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We introduce a form of Self-Organized Criticality (SOC) inspired by the new generation of evolutionary game theory, which ranges from physiology to sociology. The single individuals are the nodes of a composite network, equivalent to two interacting subnetworks, one leading to strategy choices made by the individuals under the influence of the choices of their nearest neighbors and the other measuring the Prisoner's Dilemma Game payoffs of these choices. The interaction between the two networks is established by making the imitation strength K increase or decrease according to whether the last two payoffs increase or decrease upon increasing or decreasing K. Although each of these imitation strengths is selected selfishly, and independently of the others as well, the social system spontaneously evolves toward the state of cooperation. Criticality is signaled by temporal complexity, namely the occurrence of non-Poisson renewal events, the time intervals between two consecutive crucial events being given by an inverse power law index μ = 1.3 rather than by avalanches with an inverse power law distribution as in the original form of SOC. This new phenomenon is herein labeled self-organized temporal criticality (SOTC). We compare this bottom-up self-organization process to the adoption of a global choice rule based on assigning to all the units the same value K, with the time evolution of common K being determined by consciousness of the social benefit, a top-down process implying the action of a leader. In this case self-organization is impeded by large intensity fluctuations and the global social benefit turns out to be much weaker. We conclude that the SOTC model fits the requests of a manifesto recently proposed by a number of European social scientists.

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We propose a social model of spontaneous self-organization generating criticality and resilience, called Self-Organized Temporal Criticality (SOTC). The criticality-induced long-range correlation favors the societal benefit and can be interpreted as the social system becoming cognizant of the fact that altruism generates societal benefit. We show that when the spontaneous bottom-up emergence of altruism is replaced by a top-down process, mimicking the leadership of an elite, the crucial events favoring the system's resilience are turned into collapses, corresponding to the falls of the leading elites. We also show with numerical simulation that the top-down SOTC lacks the resilience of the bottom-up SOTC. We propose this theoretical model to contribute to the mathematical foundation of theoretical sociology illustrated in 1901 by Pareto to explain the rise and fall of elites.

Natural graphite is a soft material that conventional milling methods fail to grind into nanoparticles. We found that adding NaCl into graphite during milling allows obtaining graphene nanoflakes of about 50[Formula: see text][Formula: see text][Formula: see text]200[Formula: see text]nm2 as evidenced by Transmission Electron Microscope (TEM). NaCl particles are substantially brittle and harder than graphite, serving as milling agents by both helping to chop graphite into smaller pieces and preventing graphite particles from agglomeration. After milling, NaCl can be easily washed away by water. Probable mechanism for exfoliation of graphene during the modified ball milling may be explained by NaCl and graphene slipping or sliding against and over each other, exfoliating the graphene particles into thin layers.