摘要翻译：
本文引入一个随机模型来解释社会经济系统中广泛存在的双幂律分布，该分布在上尾和下尾表现出两种不同的帕累天行为。该模型考虑了适应度和噪声波动。我们发现，当变量数（如复杂网络中节点的度或人们的收入）呈指数增长时，正态分布适应值与指数增长变量的耦合导致了双幂律分布的出现。波动不会在质量上改变结果，但会影响第二部分的标度指数。以中国航线网络的演化为例，验证了随机模型的一致性。
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英文标题：
《Emergence of double scaling law in complex system》
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作者：
D. D. Han, J. H. Qian, Y. G. Ma
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最新提交年份：
2011
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分类信息：

一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Physics        物理学
二级分类：Soft Condensed Matter        软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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一级分类：Physics        物理学
二级分类：Nuclear Theory        核理论
分类描述：Nuclear Theory Theory of nuclear structure covering wide area from models of hadron structure to neutron stars. Nuclear equation of states at different external conditions. Theory of nuclear reactions including heavy-ion reactions at low and high energies. It does not include problems of data analysis, physics of nuclear reactors, problems of safety, reactor construction
核理论涵盖从强子结构模型到中子星等广泛领域的核结构理论。不同外部条件下的核状态方程。核反应理论，包括低能和高能的重离子反应。它不包括数据分析问题、核反应堆物理问题、安全问题、反应堆建设问题
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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
  We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness consideration and noise fluctuation. We find that if the number of variables (e.g. the degree of nodes in complex networks or people's incomes) grows exponentially, normal distributed fitness coupled with exponentially increasing variable is responsible for the emergence of the double power-law distribution. Fluctuations do not change the result qualitatively but contribute to the second-part scaling exponent. The evolution of Chinese airline network is taken as an example to show a nice agreement with our stochastic model.
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PDF链接：
https://arxiv.org/pdf/1103.2001