In this paper, a family of discriminant functions is defined for searching isotropic configurations in robot manipulators. A subfamily of the functions extensively exploits properties of symmetric polynomials derived from a manipulability matrix. The complexity analysis of computing the discriminant functions is provided. Possible applications of the functions are mentioned and illustrated.

Milling behaviour is problematic when using hydroacoustics to estimate the number of migrating fish in rivers. Milling behaviour was observed for adult sockeye salmon migrating upstream in the Wannock River, to their spawning grounds in the tributaries of Owikeno Lake in the central coast area of British Columbia, Canada. We classified the acoustic salmon tracks to separate the milling fish from the actively migrating fish in an attempt to obtain an estimate of sockeye salmon flux as they migrate to their spawning grounds. We used discriminant function analysis and found that three variables measured on each track were sufficient for the classification of the acoustic tracks into milling and non-milling categories with an approximate classification accuracy of 98%. The method we present can also be used to separate tracks of targets of interest from noise or debris tracks that occur in the acoustic data, if discrete track characteristics are ascertained.

Heterochrony is commonly proposed as a mechanism producing evolutionary changes, and some researchers identify two ways that heterochrony may be conceptualized. ‘Growth heterochrony’ examines ancestor-to-descendant differences in the ontogeny of size relative to shape, while ‘sequence heterochrony’ focuses on differences in the order of occurrence of events during ontogeny. Methods introduced here are allied with sequence heterochrony in that ontogeny is modelled as if it were a sequence of events; however, events are differently defined in this study. Using data from 16 primate species, I demonstrate that discriminant function analysis of data on developmental timing provides an additional tool for exploring the relationship between ontogeny and phylogeny. Patterns in the timing of tooth eruption, craniofacial sutural closure, and postcranial epiphyseal fusion can be used to classify individuals of all ages to their correct taxon. Taxon differences in these patterns can be characterized and described by interpreting correlations between discriminant functions and developmental events. Discriminant analysis has the advantages of: (1) being applicable to taxa for which there are too few individuals to be able to reconstruct ontogenetic sequences, including fossil species; (2) preserving intraspecific developmental variation during analysis; (3) being sensitive to very subtle differences in ontogenetic timing.

A function for distinguishing between the long, intermediate and short-setaed forms of Mononychellus species complex is described. The results show that the dorsal-central body setae, variable D3, with a discriminant correlation coefficient of 0.99, was the most important variable. Five other variables, lengths of dorso-central body setae Dl, D2, laterals LI, L2 and propodosomal P2, which had significant discriminant correlations (0.28 to 0.35) with the function were, however, included in the discriminant function.

Doleritic intrusions known to post-date the obduction of the Ballantrae complex during Arenig times record changing magma provenance during the cooling and serpentinisation of obducted peridotite. There are two groups of dolerites with different petrographical and geochemical characteristics.

The earlier emplaced group, which is subordinate, is characterised by amphibole formed under low metamorphic facies conditions and the virtual absence of Fe–Ti oxides. Chemically these rocks are of primitive tholeiitic character and are similar to modern island-arc basalts. They were derived from a strongly depleted mantle source region. The source region of the later emplaced group, which is predominant, was much less depleted. Clinopyroxene and plagioclase, much of it albitised, are the dominant minerals. Fe–Ti oxides also are common and there are pronounced chilled margins and well-preserved ophitic textures. Although showing mildly alkaline tendencies, these rocks originated from a tholeiitic parental magma of “within-plate” type.

Both groups show evidence of rodingitisation and associated alteration related to serpentinisation of the peridotite. During the metasomatic activity, only some elements were mobile, while Al2O3, total Fe, MgO, TiO2, Cr, Ni, Nb, Y and Zr remained almost constant. Assessment of original magma type and geotectonic environment, and demonstration that both groups of doleritic rocks show the products of fractionation, has relied heavily on data for the apparently immobile elements and on petrographical study which identified those rocks least affected by alteration.