Glassy nature of hierarchical organizations
The question of why and how animal and human groups form temporarily stable hierarchical organizations has long been a great challenge from the point of quantitative interpretations. The prevailing observation/consensus is that a hierarchical social or technological structure is optimal considering...
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| Format: | journal article |
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2017
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| Online Access: | http://hdl.handle.net/10831/66724 |
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| Summary: | The question of why and how animal and human groups form temporarily stable hierarchical organizations has long been a great challenge from the point of quantitative interpretations. The prevailing observation/consensus is that a hierarchical social or technological structure is optimal considering a variety of aspects. Here we introduce a simple quantitative interpretation of this situation using a statistical mechanics-type approach. We look for the optimum of the efficiency function E-eff = 1/N Sigma(ij)J(ij)a(i)a(j) with J(ij) denoting the nature of the interaction between the units i and j and a(i) standing for the ability of member i to contribute to the efficiency of the system. Notably, this expression for Eeff has a similar structure to that of the energy as defined for spin-glasses. Unconventionally, we assume that J(ij)-s can have the values 0 (no interaction), +1 and -1; furthermore, a direction is associated with each edge. The essential and novel feature of our approach is that instead of optimizing the state of the nodes of a pre-defined network, we search for extrema for given a(i)-s in the complex efficiency landscape by finding locally optimal network topologies for a given number of edges of the subgraphs considered. |
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| Physical Description: | application/pdf |