arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1802.03286physics.soc-phmath.STq-fin.RMstat.TH
收藏

失效级联的显式规模分布重新定义了有限网络上的系统风险

Explicit size distributions of failure cascades redefine systemic risk on finite networks

Rebekka Burkholz, Hans J. Herrmann, Frank Schweitzer

备注：
systemic risk, finite size effects, cascades, networks
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

网络中的一些节点的初始故障放大为跨越所有节点的大部分的大级联的风险有多大？预测最终级联规模对于确保整个系统的运作至关重要。然而，这项任务受到不确定或不断变化的参数和缺失信息的阻碍。在无限大的网络中，平均级联大小通常可以很好地估计建立在局部树近似和平均场近似的方法。然而，正如我们所证明的，在有限网络中，这个平均值甚至不需要是一个可能的结果。相反，我们发现广泛的，甚至双峰级联尺寸分布。这种现象持续存在的系统规模高达$10^{7}$和不同的级联模型，即它是相关的大多数真实的系统。为了证明这一点，我们推导出显式的封闭形式的解决方案的最终级联大小的全概率分布。我们专注于两个拓扑极限的情况下，完整的网络表示一个密集的网络，一个非常窄的度分布，和星型网络表示一个稀疏的网络，一个不均匀的度分布。这些拓扑结构非常有趣，因为它们可以最小化或最大化平均级联大小，并且是许多现实世界网络中的常见图案。

英文摘要：

How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet, this task is hampered by uncertain or changing parameters and missing information. In infinitely large networks, the average cascade size can often be well estimated by established approaches building on local tree approximations and mean field approximations. Yet, as we demonstrate, in finite networks, this average does not even need to be a likely outcome. Instead, we find broad and even bimodal cascade size distributions. This phenomenon persists for system sizes up to $10^{7}$ and different cascade models, i.e. it is relevant for most real systems. To show this, we derive explicit closed-form solutions for the full probability distribution of the final cascade size. We focus on two topological limit cases, the complete network representing a dense network with a very narrow degree distribution, and the star network representing a sparse network with a inhomogeneous degree distribution. Those topologies are of great interest, as they either minimize or maximize the average cascade size and are common motifs in many real world networks.

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。

↑