ES and Advanced Adaptation Mechanisms
  
  • Akimoto Youhei
  • Hansen Nikolaus
  , 2018.
• On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard
  
  • Martinon Pierre
  • Picard Pierre
  • Raj Anasuya
  Geneva Risk and Insurance Review, Palgrave Macmillan, 2018, 43 (2), pp.137-185. We analyze the design of optimal medical insurance under ex post moral haz- ard, i.e., when illness severity cannot be observed by insurers and policyholders decide for themselves on their health expenditures. The trade-o¤ between ex ante risk sharing and ex post incentive compatibility is analyzed in an optimal revelation mechanism under hidden information and risk aversion. The optimal contract provides partial insurance at the margin, with a deductible when in- surers’ rates are affected by a positive loading, and it may also include an upper limit on coverage. The potential to audit the health state leads to an upper limit on out-of-pocket expenses. (10.1057/s10713-018-0034-y)
  DOI : 10.1057/s10713-018-0034-y
• Exact Hydrodynamic Description of Active Lattice Gases
  
  • Kourbane-Houssene Mourtaza
  • Erignoux Clément
  • Bodineau Thierry
  • Tailleur Julien
  Physical Review Letters, American Physical Society, 2018, 120 (26), pp.268003. We introduce a class of lattice gas models of active matter systems whose hydrodynamic description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviours in active matter: the motility-induced phase separation and the transition to collective motion. In both cases, we derive coupled partial differential equation describing the dynamics of the local density and polarization fields and show how they quantitatively predict the emerging properties of the macroscopic lattice gases. (10.1103/PhysRevLett.120.268003)
  DOI : 10.1103/PhysRevLett.120.268003
• Multidimensional martingale optimal transport.
  
  • de March Hadrien
  , 2018. In this thesis, we study various aspects of martingale optimal transport in dimension greater than one, from duality to local structure, and finally we propose numerical approximation methods.We first prove the existence of irreducible intrinsic components to martingal transport between two given measurements, as well as the canonicity of these components. We have then proved a duality result for optimal martingale transport in any dimension, point by-point duality is no longer true but a form of quasi safe duality is demonstrated. This duality makes it possible to demonstrate the possibility of decomposing the quasi-safe optimal transport into a series of optimal transport subproblems point by point on each irreducible component. Finally, this duality is used to demonstrate a principle of martingale monotony, analogous to the famous monotonic principle of classical optimal transport. We then study the local structure of optimal transport, deduced from differential considerations. We thus obtain a characterization of this structure using tools of real algebraic geometry. We deduce the optimal martingal transport structure in the case of the power costs of the Euclidean norm, which makes it possible to solve a conjecture that dates from 2015. Finally, we compared the existingnumerical methods and proposed a new method which proves more efficient and allows to treat an intrinsic problem of the martingale constraint which is the defect of convex order. Techniques are also provided to manage digital problems in practice.
• The Sparse Cardinal Sine Decomposition (SCSD) and its application to the simulation of suspensions
  
  • Alouges François
  • Aussal Matthieu
  • Lefebvre-Lepot Aline
  • Pigeonneau Franck
  • Sellier Antoine
  , 2018.
• Adjoint approximation of nonlinear hyperbolic systems with non-conservative products
  
  • Coquel Frédéric
  • Marmignon Claude
  • Rai Pratik
  • Renac Florent
  , 2018. We consider the approximation of adjoint-based derivatives for discontinuous solutions of the Cauchy problem associated to one-dimensional nonlinear non-conservative hyperbolic systems. We first derive the adjoint equations in strong form with a discontinuous primal solution together with the associated jump relations across the discontinuity. The adjoint solution may be discontinuous at the discontinuity in contrast to the case of conservative systems. Then, we consider first-order finite volume (FV) approximations to the primal problem and show that, using the Volpert path family of schemes, the discrete adjoint solution is consistent with the strong form adjoint solution. Numerical experiments are shown for a nonlinear 2 × 2 system with a genuinely nonlinear (GNL) field and a linearly degenerate (LD) field associated to the non-conservative product.
• EXISTENCE OF STEADY TWO-PHASE FLOWS WITH DISCONTINUOUS BOILING EFFECTS
  
  • Pichard Teddy
  , 2018. We aim at characterizing the existence and uniqueness of steady solutions to hyperbolic balance laws with source terms depending discontinu-ously on the unknown. We exhibit conditions for such differential equations to be well-posed and apply it to a model describing boiling flows.