The Routing of Complex Contagion in Kleinberg's Small-World Networks

In Kleinberg's small-world network model, strong ties are modeled as deterministic edges in the underlying base grid and weak ties are modeled as random edges connecting remote nodes. The probability of connecting a node $u$ with node $v$ through a weak tie is proportional to $1/|uv|^\alpha$, where $|uv|$ is the grid distance between $u$ and $v$ and $\alpha\ge 0$ is the parameter of the model. Complex contagion refers to the propagation mechanism in a network where each node is activated only after $k \ge 2$ neighbors of the node are activated. In this paper, we propose the concept of routing of complex contagion (or complex routing), where we can activate one node at one time step with the goal of activating the targeted node in the end. We consider decentralized routing scheme where only the weak ties from the activated nodes are revealed. We study the routing time of complex contagion and compare the result with simple routing and complex diffusion (the diffusion of complex contagion, where all nodes that could be activated are activated immediately in the same step with the goal of activating all nodes in the end). We show that for decentralized complex routing, the routing time is lower bounded by a polynomial in $n$ (the number of nodes in the network) for all range of $\alpha$ both in expectation and with high probability (in particular, $\Omega(n^{\frac{1}{\alpha+2}})$ for $\alpha \le 2$ and $\Omega(n^{\frac{\alpha}{2(\alpha+2)}})$ for $\alpha > 2$ in expectation), while the routing time of simple contagion has polylogarithmic upper bound when $\alpha = 2$. Our results indicate that complex routing is harder than complex diffusion and the routing time of complex contagion differs exponentially compared to simple contagion at sweetspot.Comment: Conference version will appear in COCOON 201

Cascade Dynamics of Multiplex Propagation

Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However we show that when the propagation requires simultaneous exposure to multiple sources of activation, called multiplex propagation, the effect of random links is just the opposite: it makes the propagation more difficult to achieve. We calculate analytical and numerically critical points for a threshold model in several classes of complex networks, including an empirical social network.Comment: 4 pages, 5 figures, for similar work visit http://hsd.soc.cornell.edu and http://www.imedea.uib.es/physdep

Wild Otherness Within: A Jungian and Zen Approach to the Untamed Self in the Ten Oxherding Pictures

The Ten Oxherding Pictures are an ancient allegory for the process of enlightenment. This article analyzes the series of ten paintings through the lenses of Jungian psychology and alterity studies to suggest an unorthodox interpretation of the images. This interpretation highlights the relationship between the oxherd and the ox, suggesting that the ox is a wild other that seeks intersubjective understanding. In questioning the meaning of domestication in these images, this investigation deconstructs the traditional allegory of enlightenment as a process of domestication, suggesting that these images instead point towards the importance of releasing the appropriative attitude. Ultimately, the oxherd in the series must surrender his perceptual lens to make space for what seems untamed and unencompassable to speak to and through him

Wild Otherness Within: A Jungian and Zen Approach to the Untamed Self in the Ten Oxherding Pictures

The Ten Oxherding Pictures are an ancient allegory for the process of enlightenment. This article analyzes the series of ten paintings through the lenses of Jungian psychology and alterity studies to suggest an unorthodox interpretation of the images. This interpretation highlights the relationship between the oxherd and the ox, suggesting that the ox is a wild other that seeks intersubjective understanding. In questioning the meaning of domestication in these images, this investigation deconstructs the traditional allegory of enlightenment as a process of domestication, suggesting that these images instead point towards the importance of releasing the appropriative attitude. Ultimately, the oxherd in the series must surrender his perceptual lens to make space for what seems untamed and unencompassable to speak to and through him

Theory of collective opinion shifts: from smooth trends to abrupt swings

We unveil collective effects induced by imitation and social pressure by analyzing data from three different sources: birth rates, sales of cell phones and the drop of applause in concert halls. We interpret our results within the framework of the Random Field Ising Model, which is a threshold model for collective decisions accounting both for agent heterogeneity and social imitation. Changes of opinion can occur either abruptly or continuously, depending on the importance of herding effects. The main prediction of the model is a scaling relation between the height h of the speed of variation peak and its width $w$ of the form h ~ w^{-kappa}, with kappa = 2/3 for well connected populations. Our three sets of data are compatible with such a prediction, with kappa ~ 0.62 for birth rates, kappa ~ 0.71 for cell phones and kappa ~ 0.64 for clapping. In this last case, we in fact observe that some clapping samples end discontinuously (w=0), as predicted by the model for strong enough imitation.Comment: 11 pages, 8 figure

Slightly generalized Generalized Contagion: Unifying simple models of biological and social spreading

We motivate and explore the basic features of generalized contagion, a model mechanism that unifies fundamental models of biological and social contagion. Generalized contagion builds on the elementary observation that spreading and contagion of all kinds involve some form of system memory. We discuss the three main classes of systems that generalized contagion affords, resembling: simple biological contagion; critical mass contagion of social phenomena; and an intermediate, and explosive, vanishing critical mass contagion. We also present a simple explanation of the global spreading condition in the context of a small seed of infected individuals.Comment: 8 pages, 5 figures; chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur

Order-disorder phase transition in a cliquey social network

We investigate the network model of community by Watts, Dodds and Newman (D. J. Watts et al., Science 296 (2002) 1302) as a hierarchy of groups, each of 5 individuals. A homophily parameter $\alpha$ controls the probability proportional to $\exp(-\alpha x)$ of selection of neighbours against distance $x$. The network nodes are endowed with spin-like variables $s_i = \pm 1$, with Ising interaction $J>0$. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature $T_c$ is close to 3.8 for $\alpha < 0.0$ and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action {\it via} weak ties, as discussed by Granovetter in 1973.Comment: 10 pages, 7 figure

Networks, Urban

For much of the twentieth century, urban networks was a term used by sociologists and others to describe social networks, their importance for bonding within communities and bridging between communities, and their relationship to the geographical mobility implied by late-nineteenth- and early-twentieth-century urbanization, mid-twentieth-century suburbanization, and late-twentieth-century globalization. This relationship is often assumed to be one in which social networks are threatened by geographical mobility. From sometime in the 1980s, in a context of globalization, network became a metaphor used across the social sciences to describe how people, ideas, and objects flow between nodes in a globalizing world, and urban networks became a term used by geographers and others to describe at least four more or less connected things: (1) archipelagos of world or global cities, in which centrality depends on networks of producer services and information and communications technology infrastructure; (2) this information and communications technology infrastructure, among other networked infrastructure, which has become unbundled in recent years, leading to fragmented or splintered cities; (3) other smaller networks of humans and nonhumans – actor networks – that help to maintain urban life; and (4) twenty-first-century social networks, characterized by their transnational geographies and relatively high levels of institutionalization and self-consciousnes

Weak ties: Subtle role of information diffusion in online social networks

As a social media, online social networks play a vital role in the social information diffusion. However, due to its unique complexity, the mechanism of the diffusion in online social networks is different from the ones in other types of networks and remains unclear to us. Meanwhile, few works have been done to reveal the coupled dynamics of both the structure and the diffusion of online social networks. To this end, in this paper, we propose a model to investigate how the structure is coupled with the diffusion in online social networks from the view of weak ties. Through numerical experiments on large-scale online social networks, we find that in contrast to some previous research results, selecting weak ties preferentially to republish cannot make the information diffuse quickly, while random selection can achieve this goal. However, when we remove the weak ties gradually, the coverage of the information will drop sharply even in the case of random selection. We also give a reasonable explanation for this by extra analysis and experiments. Finally, we conclude that weak ties play a subtle role in the information diffusion in online social networks. On one hand, they act as bridges to connect isolated local communities together and break through the local trapping of the information. On the other hand, selecting them as preferential paths to republish cannot help the information spread further in the network. As a result, weak ties might be of use in the control of the virus spread and the private information diffusion in real-world applications.Comment: Final version published in PR

Application of spectral methods for high-frequency financial data to quantifying states of market participants

Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A, 382 (2007) 258--270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation of the earth, and that the similarities among best quotation rates are associated with those among quotation frequencies. Furthermore it is shown that the Jensen-Shannon spectral divergence is proportional to a mean of the Kullback-Leibler spectral distance both empirically and numerically. It is confirmed that these spectral distances are connected with distributions for behavioral parameters of the market participants from numerical simulation. This concludes that spectral distances of representative quantities of financial markets are related into diversification of behavioral parameters of the market participants.Comment: 8 pages, 6 figures, APFA