We focus on Internet rumors and present an empirical analysis and simulation results of their diffusion and convergence during emergencies. In particular, we study one rumor that appeared in the immediate aftermath of the Great East Japan Earthquake on March 11, 2011, which later turned out to be misinformation. By investigating whole Japanese tweets that were sent one week after the quake, we show that one correction tweet, which originated from a city hall account, diffused enormously. We also demonstrate a stochastic agent-based model, which is inspired by contagion model of epidemics SIR, can reproduce observed rumor dynamics. Our model can estimate the rumor infection rate as well as the number of people who still believe in the rumor that cannot be observed directly. For applications, rumor diffusion sizes can be estimated in various scenarios by combining our model with the real data.

We propose a new type of stochastic network evolution model based on annihilation, creation, and coagulation of nodes, together with the preferential attachment rule. The system reaches a unique quasistatistically steady state in which the distribution of links follows a power law, lifetime of nodes follows an exponential distribution, and the mean number of links grows exponentially with time. The master equation of the model is solved analytically by applying Smoluchowski's coagulation equation for aerosols. The results indicate that coagulation of nodes in complex networks and mean field analysis of aerosols are similar in both the growth dynamics with irreversible processes and in the steady state statistics. We confirm that the basic properties of the model are consistent with the empirical results of a business transaction network having about 1×10(6) firms.

We analyze Japanese inter-firm network data showing scale-free properties as an example of a real complex network. The data contains information on money flow (annual transaction volume) between about 7000 pairs of firms. We focus on this money-flow data and investigate the correlation between various quantities such as sales or link numbers. We find that the flux from a buyer to a supplier is given by the product of the fractional powers of both sales with different exponents. This result indicates that the principle of detailed balance does not hold in the real transport of money; therefore, random walk type transport models such as PageRank are not suitable.

The world economy consists of highly interconnected and interdependent commercial and financial networks. Here, we develop temporal and structural network tools to analyze the state of the economy and the financial markets. Our analysis indicates that a strong clustering can be a warning sign. Reduction in diversity, which was an essential aspect of the dynamics surrounding the financial markets crisis of 2008, is seen as a key emergent feature arising naturally from the evolutionary and adaptive dynamics inherent to the financial markets. Similarly, collusion amongst construction firms in a number of regions in Japan in the 2000s can be identified with the formation of clusters of anomalous highly connected companies. V C 2013 Wiley Periodicals, Inc. Complexity 19: 22-36, 2013 Key Words: economics; evolutionary dynamics; network theory; quantitative finance. ANALYSIS 1.Dynamics of Financial MarketsI n order to investigate the dynamics of financial markets we have developed a simple multi agent network model for a basic financial system, comprising of three fundamental types of agents: Banks, Investors and Borrowers (see section 2 for details). Our approach to modeling this system is inspired by the modeling of societies and ecosystems, in which a key role is played by the This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.virtual intra and interdependence of species [1][2][3][4]. This translates in our model into a focus on: (i) the dynamics of infection of business strategies within the banking sector and of culture dissemination within the investment and fund management community, and (ii) the topological aspects of the network of interactions. In order to focus more clearly on the influence of the collective action of agents, and their interaction amongst FIGURE 1Crisis Mapping from Evolutionary Dynamics: Plot A shows the frequency of crisis and the relative number of times that each type of crisis scenario occurs. The front floor (dark blue) indicates the distributions when evolutionary dynamics are present, with realizations resulting in 1 or 2 crises being by far the most common. The back floor (green) showing the results without dynamics is entirely distributed into the first block (no crisis), indicating that evolutionary dynamics are an essential feature in order to see crises occur. Plot B illustrates the time line of crises as predicted by the model including the evolutionary dynamics for 1 crisis (light purple) and 2 crises (light yellow) simulations. Time is shown vertically, increasing downwards, while the horizontal axis denotes different realizations of the model. A crisis is defined when >2% of the Bank agents fail or require financial assistance over a year, which corresponds to the historical average registered in the first and second US banking crisis over the simulation period. 4 The fir...

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