剖析马氏链平稳分布的讲解——谈《应用随机过程》教学

通过平稳分布在Google搜索技术中的应用角度讲解马氏链的平稳分布的概念,并在此基础上对应用随机过程的教学做了粗浅的探讨.     

An adaptive improvement on PageRank algorithm

In this article, we introduce the Google’s method for quality ranking of web page in a formal mathematical format, use the power iteration to improve the PageRank, and also discuss the effect of different q to the PageRank, as well as how a PageRank will be changed if more links are added to one page or removed from some pages.     

On the eigenvalues of specially low-rank perturbed matrices

We study the eigenvalues of a matrix A perturbed by a few special low-rank matrices. The perturbation is constructed from certain basis vectors of an invariant subspace of A, such as eigenvectors, Jordan vectors, or Schur vectors. We show that most of the eigenvalues of the low-rank perturbed matrix stayed unchanged from the eigenvalues of A; the perturbation can only change the eigenvalues of A that are related to the invariant subspace. Existing results mostly studied using eigenvectors with full column rank for perturbations, we generalize the results to more general settings. Applications of our results to a few interesting problems including the Google’s second eigenvalue problem are presented.     

A Power–Arnoldi algorithm for computing PageRank

The PageRank algorithm plays an important role in modern search engine technology. It involves using the classical power method to compute the principle eigenvector of the Google matrix representing the web link graph. However, when the largest eigenvalue is not well separated from the second one, the power method may perform poorly. This happens when the damping factor is sufficiently close to 1. Therefore, it is worth developing new techniques that are more sophisticated than the power method. The approach presented here, called Power–Arnoldi, is based on a periodic combination of the power method with the thick restarted Arnoldi algorithm. The justification for this new approach is presented. Numerical tests illustrate the efficiency and convergence behaviour of the new algorithm. Copyright © 2007 John Wiley & Sons, Ltd.     

Google矩阵和它的性质

网页等级(PageRank)是一个反映网页重要性的数值.当一个网页A连向另一个网页B的时候,A就等于给网页B投了有效的一票.一个网页接受的票越多,这个网页就越重要.同时,给网页B投票的网页本身的等级也决定了该选票的重要性.Google通过每张选票本身重要性和得票多少来计算一个网页的级别(重要性).Google的核心就是计算每一个网页的等级(即PageRank).本文主要介绍Google矩阵的定义和产生,解释PageRank的一些相关概念,证明Google矩阵及其第二特征值具有的一些性质,并简要介绍这些性质的应用.     

Interdependence of Sectors of Economic Activities for World Countries from the Reduced Google Matrix Analysis of WTO Data

We apply the recently developed reduced Google matrix algorithm for the analysis of the OECD-WTO World Network of Economic Activities. This approach allows to determine interdependencies and interactions of economy sectors of several countries, including China, Russia and the USA, properly taking into account the influence of all the other world countries and their economic activities. Within this analysis, we also obtain the sensitivity of EU countries’ economies to the petroleum activity sector. We show that this approach takes into account the multiplicity of economical interactions between countries and activity sectors, thus providing a richer analysis compared to the usual export-import analysis.     

管道清管器实时远程跟踪定位系统的设计与实现

清管器在油气管道的清理过程中具有重要的作用,但若管道内杂质堆积物过多会将清管器卡堵在管道中而影响清管作业的顺利完成。为了保证油气管道的正常运营,需要对工作中的清管器进行实时远程跟踪定位。本文开发了一套管道清管器实时远程跟踪定位系统。在清管器接收机中内置GPS模块,接收机检测到清管器发射的低频信号时向GPS模块发送指令进行导航定位,并将得到的定位信息通过访问网址的方式发送给指定的服务器,由服务器调用Google地图显示清管器所在位置以及运动轨迹,从而实现清管器实时远程追踪和定位。     

COVID-19’s Impact on International Trade

We analyze how the COVID-19 pandemic affected the trade of products between countries. With this aim, using the United Nations Comtrade database, we perform a Google matrix analysis of the multiproduct World Trade Network (WTN) for the years 2018–2020, comprising the emergence of the COVID-19 as a global pandemic. The applied algorithms—PageRank, CheiRank and the reduced Google matrix—take into account the multiplicity of the WTN links, providing new insights into international trade compared to the usual import–export analysis. These complex networks analysis algorithms establish new rankings and trade balances of countries and products considering all countries on equal grounds, independent of their wealth, and every product on the basis of its relative exchanged volumes. In comparison with the pre-COVID-19 period, significant changes in these metrics occurred for the year 2020, highlighting a major rewiring of the international trade flows induced by the COVID-19 pandemic crisis. We define a new PageRank–CheiRank product trade balance, either export or import-oriented, which is significantly perturbed by the pandemic.     

基于Google Earth的无人机任务规划设计

针对无人机任务规划要求,提出了一种利用Google Earth二次开发能力实现的无人机任务规划方法。首先应用任务规划算法得到规划信息,然后将威胁数据、规划数据、飞机数据等信息通过Google Earth提供的接口引入到Google Earth中,得到无人机在Google Earth上的规划航迹。结果表明,该方法不仅省去了地形建模,而且能快速地生成一条逼真性相当高的满足无人机性能要求的规避威胁航路。