Reliable computation of the points of intersection of nn spheres in RnR^n

The problem of determining the points of intersection of n spheres in R n has many applications. Examples in 3-D include problems in navigation, in positioning of specific atoms in crystal structures, in reconstructing torso geometries in experimental cardiology, in the `Pentacle Problem,' and in many other problems of distance geometry. The problem is easily formulated as a system of n nonlinear equations in the coordinates of the unknown point(s) of intersection and it is of interest to determine an efficient and reliable method of solution. It is shown that apart from a few square roots the problem is usually easily and robustly solved without iteration by employing standard techniques from linear algebra. In some applications, however, the radii of the spheres may not be known accurately and this can lead to difficulties, particularly when the required point is close to lying in the affine subspace defined by the n centres of the spheres. In such cases it is more appropriate to formulate a nonlinear least squares problem in order to identify a `best approximate solution.' The special structure of this nonlinear least squares problem allows a solution to be calculated through an efficient safeguarded Newton iteration

Multilocal programming and applications

Preprint versionMultilocal programming aims to identify all local minimizers of unconstrained or constrained nonlinear optimization problems. The multilocal programming theory relies on global optimization strategies combined with simple ideas that are inspired in deflection or stretching techniques to avoid convergence to the already detected local minimizers. The most used methods to solve this type of problems are based on stochastic procedures and a population of solutions. In general, population-based methods are computationally expensive but rather reliable in identifying all local solutions. In this chapter, a review on recent techniques for multilocal programming is presented. Some real-world multilocal programming problems based on chemical engineering process design applications are described.Fundação para a Ciência e a Tecnologia (FCT

An adaptive scheme for the derivation of harmonic impedance contours

The aim of this paper is to make the calculation of harmonic impedances accurate and efficient. An adaptive scheme is proposed which minimises the number of frequency samples to be used in the derivation of the impedance/frequency loci. The scheme is then used to derive three-phase harmonic impedance contours which take into account any specified range of fundamental frequency variation

The Augustan Bridge at Narni: From laser survey to FEM seismic analysis

The Augustan Bridge of Narni represents one of the greatest transit infrastructure realized by the Romans. Mentioned in classical sources, partly collapsed on several occasions, the bridge has kept his strategic military role until the definitive collapse in 1053, being the obligatory transit from Rome to the North. Although subject to many studies however many technical aspects of the structure are still not fully understood: from which quarry the travertine blocks came from, the original number of arches, the absence of breakwater, the shape of the collapsed arches, its slope and physical connection to the Via Flaminia at both mountain and valley level, as well as the causes of its collapse. Recently an entire laser survey was carried out, today updated, providing comprehensive measurements for reconstructing the bridge’s original shape and overall size. Finally from FEM models was carried out a series of structural analysis

Localization of P300 sources in schizophrenia patients using constrained BSS

A robust constrained blind source separation (CBSS) algorithm has been proposed for separation and localization of the P300 sources in schizophrenia patients. The algorithm is an extension of the Infomax algorithm, based on minimization of mutual information, for which a reference P300 signal is used as a constraint. The reference signal forces the unmixing matrix to separate the sources of both auditory and visual P300 resulted from the corresponding stimulations. The constrained problem is then converted to an unconstrained problem by means of a set of nonlinear penalty functions. This leads to the modification of the overall cost function, based on the natural gradient algorithm (NGA). The P300 sources are then localized based on electrode - source correlations. © Springer-Verlag 2004

A Smoothing Newton Method for Semi-Infinite Programming

Semi-infinite programming, KKT condition, Semismooth equations, Smoothing Newton method,