An alternating least squares method for the weighted approximation of a symmetric matrix

Bailey and Gower examined the least squares approximationC to a symmetric matrixB, when the squared discrepancies for diagonal elements receive specific nonunit weights. They focussed on mathematical properties of the optimalC, in constrained and unconstrained cases, rather than on how to obtainC for any givenB. In the present paper a computational solution is given for the case whereC is constrained to be positive semidefinite and of a fixed rankr or less. The solution is based on weakly constrained linear regression analysis.The authors are obliged to John C. Gower for stimulating this research.     

Procedural fairness and self-esteem

We argue that people's self-esteem is affected by the fairness of procedures to which they are subjected; unfair treatment will lower self-esteem. Moreover, since this influence on self-esteem is presumably due to the implicit evaluation expressed by the choice of procedure and hence by the evaluation expressed by the person implementing the procedure, people's concern with the fairness of treatment will be focused on the interactional aspects of the procedure. In two experiments designed to test these hypotheses subjects received either a high or a low grade on an ability test on the basis of either fair or unfair grading procedures. The results of Experiment 1 indicated that subjects' self-esteem was lower after unfair treatment, and this influence was only apparent when subjects received high test feedback. Additionally, ratings of the fairness of the interaction were lower following unfair grading procedures. Experiment 2 also manipulated level of involvement with the test. Self-esteem was affected by procedural fairness and procedural fairness influenced perceived fairness of the interaction only in the high involvement condition.     

Racial categorization and preference among older children in The Netherlands

In this study the pervasiveness of racial categorization is investigated among children (10–12 years of age) in multi-racial schools. Subjects were asked to sort photographs of unknown contemporaries and to indicate preferences. Skin colour, sex and facial expression were used as three characteristics which varied systematically in the pictures. The results show, first, that children preferred to use different features simultaneously instead of a single feature only. Second, in a dichotomous classification task skin colour and sex were the most obvious visible features used for categorization. Gender was also used for explaining socially undesirable behaviour, and for indicating preferences. while race was not used in these tasks. In indicating preferences facial expression and not skin colour was used as a subordinate category. There were very few differences between ethnic Dutch, coloured and ethnic minority children in the use of skin colour or other features.     

Auditory spatial alternation transforms auditory time (again): Comments on Lakatos (1993), “Temporal constraints on apparent motion in auditory space”

Lakatos (1993) reported interesting data that indeed support “the hypothesis that the extent of spatial separation between successive sound events directly affects the perception of time intervals between these events” (p. 139). The present comment is an attempt to show that, as far as the horizontal plane is concerned, Lakatos’s hypothesis was already answered qualitatively by Axelrod and coworkers (Axelrod & Guzy, 1968; Axelrod, Guzy, & Diamond, 1968) in their studies of attention shifting, and by ten Hoopen and coworkers, who quantified the amount of “interaural time dilation” (Akerboom, ten Hoopen, Olierook, & van der Schaaf, 1983; ten Hoopen, 1982; ten Hoopen, Vos, & Dispa, 1982). Nonetheless, Lakatos’s study is very worthwhile. It originated from the realm of “apparent motion paradigms,” but I will argue that the study rather used an “auditory streaming paradigm,” and that the data is a welcome contribution to elucidate how the perceptual processes of auditory stream formation and interaural time dilation interact.     

A simplification of a result by zellini on the maximal rank of symmetric three-way arrays

Zellini (1979, Theorem 3.1) has shown how to decompose an arbitrary symmetric matrix of ordern ×n as a linear combination of 1/2n(n+1) fixed rank one matrices, thus constructing an explicit tensor basis for the set of symmetricn ×n matrices. Zellini's decomposition is based on properties of persymmetric matrices. In the present paper, a simplified tensor basis is given, by showing that a symmetric matrix can also be decomposed in terms of 1/2n(n+1) fixed binary matrices of rank one. The decomposition implies that ann ×n ×p array consisting ofp symmetricn ×n slabs has maximal rank 1/2n(n+1). Likewise, an unconstrained INDSCAL (symmetric CANDECOMP/PARAFAC) decomposition of such an array will yield a perfect fit in 1/2n(n+1) dimensions. When the fitting only pertains to the off-diagonal elements of the symmetric matrices, as is the case in a version of PARAFAC where communalities are involved, the maximal number of dimensions can be further reduced to 1/2n(n–1). However, when the saliences in INDSCAL are constrained to be nonnegative, the tensor basis result does not apply. In fact, it is shown that in this case the number of dimensions needed can be as large asp, the number of matrices analyzed.     

The hyperreality of clinical ethics: A unitary theory and hermeneutics

Medical ethics nowadays is dominated by a conception of ethics as the application of moral theories and principles. This conception is criticized for its depreciation of the internal morality of medical practice and its narrow view of external morality. This view reflects both a lack of interest in the empirical realities of medicine and a neglect of the socio-cultural value-contexts of medical ethical issues, including the creative development of a broader philosophical framework for a practicable medical ethics. Several alternative approaches and conceptions have been proposed. The unified clinical ethics theory, developed by Graber and Thomasma, is an interesting attempt to synthesize these alternative approaches. It correctly identifies as the crucial problem the present disconnectedness of medical ethics from theoretical philosophy as well as the practice of medicine. In this paper, however, it is argued that the unitary theory should take more serious attention to the hermeneutic character of medicine as well as ethics. This implies that the unitary theory must in fact transform itself into aninterpretive clinical ethics theory. The theoretical characteristics and practical consequences of an interpretive theory of medical ethics are discussed in the present paper.     

Some uniqueness results for PARAFAC2

Whereas the unique axes properties of PARAFAC1 have been examined extensively, little is known about uniqueness properties for the PARAFAC2 model for covariance matrices. This paper is concerned with uniqueness in the rank two case of PARAFAC2. For this case, Harshman and Lundy have recently shown, subject to mild assumptions, that PARAFAC2 is unique when five (covariance) matrices are analyzed. In the present paper, this result is sharpened. PARAFAC2 is shown to be usually unique with four matrices. With three matrices it is not unique unless a certain additional assumption is introduced. If, for instance, the diagonal matrices of weights are constrained to be non-negative, three matrices are enough to have uniqueness in the rank two case of PARAFAC2. The authors are obliged to Richard Harshman for stimulating this research, and to the Associate Editor and reviewers for suggesting major improvements in the presentation.     

Philosophy of medicine in the Netherlands

This report explores the relationship between philosophy and medicine in the Netherlands. In Section 1 we outline the ups and downs of medico-philosophical research in our country: pre-war flourishing, post-war decline, and modern renaissance. In Section 2 we review recent Dutch literature in the philosophy of medicine. The topics dealt with include methodology of medical science, alternative medicine, the basic concepts of medicine, anthropological medicine, medicalization, medicine and culture, and health care ethics.     

Attention switching is not a fatigable process: methodological comments on Axelrod and Guzy (1972)

Guzy and Axelrod investigated auditory attention switching by means of the click-counting paradigm and concluded that attention switching is a fatigable process. In the present comment it is shown that this conclusion is based on a faulty analysis of the data: The scores subjected to the analysis of variance were transformed such that they were no longer linear combinations of the factorial effects. Reanalyzing the data in the correct way renders perfectly linear conting functions that deviate from theoretical fatigue functions. It is concluded that the attention-switching mechanism is not fatigable.