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.     

Concurrent avoidance of shocks by pigeons pecking a key

Three pigeons were studied on concurrent, unsignaled, avoidance schedules in a two-key procedure. Shock-shock intervals were two seconds in both schedules. The response-shock interval on one key was always 22 seconds, while the response-shock interval associated with the other key was varied from 7 to 52 seconds in different experimental conditions. Response rates on the key associated with the varied schedule tended to decrease when the response-shock interval length was increased. Responding on the key associated with the constant schedule was not systematically affected.     

Signalled free-operant avoidance of shock by pigeons pecking a key

Two pigeons were trained to peck a key under a free-operant avoidance schedule. Then, changes in key color signalled the beginning (safe period) and the end (warning period) of the response-shock interval, with a response required to change the key color. Finally, a change in key color signalled the warning period and either a response or a shock reinstated the safe stimulus. During signalled avoidance, response rate was higher during the warning stimulus than during the safe stimulus. More responding tended to occur in the warning stimulus when it was terminated by either a response or a shock than by only a response. In either procedure, response latency during the warning stimulus was a function of the duration of the warning stimulus. In general, response and shock rate were higher during unsignalled than during signalled avoidance. When the warning stimulus was brief, the results were similar to those of unsignalled avoidance. These results confirm previous findings with pigeons, are in general agreement with data provided by other species in studies of signalled avoidance, and thereby indicate the transituationality of the key-pecking operant.     

Memory and Counterfactual Simulations for Past Wrongdoings Foster Moral Learning and Improvement

In four studies, we investigated the role of remembering, reflecting on, and mutating personal past moral transgressions to learn from those moral mistakes and to form intentions for moral improvement. Participants reported having ruminated on their past wrongdoings, particularly their more severe transgressions, and they reported having frequently thought about morally better ways in which they could have acted instead (i.e., morally upward counterfactuals; Studies 1–3). The more that participants reported having mentally simulated morally better ways in which they could have acted, the stronger their intentions were to improve in the future (Studies 2 and 3). Implementing an experimental manipulation, we then found that making accessible a morally upward counterfactual after committing a moral transgression strengthened reported intentions for moral improvement—relative to resimulating the remembered event and considering morally worse ways in which they could have acted instead (Study 4). We discuss the implications of these results for competing theoretical views on the relationship between memory and morality and for functional theories of counterfactual thinking.