The Canonical Analysis of Distance

Canonical Variate Analysis (CVA) is one of the most useful of multivariate methods. It is concerned with separating between and within group variation among N samples from K populations with respect to p measured variables. Mahalanobis distance between the K group means can be represented as points in a (K - 1) dimensional space and approximated in a smaller space, with the variables shown as calibrated biplot axes. Within group variation may also be shown, together with circular confidence regions and other convex prediction regions, which may be used to discriminate new samples. This type of representation extends to what we term Analysis of Distance (AoD), whenever a Euclidean inter-sample distance is defined. Although the N × N distance matrix of the samples, which may be large, is required, eigenvalue calculations are needed only for the much smaller K × K matrix of distances between group centroids. All the ancillary information that is attached to a CVA analysis is available in an AoD analysis. We outline the theory and the R programs we developed to implement AoD by presenting two examples.     

Canonical Analysis: Ranks,Ratios and Fits

Measurements of p variables for n samples are collected into a n×p matrix X, where the samples belong to one of k groups. The group means are separated by Mahalanobis distances. CVA optimally represents the group means of X in an r-dimensional space. This can be done by maximizing a ratio criterion (basically one- dimensional) or, more flexibly, by minimizing a rank-constrained least-squares fitting criterion (which is not confined to being one-dimensional but depends on defining an appropriate Mahalanobis metric). In modern n < p problems, where W is not of full rank, the ratio criterion is shown not to be coherent but the fit criterion, with an attention to associated metrics, readily generalizes. In this context we give a unified generalization of CVA, introducing two metrics, one in the range space of W and the other in the null space of W, that have links with Mahalanobis distance. This generalization is computationally efficient, since it requires only the spectral decomposition of a n×n matrix.     

热处理作用下碳钢氢腐蚀裂纹愈合规律

对含氢腐蚀裂纹的碳钢进行再热处理后,SEM观察表明,氢蚀裂发生了不同程度的愈合,实验结果表明：长度约为10μm的碳钢氢蚀裂纹完全愈合的热处理条件下是从室温到1000℃热循环5次,共10h,氢蚀裂纹的愈合机制是热扩散,发生氢蚀裂纹愈合的动力是氢蚀气泡或裂纹长大导致的塑性变 能E8。在铁、碳和氢原子扩散都足够快的情况下,氢蚀裂纹愈合的条件是E8大于裂纹愈合所必须克服的表面张力能。     

Henri Poincaré and bruno de finetti: Conventions and scientific reasoning

In his account of probable reasoning, Poincaré used the concept, or at least the language, of conventions. In particular, he claimed that the prior probabilities essential for inverse probable reasoning are determined conventionally. This paper investigates, in the light of Poincaré's well known claim about the conventionality of metric geometry, what this could mean, and how it is related to other views about the determination of prior probabilities. Particular attention is paid to the similarities and differences between Poincaré's conventionalism as it applies to probabilities and de Finetti's subjectivism. The aim of the paper is to suggest that in accounts of the development of ideas about probable reasoning, particularly those customarily described as Bayesian, Poincaré's discussion deserves more attention than it has so far received.     

Axillary 5α-androst-16-en-3-one in men and women: Relationships with olfactory acuity to odorous 16-androstenes

Summary Axillary 5-androst-16-en-3-one (5-androstenone) levels were found to be significantly higher in men than in women but do not vary between left and right axillae, are not related to age, handedness or degree of hirsutism (in women) nor to anosmia to this steroid. In men (but not in women), levels are related linearly to axillary cholesterol concentrations but not to squalene. Olfactory thresholds for 5-androstenone varied widely, the lowest recorded being 0.2 ppb, but there was no difference in thresholds between men and women. Women (70%) found the smell repellant but anosmia did not differ greatly between men and women (9–20%). Anosmia to the smell of 5-androst-16-en-3-ol was most marked in women (90%) rather than in men (45%). Axillary 5-androstenone values were generally consistent with the musky or strong smells of male axillary extracts, compared with the sweet smell of those from female subjects.Supported by the Herbert Dunhill Trust.