摘要翻译：
我们介绍了网络上的级联和传染过程模型的一般框架，以识别它们的共同点和不同点。特别是社会和金融级联模型，以及纤维束模型、选民模型和流行病传播模型作为特例进行了恢复。为了统一它们的描述，我们定义了一个节点的网络脆弱性，即它的脆弱性与决定它失败的阈值之间的差。如果节点的网络脆弱性大于零，那么节点就会失败，并且它们的失败增加了邻近节点的脆弱性，从而可能触发级联。在这个框架中，我们根据邻居的失败增加节点脆弱性的方式来识别三类。在微观层面，我们用具体的例子说明了故障传播模式是如何随着触发级联的节点在网络中的位置和程度而变化的。在宏观层面上，系统风险被度量为失败节点的最终分数$x^\AST$，对于这三个类别中的每一个，我们导出了一个递归方程来计算其值。作为初始条件函数的相图$x^\AST$，因此允许系统风险的预测以及三种不同模型类别的比较。我们可以识别哪一类模型导致系统风险的一级相变，即初始条件的微小变化可能导致全局失败的情况。最后，我们将我们的框架推广到包括随机传染模型。这表明有进一步推广的潜力。
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英文标题：
《Systemic Risk in a Unifying Framework for Cascading Processes on
  Networks》
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作者：
Jan Lorenz, Stefano Battiston, Frank Schweitzer
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, $X^\ast$, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of $X^\ast$ as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class lead to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions may lead to a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.
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PDF链接：
https://arxiv.org/pdf/0907.5325