Estimation of a Bivariate Extreme Value Distribution

Several threshold methods have been proposed for the purpose of estimating a bivariate extreme value distribution from a sample of data whose distribution is only in its domain of attraction. An integrated view of these methods is presented which leads to the introduction of a new asymptotically consistent estimator of the dependence function characterizing the extreme dependence structure. Through Monte Carlo simulations, the new estimator is also shown to do as well as its competitors and to outperform them in cases of weak dependence. To the authors' knowledge, this is the first time that the small-sample behavior of nonparametric bivariate threshold methods has ever been investigated.     

Uniform estimates in the Poincaré-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function ƒ with singularities in a closed set E ⋃ F as a sum of two bounded analytic functions with singularities in E and F respectively. We obtain some results under geometric restrictions on the sets E and F and we provide some examples showing the sharpness of the positive results. The first author is partially supported by RFBR grant #06-01-00313 and by the grant for Leading Scientific Schools #NSH-2266-2003.1. The last author is supported by DGICYT grant MTM2005-08984-C02-02 and the CIRIT grant 2005SGR00611.     

On the Characterization of Linear Uniquely Decodable Codes

A Uniquely Decodable (UD) Code is a code such that any vector of the ambient space has a unique closest codeword. In this paper we begin a study of the structure of UD codes and identify perfect subcodes. In particular we determine all linear UD codes of covering radius 2.     

Immersions of cohomogeneity one Riemannian manifolds

This work deals with positively curved compact Riemannian manifolds which are acted on by a closed Lie group of isometries whose principal orbits have codimension one and are isotropy irreducible homogeneous spaces. For such manifolds we can show that their universal covering manifold may be isometrically immersed as a hypersurface of revolution in an euclidean space.     

The Express heuristic for probabilistically constrained integer problems

Integer problems under joint probabilistic constraints with random coefficients in both sides of the constraints are extremely hard from a computational standpoint since two different sources of complexity are merged. The first one is related to the challenging presence of probabilistic constraints which assure the satisfaction of the stochastic constraints with a given probability, whereas the second one is due to the integer nature of the decision variables. In this paper we present a tailored heuristic approach based on alternating phases of exploration and feasibility repairing which we call Express (Explore and Repair Stochastic Solution) heuristic. The exploration is carried out by the iterative solution of simplified reduced integer problems in which probabilistic constraints are discarded and deterministic additional constraints are adjoined. Feasibility is restored through a penalty approach. Computational results, collected on a probabilistically constrained version of the classical 0–1 multiknapsack problem, show that the proposed heuristic is able to determine good quality solutions in a limited amount of time.     

Removing dead transitions in timed-arc Petri nets

Timed-arc Petri nets (TAPNs) are a timed extension of Petri nets where tokens are assigned an age indicating the time elapsed from its creation, and PT-arcs (place to transition arcs) are labelled with time intervals that are used to restrict the age of the tokens that can be used to fire the adjacent transition. This is a rather pathological model, as reachability is undecidable, whereas some other known properties of Petri nets, like boundedness, coverability and even termination, are decidable. This article focuses on the problem of detecting dead transitions, i.e. transitions that can be removed from the model since they can never become enabled. We prove that this problem is decidable for TAPNs with natural times, and we present an algorithm that can be used to find dead transitions in the particular case of 1-safe TAPNs.     

Determination of paraquat in rat brain using ion-pair solid-phase extraction and reversed-phase high-performance liquid chromatography with ultraviolet detection

A simple and sensitive procedure for the measurement of N-methylisoquinolinium ion (NMIQ+), a putative neurotoxin, was devised using high-performance liquid chromatography (HPLC) with fluorescence detection. Separation of NMIQ+ was carried out by gel filtration and reversed-phase HPLC on a column of hydrophilic polymer gels (Asahipak GS-302H). The method was sensitive enough to measure 50 fmol of NMIQ+. Uptake of NMIQ+ into rat striatal slices was confirmed by this method.     

The use of simplex optimiztion in evaluating complex chromatograms of mixtures

The application of simplex optimization to the qualitative and quantitative evaluation of chromatograms of complex mixtures is outlined. The chromatogram is considered as a linear combination of pure component chromatograms (assuming no interactions are present); if suitable components are selected and the coefficients of the linear combination are properly evaluated, the experimental chromatogram can be reproduced numerically. The simplex method is then used to evaluate the solution with minimal error. The quantitation of polychlorobiphenyls from Aroclor mixtures in marine sediments and fish, and the identification of essential oils in a perfume base extract are outlined. Errors of ≤19% (25% in environmental samples) between the experimental and reconstructed chromatograms were achieved.