Learning by mirror averaging

Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion. We define our aggregate by a simple recursive procedure which solves an auxiliary stochastic linear programming problem related to the original nonlinear one and constitutes a special case of the mirror averaging algorithm. We show that the aggregate satisfies sharp oracle inequalities under some general assumptions. The results are applied to several problems including regression, classification and density estimation.Comment: Published in at http://dx.doi.org/10.1214/07-AOS546 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Pivotal estimation in high-dimensional regression via linear programming

We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The method is based on linear programming only, so that its numerical implementation is faster than for previously known techniques using conic programs, and it allows one to deal with higher dimensional models. We provide upper bounds for estimation and prediction errors of the proposed estimator showing that it achieves the same rate as in the more restrictive situation of fixed design and i.i.d. Gaussian errors with known variance. Following Gautier and Tsybakov (2011), we obtain the results under weaker sensitivity assumptions than the restricted eigenvalue or assimilated conditions

Shape Coexistence in Pb186: Beyond-mean-field description by configuration mixing of symmetry restored wave functions

We study shape coexistence in Pb186 using configuration mixing of angular-momentum and particle-number projected self-consistent mean-field states. The same Skyrme interaction SLy6 is used everywhere in connection with a density-dependent zero-range pairing force. The model predicts coexisting spherical, prolate and oblate 0+ states at low energy.Comment: 5 pages REVTEX4, 4 eps figures, accepted by Phys. Lett. B. Revised version with some polishing of the text without changing its conten

Microscopic models for exotic nuclei

Starting from successful self-consistent mean-field models, this paper discusses why and how to go beyond the mean field approximation. To include long-range correlations from fluctuations in collective degrees of freedom, one has to consider symmetry restoration and configuration mixing, which give access to ground-state correlations and spectroscopy.Comment: invited talk at ENAM0

Pairing correlations. Part 1: description of odd nuclei in mean-field theories

In order to extract informations on pairing correlations in nuclei from experimental mass differences, the different contributions to odd-even mass differences are investigated within the Skyrme HFB method. In this first paper, the description of odd nuclei within HFB is discussed since it is the key point for the understanding of the above mentioned contributions. To go from an even nucleus to an odd one, the advantage of a two steps process is demonstrated and its physical content is discussed. New results concerning time-reversal symmetry breaking in odd-nuclei are also reported. PACS: 21.10Dr; 21.10.Hw; 21.30.-x. Keywords: Mean-field theories; Pairing correlations; odd nuclei;Comment: 34 pages, 8 figures. Submitted to Phys. Rev.

Configuration mixing of mean-field wave-functions projected on angular momentum and particle number; application to 24Mg

We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.Comment: 26 pages, 7 figures. Submitted to Nuclear Physic

Beyond mean-field description of the low-lying spectrum of 16O

Starting from constrained Skyrme-mean-field calculations, the low-energy excitation spectrum of 16O is calculated by configuration mixing of particle-number and angular-momentum projected mean-field states in the framework of the Generator Coordinate Method. Without any adjustable parameters, this approach gives a very good description of those states and their transition moments that can be described with our restriction to axially and reflection-symmetric shapes. The structure of low-lying 0+ states is analyzed in terms of self-consistent 0p-0h, 2p-2h, and 4p-4h Hartree-Fock states.Comment: 15 pages LATEX, 6 figures, 3 tables, revision of sections 4 and

Skyrme mean-field study of rotational bands in transfermium isotopes

Self-consistent mean field calculations with the SLy4 interaction and a density-dependent pairing force are presented for nuclei in the Nobelium mass region. Predicted quasi-particle spectra are compared with experiment for the heaviest known odd N and odd Z nuclei. Spectra and rotational bands are presented for nuclei around No252,4 for which experiments are either planned or already running.Comment: 13 pages LATEX, elsart style, 6 embedded eps figure

Prototyping of DSSDs for Particle Tracking and Spectroscopy within the EXL Project at Fair

Prototype double-sided silicon strip detectors (DSSD$s$) of 300 $\mu$m thickness produced at PTI St. Petersburg (Russia) were tested for the use as position sensitive, $\Delta E$ and E detectors for tracking and particle identification in the EXL (EXotic nuclei studied in Light-ion induced reactions at the NESR storage ring) setup at the FAIR (Facility for Antiproton and Ion Research) project at GSI. We describe the characteristics of detectors with $16 \times 16,\;64\times 64$ and $64\times 16$ strips, respectively. The response of these detectors for $^{241}$Am $\alpha$ particles injected either from the p or n side was examined. The test measurements were performed partially at GSI and the University of Edinburgh. A first in-beam test with a proton beam of 50 MeV with the latter two DSSDs and two 6.5 mm thick Si(Li) detectors was also done at KVI Groningen, the Netherlands. The results reveal good spectroscopic properties of these detectors

Quadrupole deformations of neutron-drip-line nuclei studied within the Skyrme Hartree-Fock-Bogolyubov approach

We introduce a local-scaling point transformation to allow for modifying the asymptotic properties of the deformed three-dimensional Cartesian harmonic oscillator wave functions. The resulting single-particle bases are very well suited for solving the Hartree-Fock-Bogoliubov equations for deformed drip-line nuclei. We then present results of self-consistent calculations performed for the Mg isotopes and for light nuclei located near the two-neutron drip line. The results suggest that for all even-even elements with $Z$=10--18 the most weakly-bound nucleus has an oblate ground-state shape.Comment: 20 pages, 7 figure