Slow-light enhanced optical detection in liquid-infiltrated photonic crystals

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals is theoretically studied. Using a scattering-matrix approach and the Wigner–Smith delay time concept, we show that optical absorbance benefits both from slow-light phenomena as well as a high filling factor of the energy residing in the liquid. Utilizing strongly dispersive photonic crystal structures, we numerically demonstrate how liquid-infiltrated photonic crystals facilitate enhanced light–matter interactions, by potentially up to an order of magnitude. The proposed concept provides strong opportunities for improving existing miniaturized absorbance cells for optical detection in lab-on-a-chip systems.     

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).     

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).     

Low-energy fission investigated in reactions of 750 AMeV 238U-ions on 208Pb. II: Isotopic distributions

Projectile fission of 750 AMeV ²³⁸U-ions interacting with a Pb target was studied by means of the spectrometer FRS, GSI-Darmstadt. One of the two fission fragments was detected with a transmission of few percent and identified in mass and charge. Low-energy fission (E^* < 25 MeV) events were selected by their magnetic rigidity. Whereas the production of asymmetric fission events is dominated by the GDR excitation, very asymmetric fission and symmetric fission take place after a GQR or DGDR excitation or after a nuclear interaction. Cross sections of more than 250 isotopes were measured. Isotopic distributions of low-energy fission were reconstructed for elements from Se to Te. The fission modes SI, SII and SL were clearly shown in these distributions and in the mass and TKE distributions. Charge polarization and mass dispersion were deduced for each fission mode. Finally, the characteristics of the low-energy fission process explain the production rates of neutron-rich species. Received: 14 July 1997 / Revised version: 6 October 1997     

On local optima in multiobjective combinatorial optimization problems

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.