Advances in Complex Systems

We study temporal networks of characters in literature focussing on Alice’s Adventures in Wonderland (1865) by Lewis Carroll and the anonymous La Chanson de Roland (around 1100). The former, one of the most influential pieces of nonsense literature ever written, describes the adventures of Alice in a fantasy world with logic plays interspersed along the narrative. The latter, a song of heroic deeds, depicts the Battle of Roncevaux in 778 A.D. during Charlemagne’s campaign on the Iberian Peninsula. We apply methods recently developed by Taylor et al. [Taylor, D., Myers, S. A., Clauset, A., Porter, M. A. and Mucha, P. J., Eigenvector-based centrality measures for temporal networks, CoRR (2015).] to find time-averaged eigenvector centralities, Freeman indices and vitalities of characters. We show that temporal networks are more appropriate than static ones for studying stories, as they capture features that the time-independent approaches fail to yield.

We study the minimum number of driver nodes control of which leads a Boolean network (BN) from an initial state to a target state in a specified number of time steps. We show that the problem is NP-hard and present an integer linear programming-based method that solves the problem exactly. We mathematically analyze the average size of the minimum set of driver nodes for random Boolean networks with bounded in-degree and with a small number of time steps. The results of computational experiments using randomly generated BNs show good agreements with theoretical analyses. A further examination in realistic BNs demonstrates the efficiency and generality of our theoretical analyses.

We propose an evolutionary game with dynamics rules derived from the consideration of field observations on human social behavior driven by self-confidence and social imitation. This dynamics turns out to be payoff nonmonotonic. The effects on the dynamics induced by this property are studied both numerically and analytically.