Glassy nature of hierarchical organizations #MMPMID28469242
Zamani M; Vicsek T
Sci Rep 2017[]; 7 (ä): ä PMID28469242show ga
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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{eff}=1/N{\sum }_{ij}{J}_{ij}{a}_{i}{a}_{j}$$\end{document}Eeff=1/N?ijJijaiaj with Jij denoting the nature of the interaction between the units i and j and ai 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 Jij-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 ai-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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Sci+Rep 2017 ; 7 (ä): ä
