Publications

2016

• Maximum likelihood estimation of a low-order building model
  
  • Nabil Tahar
  • Moulines Éric
  • Roueff François
  • Jicquel Jean-Marc
  • Girard Alexandre
  , 2016. The aim of this paper is to investigate the accuracy of the estimates learned with an open loop model of a building whereas the data is actually collected in closed loop, which corresponds to the true exploitation of buildings. We propose a simple model based on an equivalent RC network whose parameters are physically interpretable. We also describe the maximum likelihood estimation of these parameters by the EM algorithm, and derive their statistical properties. The numerical experiments clearly show the potential of the method, in terms of accuracy and robustness. We emphasize the fact that the estimations are linked to the generating process for the observations, which includes the command system. For instance, the features of the building are correctly estimated if there is a significant gap between the heating and cooling setpoint. (10.1109/EUSIPCO.2016.7760339)
  DOI : 10.1109/EUSIPCO.2016.7760339
• Team organization may help swarms of flies to become invisible in closed waveguides
  
  • Chesnel Lucas
  • Nazarov Sergei
  , 2016. We are interested in a time harmonic acoustic problem in a waveguide containing flies. The flies are modelled by small sound soft obstacles. We explain how they should arrange to become invisible to an observer sending waves from −∞ and measuring the resulting scattered field at the same position. We assume that the flies can control their position and/or their size. Both monomodal and multimodal regimes are considered. On the other hand, we show that any sound soft obstacle (non necessarily small) embedded in the waveguide always produces some non exponentially decaying scattered field at +∞ for wavenumbers smaller than a constant that we explicit. As a consequence, for such wavenumbers, the flies cannot be made completely invisible to an observer equipped with a measurement device located at +∞.
• Zero-sum games, non-archimedean convexity and sinuous central paths
  
  • Gaubert Stéphane
  , 2016.
• Correlated Extra-Reductions Defeat Blinded Regular Exponentiation
  
  • Dugardin Margaux
  • Guilley Sylvain
  • Danger Jean-Luc
  • Najm Zakaria
  • Rioul Olivier
  , 2016, 9813, pp.3-22. Walter & Thomson (CT-RSA '01) and Schindler (PKC '02) have shown that extra-reductions allow to break RSA-CRT even with message blinding. Indeed, the extra-reduction probability depends on the type of operation (square, multiply, or multiply with a constant). Regular exponentiation schemes can be regarded as protections since the operation sequence does not depend on the secret. In this article, we show that there exists a strong negative correlation between extra-reductions of two consecutive operations, provided that the first feeds the second. This allows to mount successful attacks even against blinded asymmetrical computations with a regular exponentiation algorithm, such as Square-and-Multiply Always or Montgomery Ladder. We investigate various attack strategies depending on the context - known or unknown modulus, known or unknown extra-reduction detection probability, etc.-and implement them on two devices: a single core ARM Cortex-M4 and a dual core ARM Cortex M0-M4. (10.1007/978-3-662-53140-2)
  DOI : 10.1007/978-3-662-53140-2
• Template estimation in computational anatomy: Fréchet means in top and quotient spaces are not consistent
  
  • Devilliers Loïc
  • Allassonnière Stéphanie
  • Trouvé Alain
  • Pennec Xavier
  , 2016. In this article we study the consistency of the template estimation with the Fréchet mean in the quotient space when the observations are shifted by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.
• A scalable algebraic method to infer quadratic invariants of switched systems
  
  • Allamigeon Xavier
  • Gaubert Stéphane
  • Goubault Eric
  • Putot Sylvie
  • Stott Nikolas
  ACM Transactions on Embedded Computing Systems (TECS), ACM, 2016, 15 (4). We present a new numerical abstract domain based on ellipsoids designed for the formal verification of switched linear systems. Unlike the existing approaches, this domain does not rely on a user-given template. We overcome the difficulty that ellipsoids do not have a lattice structure by exhibiting a canonical operator overapproximating the union. This operator is the only one that permits the performance of analyses that are invariant with respect to a linear transformation of state variables. It provides the minimum volume ellipsoid enclosing two given ellipsoids. We show that it can be computed in O(n3) elementary algebraic operations. We finally develop a fast nonlinear power-type algorithm, which allows one to determine sound quadratic invariants on switched systems in a tractable way, by solving fixed-point problems over the space of ellipsoids. We test our approach on several benchmarks, and compare it with the standard techniques based on linear matrix inequalities, showing an important speedup on typical instances. (10.1145/2932187)
  DOI : 10.1145/2932187
• Solving Generic Nonarchimedean Semidefinite Programs Using Stochastic Game Algorithms
  
  • Allamigeon Xavier
  • Gaubert Stéphane
  • Skomra Mateusz
  , 2016. A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility problems given by generic matrices with a Metzler-type sign pattern. Our approach is based on tropical geometry. We define tropical spectrahedra as the images by the valuation of nonarchimedean spectrahedra, and provide an explicit description of the tropical spectrahedra arising from the aforementioned class of problems. We deduce that the tropical semidefinite feasibility problems obtained in this way are equivalent to stochastic mean payoff games, which have been well studied in algorithmic game theory. This allows us to solve nonarchimedean semidefinite feasibility problems using algorithms for stochastic games. These algorithms are of a combinatorial nature and work for large instances. (10.1145/2930889.2930935)
  DOI : 10.1145/2930889.2930935
• Perturbation of Ornstein-Uhlenbeck stationary distributions: expansion and simulation
  
  • Gobet Emmanuel
  • She Qihao
  , 2016. We consider a multidimensional stochastic differential equation Y written as a drift-perturbation of an ergodic Ornstein-Uhlenbeck process X. Under the condition of time-reversibility of X, we derive a first and second order expansion of the stationary distribution µ^Y of Y in terms of X. Error estimates are established. These approximations are then turned into a simulation scheme for sampling approximately according to µ Y. Numerical experiments support the theoretical error estimates.
• Solving Hamilton-Jacobi-Bellman equations by combining a max-plus linear approximation and a probabilistic numerical method
  
  • Akian Marianne
  • Fodjo Eric
  , 2016.
• An Accretive Operator Approach to Ergodic Problems for Zero-Sum Games
  
  • Hochart Antoine
  , 2016.
• Total non-negativity via valuations in tropical algebra
  
  • Niv Adi
  , 2016.
• Reconstruction of discontinuous parameters in a second order impedance boundary operator
  
  • Chaabane Slim
  • Charfi Bilel
  • Haddar Houssem
  Inverse Problems, IOP Publishing, 2016, 32 (10). We consider the inverse problem of retrieving the coefficients of a second order boundary operator from Cauchy data associated with the Laplace operator at a measurement curve. We study the identifiability and reconstruction in the case of piecewise continuous parameters. We prove in particular the differentiability of the Khon-Vogelius functional with respect to the discontinuity points and employ the result in a gradient type minimizing algorithm. We provide validating numerical results discussing in particular the case of unknown number of discontinuity points. (10.1088/0266-5611/32/10/105004)
  DOI : 10.1088/0266-5611/32/10/105004
• Scaling to integer matrices in max-algebra
  
  • Maccaig Marie
  , 2016.
• Nonarchimedean semidefinite programming and stochastic games
  
  • Skomra Mateusz
  , 2016.
• A robust inversion method for quantitative 3D shape reconstruction from coaxial eddy-current measurements
  
  • Haddar Houssem
  • Jiang Zixian
  • Riahi Mohamed-Kamel
  Journal of Scientific Computing, Springer Verlag, 2016, pp.31. This work is motivated by the monitoring of conductive clogging deposits in steam generator at the level of support plates. One would like to use multistatic measurements from coaxial coils in order to obtain estimates on the clogging volume. We propose a 3D shape optimization technique based on simplified shape parametrization of the deposit. This parametrization is adapted to the measurement nature and resolution. The direct problem is modeled by the eddy current approximation of time-harmonic Maxwell’s equations in the low frequency regime. A potential formulation is adopted in order to easily handle the complex topology of the industrial problem setting. We first characterize the shape derivatives of the deposit impedance signal using an adjoint field technique. For the inversion procedure, the direct and adjoint problems have to be solved for each vertical probe position which is excessively time- and memory-consuming. To overcome this difficulty, we propose and discuss a steepest descent method based on a invariant mesh. Numerical experiments are presented to illustrate the convergence and the efficiency of the method. (10.1007/s10915-016-0241-6)
  DOI : 10.1007/s10915-016-0241-6
• Zero-sum games, non-archimedean convexity and sinuous central paths
  
  • Gaubert Stéphane
  , 2016.
• Studying isometry groups using the horofunction boundary
  
  • Walsh Cormac
  , 2016.
• Fourier Descriptors Based on the Structure of the Human Primary Visual Cortex with Applications to Object Recognition
  
  • Bohi Amine
  • Prandi Dario
  • Guis Vincente
  • Bouchara Frédéric
  • Gauthier Jean-Paul
  Journal of Mathematical Imaging and Vision, Springer Verlag, 2016, pp.1-17. In this paper we propose a supervised object recognition method using new global features and inspired by the model of the human primary visual cortex V1 as the semidiscrete roto-translation group $SE(2,N)=\mathbb Z_N\rtimes \mathbb{R}^2$. The proposed technique is based on generalized Fourier descriptors on the latter group, which are invariant to natural geometric transformations (rotations, translations). These descriptors are then used to feed an SVM classifier. We have tested our method against the COIL-100 image database and the ORL face database, and compared it with other techniques based on traditional descriptors, global and local. The obtained results have shown that our approach looks extremely efficient and stable to noise, in presence of which it outperforms the other techniques analyzed in the paper. (10.1007/s10851-016-0669-1)
  DOI : 10.1007/s10851-016-0669-1
• Persistance et vitesse d'extinction pour des modèles de populations stochastiques multitypes en temps discret.
  
  • Adam Etienne
  , 2016. Cette thèse porte sur l'étude mathématique de modèles stochastiques de dynamique de populations structurées.Dans le premier chapitre, nous introduisons un modèle stochastique à temps discret prenant en compte les diverses interactions possibles entre les individus, que ce soit de la compétition, de la migration, des mutations, ou bien de la prédation. Nous montrons d'abord un résultat de type ``loi des grands nombres'', où on montre que si la population initiale tend vers l'infini, alors sur un intervalle de temps fini, le processus stochastique converge en probabilité vers un processus déterministe sous-jacent. Nous quantifions aussi les écarts entre ces deux processus par un résultat de type ``théorème central limite''. Enfin, nous donnons un critère de persistance/extinction afin de déterminer le comportement en temps long de notre processus stochastique. Ce critère met en exergue un cas critique qui sera étudié plus en détail dans les chapitres suivants.Dans le deuxième chapitre, nous donnons un critère de croissance illimitée pour des processus vérifiant le cas critique évoqué plus haut. Nous illustrons en particulier ce critère avec l'exemple d'une métapopulation constituée de parcelles de type puits (c'est à dire dont la population s'éteint sans tenir compte de la migration), où l'on montre que la survie de la population est possible.Dans le troisième chapitre, nous nous intéressons au comportement du processus critique lorsqu'il croît vers l'infini. Nous montrons en particulier une convergence en loi vers une loi gamma de notre processus renormalisé et dans un cadre plus général, en renormalisant aussi en temps, nous obtenons une convergence en loi d'une fonction de notre processus vers la solution d'une équation différentielle stochastique appelée un processus de Bessel carré.Dans le quatrième et dernier chapitre, nous nous plac{c}ons dans le cas où le processus critique ne tend pas vers l'infini et étudions le temps d'atteinte de certains ensembles compacts. Nous donnons un encadrement asymptotique de la queue de ce temps d'atteinte. Lorsque le processus s'éteint, ces résultats nous permettent en particulier d'encadrer la queue du temps d'extinction. Dans le cas où notre processus est une chaîne de Markov, nous en déduisons un critère de récurrence nulle ou récurrence positive et dans ce cas, nous obtenons un taux de convergence sous-géométrique du noyau de transition de notre chaîne vers sa mesure de probabilité invariante.
• A Stochastic Continuous Time Model for Microgrid Energy Management
  
  • Heymann Benjamin
  • Frédéric Bonnans J
  • Silva Francisco
  • Jimenez Guillermo
  , 2016. We propose a novel stochastic control formulation for the microgrid energy management problem and extend previous works on continuous time rolling horizon strategy to uncertain demand. We modelize the demand dynamics with a stochastic differential equation. We decompose this dynamics into three terms: an average drift, a time-dependent mean-reversion term and a Brownian noise. We use BOCOPHJB for the numerical simulations. This optimal control toolbox implements a semi-Lagrangian scheme and handle the optimization of switching times required for the discrete on/off modes of the diesel generator. The scheme allows for an accurate modelling and is computationally cheap as long as the state dimension is small. As described in previous works, we use a trick to reduce the search of the optimal control values to six points. This increases the computation speed by several orders. We compare this new formulation with the deterministic control approach introduced in [1] using data from an isolated microgrid located in northern Chile.
• Probabilistic and deterministic analysis of the evolution : influence of a spatial structure and a mating preference.
  
  • Leman Hélène
  , 2016. We study the spatial and evolutionary dynamics of a population by using probabilistic and deterministic tools. In the first part of this thesis, we are concerned with the influence of a heterogeneous environment on the evolution of species. The population is modeled by an individual-based process with some interactions and which describes the birth, the death, the mutation and the spatial diffusion of each individual. The rates of those events depend on the characteristics of the individuals : their phenotypic trait and their spatial location. First, we study the system of partial differential equations that describes the spatial and demographic dynamics of a population composed of two traits in a large population limit. We characterize precisely the conditions of extinction and long time survival for this population. Secondly, we study the initial individual-based model under two asymptotic: large population and rare mutations such as demographic and mutational timescales are separated. Thus, when a mutant appears, the resident population has reached its demographic balance. We characterize the survival probability of the population descended from this mutant. Then, by studyingthe process in the mutational scale, we prove that the microscopic process converges to a jump process which describes the successive fixations of the most advantaged traits and the spatial distribution of populations carrying these traits. We then extend the model to introduce mutualistic interactions between two species. We study this model in a limit of large population. We also give numerical results and a detailed biological behavior analysis around two issues: the co-evolution of phenotypic and spatial niches of mutualistic species and the invasion dynamics of a homogeneous space by these species. In the second part of this thesis, we develop a probabilistic model to study the effect of the sexual preference on the speciation. Here, the population is structured on two patches and the individuals, characterized by a trait, are ecologically and demographically similar and differ only in their sexual preferences: two individuals of the same trait are more likely to reproduce than two individuals of distinct traits. We show that in the absence of any other ecological differences, the sexual preferences lead to reproductive isolation between the two patches.
• Parameter estimation of Ornstein-Uhlenbeck process generating a stochastic graph
  
  • Gobet Emmanuel
  • Matulewicz Gustaw
  Statistical Inference for Stochastic Processes, Springer Verlag, 2016, 20 (2), pp.211-235. Given Y a graph process defined by an incomplete information observation of a multivariate Ornstein-Uhlenbeck process X, we investigate whether we can estimate the parameters of X. We define two statistics of Y. We prove convergence properties and show how these can be used for parameter inference. Finally, numerical tests illustrate our results and indicate possible extensions and applications. (10.1007/s11203-016-9142-4)
  DOI : 10.1007/s11203-016-9142-4
• Nonparametric estimation of a shot-noise process
  
  • Ilhe Paul
  • Roueff François
  • Moulines Éric
  • Souloumiac Antoine
  , 2016, pp.7551709. We propose an efficient method to estimate in a nonpara-metric fashion the marks' density of a shot-noise process in presence of pile-up from a sample of low-frequency observations. Based on a functional equation linking the marks' density to the characteristic function of the observations and its derivative, we propose a new time-efficient method using B-splines to estimate the density of the underlying γ-ray spectrum which is able to handle large datasets used in nuclear physics. A discussion on the numerical computation of the algorithm and its performances on simulated data are provided to support our findings. (10.1109/SSP.2016.7551709)
  DOI : 10.1109/SSP.2016.7551709
• Mesh requirements for the finite element approximation of problems with sign-changing coefficients
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Carvalho Camille
  • Ciarlet Patrick
  , 2016. Transmission problems with sign-changing coefficients occur in electromagnetic theory in the presence of negative materials surrounded by classical materials. For general geometries, establishing Fredholmness of these transmission problems is well-understood thanks to the T-coercivity approach. Moreover, for a plane interface, there exist meshing rules that guarantee an optimal convergence rate for the finite element approximation. We propose here a new treatment at the corners of the interface which allows to design meshing rules for an arbitrary polygonal interface and then recover standard error estimates. This treatment relies on the use of simple geometrical transforms to define the meshes. Numerical results illustrate the importance of this new design.
• MIDAS: A Mixed Integer Dynamic Approximation Scheme
  
  • Philpott Andy
  • Wahid Faisal
  • Bonnans Frédéric
  , 2016, pp.22. Mixed Integer Dynamic Approximation Scheme (MIDAS) is a new sampling-based algorithm for solving finite-horizon stochastic dynamic programs with monotonic Bellman functions. MIDAS approximates these value functions using step functions, leading to stage problems that are mixed integer programs. We provide a general description of MIDAS, and prove its almost-sure convergence to an ε-optimal policy when the Bellman functions are known to be continuous, and the sampling process satisfies standard assumptions.