类Schroedinger PageRank方程及其在WWW中的局部化
Schroedinger-like PageRank equation and localization in the WWW
摘要：
万维网是我们日常生活中使用的最重要的通信系统之一。尽管它的核心作用，增长和发展的万维网是不受任何中央权威。这种情况已经创造了一个巨大的整体的连接，其复杂性可以卓有成效地描述和量化的网络理论。一个重要的应用程序，允许整理出这些连接中存在的信息是由PageRank算法给出的。这个量的计算通常是迭代进行的，大量使用计算时间。在本文中，我们表明，PageRank可以表示在一个波函数服从薛定谔方程。特别是页面之间的输出和输入链接的不平衡所引起的拓扑混乱，导致了波函数和潜在的结构。这允许直接本地化具有最大分数的页面。通过这种新的表示，我们现在可以计算PageRank而无需迭代技术。对于大多数感兴趣的情况下，我们的方法比原来的方法更快。我们的研究结果也澄清了复杂网络中的信息扩散的拓扑结构的作用。整个方法打开了可能性的新技术的启发量子物理的WWW属性的分析。
英文摘要：
The WorldWide Web is one of the most important communication systems we use in our everyday life. Despite its central role, the growth and the development of the WWW is not controlled by any central authority. This situation has created a huge ensemble of connections whose complexity can be fruitfully described and quantified by network theory. One important application that allows to sort out the information present in these connections is given by the PageRank alghorithm. Computation of this quantity is usually made iteratively with a large use of computational time. In this paper we show that the PageRank can be expressed in terms of a wave function obeying a Schroedinger-like equation. In particular the topological disorder given by the unbalance of outgoing and ingoing links between pages, induces wave function and potential structuring. This allows to directly localize the pages with the largest score. Through this new representation we can now compute the PageRank without iterative techniques. For most of the cases of interest our method is faster than the original one. Our results also clarify the role of topology in the diffusion of information within complex networks. The whole approach opens the possibility to novel techniques inspired by quantum physics for the analysis of the WWW properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
