Schizotypy,cognitive performance,and genetic risk for schizophrenia in a non-clinical population

Schizophrenia risk alleles are expected to mediate effects on cognitive task performance, and aspects of personality including schizotypy, in nonclinical populations. We investigated how 32 of the best-validated schizophrenia risk alleles, singly and as summed genetic risk, were related to measures of schizotypal personality and measures of two aspects of cognitive performance, verbal skills (vocabulary) and visual-spatial skills (mental rotation), in healthy individuals. Summed genetic risk score was not associated with levels of total schizotypy or its three main subscales. Similarly, genotypic variation at none of the individual risk loci was related to cognitive performance measures, after correction for multiple tests. Higher overall genetic risk score was, however, associated with lower performance on the mental rotation test in males, with a broad set of loci contributing to this effect. These results imply that there is a lack of linear, genetically-based continuity connecting schizotypal cognition with the expression of schizophrenia itself, and indicate that, for males, higher genetic risk of schizophrenia exerts negative effects on visual-spatial skills, as measured by mental rotation.     

Development of mental rotation in 3- to 5-year-old children

We assessed 3- to 5-year-olds’ mental rotation abilities using a new puzzle paradigm. It allows for assessment of mental rotation abilities in children younger than 5 years, using a task comparable to ones used with older children and adults. Children saw pairs of asymmetrical ghost figures, either as three-dimensional cut-outs or two-dimensional paper versions, in seven orientations. One of the ghosts fit into a hole if rotated right-side up – the other ghost was its mirror image and would not fit. Children were asked to turn the ghosts in their heads and choose the one that would fit into the hole. The number of children who chose the correct ghost above chance in the three-dimensional version of the task increased dramatically from 10% of 3-year-olds to 95% of 5-year-olds; average accuracy also increased significantly, from 54% to 83%. The two-dimensional paper version yielded similar results. These results indicate considerable development in mental rotation between 3 and 5 years.     

Tuning of human vestibulospinal reflexes by leg rotation

Changing the foot position modifies the mechanical action exerted by the ankle extensor and flexor muscles over the body. We verified, in two groups of healthy subjects standing with the heels touching or apart, whether a 90° external rotation of the right leg and foot also changes the pattern of vestibulospinal reflexes elicited by electrical stimulation of the labyrinth. With the head oriented forward, leg rotation did not modify the labyrinthine-driven displacements of the center of pressure (CoP). When the head was rotated in the horizontal plane, either to the right or to the left, the CoP displacement increased along the y axis in all subjects. Changes in the x component in most instances appropriate to preserve unmodified the direction of body sway elicited by the stimulus were observed. Right leg rotation increased the basal EMG activity of ankle extensors and flexors on the left side, while the right side activity was unaffected. The EMG responses to labyrinthine stimulation were modified only on the left side, in a way appropriate to correct the effects of the altered torque pattern exerted on the body by right leg muscles. It appears, therefore, that somatosensory signals related to leg rotation and/or copy of the corresponding voluntary motor commands modify the pattern of vestibulospinal reflexes and maintain the postural response appropriate to counteract a body sway in the direction inferred by labyrinthine signals.     

目标刺激的熟悉度和呈现角度对情绪启动的影响

本研究初步考察目标刺激的熟悉度和呈现角度对情绪启动的影响。研究采用女性面孔图片作为实验材料,随机选取30名大学生被试进行实验,采用重复测量方差分析对数据进行统计分析。结果发现:当目标刺激为熟悉图片时,出现了情绪启动效应;当目标刺激为不熟悉的图片时,未发现情绪启动效应;目标刺激的呈现角度对情绪启动效应没有影响。     

The rigid orthogonal Procrustes rotation problem

The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has proposed a method for suppressing reflections in cases where that is necessary. This paper proves that Gower’s solution does indeed give the best least squares fit over rigid rotation when the unconstrained solution is not rigid. Also, special cases that have multiple solutions are discussed. The author is obliged to Henk Kiers and Alwin Stegeman for helpful comments on a previous draft.     

A joint treatment of varimax rotation and the problem of diagonalizing symmetric matrices simultaneously in the least-squares sense

The present paper contains a lemma which implies that varimax rotation can be interpreted as a special case of diagonalizing symmetric matrices as discussed in multidimensional scaling. It is shown that the solution by De Leeuw and Pruzansky is essentially equivalent to the solution by Kaiser. Necessary and sufficient conditions for maxima and minima are derived from first and second order partial derivatives. A counter-example by Gebhardt is reformulated and examined in terms of these conditions. It is concluded that Kaiser's method or, equivalently, the method by De Leeuw and Pruzansky is the most attractive method currently available for the problem at hand.The author is obliged to Dirk Knol for computational assistance and to Dirk Knol, Klaas Nevels and Frits Zegers for critically reviewing an earlier draft of this paper.     

A general solution to Mosier's oblique procrustes problem

Browne provided a method for finding a solution to the normal equations derived by Mosier for rotating a factor matrix to a best least squares fit with a specified structure. Cramer showed that Browne's solution is not always valid, and proposed a modified algorithm. Both Browne and Cramer assumed the factor matrix to be of full rank. In this paper a general solution is derived, which takes care of rank deficient factor matrices as well. A new algorithm is offered.     

A solution to the weighted procrustes problem in which the transformation is in agreement with the loss function

This paper provides a generalization of the Procrustes problem in which the errors are weighted from the right, or the left, or both. The solution is achieved by having the orthogonality constraint on the transformation be in agreement with the norm of the least squares criterion. This general principle is discussed and illustrated by the mathematics of the weighted orthogonal Procrustes problem.     

More factors than subjects,tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling

Some methods that analyze three-way arrays of data (including INDSCAL and CANDECOMP/PARAFAC) provide solutions that are not subject to arbitrary rotation. This property is studied in this paper by means of the triple product [A, B, C] of three matrices. The question is how well the triple product determines the three factors. The answer: up to permutation of columns and multiplication of columns by scalars—under certain conditions. In this paper we greatly expand the conditions under which the result is known to hold. A surprising fact is that the nonrotatability characteristic can hold even when the number of factors extracted is greater thanevery dimension of the three-way array, namely, the number of subjects, the number of tests, and the number of treatments.This paper is being published in place of Dr. Kruskal's presidential address to the Psychometric Society, April, 1975. Further results like those in this paper, as well as a surprising connection with an area of mathematics called arithmetic complexity theory, will be found in a more recent paper [Kruskal, in press].