玻璃状分级网络的稳定性
Stability of glassy hierarchical networks
摘要：
在大多数动物和人类社会中，相互作用的结构可以用复杂的等级网络来最好地表示。为了保持接近最佳的功能，稳定性和适应性都是必要的。在这里，我们调查的稳定性的层次网络，出现从模拟的组织类型的效率函数让人想起的哈密顿的自旋玻璃。使用这种定量方法，我们发现一些预期的（来自日常观察）以及获得的局部最优网络的高度非平凡的结果，包括例如：i）稳定性随着效率和层次级别的增长而增加，ii）对于更有效的状态，相同的扰动导致更大的变化，iii）具有较低层次级别的网络在扰动之后变得更有效，iv）由于可能的最佳状态的数量巨大，它们中只有一小部分表现出弹性，最后，v）选择性地针对节点（关于它们在层次结构中的位置）的“攻击”可能导致矛盾的结果。
英文摘要：
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we investigate the stability of hierarchical networks that emerge from the simulations of an organization-type having an efficiency function reminiscent of the Hamiltonian of spin-glasses. Using this quantitative approach we find a number of expected (from everyday observations) and highly non-trivial results for the obtained locally optimal networks, including such as: i) stability increases with growing efficiency and level of hierarchy, ii) the same perturbation results in a larger change for more efficient states, iii) networks with a lower level of hierarchy become more efficient after perturbation, iv) due to the huge number of possible optimal states only a small fraction of them exhibits resilience and, finally, v) "attacks" targeting the nodes selectively (regarding their position in the hierarchy) can result in paradoxical outcomes.
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