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arXiv 1402.0501physics.soc-phcs.SIphysics.comp-ph
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运输网络弹性的大偏差性质

Large-deviation properties of resilience of transportation networks

Alexander K. Hartmann

摘要:

对运输网络的弹性分布进行了数值研究,特别是研究了大偏差尾部。因此,不仅可以研究平均值或方差等典型量,还可以研究(几乎)完全支持上的分布。为了证明的原则,一个简单的传输模型的基础上的边缘介数和三个抽象的但广泛研究的随机网络集成被认为是在这里:Erdoes-Renyi随机网络有限连接,小世界网络和空间网络嵌入在一个二维平面。使用特定的数值大偏差技术,概率密度小至10^(-80)在这里获得。这使得人们可以研究典型的网络,也可以研究最具弹性和最不具弹性的网络。由此产生的分布满足数学大偏差原理,即,可以很好地描述率函数在热力学极限。极限速率函数的分析表明,弹性几乎处处服从指数分布。网络结构的分析表明,最有弹性的网络可以获得,作为一个经验法则,通过最小化网络的直径。此外,通过包括更多的链路,通常可以使网络更具弹性。另一方面,弹性最小的网络非常罕见,其特征是所有其他节点都连接到一个(或几个)小核心。总的来说,空间网络集成是最适合获得和研究真正的大部分有限维网络的弹性。结合所提出的大偏差方法来研究这个集合,以获得更现实的,特别是动态的运输网络,似乎是非常有前途的。

英文摘要:

Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be studied. For a proof of principle, a simple transport model based on the edge-betweenness and three abstract yet widely studied random network ensembles are considered here: Erdoes-Renyi random networks with finite connectivity, small world networks and spatial networks embedded in a two-dimensional plane. Using specific numerical large-deviation techniques, probability densities as small as 10^(-80) are obtained here. This allows one to study typical but also the most and the least resilient networks. The resulting distributions fulfill the mathematical large-deviation principle, i.e., can be well described by rate functions in the thermodynamic limit. The analysis of the limiting rate function reveals that the resilience follows an exponential distribution almost everywhere. An analysis of the structure of the network shows that the most-resilient networks can be obtained, as a rule of thumb, by minimizing the diameter of a network. Also, trivially, by including more links a network can typically be made more resilient. On the other hand, the least-resilient networks are very rare and characterized by one (or few) small core(s) to which all other nodes are connected. In total, the spatial network ensemble turns out to be most suitable for obtaining and studying resilience of real mostly finite-dimensional networks. Studying this ensemble in combination with the presented large-deviation approach for more realistic, in particular dynamic transport networks appears to be very promising.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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