一句话：提出一类可组合的动态系统及其公理化代数，用格与不动点刻画级联效应、失效、韧性与脆弱性。
本文研究级联效应（可视为后果性效应）的形式化与组合问题，提出一类新的动态系统，使其天然支持系统组合。作者建立公理化的一般理论，以格与不动点为核心，刻画系统并通过两个算子描述局部系统如何组合成全局系统；理论结果可实例化到常见级联模型。进一步引入失效概念，分析何种冲击会导致系统失效；提出 mu-rank 度量系统能量，定义韧性为使系统失效所需的最小努力，并推出对偶的脆弱性概念，证明系统组合会限制脆弱性的继承程度。
We introduce a new class of (dynamical) systems that inherently capture cascading effects (viewed as consequential effects) and are naturally amenable to combinations. We develop an axiomatic general theory around those systems, and guide the endeavor towards an understanding of cascading failure. The theory evolves as an interplay of lattices and fixed points, and its results may be instantiated to commonly studied models of cascade effects. We characterize the systems through their fixed points, and equip them with two operators. We uncover properties of the operators, and express global systems through combinations of local systems. We enhance the theory with a notion of failure, and understand the class of shocks inducing a system to failure. We develop a notion of mu-rank to capture the energy of a system, and understand the minimal amount of effort required to fail a system, termed resilience. We deduce a dual notion of fragility and show that the combination of systems sets a limit on the amount of fragility inherited.Comment: 31 pages
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@article{AdamDO15,
title = {Towards an Algebra for Cascade Effects},
author = {Elie M. Adam and Munther A. Dahleh and Asuman Ozdaglar},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 3},
year = {2017},
doi = {10.23638/lmcs-13(3:1)2017}
}