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.     

A generalization of Kristof's theorem on the trace of certain matrix products

Kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form \(X_1 \hat \Gamma _1 X_2 \hat \Gamma _2 \cdots X_n \hat \Gamma _n\) where the matrices \(\hat \Gamma _i\) are diagonal and fixed and theX _i vary unrestrictedly and independently over the set of orthonormal matrices. The theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints. The present paper contains a generalization of Kristof's theorem to the case where theX _i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank. The generalized theorem contains the Schwarz inequality as a special case. Various examples from the psychometric literature, illustrating the practical use of the generalized theorem, are discussed.     

Some clarifications of the CANDECOMP algorithm applied to INDSCAL

Carroll and Chang have claimed that CANDECOMP applied to symmetric matrices yields equivalent coordinate matrices, as needed for INDSCAL. Although this claim has appeared to be valid for all practical purposes, it has gone without a rigorous mathematical footing. The purpose of the present paper is to clarify CANDECOMP in this respect. It is shown that equivalent coordinate matrices are not granted at global minima when the symmetric matrices are not Gramian, or when these matrices are Gramian but the solution not globally optimal.Part of this research has been supported by The Netherlands Organization for Scientific Research (NWO), PSYCHON-grant (560-267-011).     

The Dental Subscale of the Children's Fear Survey Schedule: Predictive Value and Clinical Usefulness

This study reports on the predictive value and clinical usefulness of the Dutch parental version of the Dental Subscale of the Children's Fear Survey Schedule (CFSS-DS). Parents of 718 children (4–12 years) completed this CFSS-DS version before or during the child's visit. The dentist rated the child's dental fear during treatment on a 5-point Likert-type Scale from 1 (not afraid at all) to 5 (very afraid). Reliability analysis was performed, and correlation coefficients between the two measures were calculated. The reliability of the scale proved to be high (Cronbach's = .93) and significant correlation coefficients were found (r = .58 and r = .68, p < .01). The negative predictive value of the CFSS-DS was high (.96), whereas its positive predictive value was relatively low (0.41). It was concluded that the CFSS-DS might be of clinical value as a screening device of dental fear, whereas its predictive value of fearful behavior should not be overestimated.     

In competitive interaction displays of red increase actors' competitive approach and perceivers' withdrawal

Colors carry meaningful psychological signals. We hypothesized that the color red serves as a powerful cue in competition, affecting both actors and perceivers. Using simplified poker games we investigated the psychological meaning of color in competitive interaction, by examining how the color of chips (red vs. blue or white) used by participants or their competitors affected behavior. Although chip color was objectively unrelated to the chips' value or competitors' strength, perceiving competitors using red chips renders competitors more intimidating, which leads perceivers to withdraw. Furthermore, actors who used red chips felt more dominant, which led them to enhanced competitive approach. Displaying red thus makes actors feel stronger and increases competitive approach; perceivers of displays of red in competitors feel intimidated and withdraw from competing.     

Does Family Life Help to be a Better Leader? A Closer Look at Crossover Processes From Leaders to Followers

Although research on family‐to‐work processes is accumulating, not many studies have looked at how the leader's family issues spillover to work and what the consequences are for their followers. We investigate whether leaders’ family‐to‐work conflict (FWC) and enrichment (FWE) influence first their own well‐being at work (i.e., job burnout and work engagement) and consequently the well‐being of their followers due to crossover processes. We test whether crossover is due to the transfer of emotions from the leader to followers (affective crossover) or due to diminished or enhanced support from the leader (behavioral crossover). Using a sample of 199 leaders and 456 followers, we found that leader FWC (Time 1) was positively related to leader feelings of burnout 4 weeks later (Time 2), consequently enhancing follower feelings of burnout 5 weeks after Time 1 (Time 3). Similarly, leader FWE had a positive relationship with follower engagement, through leader enhanced engagement. Our findings fully supported the affective crossover mechanism. In addition, leader burnout was negatively related to leader supportive behavior, indirectly increasing burnout among followers. Our results underscore that leaders’ family life matters at work, influencing not only their own well‐being but also how they motivate and support their followers.