Une formule de Landau–Zener pour un croisement non dégénéré et involutif de codimension 3Landau–Zener formula for non-degenerate involutive codimension 3 crossings

In this Note, we study a 2×2 system of evolution equations with some codimension 3 crossing. We derive two conditions of non-degeneracy. We focus on one of them and reduce our system to some Landau–Zener's type system. Using this reduction, we describe the energy transfer at the crossing by Landau–Zener formula for 2-scales semi-classical measures. To cite this article: C. Fermanian Kammerer, P. Gérard, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 915–920.     

The finite sample properties of sparse M-estimators with pseudo-observations

Annals of the Institute of Statistical Mathematics - We provide finite sample properties of general regularized statistical criteria in the presence of pseudo-observations. Under the restricted...     

Semi-Classical Analysis of a Dirac Equation Without Adiabatic Decoupling

We study adiabatic decoupling for Dirac equation with some scaling which yields that the mass appears with a coefficient where is the semi-classical parameter and > 0. Therefore, the system presents an avoided crossing. The scale = 1/2 is critical: adiabatic decoupling holds for (0,1/2) while for 1/2, there is energy transfer at leading order between the two modes. We describe this transfer in terms of two-scale Wigner measures by means of Landau-Zener formula which takes into account the change of polarization of the measures after the crossing.     

A non-stationary problem coupling PDEs and ODEs modelizing an automotive catalytic converter

In this article we prove the existence and uniqueness of the solution of a non-stationary problem that modelizes the behavior of the concentrations and the temperature of gases going through a cylindrical passage of an automotive catalytic converter. This problem couples parabolic partial differential equations (PDEs) in a domain with one parabolic partial differential equation and some ordinary differential equations (ODEs) on a part of its boundary.     

Second-Order Models for Optimal Transport and Cubic Splines on the Wasserstein Space

Foundations of Computational Mathematics - On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation....     

Single switch surface hopping for molecular dynamics with transitions

A trajectory surface hopping algorithm is proposed, which stems from a mathematically rigorous analysis of propagation through conical intersections of potential energy surfaces. Since nonadiabatic transitions are only performed when a classical trajectory attains one of its local minimal surface gaps, the algorithm is called single switch surface hopping. Numerical experiments for a two mode Jahn-Teller system are presented, which illustrate the asymptotic justification of the method as well as its good performance in the physically relevant parameter range.     

Source point discovery through high frequency asymptotic time reversal

Given local frequency domain wave data, the Numerical Micro-Local Analysis (NMLA) method (Benamou et al., 2004) [5] and its recent improved version (Benamou et al., 2011) [4] gives a pointwise numerical approximation of the number of rays, their slowness vectors and corresponding wavefront curvatures. With time domain wave data and assuming the source wavelet is given, the method also estimates the travel-time. The paper provides a non technical presentation of the improved NMLA algorithm and presents a numerical application which can be interpreted as a high frequency asymptotic version of the classical time reversal method (Borcea et al., 2003) [7]. A detailed technical presentation of the algorithm is available in Benamou et al. (2011) [4] and more numerical experiments can be found in Collino and Marmorat (2011) [15].     

Nonparametric estimation of competing risks models with covariates

In competing risks model, several failure times arise potentially. The smallest failure time and its index only are observed. Without specific assumptions, the joint or even the marginal distribution functions of the underlying failure times are not identifiable (A. Tsiatis, Proc. Natl. Acad. Sci. USA 72 (1975) 20). Nonetheless, if each individual is characterized by a “sufficiently informative” set of covariates, these distributions are identifiable under some conditions of regularity (J.J. Heckman and B. Honoré, Biometrika 76 (1989) 325). In this paper, nonparametric kernel estimators of the joint distribution function of failure times conditional on the covariates are proposed. Their weak and strong consistency are discussed.     

Semi-classical analysis on H-type groups

Science China Mathematics - In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodi fferential operators, prove the boundedness of their action on...