Publications

2016

• Inverse Scattering Theory and Transmission Eigenvalues
  
  • Cakoni Fioralba
  • Colton David
  • Haddar Houssem
  , 2016, 88.
• Jan de Leeuw and the French School of Data Analysis
  
  • Husson François
  • Josse Julie
  • Saporta Gilbert
  Journal of Statistical Software, University of California, Los Angeles, 2016, 73 (6), pp.16 p.. The Dutch and the French schools of data analysis differ in their approaches to the question: How does one understand and summarize the information contained in a data set? The commonalities and discrepancies between the schools are explored here with a focus on methods dedicated to the analysis of categorical data, which are known either as homogeneity analysis (HOMALS) or multiple correspondence analysis (MCA). (10.18637/jss.v073.i06)
  DOI : 10.18637/jss.v073.i06
• Quadratic BSDEs with jumps: Related nonlinear expectations
  
  • Kazi-Tani Mohamed Nabil
  • Possamaï Dylan
  • Zhou Chao
  Stochastics and Dynamics, World Scientific Publishing, 2016, 16 (4), pp.1650012. In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z, u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of their properties. We obtain in particular a non-linear Doob-Meyer decomposition for g-submartingales and a downcrossing inequality which implies their regularity in time. As a consequence of these results, we also obtain a converse comparison theorem for our class of BSDEs. Finally, we provide a dual representation for the corresponding dynamic risk measures, and study the properties of their inf-convolution, giving several explicit examples. (10.1142/S021949371650012X)
  DOI : 10.1142/S021949371650012X
• Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds
  
  • Boscain Ugo
  • Prandi Dario
  • Seri Marcello
  Communications in Partial Differential Equations, Taylor & Francis, 2016, 41 (1), pp.32–50. We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. As for general almost-Riemannian structures (under certain technical hypothesis), the singular set acts as a barrier for the evolution of the heat and of a quantum particle, although geodesics can cross it. This is a consequence of the self-adjointness of the Laplace-Beltrami operator on each connected component of the manifolds without the singular set. We get explicit descriptions of the spectrum, of the eigenfunctions and their properties. In particular in both cases we get a Weyl law with dominant term $E\log E$. We then study the effect of an Aharonov-Bohm non-apophantic magnetic potential that has a drastic effect on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator. (10.1080/03605302.2015.1095766)
  DOI : 10.1080/03605302.2015.1095766
• An introduction to continuous optimization for imaging
  
  • Chambolle Antonin
  • Pock Thomas
  Acta Numerica, Cambridge University Press (CUP), 2016, 25, pp.161-319. A large number of imaging problems reduce to the optimization of a cost function , with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification. (10.1017/S096249291600009X)
  DOI : 10.1017/S096249291600009X