英文标题：
《Mean field approximation for biased diffusion on Japanese inter-firm
  trading network》
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作者：
Hayafumi Watanabe
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最新提交年份：
2014
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英文摘要：
  By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7.
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中文摘要：
通过分析日本各地公司的财务数据，观察到商业伙伴数量（即公司间贸易网络的程度）与销售额之间存在指数为1.3的非线性幂律。在之前的一项使用数值模拟的研究中，我们发现，这种规模可以通过货币运输模型（企业（即客户）按照目的地的入度比例向其外部边缘（供应商）分配货币）和日本企业间交易网络之间的相关性来解释。然而，在之前的研究中，我们无法明确确定网络的哪些类型的结构属性（或相关性）决定1.3指数。在本研究中，我们通过将复杂网络中扩散的平均场近似应用于该货币运输模型，更清楚地阐明了这种非线性标度与网络结构之间的关系。通过理论分析，我们获得了该模型的平均场解，并发现，在日本企业的情况下，1.3的标度指数可以根据指数为-0.7的网络最近邻平均度的幂律确定。
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分类信息：

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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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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