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sion of the structures of hydrazines and their ionization potentials, see Klessinger, M.; Rademacher, P., Angew. Chem. Int. Ed. Engl., 1979, 18, 826. Answer to 3(a). We are asked here to provide an interaction diagram which will illustrate the nature of the molecular orbitals which contain the three electrons which are involved in binding together the two sulfur atoms. We note that in the absence of an interaction between them, each sulfur atom is a bent dicoordinated atom and as such has two frontier orbitals, a pure p orbital perpendicular to the plane of the s bonds to S and an sp n hybrid orbital of lower energy directed along the line bisecting the angle made by the s bonds and in the same plane. In the case of sulfur the p orbital is 3p, and the sp n hybrid has rather little ``p'' character n ` 1 . To set up the interaction diagram, one must have an appreciation of the limitations imposed by the s framework, which form an 8-membered ring. Inspection

10

(1972) Will a large complex system be stable Nature 238, 413 14 May, RM (1973a) Stability and Complexity in Model Ecosystems Princeton University Press, Princeton, NJ May, RM (1973b) On relationships among various types of population model American Naturalist 107, 46 57 May, RM (1976) Simple mathematical models with very complicated dynamics Nature 261, 459 67 May, RM (1978) Host-parasitoid systems in patchy environments, a phenomenological model Journal of Animal Ecology 47, 833 43 May, RM (1981) Theoretical Ecology Principles and Applications Blackwell Science, Oxford May, RM (1984) An overview: real and apparent patterns in community structure In: Ecological Communities: Conceptual Issues and the Evidence (DR Strong, D Simberloff, CG Abele and AB Thistle, eds), pp 3 18 Princeton University Press, Princeton, NJ May, RM and Oster, GF (1976) Bifurcations and dynamic complexity in simple ecological models.

Classi cation is useful when the response considered is a category variable that can be interpreted in terms of several classes to which a sample may belong The main goal of classi cation is to assign new samples reliably to preexisting classes, but classi cation results can also be used as a diagnostic tool to identify the most important variables to retain in the model or to nd outliers Applications include predicting whether a pharmaceutical product meets speci ed quality requirements, in which case the result is simply a binary response, or more generally testing or con rming the identity of a substance PCA and discriminant analysis are techniques that have found extensive use in NIR analysis for that purpose SIMCA, a multivariate technique optimized for NIR data analysis, combines PCA models for each de ned class in the training set.

American Naturalist 110, 573 99 May, RM and Watts, CH (1992) The dynamics of predator-prey and resource-harvester systems In: Natural Enemies (MJ Crawley, ed), pp 431 57 Blackwell Science, Oxford May, RM, Conway, GR, Hassell, MP and Southwood, TRE (1974) Time delays, density dependence and single-species oscillations Journal of Animal Ecology 43, 747 70 Maynard Smith, J (1968) Mathematical Ideas in Biology Cambridge University Press, Cambridge..

The approach can be applied to a more general class of problems than simple classi cation, for example, identi cation PCA is performed on a data set requiring qualitative analysis After computing the PCs, scores are calculated and used to perform qualitative analysis by surrounding each region of multidimensional space containing each group s scores with a surface Conceptually, this enclosing surface can be modeled as an ellipsoid and distances to these clouds are computed using Mahalanobis metrics based on the PC scores In practice, the optimal number of PCs should be chosen for each class model separately, according to a suitable validation scheme Each model is checked for possible outliers and improved as much as possible, like any PCA model.

Before using the models to predict class membership for new samples, the speci city of the models should be veri ed, that is, checked for class overlap and adequate interclass distance Once each class has been modeled, and class overlap is not excessive, new samples can be tted to each model Unknown samples are then compared to the class models, and assigned to classes according to their similarity to the training samples The modeling stage implies that enough samples have been identi ed as members of each class to allow reliable models to be built Accurate sample description also requires a suf cient number of variables Actual classi cation is based on statistical tests performed on Mahalanobis distances between sample and model With each unknown sample, all variable values are computed using the model scores and loadings, before being compared to the actual values.