英文标题：
《On the convergence of the Fitness-Complexity Algorithm》
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作者：
Emanuele Pugliese, Andrea Zaccaria, and Luciano Pietronero
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最新提交年份：
2014
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英文摘要：
  We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q. The algorithm was originally based on the adjacency matrix M of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of F and Q. Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied.
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中文摘要：
我们研究了最近提出的一种算法的收敛性，该算法用于衡量各国的竞争力及其出口产品的质量。这些量分别称为适应度F和复杂度Q。该算法最初基于将国家与其出口产品连接起来的双边网络的邻接矩阵M，但可以应用于任何双边网络。邻接矩阵的结构对于确定哪些国家和产品收敛到F和Q的非零值至关重要。收敛到零的速度也取决于矩阵结构。排序矩阵的形状起着主要作用，尤其是当算法到达固定点时，只有对角线不与空部分相交的矩阵才能保证其输出值为非零值。对于简化的矩阵结构，我们用解析方法证明了这个结果，对于实际情况，我们用数值方法证明了这个结果。最后，我们提出了一些实际的指示，以考虑我们的结果时，该算法的应用。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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