A decision theoretical approach for diffusion promotion

In order to maximize cost efficiency from scarce marketing resources, marketers are facing the problem of which group of consumers to target for promotions. We propose to use a decision theoretical approach to model this strategic situation. According to one promotion model that we develop, marketers balance between probabilities of successful persuasion and the expected profits on a diffusion scale, before making their decisions. In the other promotion model, the cost for identifying influence information is considered, and marketers are allowed to ignore individual heterogeneity. We apply the proposed approach to two threshold influence models, evaluate the utility of each promotion action, and provide discussions about the best strategy. Our results show that efforts for targeting influentials or easily influenced people might be redundant under some conditions.     

Modelling Moran Process with Network Dynamics for the Evolution of Cooperation

We introduce a simple model based on the Moran process with network dynamics. Using pair approximation, the cooperation frequencies at equilibrium states are deduced for general interactions. Three usual social dilemmas are discussed in the framework of our model. It is found that they all have a phase transition at the same value of cost-to-benefit ratio. For the prisoner＇s dilemma game, notably it is exactly the simple rule reported in the literature [Nature 441 （2006） 502]. In our model, the simple rule results from the parent-offspring link. Thus the basic mechanism for cooperation enhancement in network reciprocity is in line with the Hamilton rule of kin selection. Our simulations verify the analysis obtained from pair approximation.     

City size distributions for India and China

This paper studies the size distributions of urban agglomerations for India and China. We have estimated the scaling exponent for Zipf’s law with the Indian census data for the years of 1981-2001 and the Chinese census data for 1990 and 2000. Along with the biased linear fit estimate, the maximum likelihood estimate for the Pareto and Tsallis q-exponential distribution has been computed. For India, the scaling exponent is in the range of [1.88, 2.06] and for China, it is in the interval [1.82, 2.29]. The goodness-of-fit tests of the estimated distributions are performed using the Kolmogorov-Smirnov statistic.     

Evolutionary Games on Weighted Newman-Watts Small-World Networks

We investigate the evolutionary prisoner＇s dilemma game （PDG） on weighted Newman-Watts （NW） networks. In weighted NW networks, the link weight ωij is assigned to the link between the nodes i and j as： ωij = （ki · kj）^β, where ki（kj） is the degree of node i（j） and β represents the strength of the correlations. Obviously, the link weight can be tuned by only one parameter β. We focus on the cooperative behavior and wealth distribution in the system. Simulation results show that the cooperator frequency is promoted by a large range of β and there is a minimal cooperation frequency around β = -1. Moreover, we also employ the Gini coefficient to study the wealth distribution in the population. Numerical results show that the Gini coefficient reaches its minimum when β≈ -1. Our work may be helpful in understanding the emergence of cooperation and unequal wealth distribution in society.     

The effect of asymmetric payoff mechanism on evolutionary networked prisoner’s dilemma game

In social and biological systems, there are obvious individual divergence and asymmetric payoff phenomenon due to the strength, power and influence differences. In this paper, we introduce an asymmetric payoff mechanism to evolutionary Prisoner’s Dilemma Game (PDG) on scale-free networks. The co-effects of individual diversity and asymmetric payoff mechanism on the evolution of cooperation and the wealth distribution under different updating rules are investigated. Numerical results show that the cooperation is highly promoted when the hub nodes are favored in the payoff matrix, which seems to harm the interest of the majority. But the inequality of social wealth distribution grows with the unbalanced payoff rule. However, when the node difference is eliminated in the learning strategy, the asymmetric payoff rule will not affect the cooperation level. Our work may sharpen the understanding of the cooperative behavior and wealth inequality in the society.     

Randomness Effect on Cooperation in Memory-Based Snowdrift Game

A memory-based snowdrift game (MBSG) on spatial small-world networks is investigated. It is found that cooperation rate versus temptation shows some step structures on small-world networks, similar to the case on regular lattices. With the increment of rewiring probability based on four-neighbourregular lattices, more steps are observable. Interestingly, it is observed that cooperation rate peaks at a specific value of temptation, which indicates that properly encouraging selfish actions may lead to better cooperative behaviours in the MBSG on small-world networks. Memory effects are also discussed for different rewiring probabilities. Furthermore, optimal regions arefound in the parameter planes. The strategy-related average degrees of individuals are helpful to understand the obtained results.     

Role of parties in the vote distribution of proportional elections

We analyze proportional election data to show the influence of parties on the results of this kind of election. The study compiles data from different countries and dates to show that depending on how the candidate’s votes are counted, one can find that these votes have different distributions. When considering the fraction of votes received by the candidates, the vote distribution has a power law behavior with exponent α=1 for all cases studied. However, this universal behavior is modified when we normalize the fraction of votes by the mean number of votes of the candidate’s party. Considering this normalization, the Brazilian and the Finnish results are now different. The former follows an exponential while the latter a log-normal distribution.     

Herd behavior in weight-driven information spreading models for financial market

We study two weight-driven information spreading models for financial market. In these models, we find that the activity threshold below which the ‘financial crash’ occurs can be increased by uneven distribution of information weight, compared with Eguíluz and Zimmermann model [V.M. Eguíluz, M.G. Zimmermann, Phys. Rev. Lett. 85 (2000) 5659]. We also find that below the threshold the normalized return distribution, P(Z;Δt) satisfies P(Z=0;Δt)∼exp(−Δt/b) whereas P(Z=0;Δt)∼Δt^−τ above the threshold. Here Δt is the time interval where the normalized return is defined, Z(t,Δt)=Z(t+Δt)−Z(t). By approximating the relative increase of P(Z;Δt=1) for large Z as Gaussian distribution with non-zero mean, we show that the non-zero mean of the Gaussian distribution can cause such exponentially decaying behavior of P(Z=0;Δt).     

Development of friendship network among young scientists in an international Summer School

A total of 49 students, about half of them male, from various countries and 4 student helpers attended the 2008 China Complex Systems Summer School organized by the Santa Fe Institute and the Chinese Academy of Sciences held in Beijing. We studied the development of the social network among these participants during the school, which lasted for 4 weeks, by carrying out surveys at different times of the school. The students got to know each other through various activities, including being roommates, eating together everyday, attending lectures, doing group projects, sight-seeing visits, etc. The topological structures and various properties of the network are discussed. The results indicate how the participants became friends as time went by. By considering the correlations between reciprocal evaluations via the Pearson’s correlation coefficient, it is found that the ethnicity and gender are important factors in establishing personal relationships and in getting mutually consistent perceptions on the relationships. We also study the clique components and community structures in the networks.     

Network effects in a human capital based economic growth model

We revisit a recently introduced agent model [ACS, 11, 99 (2008)], where economic growth is a consequence of education (human capital formation) and innovation, and investigate the influence of the agents’ social network, both on an agent’s decision to pursue education and on the output of new ideas. Regular and random networks are considered. The results are compared with the predictions of a mean field (representative agent) model.     

Statistical Property and Model for the Inter-Event Time of Terrorism Attacks

The inter-event time of terrorism attack events is investigated by empirical data and model analysis. Empirical evidence shows that it follows a scale-free property. In order to understand the dynamic mechanism of such a statistical feature, an opinion dynamic model with a memory effect is proposed on a two-dimensional lattice network. The model mainly highlights the role of individual social conformity and self-affirmation psychology. An attack event occurs when the order parameter indicating the strength of public opposition opinion is smaller than a critical value. Ultimately, the model can reproduce the same statistical property as the empirical data and gives a good understanding for the possible dynamic mechanism of terrorism attacks.     

A triangle model of criminality

This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, and so is Z with respect to Y. Moreover, Z can also be thought of as a predator of X, since this last population is required to bear the costs of maintaining Z.We propose a system of three ordinary differential equations to account for the time evolution of X(t), Y(t) and Z(t) according to our previous assumptions. Out of the various parameters that appear in that system, we select two of them, denoted by H, and h, which are related with the efficiency of the security forces as a control parameter in our discussion. To begin with, we consider the case of large and constant owners population, which allows us to reduce (3), (4) and (5) to a bidimensional system for Y(t) and Z(t). As a preliminary step, this situation is first discussed under the additional assumption that Y(t)+Z(t) is constant. A bifurcation study is then performed in terms of H and h, which shows the key role played by the rate of casualties in Y and Z, that results particularly in a possible onset of bistability. When the previous restriction is dropped, we observe the appearance of oscillatory behaviours in the full two-dimensional system. We finally provide a exploratory study of the complete model (3), (4) and (5), where a number of bifurcations appear as parameter H changes, and the corresponding solutions behaviours are described.     

Empirical study of recent Chinese stock market

We investigate the statistical properties of the empirical data taken from the Chinese stock market during the time period from January, 2006 to July, 2007. By using the methods of detrended fluctuation analysis (DFA) and calculating correlation coefficients, we acquire the evidence of strong correlations among different stock types, stock index, stock volume turnover, A share (B share) seat number, and GDP per capita. In addition, we study the behavior of “volatility”, which is now defined as the difference between the new account numbers for two consecutive days. It is shown that the empirical power-law of the number of aftershock events exceeding the selected threshold is analogous to the Omori law originally observed in geophysics. Furthermore, we find that the cumulative distributions of stock return, trade volume and trade number are all exponential-like, which does not belong to the universality class of such distributions found by Xavier Gabaix et al. [Xavier Gabaix, Parameswaran Gopikrishnan, Vasiliki Plerou, H. Eugene Stanley, Nature, 423 (2003)] for major western markets. Through the comparison, we draw a conclusion that regardless of developed stock markets or emerging ones, “cubic law of returns” is valid only in the long-term absolute return, and in the short-term one, the distributions are exponential-like. Specifically, the distributions of both trade volume and trade number display distinct decaying behaviors in two separate regimes. Lastly, the scaling behavior of the relation is analyzed between dispersion and the mean monthly trade value for each administrative area in China.     

Statistical properties of online avatar numbers in a massive multiplayer online role-playing game

Massive multiplayer online role-playing games (MMORPGs) have been very popular in the past few years. The profit of an MMORPG company is proportional to how many users registered, and the instant number of online avatars is a key factor to assess how popular an MMORPG is. We use the online-offline logs on an MMORPG server to reconstruct the instant number of online avatars per second and investigate its statistical properties. We find that the online avatar number exhibits one-day periodic behavior and clear intraday pattern, the fluctuation distribution of the online avatar numbers has a leptokurtic non-Gaussian shape with power-law tails, and the increments of online avatar numbers after removing the intraday pattern are uncorrelated and the associated absolute values have long-term correlation. In addition, both time series exhibit multifractal nature.     

Local Events and Dynamics on Weighted Complex Networks

We examine the weighted networks grown and evolved by local events, such as the addition of new vertices and links and we show that depending on frequency of the events, a generalized power-law distribution of strength can emerge. Continuum theory is used to predict the scaling function as well as the exponents, which is in good agreement with the numerical simulation results. Depending on event frequency, power-law distributions of degree and weight can also be expected. Probability saturation phenomena for small strength and degree in many real world networks can be reproduced. Particularly, the non-trivial clustering coefficient, assortativity coefficient and degree-strength correlation in our model are all consistent with empirical evidences.     

Travel and tourism: Into a complex network

It is discussed how the worldwide tourist arrivals, about 10% of the world’s domestic product, form a largely heterogeneous and directed complex network. Remarkably the random network of connectivity is converted into a scale-free network of intensities. The importance of weights on network connections is brought into discussion. It is also shown how strategic positioning particularly benefits from market diversity and that interactions among countries prevail on a technological and economic pattern, questioning the backbone of driving forces in traveling.     

Local Minority Game with Evolutionary Strategies

We study a model of local minority game in the random Kauffman network with evolutionary strategies and propose three methods to update the strategy of poor agents, with lower points in a given generation： namely to update either the Boolean function of their strategies randomly, or their local information of randomly adjacent m agents, or the number m of randomly chosen adjacent agents. The results of extended numerical simulations show that the behaviour of strategies in the three methods may enhance significantly the entire coordination of agents in the system. It is also found that a poor agent tends to use both small m strategies and correlated strategies, and the strategies of agents will finally self-organize into a steady-state distribution for a long time playing of the game.     

Wavelet multiscale analysis for Hedge Funds: Scaling and strategies

The wide acceptance of Hedge Funds by Institutional Investors and Pension Funds has led to an explosive growth in assets under management. These investors are drawn to Hedge Funds due to the seemingly low correlation with traditional investments and the attractive returns. The correlations and market risk (the Beta in the Capital Asset Pricing Model) of Hedge Funds are generally calculated using monthly returns data, which may produce misleading results as Hedge Funds often hold illiquid exchange-traded securities or difficult to price over-the-counter securities. In this paper, the Maximum Overlap Discrete Wavelet Transform (MODWT) is applied to measure the scaling properties of Hedge Fund correlation and market risk with respect to the S&P 500. It is found that the level of correlation and market risk varies greatly according to the strategy studied and the time scale examined. Finally, the effects of scaling properties on the risk profile of a portfolio made up of Hedge Funds is studied using correlation matrices calculated over different time horizons.     

The existence of negative absolute temperatures in Axelrod’s social influence model

We introduce the concept of temperature as an order parameter in the standard Axelrod’s social influence model. It is defined as the relation between suitably defined entropy and energy functions, T=(∂S/∂E)⁻¹. We show that at the critical point, where the order/disorder transition occurs, this absolute temperature changes in sign. At this point, which corresponds to the transition homogeneous/heterogeneous culture, the entropy of the system shows a maximum. We discuss the relationship between the temperature and other properties of the model in terms of cultural traits.     

Empirical analysis of dependence between stations in Chinese railway network

A railway transportation system can be represented by a bipartite network consisting of trains and stations, where a train is connected to all stations where it stops. In this paper, motivated by the resource-allocation process taking place on networks, we design a method to project a Chinese train-station bipartite network into a weighted station network. A new metric is proposed to quantify the dependence between pairs of stations, which is shown to follow a shifted power-law distribution. In addition, we compare the resource-allocation method and the well-known multiple-edge method, and the results indicate that our proposed method is more reasonable.