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).     

Family therapy in Mexico—1978

The status of family therapy in Mexico is described. The Instituto de la Familia was formed in 1974 as a facility to train family therapists by Macias, Estrada, Dersbez, Chagoya and Barragan. In 1975 Barragan formed the Instituto Mexicano de la Familia. Various centers utilizing family therapy are noted.     

Spoonish spanerisms: A lexical bias effect in Spanish

Lexical bias is the tendency for phonological errors to form existing words at a rate above chance. This effect has been observed in experiments and corpus analyses in Germanic languages, but S. del Viso, J. M. Igoa, and J. E. García-Albea (1991) found no effect in a Spanish corpus study. Because lexical bias plays an important role in the debate on interactivity in language production, the authors reconsidered its absence in Spanish. A corpus analysis, which considered relatively many errors and which used a method of estimating chance rate that is relatively independent of total error number, and a speech-error elicitation experiment provided converging evidence for lexical bias in Spanish. The authors conclude that the processing mechanisms underlying this effect hold cross-linguistically.     

Creative thinking in adolescents with attention deficit hyperactivity disorder (ADHD).

A widened attentional focus, that is typically associated with ADHD, has been postulated to be accompanied by enhanced creative ability. However, creativity has been only limitedly examined in ADHD. Performance across several creativity measures were investigated in three groups: adolescents with ADHD, those with conduct disorder, and a healthy control sample. The ADHD group exhibited selective cognitive advantages and disadvantages by demonstrating an enhanced ability in overcoming the constraining influence of examples, but a reduced capacity to generate a functional invention during an imagery task. These findings are interpreted with reference to inhibitory control mechanisms and the contextual modulation of creative cognition.     

Anxiolytic-like activity of SB-205384 in the elevated plus-maze test in mice

Recent studies point to a major role for alpha2-containing GABA-A receptors in modulating anxiety. However, the possible implication of GABA-A receptors containing the alpha3 subunit on anxiety is less known. The aim of this study was to examine the effects of SB-205384 (0.5-4 mg/kg, i.p.), an alpha3 subunit positive modulator of GABA-A receptor, on anxiety tested in the elevated plus-maze in male mice, using classical and ethological parameters. Mice treated with SB-205384 showed an increase in the frequency of entries and the time spent in open arms, as well as a reduction in the time spent in closed arms, as compared with the control group. A notable increase of "head-dipping" unprotected and a reduction of "stretched-attend posture" protected was also evident. These findings indicate that SB-205384 exhibits an anxiolytic-like profile in the elevated plus-maze test, suggesting that GABA-A receptors which contain the alpha3 subunit might be involved in regulation of anxiety.     

Determinants of instrumental extinction in terrestrial toads (Bufo arenarum)

Previous research in a water-reinforced instrumental training situation with toads (Bufo arenarum) has shown that performance in both acquisition and extinction is poorer after partial, rather than continuous reinforcement training. In Experiment 1, the performance of a group receiving 24 trials on a 50% partial reinforcement schedule was poorer in acquisition and extinction than that of continuously reinforced groups matched for trials or reinforcements. However, partially reinforced toads extinguished at the same rapid rate as a continuously reinforced group that received training only on the days in which the partial toads received water reinforcement. In Experiment 2, extinction was faster after 10 reinforced acquisition trials than after 30 trials. This evidence suggests that the deleterious effects of partial reinforcement in toads can be explained by a combination of two factors, namely, the distribution of reinforced trials across days and the total number of reinforcements.     

Saccadic latency as a function of target duration in a spatial localization task

This study examined a potential confound in the inverse relationship between target duration and saccadic latency reported by Adam, Ketelaars, Kingma, and Hoek in 1993. Eight participants located a briefly flashed target by moving the eyes and the cursor toward its position in a (backward) mask condition and in a no-mask condition. Analysis showed similar saccadic latencies in both conditions, thereby refuting the potentially confounding role of the backward masking procedure. It is tenatively suggested that the longer saccadic latencies noted for shorter target durations may be associated with delayed accumulation of evidence for the detection of the target.