Smoothing Sample Extremes with Dynamic Models

The study of extreme values is of crucial interest in many contexts. The concentration of pollutants, the sea-level and the closing prices of stock indexes are only a few examples in which the occurrence of extreme values may lead to important consequences. In the present paper we are interested in detecting trend in sample extremes. A common statistical approach used to identify trend in extremes is based on the generalized extreme value distribution, which constitutes a building block for parametric models. However, semiparametric procedures imply several advantages when exploring data and checking the model. This paper outlines a semiparametric approach for smoothing sample extremes, based on nonlinear dynamic modelling of the generalized extreme value distribution. The relative merits of this approach are illustrated through two real examples.AMS 2000 Subject Classification. Primary—62G32, 62G05, 62M10     

A Spectroscopic and Molecular Modelling Study of the Nature of the Association Complexes of Nile Red with Cyclodextrins

The polarity-sensitive fluorescent dye Nile Red forms association complexes with various cyclodextrins in aqueous solution. The formation of such association complexes has a significant effect on the Nile Red fluorescence, with the largest effect being observed in -cyclodextrin solution. When -cyclodextrin is used to increase the Nile Red concentration in solution, the absorption spectrum shows a large blue shift indicating the formation of an inclusion complex, but surprisingly the Nile Red fluorescence is strongly suppressed. A proposed explanation for this observation involves the formation of 1:2 host:guest complexes, in which the Nile Red guests are included as relatively non-fluorescent dimers. When the solutions were prepared by adding -cyclodextrinto a near-saturated aqueous solution of Nile Red (so that 1:1 or 2:1 complexation shouldbe favoured), significant fluorescence enhancement was observed. Analysis of thefluorescence enhancement as a function of host concentration indicated the formationof 2:1 host:guest complexes in these solutions. However, electrospray mass spectroscopic studies show no evidence for the formation of any such inclusion complexes. Furthermore, molecular modelling shows that the formation of a complex involving full insertion of Nile Red in the -cyclodextrin cavity is not stable, and will quickly eject the Nile Red guest molecule. These modelling results suggest that an association complex involving capping (via the association of Nile Red parallel to the cavity opening, or by partial insertion into the cavity) of the -cyclodextrin cavity by one or two Nile Red molecules is much more likely.     

Generation of Accurate Finite Element Models of Nonlinear Systems – Application to an Aeroplane-Like Structure

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the other hand, updating nonlinear models is something the structural dynamicist prefers to avoid mainly because tools such as modal analysis are no longer available. The objective of the present study is to propose a two-step methodology for dealing with nonlinear systems. Its most appealing feature is that it decouples the estimation of the linear and nonlinear parameters. A numerical application consisting of an aeroplane-like structure is used to assess the efficiency of the procedure.