The effect of dissipation on coherent quantum tunnelling in a double-well system: Two-level model using an adjoint equation approach

We examine the effect of dissipation on coherent quantum tunnelling between the two lowest levels of a double-well system using an adjoint equation approach developed previously in the treatment of quantum-optical problems. Dissipation is modelled by a linear coupling to a bath of harmonic oscillators. The high frequency portion of the bath is adiabatically eliminated using a cumulant expansion technique, which generates frequency renormalisation terms. Making a low temperature assumption, an approximate two-level model is developed in the form of three coupled stochastic differential equations. With a decorrelation approximation, the two-level equations can be solved to yield familiar results. However, the adjoint equation also permits the use of direct stochastic simulation as a means of solution, and simulations are carried out for a range of parameters. A comparison with the decorrelation approximation is made.     

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An iterative procedure for differential analysis of gene expression

Microarrays are a popular technology to study genes that are differentially expressed between two conditions. In this Note, we propose an iterative procedure to determine the biggest subset of non-differentially expressed genes. We prove a pseudo Markov relationship that allows practical computations. We obtain explicit expressions for FDR and the level of the proposed test at each step. To cite this article: A. Bar-Hen, S. Robin, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument

In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (₀ F ₁) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these ₀ F ₁functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( _r F _s ) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments. In the case of the generalized hypergeometric functions of two Hermitian matrix arguments, we prove that these functions satisfy certain modified pairwise TP₂properties; the proofs of these results are based on Sylvester's formula for compound determinants and the condensation formula of C. L. Dodgson [Lewis Carroll] (1866).     

Oxygen on Fe(100) and Fe(110)

Investigations of the electronic and magnetic properties of oxygen adsorbed on magnetized iron films have been carried out by means of angle and spin resolving photoelectron spectroscopy. Iron, epitaxially grown on W(100) and W(110) crystals, served as the ferromagnetic substrate. Exchange splittings of the O 2p_x derived level have been detected, demonstrating a magnetic coupling between the chemisorbate and the iron layer. Variations of the exchange splitting have occurred as a function of the oxygen coverage, photon energy, and emission angle. High oxygen exposures have lead to a FeO overlayer at the surface.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).