Popularity and Entropy in Friendship and Enmity Networks in Classrooms.

Looking for regular statistical trends of relations in schools, we constructed 42 independent weighted directed networks of simultaneous friendship and animosity from surveys we made in the Mexico City Metropolitan area in classrooms with students of different ages and levels by asking them to nominate and order five friends and five foes. However, the data show that older students nominated fewer than the five required five foes. Although each classroom was independent of the others, we found several general trends involving students of different ages and grade levels. In all classrooms, friendship entropy was found to be higher than enmity entropy, indicating that fewer students received enmity links than received friendship nominations. Popular agents exhibited more reciprocal nominations among themselves than less popular agents, and opposite-sex friendships increased with age.

Move-by-move dynamics of the advantage in chess matches reveals population-level learning of the game.

The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a complex system. We systematically investigate the move-by-move dynamics of the white player's advantage from over seventy thousand high level chess matches spanning over 150 years. We find that the average advantage of the white player is positive and that it has been increasing over time. Currently, the average advantage of the white player is 0.17 pawns but it is exponentially approaching a value of 0.23 pawns with a characteristic time scale of 67 years. We also study the diffusion of the move dependence of the white player's advantage and find that it is non-Gaussian, has long-ranged anti-correlations and that after an initial period with no diffusion it becomes super-diffusive. We find that the duration of the non-diffusive period, corresponding to the opening stage of a match, is increasing in length and exponentially approaching a value of 15.6 moves with a characteristic time scale of 130 years. We interpret these two trends as a resulting from learning of the features of the game. Additionally, we find that the exponent [Formula: see text] characterizing the super-diffusive regime is increasing toward a value of 1.9, close to the ballistic regime. We suggest that this trend is due to the increased broadening of the range of abilities of chess players participating in major tournaments.

Axelrod models of social influence with cultural repulsion.

Since both attractive and repulsive effects among agents are important in social systems, we present simulations of two models based on Axelrod's homogenization mechanism that includes repulsion. These models are the repulsive model, where all individuals can repel, and the partially repulsive model where only a fraction of repelling agents are considered. In these two models, attractive dynamics is implemented for agents with the ability to repel each other only if the number of features shared by them is greater than a threshold parameter. Otherwise, repelling dynamics is used. In the repulsive model, the transition from a monocultural state to a fragmented one often occurs abruptly from one cultural-variability value to the next one and a second transition emerges. For the partially repulsive model, there are also two different transitions present: the initial one being as abrupt as the one found for the repulsive model, whereas the second one follows a less abrupt behavior and resembles that of the original Axelrod model. However, the second transition for this model occurrs from a partially fragmented state and not from a monocultural one.