Publications

2014

• Le véritable système solaire pendant 243 années vu depuis une planète virtuelle verte -cette derniere appartient approximativement au plan de Pluton et est à même distance du Soleil que la Terre
  
  • Colonna Jean-François
  , 2014. The actual Solar System viewed during 243 years from a green virtual planet -this last one approximately belongs to the plane of Pluto and its distance from the Sun equals the one of the Earth- (Le véritable système solaire pendant 243 années vu depuis une planète virtuelle verte -cette derniere appartient approximativement au plan de Pluton et est à même distance du Soleil que la Terre-)
• Le véritable système solaire pendant 243 années vu depuis une planète virtuelle verte -cette derniere appartient approximativement au plan de Pluton et est à même distance du Soleil que Neptune
  
  • Colonna Jean-François
  , 2014. The actual Solar System viewed during 243 years from a green virtual planet -this last one approximately belongs to the plane of Pluto and its distance from the Sun equals the one of Neptune- (Le véritable système solaire pendant 243 années vu depuis une planète virtuelle verte -cette derniere appartient approximativement au plan de Pluton et est à même distance du Soleil que Neptune-)
• Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle
  
  • Colonna Jean-Francois
  , 2014. The Solar System with a green virtual planet -virtual planet point of view- (Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle-)
• Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle
  
  • Colonna Jean-Francois
  , 2014. The Solar System with a green virtual planet -virtual planet point of view- (Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle-)
• A convergent and precise finite element scheme for Landau–Lifschitz–Gilbert equation
  
  • Alouges François
  • Kritsikis Evaggelos
  • Steiner Jutta
  • Toussaint Jean-Christophe
  Numerische Mathematik, Springer Verlag, 2014, 128 (3), pp.407-430. (10.1007/s00211-014-0615-3)
  DOI : 10.1007/s00211-014-0615-3
• Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle
  
  • Colonna Jean-Francois
  , 2014. The Solar System with a green virtual planet -virtual planet point of view- (Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle-)
• Le voyage d'une planète virtuelle identique à la Terre (verte) dans le système solaire -point de vue de la planète virtuelle
  
  • Colonna Jean-Francois
  , 2014. The journey of an Earth-like planet (green) in the Solar System -point of view of the virtual planet- (Le voyage d'une planète virtuelle identique à la Terre (verte) dans le système solaire -point de vue de la planète virtuelle-)
• Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle
  
  • Colonna Jean-Francois
  , 2014. The Solar System with a green virtual planet -virtual planet point of view- (Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle-)
• Le voyage d'une planète virtuelle identique à la Terre (verte) dans le système solaire -point de vue héliocentrique
  
  • Colonna Jean-Francois
  , 2014. The journey of an Earth-like virtuel planet (green) in the Solar System -heliocentric view- (Le voyage d'une planète virtuelle identique à la Terre (verte) dans le système solaire -point de vue héliocentrique-)
• Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle
  
  • Colonna Jean-Francois
  , 2014. The Solar System with a green virtual planet -virtual planet point of view- (Le système solaire avec une planète virtuelle verte -point de vue de la planète virtuelle-)
• Les 126.922 premières décimales -base 6- de 'e' visualisées comme une marche aléatoire tridimensionnelle 'absolue
  
  • Colonna Jean-Francois
  , 2014. The 126.922 first digits -base 6- of 'e' displayed as an 'absolute' tridimensional random walk (Les 126.922 premières décimales -base 6- de 'e' visualisées comme une marche aléatoire tridimensionnelle 'absolue')
• Les 126.646 premières décimales -base 6- de 'pi' visualisées comme une marche aléatoire tridimensionnelle 'absolue
  
  • Colonna Jean-François
  , 2014. The 126.646 first digits -base 6- of 'pi' - displayed as an 'absolute' tridimensional random walk (Les 126.646 premières décimales -base 6- de 'pi' visualisées comme une marche aléatoire tridimensionnelle 'absolue')
• Les 126.646 premières décimales -base 6- de 'phi' -le nombre d'or- visualisées comme une marche aléatoire tridimensionnelle 'absolue
  
  • Colonna Jean-François
  , 2014. The 126.646 first digits -base 6- of 'phi' -the golden ratio- displayed as an 'absolute' tridimensional random walk (Les 126.646 premières décimales -base 6- de 'phi' -le nombre d'or- visualisées comme une marche aléatoire tridimensionnelle 'absolue')
• Les 126.646 premières décimales -base 6- de la racine carrée de 2 visualisées comme une marche aléatoire tridimensionnelle 'absolue
  
  • Colonna Jean-François
  , 2014. The 126.646 first digits -base 6- of the square root of 2 - displayed as an 'absolute' tridimensional random walk (Les 126.646 premières décimales -base 6- de la racine carrée de 2 visualisées comme une marche aléatoire tridimensionnelle 'absolue')
• Une double hélice fractale
  
  • Colonna Jean-François
  , 2014. A fractal double helix (Une double hélice fractale)
• Une double hélice fractale
  
  • Colonna Jean-François
  , 2014. A fractal double helix (Une double hélice fractale)
• A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options
  
  • Galichon Alfred
  • Henri-Labordère Pierre
  • Touzi Nizar
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2014, 24 (1), pp.312-336. We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows us to recover previously known results about lookback options. In particular, our methodology induces a new proof of the optimality of Azéma–Yor solution of the SEP for a certain class of lookback options. Unlike the SEP technique, our approach applies to a large class of exotics and is suitable for numerical approximation techniques. (10.1214/13-AAP925)
  DOI : 10.1214/13-AAP925
• Computing the smallest fixed point of order-preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs
  
  • Adjé Assalé
  • Gaubert Stéphane
  • Goubault Eric
  Journal of Mathematical Analysis and Applications, Elsevier, 2014, 410, pp.227-240. The problem of computing the smallest fixed point of an order-preserving map arises in the study of zero-sum positive stochastic games. It also arises in static analysis of programs by abstract interpretation. In this context, the discount rate may be negative. We characterize the minimality of a fixed point in terms of the nonlinear spectral radius of a certain semidifferential. We apply this characterization to design a policy iteration algorithm, which applies to the case of finite state and action spaces. The algorithm returns a locally minimal fixed point, which turns out to be globally minimal when the discount rate is nonnegative. (10.1016/j.jmaa.2013.07.076)
  DOI : 10.1016/j.jmaa.2013.07.076
• Synchronisation and control of proliferation in cycling cell population models with age structure
  
  • Billy Frédérique
  • Clairambault Jean
  • Fercoq Olivier
  • Gaubert Stéphane
  • Lepoutre Thomas
  • Ouillon Thomas
  • Saito Shoko
  Mathematics and Computers in Simulation, Elsevier, 2014, 96, pp.66-94. We present and analyse in this article a mathematical question with a biological origin, the theoretical treatment of which may have far-reaching implications in the practical treatment of cancers. Starting from biological and clinical observations on cancer cells, tumourbearing laboratory rodents, and patients with cancer, we ask from a theoretical biology viewpoint questions that may be transcribed, using physiologically based modelling of cell proliferation dynamics, into mathematical questions. We then show how recent fluorescence-based image modelling techniques performed at the single cell level in proliferating cell populations allow to identify model parameters and how this may be applied to investigate healthy and cancer cell populations. Finally, we show how this modelling approach allows us to design original optimisation methods for anticancer therapeutics, in particular chronotherapeutics, by controlling eigenvalues of the differential operators underlying the cell proliferation dynamics, in tumour and in healthy cell populations. We propose a numerical algorithm to implement these principles. (10.1016/j.matcom.2012.03.005)
  DOI : 10.1016/j.matcom.2012.03.005
• Le feu de la vie
  
  • Colonna Jean-François
  , 2014. The fire of life (Le feu de la vie)
• Manufacturing Constraints and Multi-Phase Shape and Topology Optimization via a Level-Set Method
  
  • Michailidis Georgios
  , 2014. The main contribution of this thesis is the implementation of manufacturing constraints in shape and topology optimization. Fabrication limitations related to the casting process are formulated as mathematical constraints and introduced in the optimization algorithm. In addition, based on the same theoretical and modelization tools, we propose a novel formulation for multi-phase optimization problems, which can be extended to the optimization of structures with functionally-graded properties. A key ingredient for the mathematical formulation of most problems throughout our work is the notion of the signed distance function to a domain. This work is divided into three parts. The rst part is bibliographical and contains the necessary background material for the understanding of the thesis' main core. It includes the rst two chapters. Chapter 1 provides a synopsis of shape and topology optimization methods and emphasizes the combination of shape sensitivity analysis and the level-set method for tracking a shape's boundary. In Chapter 2 we give a short description of the casting process, from which all our manufacturing constraints derive. We explain how industrial designers account for these limitations and propose a strategy to incorporate them in shape and topology optimization algorithms. The second part is about the mathematical formulation of manufacturing constraints. It starts with Chapter 3, where the control of thickness is discussed. Based on the signed distance function, we formulate three constraints to ensure a maximum and minimm feature size, as well as a minimal distance between structural members. Then, in Chapter 4, we propose ways to handle molding direction constraints and combine them with thickness constraints. Finally, a thermal constraint coming from the solidi cation of cast parts is treated in Chapter 5 using several thermal models. Multi-phase optimization is discussed in the third part. The general problem of shape and topology optimization using multiple phases is presented in detail in Chapter 6. A "smoothed-interface" approach, based again on the signed distance function, is proposed to avoid numerical di culties related to classical "sharp-interface" problems and a shape derivative is calculated. An extension of this novel formulation to general types of material properties' gradation is shown in the Appendix A.
• Quelques formes 'naturelles' à l'intèrieur d'une texture fractale
  
  • Colonna Jean-François
  , 2014. Some 'natural' patterns inside a fractal texture (Quelques formes 'naturelles' à l'intèrieur d'une texture fractale)
• Some inversion methods applied to non-destructive testings of steam generator via eddy current probe
  
  • Jiang Zixian
  , 2014. The main objective of this thesis is to propose and test some shape optimization techniques to identify and reconstruct deposits at the shell side of conductive tubes in steam generators using signals from eddy current coils. This problem is motivated by non-destructive testing applications in the nuclear power industry where the deposit clogging the cooling circuit may affect power productivity and structural safety. We consider in a first part an axisymmetric case for which we set the model by establishing a 2-D differential equation describing the eddy current phenomenon, which enable us to simulate the impedance measurements as the observed signals to be used in the inversion. To speed up numerical simulations, we discuss the behavior of the solution of the eddy current problem and build artificial boundary conditions, in particular by explicitly constructing DtN operators, to truncate the domain of the problem. In the deposit reconstruction, we adapt two different methods according to two distinct kinds of deposits. The first kind of deposit has relatively low conductivity (about 1e4 S/m). We apply the shape optimization method which consists in expliciting the signal derivative due to a shape perturbation of the deposit domain and to build the gradient by using the adjoint state with respect to the derivative and the cost functional. While for the second kind of deposit with high conductivity (5.8e7 S/m) but in the form of thin layer (in micrometers), the previous method encounter a high numerical cost due to the tiny size of the mesh used to model the layer. To overcome this difficulty, we build an adapted asymptotic model by appropriately selecting the the family of effective transmissions conditions on the interface between the deposit and the tube. The name of the asymptotic model is due to the fact that the effective transmissions conditions are derived from the asymptotic expansion of the solution with respect to a small parameter "delta" characterizing the thickness of the thin layer and the conductivity behavior. Then the inverse problem consists in reconstructing the parameters representing the layer thickness of the deposit. For both of the two approaches, we validate numerically the direct and inverse problems. In a second part we complement this work by extending the above methods to the 3-D case for a non-axisymmetric configuration. This is motivated by either non axisymmetric deposits or the existence of non axisymmetric components like support plates of steam generator tubes.
• Coupes dans un milieu tridimensionnel érodé
  
  • Colonna Jean-François
  , 2014. Cross-sections inside an eroded tridimensional medium (Coupes dans un milieu tridimensionnel érodé)
• Limit theorems for nearly unstable Hawkes processes: Version with technical appendix
  
  • Jaisson Thibault
  • Rosenbaum Mathieu
  , 2014. Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high frequency finance. However, in practice, the statistical estimation results seem to show that very often, only "nearly unstable Hawkes processes" are able to fit the data properly. By nearly unstable, we mean that the L1 norm of their kernel is close to unity. We study in this work such processes for which the stability condition is almost violated. Our main result states that after suitable rescaling, they asymptotically behave like integrated Cox Ingersoll Ross models. Thus, modeling financial order flows as nearly unstable Hawkes processes may be a good way to reproduce both their high and low frequency stylized facts. We then extend this result to the Hawkes based price model introduced by Bacry et al. We show that under a similar criticality condition, this process converges to a Heston model. Again, we recover well known stylized facts of prices, both at the microstructure level and at the macroscopic scale.