Made available in DSpace on 2008-05-13T13:16:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-05-10 / Recent advances in dynamic Mirrlees economies have incorporated the treatment of human capital investments as an important dimension of government policy. This paper adds to this literature by considering a two period economy where agents are di erentiated by their preferences for leisure and their productivity, both private information. The fact that productivity is only learnt later in an agent's life introduces uncertainty to agent's savings and human capital choices and makes optimal the use of multi-period tie-ins in the mechanism that characterizes the government policy. We show that optimal policies are often interim ine cient and that the introduction of these ine ciencies may take the form of marginal tax rates on labor income of varying sign and educational policies that include the discouragement of human capital acquisition. With regards to implementation, state-dependent linear taxes implement optimal savings, while human capital policies may require labor income taxes that depend directly on agents' schooling.

Recent experimentation with excitation of surface plasmons on a gold film in the Kretschmann configuration have shown what appears to be a superconductive effect. Researchers claimed to see the existence of electron pairing during scattering as well as magnetic field repulsion while twisting the polarization of the laser. In an attempt to explain this, they pointed to a combination of electron-electron scattering in external fields as well as dynamic screening via intense laser radiation. This paper expands upon the latter, taking a look at the properties of a dynamic polarization function, its effects on bulk and surface plasmon dispersion relations, and its various consequences.

The dissociation of fast hydrogen and nitrogen molecular ions with kinetic energies ranging from 200 to 2000 eV/atom is studied for grazing collisions with various fcc metal surfaces. Within this energy range, the dissociation is either caused by electron capture into antibonding molecular states or by vibrational and rotational excitation. In contrast to hydrogen, nitrogen is chemically inert and interacts mainly elastically with the surfaces; thus there is no dissociation via electron capture. The processes of vibrational and rotational excitation are simulated using a molecular dynamics simulation with interaction potentials based on density functional theory. The comparison with the data obtained from Time-Of-Flight experiments reveals that an additional electronic effect has to be taken into account: The intramolecular bond of the molecules is softened due to electronic screening during the interaction with the surface. Hence, the softened molecules are more likely to dissociate through elastic collisions with surface atoms. The dissociation of hydrogen at low energies on metallic surfaces is dominated by electronic processes. An analysis of the kinetic energy distributions of the scattered dissociation products reveals information about the energy which is released during the dissociation process. The model of electronically induced dissociation is clearly confirmed by this method. However, an increasing contribution of additional mechanical processes becomes apparent at higher energies.

Les algorithmes convexes de résolution pour les régressions linéaires parcimonieuses possèdent de bonnes performances pratiques et théoriques. Cependant, ils souffrent tous des dimensions du problème qui dictent la complexité de chacune de leur itération. Nous proposons une approche pour réduire ce coût calculatoire au niveau de l'itération. Des stratégies récentes s'appuyant sur des tests d'élimination de variables ont été proposées pour accélérer la résolution des problèmes de régressions parcimonieuse pénalisées tels que le LASSO. Ces approches reposent sur l'idée qu'il est profitable de dédier un petit effort de calcul pour localiser des atomes inactifs afin de les retirer du dictionnaire dans une étape de prétraitement. L'algorithme de résolution utilisant le dictionnaire ainsi réduit convergera alors plus rapidement vers la solution du problème initial. Nous pensons qu'il existe un moyen plus efficace pour réduire le dictionnaire et donc obtenir une meilleure accélération : à l'intérieur de chaque itération de l'algorithme, il est possible de valoriser les calculs originalement dédiés à l'algorithme pour obtenir à moindre coût un nouveau test d'élimination dont l'effet d'élimination augmente progressivement le long des itérations. Le dictionnaire est alors réduit de façon dynamique au lieu d'être réduit de façon statique, une fois pour toutes, avant la première itération. Nous formalisons ce principe d'élimination dynamique à travers une formulation algorithmique générique, et l'appliquons en intégrant des tests d'élimination existants, à l'intérieur de plusieurs algorithmes du premier ordre pour résoudre les problèmes du LASSO et Group-LASSO. / Applications in signal processing and machine learning make frequent use of sparse regressions. Resulting convex problems, such as the LASSO, can be efficiently solved thanks to first-order algorithms, which are general, and have good convergence properties. However those algorithms suffer from the dimension of the problem, which impose the complexity of their iterations. In this thesis we study approaches, based on screening tests, aimed at reducing the computational cost at the iteration level. Such approaches build upon the idea that it is worth dedicating some small computational effort to locate inactive atoms and remove them from the dictionary in a preprocessing stage so that the regression algorithm working with a smaller dictionary will then converge faster to the solution of the initial problem. We believe that there is an even more efficient way to screen the dictionary and obtain a greater acceleration: inside each iteration of the regression algorithm, one may take advantage of the algorithm computations to obtain a new screening test for free with increasing screening effects along the iterations. The dictionary is henceforth dynamically screened instead of being screened statically, once and for all, before the first iteration. Our first contribution is the formalisation of this principle and its application to first-order algorithms, for the resolution of the LASSO and Group-LASSO. In a second contribution, this general principle is combined to active-set methods, whose goal is also to accelerate the resolution of sparse regressions. Applying the two complementary methods on first-order algorithms, leads to great acceleration performances.