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    Does human imitate successful behaviors immediately?

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    The emergence and abundance of cooperation in animal and human societies is a challenging puzzle to evolutionary biology. Over the past decades, various mechanisms have been suggested which are capable of supporting cooperation. Imitation dynamics, however, are the most representative microscopic rules of human behaviors on studying these mechanisms. Their standard procedure is to choose the agent to imitate at random from the population. In the spatial version this means a random agent from the neighborhood. Hence, imitation rules do not include the possibility to explore the available strategies, and then they have the possibility to reach a homogeneous state rapidly when the population size is small. To prevent evolution stopping, theorists allow for random mutations in addition to the imitation dynamics. Consequently, if the microscopic rules involve both imitation and mutation, the frequency of agents switching to the more successful strategy must be higher than that of them transiting to the same target strategy via mutation dynamics. Here we show experimentally that the frequency of switching to successful strategy approximates to that of mutating to the same strategy. This suggests that imitation might play an insignificant role on the behaviors of human decision making. In addition, our experiments show that the probabilities of agents mutating to different target strategies are significantly distinct. The actual mutation theories cannot give us an appropriate explanation to the experimental results. Hence, we argue that the mutation dynamics might have evolved for other reasons

    Topological Weyl and Node-Line Semimetals in Ferromagnetic Vanadium-Phosphorous-Oxide β\beta-V2_2OPO4_4 Compound

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    We propose that the topological semimetal features can co-exist with ferromagnetic ground state in vanadium-phosphorous-oxide β\beta-V2_2OPO4_4 compound from first-principles calculations. In this magnetic system with inversion symmetry, the direction of magnetization is able to manipulate the symmetric protected band structures from a node-line type to a Weyl one in the presence of spin-orbital-coupling. The node-line semimetal phase is protected by the mirror symmetry with the reflection-invariant plane perpendicular to magnetic order. Within mirror symmetry breaking due to the magnetization along other directions, the gapless node-line loop will degenerate to only one pair of Weyl points protected by the rotational symmetry along the magnetic axis, which are largely separated in momentum space. Such Weyl semimetal phase provides a nice candidate with the minimum number of Weyl points in a condensed matter system. The results of surface band calculations confirm the non-trivial topology of this proposed compound. This findings provide a realistic candidate for the investigation of topological semimetals with time-reversal symmetry breaking, particularly towards the realization of quantum anomalous Hall effect in Weyl semimetals.Comment: 5 pages, 4 figure