Balancing selfishness and norm conformity can explain human behavior in large-scale prisoner's dilemma games and can poise human groups near criticality.

Cooperation is central to the success of human societies as it is crucial for overcoming some of the most pressing social challenges of our time; still, how human cooperation is achieved and may persist is a main puzzle in the social and biological sciences. Recently, scholars have recognized the importance of social norms as solutions to major local and large-scale collective action problems, from the management of water resources to the reduction of smoking in public places to the change in fertility practices. Yet a well-founded model of the effect of social norms on human cooperation is still lacking. Using statistical-physics techniques and integrating findings from cognitive and behavioral sciences, we present an analytically tractable model in which individuals base their decisions to cooperate both on the economic rewards they obtain and on the degree to which their action complies with social norms. Results from this parsimonious model are in agreement with observations in recent large-scale experiments with humans. We also find the phase diagram of the model and show that the experimental human group is poised near a critical point, a regime where recent work suggests living systems respond to changing external conditions in an efficient and coordinated manner.

High-pressure polymeric phases of carbon dioxide.

Understanding the structural transformations of solid CO(2) from a molecular solid characterized by weak intermolecular bonding to a 3-dimensional network solid at high pressure has challenged researchers for the past decade. We employ the recently developed metadynamics method combined with ab initio calculations to provide fundamental insight into recent experimental reports on carbon dioxide in the 60-80 GPa pressure region. Pressure-induced polymeric phases and their transformation mechanisms are found. Metadynamics simulations starting from the CO(2)-II (P4(2)/mnm) at 60 GPa and 600 K proceed via an intermediate, partially polymerized phase, and finally yield a fully tetrahedral, layered structure (P-4m2). Based on the agreement between calculated and experimental Raman and X-ray patterns, the recently identified phase VI [Iota V, et al. (2007) Sixfold coordinated carbon dioxide VI. Nature Mat 6:34-38], assumed to be disordered stishovite-like, is instead interpreted as the result of an incomplete transformation of the molecular phase into a final layered structure. In addition, an alpha-cristobalite-like structure (P4(1)2(1)2), is predicted to be formed from CO(2)-III (Cmca) via an intermediate Pbca structure at 80 GPa and low temperatures (<300 K). Defects in the crystals are frequently observed in the calculations at 300 K whereas at 500 to 700 K, CO(2)-III transforms to an amorphous form, consistent with experiment [Santoro M, et al. (2006) Amorphous silica-like carbon dioxide. Nature 441:857-860], but the simulation yields additional structural details for this disordered solid.