Publications

2016

• A two-pool model to describe the IVIM cerebral perfusion
  
  • Fournet Gabrielle
  • Li Jing-Rebecca
  • Cerjanic Alex M
  • Sutton Bradley P
  • Ciobanu Luisa
  • Le Bihan Denis
  Journal of Cerebral Blood Flow and Metabolism, Nature Publishing Group, 2016. IntraVoxel Incoherent Motion (IVIM) is a magnetic resonance imaging (MRI) technique capable of measuring perfusion-related parameters. In this manuscript, we show that the mono-exponential model commonly used to process IVIM data might be challenged, especially at short diffusion times. Eleven rat datasets were acquired at 7T using a diffusion-weighted pulsed gradient spin echo sequence with b-values ranging from 7 to 2500 s/mm2 at three diffusion times. The IVIM signals, obtained by removing the diffusion component from the raw MR signal, were fitted to the standard mono-exponential model, a bi-exponential model and the Kennan model. The Akaike information criterion used to find the best model to fit the data demonstrates that, at short diffusion times, the bi-exponential IVIM model is most appropriate. The results obtained by comparing the experimental data to a dictionary of numerical simulations of the IVIM signal in microvascular networks support the hypothesis that such a bi-exponential behavior can be explained by considering the contribution of two vascular pools: capillaries and somewhat larger vessels. (10.1177/0271678X16681310)
  DOI : 10.1177/0271678X16681310
• Introduction to geodesics in sub-Riemannian geometry
  
  • Agrachev Andrei
  • Barilari Davide
  • Boscain Ugo
  , 2016.
• Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensions
  
  • Novikov Roman
  The Journal of Geometric Analysis, Springer, 2016, 26 (1), pp.346-359. We consider phaseless inverse scattering for the Schrödinger equation with compactly supported potential in dimension d ≥ 2. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we give also a global uniqueness result for this problem with appropriate data on a fixed energy neighborhood. (10.1007/s12220-014-9553-7)
  DOI : 10.1007/s12220-014-9553-7
• Second order analysis of state-constrained control-affine problems
  
  • Aronna Maria Soledad
  • Bonnans J. Frederic
  • Goh Bean San
  Mathematical Programming, Series A, Springer, 2016, 160 (1), pp.115-147. In this article we establish new second order necessary and suffi-cient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.
• Avis en réponse à la saisine HCB - dossier EFSA-GMO-RX-003. Paris, le 9 décembre 2016
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Berny Philippe
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Eychenne Nathalie
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Jestin André
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémi
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Parzy Daniel
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2016.
• A Shrinkage-Thresholding Metropolis Adjusted Langevin Algorithm for Bayesian Variable Selection
  
  • Schreck Amandine
  • Fort Gersende
  • Le Corff Sylvain
  • Moulines Éric
  IEEE Journal of Selected Topics in Signal Processing, IEEE, 2016, 10, pp.366 - 375. This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on simulated and real data, is presented to illustrate the performance of the proposed algorithm in comparison with some more classical trans-dimensional algorithms. Index Terms—Bayesian variable selection, Metropolis Adjusted Langevin Algorithm (MALA), Markov chain Monte Carlo (MCMC), proximal operators, sparsity. (10.1109/JSTSP.2015.2496546)
  DOI : 10.1109/JSTSP.2015.2496546
• Geometry, Analysis and Dynamics on sub-Riemannian Manifolds - Volume II
  
  • Barilari Davide
  • Boscain Ugo
  • Sigalotti Mario
  , 2016. (10.4171/163)
  DOI : 10.4171/163
• Avis en réponse à la saisine HCB - dossier NL-2011-96. Paris, le 13 janvier 2016
  
  • 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
  • de Verneuil Hubert
  • 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
  • Vilotte Jean-Luc
  , 2016.
• Thickness control in structural optimization via a level set method
  
  • Allaire Grégoire
  • Jouve François
  • Michailidis Georgios
  Structural and Multidisciplinary Optimization, Springer Verlag, 2016, 53, pp.1349-1382. In the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape. We formulate global constraints using integral functionals and compute their shape derivatives. We discuss diff erent strategies and possible approximations to handle the geometric constraints. We implement our approach in two and three space dimensions for a model of linearized elasticity. As can be expected, the resulting optimized shapes are strongly dependent on the initial guesses and on the speci fic treatment of the constraints since, in particular, some topological changes may be prevented by those constraints.
• Sub-Riemannian curvature in contact geometry
  
  • Agrachev Andrei
  • Barilari Davide
  • Rizzi Luca
  The Journal of Geometric Analysis, Springer, 2016. We compare different notions of curvature on contact sub-Riemannian manifolds. In particular we introduce canonical curvatures as the coefficients of the sub-Riemannian Jacobi equation. The main result is that all these coefficients are encoded in the asymptotic expansion of the horizontal derivatives of the sub-Riemannian distance. We explicitly compute their expressions in terms of the standard tensors of contact geometry. As an application of these results, we obtain a sub-Riemannian version of the Bonnet-Myers theorem that applies to any contact manifold. (10.1007/s12220-016-9684-0)
  DOI : 10.1007/s12220-016-9684-0
• The Newtonian Potential and the Demagnetizing Factors of the General Ellipsoid
  
  • Di Fratta Giovanni
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2016, 472 (2190), pp.20160197. The objective of this paper is to present a modern and concise new derivation for the explicit expression of the interior and exterior Newtonian potential generated by homogeneous ellipsoidal domains in $\mathbb{R}^N$ (with $N \geqslant 3$). The very short argument is essentially based on the application of Reynolds transport theorem in connection with Green-Stokes integral representation formula for smooth functions on bounded domains of $\mathbb{R}^N$, which permits to reduce the N-dimensional problem to a 1-dimensional one. Due to its high physical relevance, a separate section is devoted to the derivation of the demagnetizing factors of the general ellipsoid which are one of the most fundamental quantities in ferromagnetism. (10.1098/rspa.2016.0197)
  DOI : 10.1098/rspa.2016.0197
• Approximation of Markov semigroups in total variation distance
  
  • Bally Vlad
  • Rey Clément
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2016, 21 (none). (10.1214/16-EJP4079)
  DOI : 10.1214/16-EJP4079
• Existence and Uniqueness for a Crystalline Mean Curvature Flow
  
  • Chambolle Antonin
  • Morini Massimiliano
  • Ponsiglione Marcello
  Communications on Pure and Applied Mathematics, Wiley, 2016. An existence and uniqueness result, up to fattening, for a class of crystalline mean curvature flows with natural mobility is proved. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The comparison principle is obtained by means of a suitable weak formulation of the flow, while the existence of a global-in-time solution follows via a minimizing movements approach. (10.1002/cpa.21668)
  DOI : 10.1002/cpa.21668
• Molding direction constraints in structural optimization via a level-set method
  
  • Allaire Grégoire
  • Jouve François
  • Michailidis Georgios
  , 2016, pp.1-39. In the framework of structural optimization via a level-set method, we develop an approach to handle the directional molding constraint for cast parts. A novel molding condition is formulated and a penalization method is used to enforce the constraint. A first advantage of our new approach is that it does not require to start from a feasible initialization, but it guarantees the convergence to a castable shape. A second advantage is that our approach can incorporate thickness constraints too. We do not adress the optimization of the casting system, which is considered a priori defined. We show several 3d examples of compliance minimization in linearized elasticity under molding and minimal or maximal thickness constraints. We also compare our results with formulations already existing in the literature. (10.1007/978-3-319-45680-5)
  DOI : 10.1007/978-3-319-45680-5
• Choice of measure source terms in interface coupling for a model problem in gas dynamics.
  
  • Coquel Frédéric
  • Godlewski Edwige
  • Haddaoui Khalil
  • Marmignon Claude
  • Renac Florent
  Mathematics of Computation, American Mathematical Society, 2016, 85, pp.2305-2339. This paper is devoted to the mathematical and numerical analysis of a coupling procedure for one-dimensional Euler systems. The two systems have different closure laws and are coupled through a thin fixed interface. Following the work of [5], we propose to couple these systems by a bounded vector-valued Dirac measure, concentrated at the coupling interface, which in the applications may have a physical meaning. We show that the proposed framework allows to control the coupling conditions and we propose an approximate Riemann solver based on a relaxation approach preserving equilibrium solutions of the coupled problem. Numerical experiments in constrained optimization problems are then presented to assess the performances of the present method. 1. Introduction The study of large-scale and complex problems exhibiting a wide range of physical space and time scales (see for instance [62, 35, 14]), usually requires separate solvers adapted to the resolution of specific scales. This is the case of many industrial flows. Let us quote, for example, the numerical simulation of two-phase flows applied to the burning liquid oxygen-hydrogen gas in rocket engines [58]. This kind of flow contains both separated and dispersed two-phase flows, due to atomization and evaporation phenomena. This requires appropriate models and solvers for separated and dispersed phases that have to be appropriately coupled. Another example concerns turbomachine flows which can be modeled by the Euler equations of gas dynamics with different closure laws between the stages of the turbine, where the conditions of temperature and pressure are strongly heterogeneous. The coupling of these different systems is thus necessary to give a complete description of the flow inside the whole turbine. The method of interface coupling allows to represent the evolution of such flows, where different models are separated by fixed interfaces. First, coupling conditions are specified at the interface to exchange information between the systems. The definition of transmission conditions generally results from physical consideration, e.g. the conservation or the continuity of given variables. Then, the transmission conditions are represented at the discrete level. The study of interface coupling for nonlinear hyperbolic systems has received attention for several years. In [43], the authors study the scalar case from both mathematical and numerical points of view. (10.1090/mcom%2F3063)
  DOI : 10.1090/mcom%2F3063
• Moutard transform for the generalized analytic functions
  
  • Grinevich Piotr
  • Novikov Roman
  The Journal of Geometric Analysis, Springer, 2016, 26 (4), pp.2984–2995. We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.
• Self-adjoint extensions and stochastic completeness of the Laplace–Beltrami operator on conic and anticonic surfaces
  
  • Boscain Ugo
  • Prandi Dario
  Journal of Differential Equations, Elsevier, 2016, 260 (4), pp.3234–3269. We study the evolution of the heat and of a free quantum particle (described by the Schrödinger equation) on two-dimensional manifolds endowed with the degenerate Riemannian metric $ds^2=dx^2+|x|^{-2\alpha}d\theta^2$, where $x\in \mathbb{R}$, $\theta\in\mathbb{T}$ and the parameter $\alpha\in\mathbb{R}$. For $\alpha\le-1$ this metric describes cone-like manifolds (for $\alpha=-1$ it is a flat cone). For $\alpha=0$ it is a cylinder. For $\alpha\ge 1$ it is a Grushin-like metric. We show that the Laplace-Beltrami operator $\Delta$ is essentially self-adjoint if and only if $\alpha\notin(-3,1)$. In this case the only self-adjoint extension is the Friedrichs extension $\Delta_F$, that does not allow communication through the singular set $\{x=0\}$ both for the heat and for a quantum particle. For $\alpha\in(-3,-1]$ we show that for the Schrödinger equation only the average on $\theta$ of the wave function can cross the singular set, while the solutions of the only Markovian extension of the heat equation (which indeed is $\Delta_F$) cannot. For $\alpha\in(-1,1)$ we prove that there exists a canonical self-adjoint extension $\Delta_B$, called bridging extension, which is Markovian and allows the complete communication through the singularity (both of the heat and of a quantum particle). Also, we study the stochastic completeness (i.e., conservation of the $L^1$ norm for the heat equation) of the Markovian extensions $\Delta_F$ and $\Delta_B$, proving that $\Delta_F$ is stochastically complete at the singularity if and only if $\alpha\le -1$, while $\Delta_B$ is always stochastically complete at the singularity. (10.1016/j.jde.2015.10.011)
  DOI : 10.1016/j.jde.2015.10.011
• A Pseudo-Markov Property for Controlled Diffusion Processes
  
  • Claisse Julien
  • Talay Denis
  • Tan Xiaolu
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (2), pp.1017 - 1029. In this note, we propose two different approaches to rigorously justify a pseudo-Markov property for controlled diffusion processes which is often (explicitly or implicitly) used to prove the dynamic programming principle in the stochastic control literature. The first approach develops a sketch of proof proposed by Fleming and Souganidis [9]. The second approach is based on an enlargement of the original state space and a controlled martingale problem. We clarify some measurability and topological issues raised by these two approaches. (10.1137/151004252)
  DOI : 10.1137/151004252
• Spatial Prediction Under Location Uncertainty in Cellular Networks
  
  • Braham Hajer
  • Jemaa Sana Ben
  • Fort Gersende
  • Moulines Éric
  • Sayrac Berna
  IEEE Transactions on Wireless Communications, Institute of Electrical and Electronics Engineers, 2016, 15, pp.7633 - 7643. Coverage optimization is an important process for the operator, as it is a crucial prerequisite toward offering a satisfactory quality of service to the end users. The first step of this process is coverage prediction, which can be performed by interpolating geo-located measurements reported to the network by mobile user's equipments. In the previous works, we proposed a low complexity coverage prediction algorithm based on the adaptation of the geo-statistics fixed rank kriging (FRK) algorithm. We supposed that the geo-location information reported with the radio measurements was perfect, which is not the case in reality. In this paper, we study the impact of location uncertainty on the coverage prediction accuracy and we extend the previously proposed algorithm to include geo-location error in the prediction model. We validate the proposed algorithm using both simulated and real-field measurements. The FRK is extended to take into account that the location uncertainty proves to enhance the prediction accuracy while keeping a reasonable computational complexity. (10.1109/TWC.2016.2605676)
  DOI : 10.1109/TWC.2016.2605676
• Geometry, Analysis and Dynamics on sub-Riemannian Manifolds - Volume I
  
  • Barilari Davide
  • Boscain Ugo
  • Sigalotti Mario
  , 2016. (10.4171/162)
  DOI : 10.4171/162
• Generalized linear sampling method for elastic-wave sensing of heterogeneous fractures
  
  • Pourahmadian Fatemeh
  • Guzina Bojan B
  • Haddar Houssem
  Inverse Problems, IOP Publishing, 2016, pp.28. A theoretical foundation is developed for active seismic reconstruction of fractures endowed with spatially-varying interfacial condition (e.g. partially-closed fractures, hydraulic fractures). The proposed indicator functional carries a superior localization property with no significant sensitivity to the fracture's contact condition, measurement errors, and illumination frequency. This is accomplished through the paradigm of the F-factorization technique and the recently developed Generalized Linear Sampling Method (GLSM) applied to elastodynamics. The direct scattering problem is formulated in the frequency domain where the fracture surface is illuminated by a set of incident plane waves, while monitoring the induced scattered field in the form of (elastic) far-field patterns. The analysis of the well-posedness of the forward problem leads to an admissibility condition on the fracture's (linearized) contact parameters. This in turn contributes toward establishing the applicability of the F-factorization method, and consequently aids the formulation of a convex GLSM cost functional whose minimizer can be computed without iterations. Such minimizer is then used to construct a robust fracture indicator function, whose performance is illustrated through a set of numerical experiments. For completeness, the results of the GLSM reconstruction are compared to those obtained by the classical linear sampling method (LSM).
• The influence of acquisition parameters on the metrics of the bi-exponential IVIM model
  
  • Fournet Gabrielle
  • Li Jing-Rebecca
  • Le Bihan Denis
  • Ciobanu Luisa
  , 2016. The IntraVoxel Incoherent Motion (IVIM) MRI signal, typically described as a mono-exponential decay, can sometimes be better modeled as a bi-exponential function accounting for two vascular pools, capillaries and medium-size vessels. The goal of this work is to define precisely in which conditions the IVIM signal shape becomes bi-exponential and to understand the evolution of the IVIM outputs with different acquisition parameters. Rats were scanned at 7T and 11.7T using diffusion-weighted pulsed-gradient spin-echo (SE) and stimulated-echo (STE) sequences with different repetition times (TR) and diffusion encoding times. The obtained IVIM signals were fit to the mono- and bi-exponential models and the output parameters compared. The bi-exponential and mono-exponential models converge at long diffusion encoding times and long TRs. The STE is less sensitive to inflow effects present at short TRs, leading to a smaller volume fraction for the fast pool when compared to the SE sequence. The two vascular components are more easily separated at short diffusion encoding times, short TRs and when using a SE sequence. The volume fractions of the two blood pools depend on the pulse sequence, TR and diffusion encoding times while the pseudo-diffusion coefficients are only affected by the diffusion encoding time.
• A volume integral method for solving scattering problems from locally perturbed infinite periodic layers
  
  • Haddar Houssem
  • Nguyen Thi Phong
  Applicable Analysis, Taylor & Francis, 2016, pp.29. We investigate the scattering problem for the case of locally perturbed periodic layers in $\R^d$, $d=2,3$. Using the Floquet-Bloch transform in the periodicity direction we reformulate this scattering problem as an equivalent system of coupled volume integral equations. We then apply a spectral method to discretize the obtained system after periodization in the direction orthogonal to the periodicity directions of the medium. The convergence of this method is established and validating numerical results are provided. (10.1080/00036811.2016.1221942)
  DOI : 10.1080/00036811.2016.1221942
• A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
  
  • Lakshtanov Evgeny
  • Novikov Roman
  • Vainberg Boris
  Rendiconti dell'Istituto di Matematica dell'Universita di Trieste: an International Journal of Mathematics, Università di Trieste, 2016, 48, pp.21-47. We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported potentials. In particular, we do not assume that the potential is small or that Faddeev scattering solutions do not have singularities (i.e. we allow the Faddeev exceptional points to exist). Applications of these results to the Novikov-Veselov equation are also considered.
• Nondestructive testing of the delaminated interface between two materials
  
  • Cakoni Fioralba
  • de Teresa Irene
  • Haddar Houssem
  • Monk Peter
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2016, 76 (6), pp.2306–2332. We consider the problem of detecting if two materials that should be in contact have separated or delaminated. The goal is to find an acoustic technique to detect the delamination. We model the delamination as a thin opening between two materials of different acoustic properties, and using asymptotic techniques we derive a asymptotic model where the delaminated region is replaced by jump conditions on the acoustic field and flux. The asymptotic model has potential singularities due to the edges of the delaminated region, and we show that the forward problem is well posed for a large class of possible delaminations. We then design a special Linear Sampling Method (LSM) for detecting the shape of the delamination assuming that the background, undamaged, state is known. Finally we show, by numerical experiments, that our LSM can indeed determine the shape of delaminated regions. (10.1137/16M1064167)
  DOI : 10.1137/16M1064167