Shortest Path Auction Algorithm Without Contractions Using Virtual Source Concept

In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a virtual source.We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n ²), where n is the number of nodes.Numerical experimentsare reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.     

Primal separation for 0/1 polytopes

 The 0/1 primal separation problem is: Given an extreme point xˉ of a 0/1 polytope P and some point x ^*, find an inequality which is tight at xˉ, violated by x ^* and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent. Then we provide polynomial time primal separation procedures for matching, stable set, maximum cut, and maximum bipartite graph problems, giving evidence that these algorithms are conceptually simpler and easier to implement than their corresponding counterparts for standard separation. In particular, for perfect matching we present an algorithm for primal separation that rests only on simple max-flow computations. In contrast, the known standard separation method relies on an explicit minimum odd cut algorithm. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time. Received: August 20, 2001 / Accepted: April 2002 Published online: December 9, 2002 RID="⋆" ID="⋆" This research was developed while the author was on leave at the Istituto di Analisi dei Sistemi ed Informatica, Viale Manzoni 30, 00185 Roma, supported by the project TMR-DONET nr. ERB FMRX-CT98-0202 of the European Union. Mathematics Subject Classification (2000): 90C10, 90C60, 90C57     

Convex curves, Radon transforms and convolution operators defined by singular measures

Let be a convex curve in the plane and let be the arc-length measure of Let us rotate by an angle and let be the corresponding measure. Let . Then This is optimal for an arbitrary . Depending on the curvature of , this estimate can be improved by introducing mixed-norm estimates of the form where and are conjugate exponents.     

Geometrical fitting of experimental XANES spectra by a full multiple-scattering procedure

In this paper a new software procedure is presented, named MXAN, able to fit the XANES part (from the edge to about 200 eV) of experimental X-ray absorption data. The method is based on the fitting between the experimental spectrum and several theoretical calculations generated by changing the relevant geometrical parameters of the site around the absorbing atom. The X-ray photo-absorption cross section is calculated using the full multiple-scattering scheme; different choices of the exchange correlation part of the potential can be utilised. To show the potentialities of the method the analysis of the nickel K-edge of the nickel ion in aqueous solution is presented. The procedure is able to recover the correct information on the symmetry and atomic distances from the experimental Ni K-edge XANES spectrum. The recovered structure is found to be independent of the starting conditions, showing the theoretical uniqueness of the structural solution.     

The heavy-ion magnetic spectrometer PRISMA

PRISMA is a magnetic spectrometer installed at Laboratori Nazionali di Legnaro (Italy) and designed for A=100–200, E=5–10 MeV-per-nucleon beams, and for possible use with the proposed radioactive beam facility SPES. The foremost features of the instrument are presented, along with the outline of two data analyses exemplifying the effectiveness of PRISMA-CLARA in studies of reaction dynamics.     

A sensitive and specific precursor ion scanning approach in liquid chromatography/electrospray ionization tandem mass spectrometry to detect methylprednisolone acetate and its metabolites in rat urine

A new, simple, sensitive and specific liquid chromatography/electrospray ionization tandem mass spectrometric (LC/ESI‐MS/MS) method in precursor ion scanning (PIS) mode has been developed for the rapid detection of methylprednisolone acetate (MPA) and its metabolites in rat urine. A suitable product ion specific for methylprednisolone (MP) and MPA was selected after a fragmentation study on 20 (cortico)steroids at different collision energies (5–40 eV). Urine samples were simply treated with acetonitrile then dried in a SpeedVac system. The method was validated and compared with other PIS methods for detecting corticosteroids in human urine. It was more sensitive, with limit of detection (LOD) and lower limit of quantitation (LLOQ), respectively, of 5 and 10 ng mL^?1. The method was applied for the analysis of rat urine collected before and after (24, 48, 72 h) intra‐articular (IA) injection of a marketed formulation of MPA (Depo‐Medrol®). MS/MS acquisitions were taken at different collision energies for the precursor ions of interest, detected in PIS mode, to verify the MP‐related structure. Six different metabolites were detected in rat urine, and their chemical structures were assigned with a computational study. Copyright © 2010 John Wiley & Sons, Ltd.     

Composition of Lie transforms with rigorous estimates and applications to Hamiltonian perturbation theory

In this paper we exhibit a rigorous perturbation theory for nearly integrable Hamiltonian systems, based on the composition of Lie Transforms. Precisely, we first study the algorithm for the composition of Lie transforms, and provide rigorous estimates for the convergence radius and the truncation errors of the series; then we use our estimates for a particular model-example, namely a system of weakly coupled harmonic oscillators having Diophantine frequencies, and work out Nekhoroshev-like exponential estimates for the stability times.