Retrieving the correlation matrix from a truncated PCA solution: The inverse principal component problem

Whenr Principal Components are available fork variables, the correlation matrix is approximated in the least squares sense by the loading matrix times its transpose. The approximation is generally not perfect unlessr =k. In the present paper it is shown that, whenr is at or above the Ledermann bound,r principal components are enough to perfectly reconstruct the correlation matrix, albeit in a way more involved than taking the loading matrix times its transpose. In certain cases just below the Ledermann bound, recovery of the correlation matrix is still possible when the set of all eigenvalues of the correlation matrix is available as additional information.     

Development of spatial memory and spatial orientation in preschoolers and primary school children

The present study addresses the question of what kind of information children use when orientating in new environments, if given proximal and distal landmarks, and how spatial memory develops in the investigated age groups. Ten 5-year-old, ten 7-year-old and ten 10-year-old children were presented with the ‘Kiel Locomotor Maze’, containing features of the Radial Arm Maze and the Morris Water Maze, in order to assess spatial memory and orientation. Children had to learn to approach baited locations only. Task difficulty was equated with respect to the children's age. Training was given until the children reached criterion. During testing, the maze configuration and response requirements were systematically altered, including response rotation, cue rotation, cue deletion and response rotation with cue deletion in order to assess the spatial strategies used by the children. During training and testing, working-memory errors (WM), reference-memory errors (RM) and working-reference memory errors (WR) were recorded. As expected, no difference between age groups appeared during training, thus confirming comparable task difficulty across age groups. During testing, age groups differed significantly with regard to the orientation strategy used. The 5-year-olds were bound to a cue strategy, orientating towards local, proximal cues. The 10-year-olds mastered all tasks, thus displaying a place strategy, being able to use distal cues for orientation, and were even able to do so after being rotated 180°. The 7-year-olds proved to be at an age of transition: five of them were bound to a cue strategy, five children were able to adopt a place strategy. The differences in the orientation strategies used by children of different age groups was reflected by the sum of errors they made, also by RM. WM were found to be rare, especially in older children. We conclude that preschoolers use a cue strategy, that the development of place strategies occurs during primary school age and seems to be complete by the age of 10 years.     

A Gabbay-Rule Free Axiomatization of T×W Validity

The semantical structures called T×W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, _O, which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator . However, these structures are also suitable for interpreting an extended language, _SO, containing a further possibility operator ^s which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history simultaneity operator. In the present paper we provide an infinite set of axioms in _SO, which is shown to be strongly complete forT ×W-validity. Von Kutschera (1997) contains a finite axiomatization of T×W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions.     

A case of extreme simplicity of the core matrix in three-mode principal components analysis

In three-mode Principal Components Analysis, theP ×Q ×R core matrixG can be transformed to simple structure before it is interpreted. It is well-known that, whenP=QR,G can be transformed to the identity matrix, which implies that all elements become equal to values specified a priori. In the present paper it is shown that, whenP=QR − 1,G can be transformed to have nearly all elements equal to values spectified a priori. A cllsed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation ofG are discussed. Constructive comments from anonymous reviewers are gratefully acknowledged.     

Individual characteristics and career exploration in adolescence

The effects of gender, age and school grade on several career exploration dimensions measured by the Career Exploration Survey were investigated. Subjects were high school students facing an imminent career decision. Regression analyses indicated that sex and grade-level were the most significant and prevailing individual characteristics related to the adolescents' career exploration behaviours, reactions and beliefs. Implications for career exploration interventions are discussed.     

Perceptual and Response Bias in Unilateral Neglect: Two Modified Versions of the Milner Landmark Task

Perceptual and response bias in estimating the proportion of the two segments of prebisected lines were disambiguated in a group of 121 patients suffering from left neglect by means of two variants of the Milner Landmark task (Milner et al., 1993). The first variant, LANDMARK-V, required a verbal response; the second variant, LANDMARK-M, required manual pointing. The paper reports and discusses the results obtained on each task and their correlations, as well as the relationships between either kind of bias and the intrahemispheric location of the lesion. It is argued that besides their usefulness as a diagnostic tool the proposed variants of the Milner Landmark task provide results that are worth further investigation in their own right.     

Symmetry in haptic and in visual shape perception

Four experiments tested the hypothesis that bilateral symmetry is an incidental encoding property in vision, but can also be elicited as an incidental effect in touch, provided that sufficient spatial reference information is available initially for haptic inputs to be organized spatially. Experiment 1 showed that symmetry facilitated processing in vision, even though the task required judgments of stimulus closure rather than the detection of symmetry. The same task and stimuli failed to show symmetry effects in tactual scanning by one finger (Experiment 2). Experiment 3 found facilitating effects for vertically symmetric open stimuli, although not for closed patterns, in two-forefinger exploration when the fore-fingers had previously been aligned to the body midaxis to provide body-centered spatial reference. The one-finger exploration condition again failed to show symmetry effects. Experiment 4 replicated the facilitating effects of symmetry for open symmetric shapes in tactual exploration by the two (previously aligned) forefingers. Closed shapes again showed no effect. Spatial-reference information, finger movements, and stimulus factors in shape perception by touch are discussed.     

Effects of chronic ethanol consumption on gestation and lactation in rats

Chronic consumption of ethanol during pregnancy and lactation may lead to abnormalities in the fetus or infant. A group of female Wistar rats was submitted to ethanol treatment over a period of a month. A pair-fed control group received sucrose solution isocaloric to ethanol and the control group received water “ad libitum.” Afterward, the females were mated with males over a period of 20 days. At birth, each litter was maximized to eight pups and the remaining ones were decapitated to remove the fetal blood and brains. No significant difference was observed in fetal body and brain weight at birth. During lactation the ethanol and pair-fed groups gained less weight than the control group. After weaning, their weight became similar. Fetal blood glucose levels were decreased in the ethanol-treated group. One hundred percent of the pair-fed and control females delivered live fetuses at term and all survived; only 40% of the females in the ethanol group delivered, and one pup did not survive. Chronic ethanol treatment pointed to a possible reduction in the fertility. It seems likely that the change in body weight of ethanol-fed dams was caused by undernutrition.