The approximation of two-mode proximity matrices by sums of order-constrained matrices

A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered define Q-forms (or anti-Q-forms) for a two-mode matrix, where after suitable and separate row and column reorderings, the entries within each row and within each column are nondecreasing (or nonincreasing) to a maximum (or minimum) and thereafter nonincreasing (or nondecreasing). Several other types of order constraints are also mentioned to show how alternative structures can be considered using the same computational strategy.     

Enumeration and simulation methods for 0–1 matrices with given marginals

Data in the form of zero-one matrices where conditioning on the marginals is relevant arise in diverse fields such as social networks and ecology; directed graphs constitute an important special case. An algorithm is given for the complete enumeration of the family of all zero-one matrices with given marginals and with a prespecified set of cells with structural zero entries. Complete enumeration is computationally feasible only for relatively small matrices. Therefore, a more useable Monte Carlo simulation method for the uniform distribution over this family is given, based on unequal probability sampling and ratio estimation. This method is applied to testing reciprocity of choices in social networks.The author wishes to thank Cajo ter Braak and John Birks for pointing out the relevance of this subject for ecology; and also Albert Verbeek and Ivo Molenaar, a referee, the Editor, and the Associate Editor for their comments. An earlier version of this paper was presented at the Stockholm Conference on Random Graphs and Applications (April 25–27, 1989), organized with financial support from the Swedish Council of Research in the Humanities and the Social Sciences.     

On the validity of Raven’s matrices test: Does spatial ability contribute to performance?

The paper reports on an investigation of the convergent and discriminant validity of Raven’s matrices in considering reasoning and spatial abilities. Raven’s advanced progressive matrices (APM) and four scales representing reasoning, visualization, mental rotation and closure were applied to a sample of N = 280 university students. The data were investigated by means of structural equation modeling. The results demonstrated convergent validity of APM with respect to reasoning. In contrast, in investigating discriminant validity substantial correlations of moderate size between APM and the scales representing spatial abilities were observed. However, the investigation of the structure of the prediction of APM revealed that the scales representing spatial abilities did not improve the prediction based on the reasoning scale alone at the latent level. Consequently, it is suggested that Raven’s matrices show good convergent validity and slightly impaired discriminant validity.     

A shortened version of Raven’s standard progressive matrices for children and adolescents

Numerous developmental studies assess general cognitive ability, not as the primary variable of interest, but rather as a background variable. Raven’s Progressive Matrices is an easy to administer non-verbal test that is widely used to measure general cognitive ability. However, the relatively long administration time (up to 45 min) is still a drawback for developmental studies as it often leaves little time to assess the primary variable of interest. Therefore, we used a machine learning approach – regularized regression in combination with cross-validation – to develop a short 15-item version. We did so for two age groups, namely 9 to 12 years and 13 to 16 years. The short versions predicted the scores on the standard full 60-item versions to a very high degree r = 0.89 (9–12 years) and r = 0.93 (13–16 years). We, therefore, recommend using the short version to measure general cognitive ability as a background variable in developmental studies.     

The model of a simple self-reproducing system

The model of a simple self-reproducing system has been investigated. The current model has been developed in the framework of syser systems. The term syser is the abbreviation of the words “SYstem of SElf-Reproduction”. The syser model can be considered as a reasonable model of the prebiological macromolecular self-reproducing systems. The syser includes a polynucleotide matrix, a replication enzyme, a translation enzyme, and other enzymes and protein. Earlier, we studied the model of sysers with a large number of macromolecules. However, a large number of macromolecules is a certain disadvantage of models of prebiological systems. In order to overcome this disadvantage, a new syser model with a small number of macromolecules has been constructed and investigated in the present work. The macromolecules of the syser are located inside the protocell. Additionally, we consider special macromolecules that provide sysers with energy. There is a mechanism for duplication of protocells. We consider the evolution of the population of sysers. The dynamics of macromolecules in protocells and evolution of sysers populations have been analyzed by means of computer simulation. It was shown that during the evolution of the sysers population, the comparative number and rate of synthesis of macromolecules, which provide protocells with energy, could be increased. The decrease of the synthesis rate of polynucleotide matrices is also possible.