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Sumiyoshi Abe Mie University
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An article for the Springer Encyclopedia of Complexity and System Science
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Recent observation studies have revealed that earthquakes are classified into several different categories. Each category might be characterized by the unique statistical feature in the time series, but the present understanding is still limited due to their nonlinear and nonstationary nature. Here we utilize complex network theory to shed new light on the statistical properties of earthquake time series. We investigate two kinds of time series, which are magnitude and inter-event time (IET), for three different categories of earthquakes: regular earthquakes, earthquake swarms, and tectonic tremors. Following the criterion of visibility graph, earthquake time series are mapped into a complex network by considering each seismic event as a node and determining the links. As opposed to the current common belief, it is found that the magnitude time series are not statistically equivalent to random time series. The IET series exhibit correlations similar to fractional Brownian motion for all the categories of earthquakes. Furthermore, we show that the time series of three different categories of earthquakes can be distinguished by the topology of the associated visibility graph. Analysis on the assortativity coefficient also reveals that the swarms are more intermittent than the tremors.
Earthquake network is known to be complex in the sense that it is scale-free, small-world, hierarchically organized and assortatively mixed. Here, the time evolution of earthquake network is analyzed around main shocks in the context of the community structure. It is found that the maximum of the modularity measure quantifying existence of communities exhibits a peculiar behavior: its maximum value stays at a large value before a main shock, suddenly drops to a small value at the main shock, and then increases to relax to a large value again relatively slowly. Thus, a main shock absorbs and merges communities to create a larger community, showing how a main shock can be characterized in the complex-network representation of seismicity.
Earthquake network is known to be of the small-world type. The values of the network characteristics, however, depend not only on the cell size (i.e., the scale of coarse graining needed for constructing the network) but also on the size of a seismic data set. Here, discovery of a scaling law for the clustering coefficient in terms of the data size, which is refereed to here as finite data-size scaling, is reported. Its universality is shown to be supported by the detailed analysis of the data taken from California, Japan and Iran. Effects of setting threshold of magnitude are also discussed.
We base our study on the statistical analysis of the Rigan earthquake 2010 December 20, which consists of estimating the earthquake network by means of virtual seismometer technique, and also considering the avalanche-type dynamics on top of this complex network.The virtual seismometer complex network shows power-law degree distribution with the exponent $gamma=2.3pm 0.2$. Our findings show that the seismic activity is strongly intermittent, and have a textit{cyclic shape} as is seen in the natural situations, which is main finding of this study. The branching ratio inside and between avalanches reveal that the system is at (or more precisely close to) the critical point with power-law behavior for the distribution function of the size and the mass and the duration of the avalanches, and with some scaling relations between these quantities. The critical exponent of the size of avalanches is $tau_S=1.45pm 0.02$. We find a considerable correlation between the dynamical Green function and the nodes centralities.
Global supply networks in agriculture, manufacturing, and services are a defining feature of the modern world. The efficiency and the distribution of surpluses across different parts of these networks depend on choices of intermediaries. This paper conducts price formation experiments with human subjects located in large complex networks to develop a better understanding of the principles governing behavior. Our first finding is that prices are larger and that trade is significantly less efficient in small-world networks as compared to random networks. Our second finding is that location within a network is not an important determinant of pricing. An examination of the price dynamics suggests that traders on cheapest -- and hence active -- paths raise prices while those off these paths lower them. We construct an agent-based model (ABM) that embodies this rule of thumb. Simulations of this ABM yield macroscopic patterns consistent with the experimental findings. Finally, we extrapolate the ABM on to significantly larger random and small world networks and find that network topology remains a key determinant of pricing and efficiency.
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