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How evolution favors cooperation is a fundamental issue in social and economic systems. In the business world, actively selecting a suitable project is usually helpful for a businessman to be in an advantageous position. By incorporating project selection mechanism into the threshold public goods game, we have investigated the coupling effect of mutation and imitation in updating one's preferred project scale on the evolution of cooperation. Compared with the situation where there is no project selection mechanism, the existence of project selection may suppress or promote cooperation depending upon different updating rules. There exists a critical ratio of the imitators in the population, below which cooperation is suppressed while above which cooperation is promoted. With the coevolving of individual strategies and preferred project scales, a higher level of cooperation corresponds to a larger average value of the preferred project scales. A theoretical analysis indicates that, as most of the individuals are mutants, the coevolving process is governed by the mutation process, which leads to a smaller average value of the preferred project scales and a lower level of cooperation. As most of the individuals are imitators, the coevolving process is governed by the coupling of the mutation and imitation processes, which leads to a larger average value of the preferred project scales and a higher level of cooperation. As all the individuals are imitators, the coevolving process is governed by the imitation process, which leads to an intermediate average value of the preferred project scales and an intermediate level of cooperation.

Facing a heavy task, any single person can only make a limited contribution and team cooperation is needed. As one enjoys the benefit of the public goods, the potential benefits of the project are not always maximized and may be partly wasted. By incorporating individual ability and project benefit into the original public goods game, we study the coupling effect of the four parameters, the upper limit of individual contribution, the upper limit of individual benefit, the needed project cost and the upper limit of project benefit on the evolution of cooperation. Coevolving with the individual-level group size preferences, an increase in the upper limit of individual benefit promotes cooperation while an increase in the upper limit of individual contribution inhibits cooperation. The coupling of the upper limit of individual contribution and the needed project cost determines the critical point of the upper limit of project benefit, where the equilibrium frequency of cooperators reaches its highest level. Above the critical point, an increase in the upper limit of project benefit inhibits cooperation. The evolution of cooperation is closely related to the preferred group-size distribution. A functional relation between the frequency of cooperators and the dominant group size is found.

By incorporating a multilayer network and time-decaying memory into the original voter model, the coupled effects of spatial and temporal cumulation of peer pressure on consensus are investigated. Heterogeneity in peer pressure and time-decaying mechanism are both found to be detrimental to consensus. The transition points, below which a consensus can always be reached and above which two opposed opinions are more likely to coexist, are found. A mean-field analysis indicates that the phase transitions in the present model are governed by the cumulative influence of peer pressure and the updating threshold. A functional relation between the consensus threshold and the decaying rate of the influence of peer pressure is found. As to the time to reach a consensus, it is governed by the coupling of the memory length and the decaying rate. An intermediate decaying rate may lead to much lower time to reach a consensus.

By incorporating market impact and asymmetric sensitivity into the evolutionary minority game, we study the coevolutionary dynamics of stock prices and investment strategies in financial markets. Both the stock price movement and the investors' global behavior are found to be closely related to the phase region they fall into. Within the region where the market impact is small, investors' asymmetric response to gains and losses leads to the occurrence of herd behavior, when all the investors are prone to behave similarly in an extreme way and large price fluctuations occur. A linear relation between the standard deviation of stock price changes and the mean value of strategies is found. With full market impact, the investors tend to self-segregate into opposing groups and the introduction of asymmetric sensitivity leads to the disappearance of dominant strategies. Compared with the situations in the stock market with little market impact, the stock price fluctuations are suppressed and an efficient market occurs. Theoretical analyses indicate that the mechanism of phase transition from clustering to self-segregation in the present model is similar to that in the majority-minority game and the occurrence and disappearance of efficient markets are related to the competition between the trend-following and the trend-aversion forces. The clustering of the strategies in the present model results from the majority-wins effect and the wealth-driven mechanism makes the market become predictable., Comment: 21pages,7figures

In a static environment, optional participation and a local agglomeration of cooperators are found to be beneficial for the occurrence and maintenance of cooperation. In the optional public goods game, the rock-scissors-paper cycles of different strategies yield oscillatory cooperation but not stable cooperation. In this paper, by incorporating population density and individual mobility into the spatial optional public goods game, we study the coevolutionary dynamics of strategy updating and benefit-seeking migration. With low population density and slow movement, an optimal level of cooperation is easy to be reached. An increase in population density and speed-up of free-floating of competitive agents will suppress cooperation. A log-log relation between the levels of cooperation and the free-floating probability is found. Theoretical analysis indicates that the decrease of cooperator frequency in the present model should result from the increased interactions between different agents, which may originate from the increased cluster size or the speed-up of random-movement.

We derive a formula of the nonadiabatic noncyclic Pancharatnam phase for a quantum spin-1/2 particle subject to an arbitrary magnetic field. The formula is applied to three specific kinds of magneic fields. (i) For an orientated magnetic field, the Pancharatnam phase is derived exactly. (ii) For a rotating magnetic field, the evolution equation is solved analytically. The Aharonov-Anandan phase is obtained exactly and the Pancharatnam phase is computed numerically. (iii) We propose a kind of topological transition in one-dimensional mesoscopic ring subject to an in-plane magnetic field, and then address the nonadiabatic noncyclic effect on this phenomenon., Comment: 6 pages and 3 figures