Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

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Collective dynamics of small-world networks

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Cooperation in organisms, whether bacteria or primates, has been a difficulty for evolutionary theory since Darwin. On the assumption that interactions between pairs of individuals occur on a probabilistic basis, a model is developed based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game. Deductions from the model, and the results of a computer tournament show how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established. Potential applications include specific aspects of territoriality, mating, and disease.

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The Evolution of Cooperation

A hypothesized need to form and maintain strong, stable interpersonal relationships is evaluated in light of the empirical literature. The need is for frequent, nonaversive interactions within an ongoing relational bond. Consistent with the belongingness hypothesis, people form social attachments readily under most conditions and resist the dissolution of existing bonds. Belongingness appears to have multiple and strong effects on emotional patterns and on cognitive processes. Lack of attachments is linked to a variety of ill effects on health, adjustment, and well-being. Other evidence, such as that concerning satiation, substitution, and behavioral consequences, is likewise consistent with the hypothesized motivation. Several seeming counterexamples turned out not to disconfirm the hypothesis. Existing evidence supports the hypothesis that the need to belong is a powerful, fundamental, and extremely pervasive motivation.

The need to belong: Desire for interpersonal attachments as a fundamental human motivation.

Scholars in various disciplines have considered the causes, nature, and effects of trust. Prior approaches to studying trust are considered, including characteristics of the trustor, the trustee, and the role of risk. A definition of trust and a model of its antecedents and outcomes are presented, which integrate research from multiple disciplines and differentiate trust from similar constructs. Several research propositions based on the model are presented.

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An Integrative Model Of Organizational Trust

A collection of seven essays that serves as an introductory text on complexity theory and computer modelling in the social sciences, and as an overview of the current state of the art in this field. The articles move beyond the basic paradigm of the "Prisoner's Dilemma" to study a rich set of issues, including how to cope with errors in perception or implementation, how norms emerge, and how political actors and regions of shared culture can develop. They use the shared methodology of agent-based modelling, a technique that specifies the rules of interaction between individuals and uses computer simulation to discover emergent properties of the social system.

The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration

Iorms provide a powerful mechanism for regulating conflict in groups, even when there are more than two people and no central authority. This paper investigates the emergence and stability of behavioral norms in the context of a game played by people of limited rationality. The dynamics of this new norms game are analyzed with a computer simulation based upon the evolutionary principle that strategies shown to be relatively effective will be used more in the future than less effective strategies. The results show the conditions under which norms can evolve and prove stable. One interesting possibility is the employment of metanorms, the willingness to punish someone who did not enforce a norm. Many historical examples of domestic and international norms are used to illustrate the wide variety of mechanisms that can support norms, including metanorms, dominance, internalization, deterrence, social proof, membership in groups, law, and reputation.

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An evolutionary approach to norms

Despite tendencies toward convergence, differences between individuals and groups continue to exist in beliefs, attitudes, and behavior. An agent-based adaptive model reveals the effects of a mechanism of convergent social influence. The actors are placed at fixed sites. The basic premise is that the more similar an actor is to a neighbor, the more likely that that actor will adopt one of the neighbor's traits. Unlike previous models of social influence or cultural change that treat features one at a time, the proposed model takes into account the interaction between different features. The model illustrates how local convergence can generate global polarization. Simulations show that the number of stable homogeneous regions decreases with the number of features, increases with the number of alternative traits per feature, decreases with the range of interaction, and (most surprisingly) decreases when the geographic territory grows beyond a certain size. MAINTENANCE OF DIFFERENCES If people tend to become more alike in their beliefs, attitudes, and behavior when they interact, why do not all such differences eventually disappear? Social scientists have proposed many mechanisms to answer this question. The purpose of this article is to explore one more mechanism. The mechanism proposed here deals with how people do indeed become more similar as they interact, but also provides an explanation of why the tendency to converge stops before it reaches completion. It therefore provides a new type of explanation of why we do not all become alike. Because the proposed mechanism can exist alongside other mechanisms, it can be regarded as complementary with older explanations rather than necessarily competing with them. Unfortunately, no good term describes the range of things about which people can influence each other. Although beliefs, attitudes, and behavior cover a wide range indeed, there are still more things over which interpersonal influence extends, such as language, art, technical standards, and social norms. The most generic term for the

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Robert Axelrod

Papers

The Evolution of Cooperation

The Evolution of Cooperation

The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration

An evolutionary approach to norms

The Dissemination of Culture: A Model with Local Convergence and Global Polarization