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This chapter gives a survey of optimization algorithms seen as discrete forms of dynamical systems. The presentation is not intended to be exhaustive but rather reflects our practical experience. Local and global optimizations are discussed. A unified formulation is proposed for both deterministic and stochastic optimizations. This formulation is suitable for multi-physics problems where a coupling between different models is necessary.

Global optimisation methods that involve the assessment of multiple trial crystal structures against measured diffraction data offer a powerful alternative to Direct methods of structure solution. This chapter describes the problem of searching an N-dimensional hypersurface, populated with a great many function minima, for the global minimum that corresponds to the true crystal structure. Key factors discussed include model construction, agreement factor calculation and estimating the likelihood of success. Various global optimisation methods including simulated annealing and genetic algorithms are covered, and the chapter is illustrated with numerous examples of solved molecular crystal structures.

This chapter describes general approaches to the ab initio solution of crystal structures from X-ray or neutron powder diffraction data. The steps in the process, unit cell determination and indexing, intensity extraction, space group determination, structure solution, and structure refinement are described. Indexing methods such as zone indexing, exhaustive methods or recently developed whole pattern methods, and the use of a figure of merit (M₂₀) are presented. Intensity extraction is shown to be reasonably straightforward but for the problem of peak overlap that occurs in powder patterns. The phase problem makes structure solution more difficult: Fourier and Patterson methods, direct methods, or global optimization methods (simulated annealing, genetic algorithms) are brought to bear. The chapter concludes with a section on advanced refinement techniques, including the interpretation of displacement and site occupancy parameters, and the use of constraints. The discussion is illustrated by frequent reference to structure solution for the Ruddlesden-Popper compound Ca₃Ti₂O₇.

The nature of the interface between phonology and morphology has long been a matter of intense debate. One area that has received increased attention in recent years concerns a class of allomorphy called phonologically conditioned suppletive allomorphy (PCSA). This article offers two case studies of PCSA, one from Tiene, a Bantu language, and another from Katu, a Mon-Khmer language. The PCSAs in these languages are unique in that they both involve infixation. Our investigation suggests that a strictly input-driven subcategorization-based approach to PCSA does not offer a satisfactory account of this class of PCSA. Global optimization, which crucially references the well-formedness of output structures, is needed in allomorph selection to complement the often limited selectional power of subcategorization restrictions.