Minimum entropy collaborative groupings: A tool for an automatic heterogeneous learning group formation.

For some decades now, theories on learning methodologies have advocated collaborative learning due to its good results in terms of effectiveness and learning types and its promotion of educational and social values. This means that teachers need to be able to apply different criteria when forming heterogeneous groups of students and to use automated techniques to assist them. In this study, we have created an approach based on complex network theory to design an algorithm called Minimum Entropy Collaborative Groupings (MECG) in order to form these heterogeneous groups more effectively. The algorithm was tested firstly under a synthetic framework and secondly in a real situation. In the first case, we generated 30 synthetic classrooms of different sizes and compared our approach with a genetic algorithm and a random grouping. In the latter case, the approach was tested on a group of 200 students on two subjects of a master's degree in teacher training. For each subject there were 4 large groups of 50 students each, in which collaborative groups of 4 students were created. Two of these large groups were used as random groups, another group used the CHAEA test and the fourth group used the LML test. The results showed that the groups created with MECG were more effective, had less uncertainty and were more interrelated and mature. It was observed that the randomized groups did not obtain significantly better LML results and that this cannot be related to any emotional or motivational effect because the students performed the test as a placebo measure. In terms of learning styles, the results were significantly better with LML than with CHAEA, whereas no significant difference was observed in the randomized groups.

Consistencies and inconsistencies between model selection and link prediction in networks.

A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in general, the predictive performance is higher when we average over collections of models that are individually less plausible than when we consider only the single most plausible model.

Bone Fusion in Normal and Pathological Development is Constrained by the Network Architecture of the Human Skull.

Craniosynostosis, the premature fusion of cranial bones, affects the correct development of the skull producing morphological malformations in newborns. To assess the susceptibility of each craniofacial articulation to close prematurely, we used a network model of the skull to quantify the link reliability (an index based on stochastic block models and Bayesian inference) of each articulation. We show that, of the 93 human skull articulations at birth, the few articulations that are associated with non-syndromic craniosynostosis conditions have statistically significant lower reliability scores than the others. In a similar way, articulations that close during the normal postnatal development of the skull have also lower reliability scores than those articulations that persist through adult life. These results indicate a relationship between the architecture of the skull and the specific articulations that close during normal development as well as in pathological conditions. Our findings suggest that the topological arrangement of skull bones might act as a structural constraint, predisposing some articulations to closure, both in normal and pathological development, also affecting the long-term evolution of the skull.