Publications

2012

• Monument Valley paradoxale au lever du Soleil
  
  • Colonna Jean-François
  , 2012. Paradoxal Monument Valley at sunrise (Monument Valley paradoxale au lever du Soleil)
• Monument Valley nuageuse
  
  • Colonna Jean-François
  , 2012. Cloudy Monument Valley (Monument Valley nuageuse)
• Monument Valley nuageuse
  
  • Colonna Jean-François
  , 2012. Cloudy Monument Valley (Monument Valley nuageuse)
• First and second order necessary conditions for stochastic optimal control problems
  
  • Bonnans Joseph Frédéric
  • Silva Francisco J.
  Applied Mathematics and Optimization, Springer Verlag (Germany), 2012, 65 (3), pp.403-439. In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.
• Entrelacs
  
  • Colonna Jean-François
  , 2012. Intertwining (Entrelacs)
• Entrelacs récursif
  
  • Colonna Jean-François
  , 2012. Recursive intertwining (Entrelacs récursif)
• Un détail d'un 'MandelBox' brumeux -ou 'Sous la coupole
  
  • Colonna Jean-François
  , 2012. Close-up on a foggy 'MandelBox' (Un détail d'un 'MandelBox' brumeux -ou 'Sous la coupole')
• Un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'MandelBulb') -'la ronde des enfants' ou 'la conscience émergeant des Mathématiques'
  
  • Colonna Jean-François
  , 2012. A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -'the children round' or 'the consciousness emerging from Mathematics'- (Un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'MandelBulb') -'la ronde des enfants' ou 'la conscience émergeant des Mathématiques'-)
• De l'infiniment petit à l'infini grand
  
  • Colonna Jean-François
  , 2012. From the infinitely small to the infinitely big (De l'infiniment petit à l'infini grand)
• Two-Component Two-Compressible Flow in a Porous Medium
  
  • Caro Florian
  • Saad Bilal
  • Saad Mazen
  Acta Applicandae Mathematicae, Springer Verlag, 2012, 117 (1), pp.15-46. (10.1007/s10440-011-9648-0)
  DOI : 10.1007/s10440-011-9648-0
• Visualisation tridimensionnelle de la fonction Zêta de Riemann dans la bande (+0.1,+0.9)x(0,+50)
  
  • Colonna Jean-François
  , 2012. Tridimensional display of the Riemann Zeta function inside (+0.1,+0.9)x(0,+50) (Visualisation tridimensionnelle de la fonction Zêta de Riemann dans la bande (+0.1,+0.9)x(0,+50))
• Qualitative Methods for Inverse Scattering by an Impedant Crack
  
  • Boukari Yosra
  , 2012. The inverse scattering problem for crack identification is increasingly gaining applications in many domains. Examples of applications include non destructive testing, geophysical prospection... The research work in this thesis focuses on the crack identification using qualitative methods, particularly the sampling methods. We use the Linear Sampling Method and the Factorization method to retrieve the geometry of cracks from multi-static far field data in the case of impedance boundary conditions on both sides of the crack embedded in a homogeneous domain. Moreover, an application of the Reciprocity Gap Linear Sampling Method is proposed to retrieve the geometry of cracks embedded in an inhomogeneous domain with the same boundary conditions. A completion method for the Helmholtz-Cauchy problem is also proposed to widen the applicability of the latter method. The efficiency of the proposed methods is shown through numerical experiments for different crack shapes and for several impedance values.
• Market Microstructure and Modeling of the Trading Flow
  
  • Dayri Khalil Antoine
  , 2012. We offer an original way to analyse at the various high frequency streams of information originating from financial markets and to provide simple intuitive models that closely mirror reality. We observe empirical data and report some of its stylized facts and propose models to capture these facts. In chapter 1, we review the basic definitions and properties of electronic exchanges. In particular, we review the background work done in microstructure and trade modeling, show how they relate to our work and introduce the tick size, used to classify our assets and interpret the various results. In chapter 2, we bring qualitative empirical evidence that the impact of a single trade depends on the intertrade time lags. We find that when the trading rate becomes faster, the return variance per trade strongly increases and that this behavior persists at coarser time scales. We also show that the spread value is an increasing function of the activity and deduce that orderbooks are more likely empty when the trading rate is high. In chapter 3, we present a model to capture microstructure noise. Asset prices are represented as the sum of tick returns arriving at random Poisson times. The model consists of an underlying diffusive martingale which is contaminated by some vanishing autocorrelated noise. We are able to capture the signature form of the sampled realized variance and the weak but significant autocorrelation of tick returns. In chapter 4, we use Hawkes point processes to model the random arrival of trades in the market. We model fine to coarse behavior of prices and how it affects the moments of price returns. We propose a simple non parametric estimation technique of the dependence structure of Hawkes processes in the one dimensional case and very particular multidimensional cases. We apply the method to Futures assets and find decay kernels having a power law form.
• A Non-Local Mean Curvature Flow and its semi-implicit time-discrete approximation
  
  • Chambolle Antonin
  • Morini Massimiliano
  • Ponsiglione Marcello
  , 2012. We address in this paper the study of a geometric evolution of sets, corresponding to a curvature which is non-local and singular at the origin. The curvature represents the first variation of an energy which is the volume of the set of points at a given distance to the boundary of the set. It was proposed in a a recent work of Barchiesi, Kang, Le, Morini, Ponsiglione (SIAM MMS, 2010) as a variant of the standard perimeter penalization, for the denoising of nonsmooth curves. To deal with its degeneracies, we first give an abstract existence and uniqueness result for viscosity solutions of non-local degenerate Hamiltonians, satisfying suitable continuity assumption with respect to Kuratowsky convergence of the level sets. This abstract setting applies to an approximated flow. Then, by the method of minimizing movements, we also build an ''exact'' curvature flow. We illustrate this flow with some examples, comparing our results with the standard mean curvature flow.
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation 'complexe' dans l'ensemble des pseudo-octonions
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 'complex' transformation in the pseudo-octonionic space (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation 'complexe' dans l'ensemble des pseudo-octonions)
• Le volume d'un cube
  
  • Colonna Jean-François
  , 2012. The volume of a cube (Le volume d'un cube)
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. A pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Zoom sur un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Zoom in on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Zoom sur un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))