11 research outputs found
A non parametric approach for calibration with functional data
International audienceA new nonparametric approach for statistical calibration with functional data is studied. The practical motivation comes from calibration problems in chemometrics in which a scalar random variable Y needs to be predicted from a functional random variable X. The proposed predictor takes the form of a weighted average of the observed values of Y in the training data set, where the weights are determined by the conditional probability density of X given Y. This functional density, which represents the data generation mechanism in the context of calibration , is so incorporated as a key information into the estimator. The new proposal is computationally simple and easy to implement. Its statistical consistency is proved, and its relevance is shown through simulations and an application to data
On combining wavelets expansion and sparse linear models for Regression on metabolomic data and biomarker selection
International audienceWavelet thresholding of spectra has to be handled with care when the spectra are the predictors of a regression problem. Indeed, a blind thresholding of the signal followed by a regression method often leads to deteriorated predictions. The scope of this article is to show that sparse regression methods, applied in the wavelet domain, perform an automatic thresholding: the most relevant wavelet coefficients are selected to optimize the prediction of a given target of interest. This approach can be seen as a joint thresholding designed for a predictive purpose. The method is illustrated on a real world problem where metabolomic data are linked to poison ingestion. This example proves the usefulness of wavelet expansion and the good behavior of sparse and regularized methods. A comparison study is performed between the two-steps approach (wavelet thresholding and regression) and the one-step approach (selection of wavelet coefficients with a sparse regression). The comparison includes two types of wavelet bases, various thresholding methods, and various regression methods and is evaluated by calculating prediction performances. Information about the location of the most important features on the spectra was also obtained and used to identify the most relevant metabolites involved in the mice poisoning
Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data
Using a new probabilistic approach we model the relationship between
sequences of auditory stimuli generated by stochastic chains and the
electroencephalographic (EEG) data acquired while 19 participants were exposed
to those stimuli. The structure of the chains generating the stimuli are
characterized by rooted and labeled trees whose leaves, henceforth called
contexts, represent the sequences of past stimuli governing the choice of the
next stimulus. A classical conjecture claims that the brain assigns
probabilistic models to samples of stimuli. If this is true, then the context
tree generating the sequence of stimuli should be encoded in the brain
activity. Using an innovative statistical procedure we show that this context
tree can effectively be extracted from the EEG data, thus giving support to the
classical conjecture.Comment: 16 pages, 7 figure
Wannier-Bloch approach to localization in high harmonics generation in solids
Emission of high-order harmonics from solids provides a new avenue in
attosecond science. On one hand, it allows to investigate fundamental processes
of the non-linear response of electrons driven by a strong laser pulse in a
periodic crystal lattice. On the other hand, it opens new paths toward
efficient attosecond pulse generation, novel imaging of electronic wave
functions, and enhancement of high-order harmonic generation (HHG) intensity. A
key feature of HHG in a solid (as compared to the well-understood phenomena of
HHG in an atomic gas) is the delocalization of the process, whereby an electron
ionized from one site in the periodic lattice may recombine with any other.
Here, we develop an analytic model, based on the localized Wannier wave
functions in the valence band and delocalized Bloch functions in the conduction
band. This Wannier-Bloch approach assesses the contributions of individual
lattice sites to the HHG process, and hence addresses precisely the question of
localization of harmonic emission in solids. We apply this model to investigate
HHG in a ZnO crystal for two different orientations, corresponding to wider and
narrower valence and conduction bands, respectively. Interestingly, for
narrower bands, the HHG process shows significant localization, similar to
harmonic generation in atoms. For all cases, the delocalized contributions to
HHG emission are highest near the band-gap energy. Our results pave the way to
controlling localized contributions to HHG in a solid crystal, with hard to
overestimate implications for the emerging area of atto-nanoscience
Symphony on strong field approximation
This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum–continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60
Symphony on strong field approximation
This paper has been prepared by the Symphony collaboration (University of Warsaw,
Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of
the ‘simple man’s models’ which underlie most of the phenomena that occur when intense
ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic
generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron
ionization (NSMI). ‘Simple man’s models’ provide both an intuitive basis for understanding
the numerical solutions of the time-dependent Schrödinger equation and the motivation for the
powerful analytic approximations generally known as the strong field approximation (SFA).
In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions
are described by including continuum–continuum interactions in a systematic perturbation-like
theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from
multi-electron atoms and from multi-atom molecules. The main novel part of the presented
theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron
atoms, allowing for studies of an interplay between electron impact ionization and resonant
excitation with subsequent ionization; (ii) time-dependent treatment in the single active
electron approximation of ‘large’ molecules and targets which are themselves undergoing
dynamics during the HHG or ATI processes. In particular, we formulate the general expressions
for the case of arbitrary molecules, combining input from quantum chemistry and quantum
dynamics. We formulate also theory of time-dependent separable molecular potentials to model
analytically the dynamics of realistic electronic wave packets for molecules in strong laser
fields.Peer Reviewe