University of Paris

About: University of Paris is a education organization based out in Paris, France. It is known for research contribution in the topics: Population & Medicine. The organization has 102426 authors who have published 174180 publications receiving 5041753 citations. The organization is also known as: Sorbonne.

Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory

Abstract: Since several years Lyapunov Characteristic Exponents are of interest in the study of dynamical systems in order to characterize quantitatively their stochasticity properties, related essentially to the exponential divergence of nearby orbits. One has thus the problem of the explicit computation of such exponents, which has been solved only for the maximal of them. Here we give a method for computing all of them, based on the computation of the exponents of order greater than one, which are related to the increase of volumes. To this end a theorem is given relating the exponents of order one to those of greater order. The numerical method and some applications will be given in a forthcoming paper.

Image recovery via total variation minimization and related problems

Abstract: We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original TV minimization problem that handles correctly some situations where TV fails.

Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms

Abstract: This paper examine the Euler-Lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in Dupuis et al. (1998) and Trouve (1995) in which two images I 0, I 1 are given and connected via the diffeomorphic change of coordinates I 0???1=I 1 where ?=?1 is the end point at t= 1 of curve ? t , t?[0, 1] satisfying .? t =v t (? t ), t? [0,1] with ?0=id. The variational problem takes the form $$\mathop {\arg {\text{m}}in}\limits_{\upsilon :\dot \phi _t = \upsilon _t \left( {\dot \phi } \right)} \left( {\int_0^1 {\left\| {\upsilon _t } \right\|} ^2 {\text{d}}t + \left\| {I_0 \circ \phi _1^{ - 1} - I_1 } \right\|_{L^2 }^2 } \right),$$ where ?v t? V is an appropriate Sobolev norm on the velocity field v t(·), and the second term enforces matching of the images with ?·?L 2 representing the squared-error norm. In this paper we derive the Euler-Lagrange equations characterizing the minimizing vector fields v t, t?[0, 1] assuming sufficient smoothness of the norm to guarantee existence of solutions in the space of diffeomorphisms. We describe the implementation of the Euler equations using semi-lagrangian method of computing particle flows and show the solutions for various examples. As well, we compute the metric distance on several anatomical configurations as measured by ?0 1?v t? V dt on the geodesic shortest paths.

Wavelet Shrinkage: Asymptopia?

Abstract: Much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects-curves, densities, spectral densities, images-from noisy data A now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems Unfortunately, the results have rarely moved into practice, for a variety of reasons-among them being similarity to known methods, computational intractability and lack of spatial adaptivity We discuss a method for curve estimation based on n noisy data: translate the empirical wavelet coefficients towards the origin by an amount √(2 log n) /√n The proposal differs from those in current use, is computationally practical and is spatially adaptive; it thus avoids several of the previous objections Further, the method is nearly minimax both for a wide variety of loss functions-pointwise error, global error measured in L p -norms, pointwise and global error in estimation of derivatives-and for a wide range of smoothness classes, including standard Holder and Sobolev classes, and bounded variation This is a much broader near optimality than anything previously proposed: we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves Finally, the theory underlying the method is interesting, as it exploits a correspondence between statistical questions and questions of optimal recovery and information-based complexity

Large-scale meta-analysis of genome-wide association data identifies six new risk loci for Parkinson's disease

Abstract: We conducted a meta-analysis of Parkinson's disease genome-wide association studies using a common set of 7,893,274 variants across 13,708 cases and 95,282 controls. Twenty-six loci were identified as having genome-wide significant association; these and 6 additional previously reported loci were then tested in an independent set of 5,353 cases and 5,551 controls. Of the 32 tested SNPs, 24 replicated, including 6 newly identified loci. Conditional analyses within loci showed that four loci, including GBA, GAK-DGKQ, SNCA and the HLA region, contain a secondary independent risk variant. In total, we identified and replicated 28 independent risk variants for Parkinson's disease across 24 loci. Although the effect of each individual locus was small, risk profile analysis showed substantial cumulative risk in a comparison of the highest and lowest quintiles of genetic risk (odds ratio (OR) = 3.31, 95% confidence interval (CI) = 2.55–4.30; P = 2 × 10−16). We also show six risk loci associated with proximal gene expression or DNA methylation.