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The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper presents convergence properties of the Nelder–Mead algorithm applied to(More)
How many sublattices of index N are there in the planar hexagonal lattice? Which of them are the best from the point of view of packing density, signal-to-noise ratio, or energy? We answer the first question completely and give partial answers to the other questions. Let A denote the familiar hexagonal lattice shown in Fig. 1. We shall investigate four(More)
In ischaemic stroke, expansion of the infarct core occurs at the expense of surrounding hypoxic, metabolically compromised tissue over a period of 24 h or more in a considerable proportion of patients. It is uncertain whether hypoxic tissue observed at later times after stroke onset retains the potential for survival or whether such survival has an impact(More)
Fast, efficient parallel algorithms are presented for discrete event simulations of dynamic channel assignment schemes for wireless cellular communication networks. The driving events are called arrivals and departures, in continuous time, to cells geographically distributed across the service area. A dynamic channel assignment scheme decides which call(More)