Glassy nature of hierarchical organizations
Abstract 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 con...
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Nature Portfolio
2017
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oai:doaj.org-article:8b8bd9ea9f6d4d7a875a71a31580f8372021-12-02T15:05:06ZGlassy nature of hierarchical organizations10.1038/s41598-017-01503-y2045-2322https://doaj.org/article/8b8bd9ea9f6d4d7a875a71a31580f8372017-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-01503-yhttps://doaj.org/toc/2045-2322Abstract 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 $${E}_{eff}=1/N{\sum }_{ij}{J}_{ij}{a}_{i}{a}_{j}$$ E e f f = 1 / N ∑ i j J i j 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 E eff 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.Maryam ZamaniTamas VicsekNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-9 (2017) |
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Medicine R Science Q |
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Medicine R Science Q Maryam Zamani Tamas Vicsek Glassy nature of hierarchical organizations |
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Abstract 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 $${E}_{eff}=1/N{\sum }_{ij}{J}_{ij}{a}_{i}{a}_{j}$$ E e f f = 1 / N ∑ i j J i j 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 E eff 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. |
| format |
article |
| author |
Maryam Zamani Tamas Vicsek |
| author_facet |
Maryam Zamani Tamas Vicsek |
| author_sort |
Maryam Zamani |
| title |
Glassy nature of hierarchical organizations |
| title_short |
Glassy nature of hierarchical organizations |
| title_full |
Glassy nature of hierarchical organizations |
| title_fullStr |
Glassy nature of hierarchical organizations |
| title_full_unstemmed |
Glassy nature of hierarchical organizations |
| title_sort |
glassy nature of hierarchical organizations |
| publisher |
Nature Portfolio |
| publishDate |
2017 |
| url |
https://doaj.org/article/8b8bd9ea9f6d4d7a875a71a31580f837 |
| work_keys_str_mv |
AT maryamzamani glassynatureofhierarchicalorganizations AT tamasvicsek glassynatureofhierarchicalorganizations |
| _version_ |
1718388968621342720 |