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We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agents interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdos-Renyi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdos-Renyi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.
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In this paper we discuss some features of the BCRE model. We show that this model can be understood as a mapping from a two-dimensional to a one-dimensional problem, if some conditions are satisfied. We propose some modifications that (a) guarantee mass conservation in the model (what is not assured in its original form) and (b) correct undesired behaviors that appear when there are irregularities in the surface of the static phase. We also show that a similar model can be deduced both from the principle of mass conservation (first equation) and a simple thermodynamic model (from which the exchange equation can be obtained). Finally, we solve the model numerically, using different velocity profiles and studying the influence of the different parameters present in this model.
Scientific journals are the repositories of the gradually accumulating knowledge of mankind about the world surrounding us. Just as our knowledge is organised into classes ranging from major disciplines, subjects and fields to increasingly specific topics, journals can also be categorised into groups using various metrics. In addition to the set of topics characteristic for a journal, they can also be ranked regarding their relevance from the point of overall influence. One widespread measure is impact factor, but in the present paper we intend to reconstruct a much more detailed description by studying the hierarchical relations between the journals based on citation data. We use a measure related to the notion of m-reaching centrality and find a network which shows the level of influence of a journal from the point of the direction and efficiency with which information spreads through the network. We can also obtain an alternative network using a suitably modified nested hierarchy extraction method applied to the same data. The results are weakly methodology-dependent and reveal non-trivial relations among journals. The two alternative hierarchies show large similarity with some striking differences, providing together a complex picture of the intricate relations between scientific journals.
Many of the essential features of the evolution of scientific research are imprinted in the structure of citation networks. Connections in these networks imply information about the transfer of knowledge among papers, or in other words, edges describe the impact of papers on other publications. This inherent meaning of the edges infers that citation networks can exhibit hierarchical features, that is typical of networks based on decision-making. In this paper, we investigate the hierarchical structure of citation networks consisting of papers in the same field. We find that the majority of the networks follow a universal trend towards a highly hierarchical state, and i) the various fields display differences only concerning their phase in life (distance from the birth of a field) or ii) the characteristic time according to which they are approaching the stationary state. We also show by a simple argument that the alterations in the behavior are related to and can be understood by the degree of specialization corresponding to the fields. Our results suggest that during the accumulation of knowledge in a given field, some papers are gradually becoming relatively more influential than most of the other papers.
Groups of people or even robots often face problems they need to solve together. Examples include collectively searching for resources, choosing when and where to invest time and effort, and many more. Although a hierarchical ordering of the relevance of the group members inputs during collective decision making is abundant, a quantitative demonstration of its origin and advantages using a generic approach has not been described yet. Here we introduce a family of models based on the most general features of group decision making to show that the optimal distribution of competences is a highly skewed function with a structured fat tail. Our results have been obtained by optimizing the groups compositions through identifying the best performing distributions for both the competences and for the members flexibilities/pliancies. Potential applications include choosing the best composition for a group intended to solve a given task.
We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the networks degree distribution. We rigorously prove that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.
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