Proper aspiration level promotes generous behavior in the spatial prisoner’s dilemma game

Zero-determinant strategies, which can unilaterally define a linear relationship between two individuals’ long-term payoff, have drawn much attention to comprehend the emergence of cooperation among individuals with repeated interactions. A subset of zero-determinant strategies, extortion strategy, can let an extortioner’s surplus exceed her opponent’s by a fixed percentage. On the other hand, the dual generosity strategy can ensure that a complier’s payoff is never larger than her opponent’s. In the framework of the prisoner’s dilemma game driven by payoff aspiration, we investigate in this paper the evolution of generosity strategy, in competition with extortion and unconditional defection strategies. We show that extortioners act as a catalyst to induce more defectors to change to compliers. Such influence will enhance when extortioners become more greedy. At a low aspiration level where individuals are easy to be satisfied with their current payoffs, different strategies can coexist. With the increase of aspiration level, unsatisfied individuals are likely to turn to compliers and build long-term reciprocity with their neighbors. However, at a high aspiration level, individuals are difficult to be satisfied with their payoffs and may randomly change their behaviors. Thus proper aspiration level promotes the emergence of generous behavior in the spatial prisoner’s dilemma game.     

Canonical Form and Separability of PPT States in C2(×)C2(×)C2(×)CN Composite Quantum Systems

We give a canonical form of PPT states in C2(×)C2(×)C2(×)CN with rank = N. From this canonical form a sufficient separability condition for these states is presented.     

硅钙合金中钙含量的测定

研究了用一氧化二氮-乙炔火焰原子吸收光谱法测定硅钙合金中钙,并对样品消化处理条件和干扰因素进行了综合考虑.该法灵敏度高、步骤简单,操作容易掌握,干扰少等特点.其相对标准偏差均小于1.0%(n=6).加标回收率均为97.0%-100.0%范围内,本法完全达到了仪器分析质量与质量控制要求.     

Prisoner＇s Dilemma Game with Heterogeneous Influential Effect on Regular Small-World Networks

The effect of heterogeneous influence of different individuals on the maintenance of co-operative behaviour is studied in an evolutionary Prisoner＇s Dilemma game with players located on the sites of regular small-world networks. The players interacting with their neighbours can either co-operate or defect and update their states by choosing one of the neighbours and adopting its strategy with a probability depending on the pay off difference. The selection of the neighbour obeys a preferential rule： the more influential a neighbour, the larger the probability it is picked. It is found that this simple preferential selection rule can promote continuously the co-operation of the whole population with the strengthening of the disorder of the underlying network.     

Prisoner＇s Dilemma Game with Nonlinear Attractive Effect on Regular Small-World Networks

We investigate a spatial Prisoner＇s Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbours with a probability proportional to .A^α denoting the attractiveness of the neighbour, where .4 is the collected payoff and ^α （-〉0） is a free parameter characterizing the extent of nonlinear effect. Then each player adopts its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density pc of cooperators in the stationary state for various values of α and the rewiring probability q of the network. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect for the same network structures. We also point out that long-range connections either enhance or inhibit the cooperation, which depends on the value of α and the payoff parameter b.     

Synchronization of Coupled Oscillators on Newman-Watts Small-World Networks

We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scaling. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.     

Entanglement of Formation for Quantum States

We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generallzed concurrence, from the monotonicity and convexity the entanglement of formafion for a class of high-dimensional mixed states has been calculated analytically,     

Bound entangled states invariant under Ux

This paper obtains an entangled condition for isotropic-like states by using an atomic map. It constructs a class of bound entangled states from the entangled condition and shows that the partial transposition of the state from the constructed bound entangled class is an edge bound entangled state by using range criterion.     

Tighter Constraints of Multiqubit Entanglement

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems.We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-q entanglement, and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.     

Mutually Unbiased Measurement Based Entanglement Witnesses

We study entanglement witness and present a construction of entanglement witnesses in terms of the mutually unbiased measurements (MUMs). These witnesses include the entanglement witnesses constructed from mutually unbiased bases (MUBs) as a special case. Comparing with the dimension dependence of MUBs, the witnesses can be always constructed from a complete set of d + 1 MUMs for any dimension d. We show that our witness can detect entanglement better than previous separability criterion given also by MUMs. And the approach can be experimentally implemented.