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2017 ; 7
(1
): 1382
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Glassy nature of hierarchical organizations
#MMPMID28469242
Zamani M
; Vicsek T
Sci Rep
2017[May]; 7
(1
): 1382
PMID28469242
show 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 [Formula: see text] 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.
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