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.     

Modifications of the Poggendorff effect as a function of random dot textures between the verticals

In the present research, we investigated the modification of the strength of the Poggendortf illusion as a function of different densities ofrandom dot textures failing the space between the verticals. The results ofExperiment 1 show that the illusory effect is a nonlinear function ofthe texture parameterr, the ratio of black pixels to white and black pixels, with a minimum forr=0.5, approximately, and a maximum forr=0 andr=1. The results may be interpreted by an analytical model of perceptual space dynamics, in which the effect dependson the amount of interaction between points of different light intensity. A computer simulation performed by applying the analytical model to different values ofr shows a good agreement between the predictions and the experimental data. To test the hypothesis underlying the model, a second experiment was carried out to measure the magnitude of the expansion ofthe space between the verticals as a function of the parameterr. The results are consistent with the hypothesis of the model. The overall data are discussed in terms of their implications on various theories proposed for the Poggeadorff illusion.     

Quantum MV algebras

We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.I should like to thank Prof. M.L. Dalla Chiara and Dr. P. Minari for many interesting comments and remarks. Daniele Mundici     

The outlook of the Tekhne Iatrike and the medical act to the third millenium

Medicine is arriving at a new millenium. One of its most urgent tasks is to reconcile social health demands with a renewed medical paradigm capable of including them. This challenge requires a reexamination of the definition of medicine. This work takes up the original greek definition of medicine (Tekhne Iatrike) and the Medical Act according to P. Lain Entrago, and analyzes Heidegger's interpretation of Tekhne. It points out the two main ways in which current medical practice is sustained: the Instrumental Medical Act (IMA), which organizes medical production, and the Productive Medical Act (PMA), which motivates it. An overwhelmed Medical Act, fighting but incapable of optimizing an insufficient medical production, is observed. This medical act is searching for foundations: an hegemonic IMA, associated disciplines and a new medical hierarchy.     

Point of view in personal memories

A structural aspect of personal memories was examined in four studies. In some memories, one has the perspective of an observer, seeing oneself “from the outside.” In other memories, one sees the scene from one's own perspective; the field of view in such memories corresponds to that of the original situation. The existence of “observer” and “field” memories was confirmed in Study 1, using a recall questionnaire. In Study 2, the similarity structure of a specified set of eight to-be-recalled situations was established: the significant dimensions were “emotionality” and “self-awareness.” Study 3 related these dimensions to the observer-field distinction; situations involving a high degree of emotion and selfawareness were most likely to be recalled with an observer perspective. Recall set was varied in Study 4: a focus on feelings (as opposed to objective circumstances) produced relatively more field memories. Studies 3 and 4 also showed that events reported as more recent tend to be recalled in the field mode. Thus a qualitative characteristic of personal memories—the perspective from which they are experienced—is apparently related to characteristics of the original event, to the individual's purpose in recalling that event, and to the reported recall interval.