Validity and quantification in intuitionism

We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logical notions considered we suggest that the most natural reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.This paper was partly written while the first author, H. C. M. de Swart, was a Visiting Fellow at Princeton University for the academic year 1976–1977. This opportunity was given to him by the Niels Stensen Stichting in Amsterdam, the department of philosophy of the Catholic University in Nijmegen and by Princeton University. He is happy to express his appreciation for that opportunity.     

Learned helplessness in groups

Group learned helplessness is demonstrated in Experiment I. Groups of 2 tried to turn off noise by their joint action. In the solvable group (S), noise offset was contingent on their sequence of button pushing. In the yoked, unsolvable group (U), noise offset was independent of all sequences of button pushes they produced. In a practice group (O). subjects practiced coordinated sequences of button pushes with their partners, but heard no noise. Later, all 3 groups were tested in pairs in a shuttlebox which required coordinated joint responding to turn off noise. The unsolvable group escaped more poorly than the other 2 groups, paralleling helplessness effects with individuals. Experiment 2 and 3 found no transfer from individual helplessness training to group testing and no transfer from group helplessness training to individual testing. We suggest that the same mechanism, the expectation of response ineffectiveness, may mediate both individual and group learned helplessness.     

Assertive training for agoraphobics

Twenty-one unassertive agoraphobic patients were assigned to one of three treatments: (1) prolonged exposure in vivo, (2) assertive training and (3) a combination of assertive training and prolonged exposure in vivo. Each treatment was conducted in groups which were led by two therapists. Assessments involved both phobic targets and assertiveness, and were made before and after treatment, and at 1-month follow-up. Exposure in vivo was found to be superior to assertive training on phobic targets. Assertive training produced greater gains in assertiveness than exposure in vivo. The combination of treatments produced results comparable to exposure in viro. Results indicated that the type of change produced by the treatments is a rather specific one and is related to the specific target of treatment.     

Group psychotherapy in chronic psychiatric outpatients: a Toronto model.

Seventy to 80 chronic psychiatric patients are treated in an aftercare clinic with a goal of tertiary preventive care. The major component of the treatment approach is reality-oriented group psychotherapy with an emphasis on interpersonal relationships. Attention to three factors in group psychotherapy with this population of patients has facilitated our work and outcome. These are the concept of the core group, diagnostic heterogeneity, and staff structure.     

Fitting longitudinal reduced-rank regression models by alternating least squares

An alternating least squares method for iteratively fitting the longitudinal reduced-rank regression model is proposed. The method uses ordinary least squares and majorization substeps to estimate the unknown parameters in the system and measurement equations of the model. In an example with cross-sectional data, it is shown how the results conform closely to results from eigenanalysis. Optimal scaling of nominal and ordinal variables is added in a third substep, and illustrated with two examples involving cross-sectional and longitudinal data.Financial support by the Institute for Traffic Safety Research (SWOV) in Leidschendam, The Netherlands is gratefully acknowledged.     

The enhancement of retention induced by vasopressin in mice may be mediated by an activation of central nicotinic cholinergic mechanisms.

Immediate post-training subcutaneous administration of lysine vasopressin (LVP, 0.003-1.00 microgram/kg) enhanced retention, whereas the vasopressin antagonist AAVP (0.01-0.30 microgram/kg) impaired it, in male Swiss mice tested 48 h after training in an inhibitory avoidance task. Both effects were dose-dependent. Neither LVP nor AAVP affected response latencies in mice not given the footshock on the training trial. The simultaneous administration of AAVP at a dose (0.01 microgram/kg) which had no effect on retention shifted the dose-response curve of LVP to the right. Nicotine (1.0-30.0 micrograms/kg, sc), a central nicotinic cholinergic agonist, also facilitated retention in a dose-related manner without affecting the retention performance of unshocked mice. The effect of nicotine was prevented by the central acting nicotinic cholinergic receptor antagonist mecamylamine (5 mg/kg, sc.). In contrast, neither hexamethonium (5 mg/kg, sc), a peripheral acting nicotinic receptor blocker, nor atropine (0.5 mg/kg, sc) or methylatropine (0.5 mg/kg, sc), two anticholinergic drugs which are known to act on muscarinic cholinergic receptors, prevented the effect of post-training nicotine. The effects of LVP and nicotine were time-dependent, suggesting that both treatments enhanced retention by influencing post-training processes involved in memory storage. Low doses of nicotine (1.50 microgram/kg, sc) or the central anticholinesterase physostigmine (35 micrograms/kg, sc) and LVP (0.003 microgram/kg, sc), which had no effect on retention when administered alone, produced a synergistic interaction when given together following training. The influence of LVP (0.03 microgram/kg, sc) on retention was prevented not only by AAVP (0.01 microgram/kg, sc) but also by mecamylamine (5 mg/kg, sc), whereas the effects of nicotine (10.0 micrograms/kg, sc) were prevented only by mecamylamine. These results suggest that the enhancement of retention induced by vasopressin is probably due to an activation of central nicotinic cholinergic mechanisms which are critical for memory formation.     

A note on partitioned determinants

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.     

Generalized eigenvalue problems with positive semi-definite matrices

In a recent paper in this journal McDonald, Torii, and Nishisato show that generalized eigenvalue problems in which both matrices are singular can sometimes be solved by reducing them to similar problems of smaller order. In this paper a more extensive analysis of such problems is used to sharpen and clarify the results of McDonald, Torii, and Nishisato. Possible extensions are also indicated. The relevant mathematical literature is reviewed briefly.