Behavioural family therapy and the influence of a systems framework

A family approach using the techniques of behaviour modification, to a family presenting with problems of encopressis in a five-year-old boy, is described. The usefulness of taking a broader analysis of the context of the behaviours targeted for modification under the impact of systems theories is emphasized. A one-year follow-up after treatment demonstrated both symptomatic and family changes.     

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.     

“Impossible figures” and interpretations of polyhedral figures

The concept “impossible figure” is analyzed by formalizing the interpretations of a polyhedral figure by an observer, and defining several types of inconsistency in such interpretations. Tests for these inconsistencies are developed using simple graph theory, and a sufficient condition is established for the feasibility of an interpretation. Finally, techniques are derived for the automatic construction of usual or unusual multibar figures.     

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.     

Human figure drawings of gender-problem children: A comparison to sibling,psychiatric, and normal controls

The Draw-a-Person test was used to evaluate a number of questions regarding children referred for potential problems in their gender-identity development (N = 36). Sibling (N = 31), psychiatric (N = 23), and normal (N = 30) children served as comparison groups. The major results included the following: (1) The gender-referred children were more likely to draw an opposite-sex person when requested to "draw a person" than were the other three groups; (2) the gender-referred children who drew an opposite-sex person were more likely to play with opposite-sex toys and dress-up apparel on a free-play task than were the gender-referred children who drew a same-sex person; (3) the gender-referred children drew taller opposite-sex persons than same-sex persons; (4) using Koppitz's (1968) criteria, the normal children had a smaller proportion of emotional disturbance indicators in their same-sex drawings than did the other three groups. These findings were discussed with regard to psychometric and interpretive issues in the assessment of children with atypical gender-role behavior.     

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.     

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 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.