Approximation Algorithms for Steiner and Directed Multicuts

In this paper we consider theSteiner multicutproblem. This is a generalization of the minimum multicut problem where instead of separating nodepairs, the goal is to find a minimum weight set of edges that separates all givensetsof nodes. A set is considered separated if it is not contained in a single connected component. We show anO(log³(kt)) approximation algorithm for the Steiner multicut problem, wherekis the number of sets andtis the maximum cardinality of a set. This improves theO(t log k) bound that easily follows from the previously known multicut results. We also consider an extension of multicuts to directed case, namely the problem of finding a minimum-weight set of edges whose removal ensures that none of the strongly connected components includes one of the prespecifiedknode pairs. In this paper we describe anO(log² k) approximation algorithm for this directed multicut problem. Ifk ? n, this represents an improvement over theO(log n log log n) approximation algorithm that is implied by the technique of Seymour.     

La densité de la loi-limite d'un processus en cascade expansif

Sans résumé     

Non-quasi-stationary state pyrolysis of ethane

An induction period has been observed in the pyrolysis of ethane in a continuous-flow stirred tank reactor at 530°C. The rate constants of the initiation, determining propagation and termination steps, have been determined.     

Inductive (direct) limits in the categories of heterogeneous algebras and of abstract automata

In our preceding paper [2], we have studied the fundamental properties of the heterogeneous algebras, and constructed the projective limits in the category of these algebras and in the category of abstract automata. The present article is devoted to the study ofdirect limits in the same categories.     

Anisotropy profiles of optical fibers and preforms

An experimental method to measure the optical anisotropy profiles of optical fibers and preforms is presented. The local values of n_z?n_r and n_z?n_?, (r,?,z) being a cylindrical coordinate system associated with the fiber or preform, are obtained.     

How to reduce the experimental time in isotopic 2H NMR using the ERETIC method

Deuterium site-specific natural isotope abundance (Ai) is routinely measured by NMR spectroscopy and quantified using an internal reference peak. This study demonstrates that the substitution of the chemical compound used as internal reference by an electronically generated signal (the ERETIC method) allows a dramatic reduction of the experimental time. Measurements of Ai on eight samples of methylsalicylate have been performed using either an internal reference (TMU) or ERETIC. No significant difference in accuracy or precision had been found between the two methods. However, because the method is applicable in partially saturated conditions, the experiment time was divided by a factor of 4 and the drawbacks associated with an internal chemical reference were avoided when ERETIC was used.     

Reconstruction method for weak-phase optical interferometry

Current optical interferometers are affected by unknown turbulent phases on each telescope. We account for this lack of phase information by introducing system aberration parameters, and we solve the image reconstruction problem by minimizing an original joint criterion in the aberrations and in the object. We validate this method by means of simulations. Tests on experimental data are under way.     

Ultrafast laser excitation of CO/Pt(111) probed by sum frequency generation: coverage dependent desorption efficiency

CO photodesorption from Pt(111) induced by femtosecond laser pulses is probed by IR+visible sum frequency generation (SFG). Steady state analysis of SFG spectra at varying CO pressure and laser fluence allows one to measure a approximately 5 orders of magnitude decrease of the photodesorption rate constant when CO coverage decreases from 0.37 to 0.07 monolayer. We ascribe this effect in the framework of the Menzel-Gomer-Redhead mechanism to electron delocalization in the CO layer. The lifetime of electronic excitation decreases when coverage decreases.