Publications

2015

• Role of Caribbean Islands in the diversification and biogeography of Neotropical Heraclides swallowtails
  
  • Lewis Delano
  • Sperling Felix A.H.
  • Nakahara Shinichi
  • Cotton Adam M
  • Kawahara Akito y
  • Condamine Fabien L.
  Cladistics, Wiley, 2015, 31 (3), pp.291-314. Numerous hypotheses on the evolution of Neotropical biodiversity have stimulated research to provide a better understandingof diversity dynamics and distribution patterns of the region. However, few studies integrate molecular and morphological datawith complete sampling of a Neotropical group, and so there has been little synthesis of the multiple processes governing biodi-versity through space and time. Here, a total-evidence phylogenetic approach is used to reconstruct the evolutionary history ofthe butterfly subgenusHeraclides. We used DNA sequences for two mitochondrial genes and one nuclear gene and coded 133morphological characters of larvae and adults. A robust and well-resolved phylogeny was obtained using several analyticalapproaches, while molecular dating and biogeographical analyses indicated an early Miocene origin (22 Mya) in the CaribbeanIslands. We inferred six independent dispersal events from the Caribbean to the mainland, and three from the mainland to theCaribbean, and we suggest that cooling climates with decreasing sea levels may have contributed to these events. The time-cali-brated tree is best explained by a museum model of diversity in which both speciation and extinction rates remained constantthrough time. By assessing both continental and fine-scale biodiversity patterns, this study provides new findings, for instancethat islands may act as source of diversity rather than as a sink, to explain spatio-temporal macroevolutionary processes withinthe Neotropical region. (10.1111/cla.12092)
  DOI : 10.1111/cla.12092
• A General Optimal Multiple Stopping Problem with an Application to Swing Options
  
  • Ben Latifa Imene
  • Bonnans Joseph Frédéric
  • Mnif Mohamed
  Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2015, 33 (4), pp.715-739. In their paper, Carmona and Touzi [8] studied an optimal multiple stopping time problem in a market where the price process is continuous. In this article, we generalize their results when the price process is allowed to jump. Also, we generalize the problem associated to the valuation of swing options to the context of jump diffusion processes. We relate our problem to a sequence of ordinary stopping time problems. We characterize the value function of each ordinary stopping time problem as the unique viscosity solution of the associated Hamilton–Jacobi–Bellman variational inequality. (10.1080/07362994.2015.1037592)
  DOI : 10.1080/07362994.2015.1037592
• Optimisation de forme appliquée aux matériaux micro-architecturés incluant la gestion d'interfaces graduées
  
  • Faure Alexis
  • Michailidis Georgios
  • Estevez Rafael
  • Parry Guillaume
  • Bréchet Yves
  • Vermaak Natasha
  • Allaire Grégoire
  • Jouve François
  , 2015. Nous nous intéressons au problème d'optimisation de propriétés mécaniques ou thermomécaniques d'un volume élémentaire représentatif hétérogène constitué de phases thermo-élastiques linéaires isotropes. Cette question a déjà été abordé dans les approches d'optimisation et apparaît documentés dans la littérature, majoritairement pour des mélanges de deux constituants. Sur la base de travaux récents (Michailidis, 2014 ; Vermaak et al. 2014), nous proposons une analyse du problème multi-constituants en tenant compte des interfaces et de leurs effets sur les propriétés homogénéisées.
• Topological shape optimization using level-set method
  
  • Lachouette Damien
  • Allaire Grégoire
  • Jouve François
  • Albertelli Marc
  • Srithammavanh Vasili
  , 2015. Software edition company ESI-Group in collaboration with industrial and academic partners (part of the RODIN consortium) has started to industrialize a recent method for optimizing the shape of structures. This method relies on the use of shape derivative based on mechanical computation. An ESI Software has been modified to solve the shape derivatives. The shape is described using the level-set method to precisely represent the shape evolution on a fixed mesh.
• Stochastic partial differential equations with singular terminal condition
  
  • Matoussi A
  • Piozin Lambert
  • Popier A
  , 2015. In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the generator. Then we study the case where the terminal data is singular, in the sense that it can be equal to +∞ on a set of positive measure. In this setting we show that there exists a minimal solution, both for the BDSDE and for the SPDE. Note that solution of the SPDE means weak solution in the Sobolev sense.
• Characterization of oxide scales formed on Alloy 82 in nominal PWR primary water at 340 degrees C and in hydrogenated steam at 400 degrees C
  
  • Duhamel C.
  • Sennour M.
  • Georgi Frédéric
  • Guerre C.
  • Chaumun E.
  • Crepin J.
  • Heripre E.
  • de Curieres I.
  , 2015.
• SCC crack initiation of alloy 82 in hydrogenated steam at 400 degrees c
  
  • Guerre C.
  • Crepin J.
  • Sennour M.
  • Duhamel C.
  • Heripre E.
  • de Curieres I.
  , 2015.
• Derivation of nonlinear shell models combining shear and flexure: application to biological membranes
  
  • Pantz Olivier
  • Trabelsi Karim
  Mathematics and Mechanics of Complex Systems, International Research Center for Mathematics & Mechanics of Complex Systems (M&MoCS),University of L’Aquila in Italy, 2015, 3 (2), pp.101-138. (10.2140/memocs.2015.3.101)
  DOI : 10.2140/memocs.2015.3.101
• An a posteriori error estimator for shape optimization: application to EIT
  
  • Giacomini Matteo
  • Pantz Olivier
  • Trabelsi Karim
  , 2015, 657 (012004). (10.1088/1742-6596/657/1/012004)
  DOI : 10.1088/1742-6596/657/1/012004
• Commande optimale
  
  • Bonnans Joseph Frédéric
  , 2015, pp.29. L'objet de la commande optimale est l'optimisation de systèmes dynamiques suivant différents objectifs : atteinte d'une cible en temps ou énergie minimale, maximisation du rendement d'un processus industriel par exemple. Pour cela on joue à la fois sur des paramètres indépendants du temps et sur les commandes qui, elles, dépendent du temps. L'article analyse les conditions d'optimalité du premier et second ordre, et leur résolution par discrétisation temporelle, algorithme de tir, ou programmation dynamique.
• Out of Himalaya: the impact of past Asian environmental changes on the evolutionary and biogeographical history of Dipodoidea (Rodentia)
  
  • Pisano Julie
  • Condamine Fabien L.
  • Lebedev Vladimir
  • Bannikova Anna
  • Quéré Jean-Pierre
  • Shenbrot Gregory I.
  • Pagès Marie
  • Michaux Johan R.
  Journal of Biogeography, Wiley, 2015, 42 (5), pp.856-870. Aim: We assessed the influence of past environmental changes, notably the importance of palaeogeographical and climatic drivers, in shaping the distribution patterns of Dipodoidea (Rodentia), the superfamily most closely related to the large species-rich superfamily Muroidea (c. 1300-1500 species). Dipodoids are suitable for testing several biogeographical hypotheses because of their disjunct distribution patterns in the Northern Hemisphere and the numerous species distributed in Asian deserts. Location: Holarctic. Methods: We inferred molecular phylogenetic relationships for Dipodoidea (34 out of 51 species and 15 out of 16 genera) based on five coding genes. A time-calibrated phylogeny was estimated using a Bayesian relaxed molecular clock with four fossil calibrations. A cross-validation procedure was adopted to examine the impact of each fossil on our estimates. The ancestral area of origin and biogeographical scenarios were reconstructed using time-stratified dispersal-extinction-cladogenesis models. Results: Phylogenetic analyses recovered a well-resolved and supported topology. The divergence between Dipodoidea and Muroidea occurred in the late Palaeocene (c. 57.72Ma) and modern Dipodoidea diversified during the middle Eocene (c. 40.62Ma). Similar results were found with each calibration strategy used with the cross-validation procedure. The reconstruction of ancestral areas and biogeographical events indicated that modern Dipodoidea originated in the Himalaya-Tibetan and Central Asian region. Main conclusions: At the time when Dipodoidea diversified (middle Eocene), the Central Asia and Himalaya-Tibetan Plateau region experienced major uplift episodes due to the collision of India with Asia, which also induced diversification events in many other groups. Other important diversification events (e.g. divergence between Zapodidae and Dipodidae in Central Asia) took placed during the Eocene-Oligocene transition when the global temperature decreased significantly and rodent/lagomorph-dominant faunas replaced Eocene perissodactyl-dominant faunas. All of these climatic and geological disruptions in the Central Asia and Himalaya-Tibetan Plateau region modified landscapes and offered new habitats that favoured diversification events, thus triggering the evolutionary history of Dipodoidea. (10.1111/jbi.12476)
  DOI : 10.1111/jbi.12476
• Speed of coming down from infinity for birth and death processes
  
  • Bansaye Vincent
  • Méléard Sylvie
  • Richard Mathieu
  , 2015. We finely describe the speed of "coming down from infinity" for birth and death processes which eventually become extinct. Under general assumptions on the birth and death rates, we firstly determine the behavior of the successive hitting times of large integers. We put in light two different regimes depending on whether the mean time for the process to go from $n+1$ to $n$ is negligible or not compared to the mean time to reach $n$ from infinity. In the first regime, the coming down from infinity is very fast and the convergence is weak. In the second regime, the coming down from infinity is gradual and a law of large numbers and a central limit theorem for the hitting times sequence hold. By an inversion procedure, we deduce that the process is a.s. equivalent to a non-increasing function when the time goes to zero. Our results are illustrated by several examples including applications to population dynamics and population genetics. The particular case where the death rate varies regularly is studied in details.
• An accurate method to include lubrication forces in numerical simulations of dense Stokesian suspensions
  
  • Lefebvre-Lepot Aline
  • Merlet Benoit
  • Nguyen Thanh Nhan
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2015, 769, pp.369-386. (10.1017/jfm.2015.101)
  DOI : 10.1017/jfm.2015.101
• Factorization of tropical matrices
  
  • Niv Adi
  , 2015. In contrast to the situation in classical linear algebra, not every tropically non-singular matrix can be factored into a product of tropical elementary matrices. We prove the factorizability of any tropically non-singular 2\times 2 matrix, relating to the tropicalization of the existing Bruhat decomposition, and determine which 3\times 3 matrices are factorizable. Nevertheless, there is a closure operation, obtained by means of the tropical adjoint, which is always factorizable, generalizing the decomposition of the tropical closure operation: Kleene star.
• Tropicalizing the simplex algorithm
  
  • Allamigeon Xavier
  • Benchimol Pascal
  • Gaubert Stéphane
  • Joswig Michael
  SIAM Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2015, 29 (2). We develop a tropical analog of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in O(n(m+n)) time, where m is the number of constraints and n is the dimension. (10.1137/130936464)
  DOI : 10.1137/130936464
• On some stochastic control problems with state constraints
  
  • Picarelli Athena
  , 2015. This thesis deals with Hamilton-Jacobi-Bellman (HJB) approach for some stochastic control problems in presence of state-constraints. This class of problems arises in many challenging applications, and a wide literature has already analysed such problems under some strong compatibility conditions. The main features of the present thesis is to provide new ways to face the presence of constraints without assuming any controllability condition. The first contribution of the thesis in this direction is obtained by exploiting the existing link between backward reachability and optimal control problems. It is shown that by considering a suitable auxiliary unconstrained optimal control problem, the level set approach can be extended to characterize the backward reachable sets under state-constrained. On the other hand the value function associated with a general state constrained stochastic optimal control problem is characterized by means of a state constrained backward reachable set, enabling the application of the level set method for handling the presence of the state constraints. This link between optimal control problems and reachability sets led to the theoretical and numerical analysis of HJB equations with oblique derivative boundary conditions and problems with unbounded controls. Error estimates for Markov-chain approximation represent another contribution of this manuscript. Furthermore, the properties of asymptotic controllability of a stochastic system have also been studied. A generalization of the Zubov method to state constrained stochastic systems is presented. In the last part of the thesis an ergodic optimal control problems in presence of state-constraints are considered.
• Parameter estimation using macroscopic diffusion MRI signal models
  
  • Nguyen Hang Tuan
  • Grebenkov Denis S
  • van Nguyen Dang
  • Poupon Cyril
  • Le Bihan Denis
  • Li Jing-Rebecca
  Physics in Medicine and Biology, IOP Publishing, 2015, 60 (8). (10.1088/0031-9155/60/8/3389)
  DOI : 10.1088/0031-9155/60/8/3389
• Linear processes in high dimensions: Phase space and critical properties
  
  • Mastromatteo Iacopo
  • Bacry Emmanuel
  • Muzy Jean-François
  Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], American Physical Society, 2015, 91, pp.042142. no abstract (10.1103/PhysRevE.91.042142)
  DOI : 10.1103/PhysRevE.91.042142
• On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra
  
  • Niv Adi
  Linear Algebra and its Applications, Elsevier, 2015, 471, pp.264–290. The only invertible matrices in tropical algebra are diagonal matrices, permutation matrices and their products. However, the pseudo-inverse A ∇ , defined as 1 det(A) adj(A), with det(A) being the tropical permanent (also called the tropical determinant) of a matrix A, inherits some classical algebraic properties and has some surprising new ones. Defining B and B to be tropically similar if B = A ∇ BA, we examine the characteristic (max-)polynomials of tropically similar matrices as well as those of pseudo-inverses. Other miscellaneous results include a new proof of the identity for det(AB) and a connection to stabilization of the powers of definite matrices. (10.1016/j.laa.2014.12.038)
  DOI : 10.1016/j.laa.2014.12.038
• Complexity of control-affine motion planning
  
  • Jean Frédéric
  • Prandi Dario
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.816-844. In this paper we study the complexity of the motion planning problem for control- affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time- rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quanti- tative estimates on the cost of stabilizing the system near a non-equilibrium point of the drift. (10.1137/130950793)
  DOI : 10.1137/130950793
• Theoretical and Numerical Study of the Problem of Abort Landing in the Presence of Windshear
  
  • Cadena Guaqueta Ivan
  , 2015. We analyze both theoretically and numerically the problem of abort landing in the presence of windshear. A pertinent model of optimal control is constructed in order to allow numerical simulations through an open source software. We verify that the numerical results correspond to the mathematical theory and in particular we analyze as much as possible the junction conditions in presence of state constraints. The code written to analyze the problem will be available as a contribution in bocop.org.
• RODIN project, Topology Optimization 2.0?
  
  • Abballe Thomas
  • Albertelli Marc
  • Allaire Grégoire
  • Caron Axelle
  • Conraux Philippe
  • Dall 'Olio Luca
  • Dapogny Charles
  • Dobrzynski Cecile
  • Jeannin Benoit
  • Jouve François
  • Lachouette Damien
  • Le Sommer Thierry
  • Maquin Kevin
  • Michailidis Georgios
  • Siavelis Maximilien
  • Srithammavanh Vassili
  , 2015. RODIN project is an attempt to propose a new kind of topology optimization tools. It has been motivated by the combination of two events: (1) the industrials demands for getting past serious limits identified in the available tools, (2) the advent of a new mathematical approach in the mid 2000's presenting very interesting properties. This project has been launched in July 2012 and is supported by French public funding. It is a collaborative project that gathers ten partners (ranging from academics to software editors and industrials end-users) and firmly aims at overcoming technical and scientific locks in the area of topology optimization. RODIN is therefore an ambitious and risky project that will possibly mark the birth of a new numerical tool.
• Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Chesnel Lucas
  • Nazarov Sergei
  Inverse Problems, IOP Publishing, 2015. We investigate a time harmonic acoustic scattering problem by a penetrable inclusion with compact support embedded in the free space. We consider cases where an observer can produce inci-dent plane waves and measure the far field pattern of the resulting scattered field only in a finite set of directions. In this context, we say that a wavenumber is a non-scattering wavenumber if the associated relative scattering matrix has a non trivial kernel. Under certain assumptions on the physical coeffi-cients of the inclusion, we show that the non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a second step, for a given real wavenumber and a given domain D, we present a construc-tive technique to prove that there exist inclusions supported in D for which the corresponding relative scattering matrix is null. These inclusions have the important property to be impossible to detect from far field measurements. The approach leads to a numerical algorithm which is described at the end of the paper and which allows to provide examples of (approximated) invisible inclusions.
• The reconstructed tree in the lineage-based model of protracted speciation
  
  • Lambert Amaury
  • Morlon Hélène
  • Etienne Rampal S.
  Journal of Mathematical Biology, Springer, 2015, 70 (1-2), pp.367-397. A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree produced by a given model of diversification. Etienne and Rosindell in Syst Biol 61(2):204–213, (2012) proposed a lineage-based model of diversification, called protracted speciation, where species remain incipient during a random duration before turning good species, and showed that this can explain the slowdown in lineage accumulation observed in real phylogenies. However, they were unable to provide a general likelihood formula. Here, we present a likelihood formula for protracted speciation models, where rates at which species turn good or become extinct can depend both on their age and on time. Our only restrictive assumption is that speciation rate does not depend on species status. Our likelihood formula utilizes a new technique, based on the contour of the phylogenetic tree and first developed by Lambert in Ann Probab 38(1):348–395, (2010). We consider the reconstructed trees spanned by all extant species, by all good extant species, or by all representative species, which are either good extant species or incipient species representative of some good extinct species. Specifically, we prove that each of these trees is a coalescent point process, that is, a planar, ultrametric tree where the coalescence times between two consecutive tips are independent, identically distributed random variables. We characterize the common distribution of these coalescence times in some, biologically meaningful, special cases for which the likelihood reduces to an elegant analytical formula or becomes numerically tractable. (10.1007/s00285-014-0767-x)
  DOI : 10.1007/s00285-014-0767-x
• A piecewise deterministic model for prey-predator communities
  
  • Costa Manon
  , 2015. We are interested in prey-predator communities where the predator population evolves much faster than the prey's (e.g. insect-tree communities). We introduce a piecewise deterministic model for these prey-predator communities that arises as a limit of a microscopic model when the number of predators goes to infinity. We prove that the process has a unique invariant probability measure and that it is exponentially ergodic. Further on, we rescale the predator dynamics in order to model predators of smaller size. This slow-fast system converges to a community process in which the prey dynamics is averaged on the predator equilibria. This averaged process has an invariant probability measure which can be computed explicitly. We prove that this invariant probability is the weak limit of the invariant probability measures of the rescaled processes.