求解PageRank问题的GMRES重启的松弛两步分裂法

正1引言随着互联网信息的快速发展,网络搜索引擎是人们通过互联网获取信息的重要工具.搜索引擎的关键技术就是网页排序,其核心是搜索引擎算法的设计.斯坦福大学的Larry和Sergey Brin在1996年提出的PageRank算法,主要是用于网页评级的系统,该算法在Google搜索引擎中取得了很大的成功.所谓PageRank问题就是求解Google矩阵A的首特征值1所对应的特征向量,即线     

求解PageRank问题的Arnoldi-MSI算法

正1引言信息时代互联网技术的飞速发展,使得网络搜索引擎成为重要的信息检索工具.搜索引擎最核心的部分就是搜索算法的设计,在搜索算法中最著名的算法之一就是PageRank算法~([2]).PageRank问题就是求解Google矩阵A的首特征值1所对应的特征向量,即线性系统     

PageRank的改进算法——调整阻尼因子

Google将PageRank定义成某个非周期不可约Markov转移概率矩阵的平稳分布,于是对PageRank算法的改进所得到的矩阵一定要是非周期不可约Markov转移概率矩阵,结合RageRank算法和林共进修正算法思想,以及修正算法存在的问题,本文给出了改进算法,并通过简单试验对改进算法进行调整,调整后的改进算既满足Google的初衷又解决其算法的问题,也没有增加算法的复杂度.     

一类析取矩阵的构作和性质

利用BIB设计构作了一个d-析取矩阵A,研究了它的一些性质;然后,通过给矩阵A加行构作了一个新矩阵A+,研究了这个新矩阵的性质,并比较了两个矩阵的检纠错性.     

关于矩阵张量积的谱

<正> 设 A=(a_(jk))_(m_1×m_2),B=(b_(jk))_(n_1×n_2),则 m_1n_1×m_2n_2矩阵(?)称为 A 与 B 的张量积(也称直积或 Kronecker 积).矩阵的张量积是多重线性代数的重要工具之一,在群表示论中也有重要应用.本文的主要目的是在作者过去工作的基础上给出矩阵张量积的一些谱性质.     

两类网页重要性排序算法的概率对比

PageRank和BrowseRank算法是近年来针对网页重要性排序提出的两类典型算法.本文基于更新过程,通过遍历理论分析对比两类网页重要性排序算法,发现它们都利用随机游走的思想来模拟用户在互联网上浏览网页的行为,不同的是前者是离散时间参数的马尔可夫链而后者是连续时间参数的.而且它们所利用的数据也不同,前者基于网络链接图而后者是从真实用户浏览日志中生成的用户浏览图.此外,我们还证明随机游走的平稳分布是对网页重要性的一个合理且可行的衡量方法,并给出目前一些文献中所获得的实验结果的概率解释和意义.     

广义逆矩阵A~-的计算方法及应用

根据广义逆矩阵(减号逆)的定义AA-A=A,给出了求任意矩阵A的一个或全部广义逆矩阵A-的计算方法.当A-为A的全部广义逆矩阵时,得出了矩阵方程(或线性方程组)AX=B的统一通解公式X=A-B.     

矩阵方程XA-YB=D的广义中心对称解及其最佳逼近

1 引言 首先引入一些记号.记Cn×m为n×m复矩阵的集合.UCn×n表示所有n阶酉矩阵的集合.In表示n阶单位矩阵.AH和A+分别表示矩阵A的共轭转置及Moore-Penrose广义逆.对A=(n玎).…B=(bij).煳用A}B=(aijbij)sXt表示A与B的Hadamard积.     

矩阵Hadamard积和Fan积的特征值界的一些新估计式（英文）

本文研究了非奇异M-矩阵A与B的Fan积的最小特征值下界和非负矩阵A与B的Hadamard积的谱半径上界的估计问题.利用Brauer定理,得到了一些只依赖于矩阵的元素且易于计算的新估计式,改进了文献[41现有的一些结果.     

任意矩阵的特征值的扰动界

Hoffman和Wielandt对A和C都是正规矩阵(即AA~H=A~HA,A~H表示A的共轭转置矩阵)的情形给出了σ的一个上界为||B||_F,其中||·||_F表示矩阵的Frobenius(或Euclld)范数([9]和[10]分别对A,C均为对称矩阵和Hermite矩阵时证明了这一结果).但他们也指出,当A和C至少有一个不是正规矩阵时,这个界不成立.于是,如何推广Hoffman和Wielandt的结果(下面简称为W-H定理),一直成为人们感兴趣的课题.     

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.     

Ghost seats in parliaments

In several European Countries citizens’ movements have formed parties whose programme is to reform electoral legislation so that blank votes are transformed into vacant seats in parliament. The first objective of this paper is to offer some tools in order to quantify the potential effect of a reform that would allow citizens to cast a dissatisfaction vote. We show that such a reform would reduce the ease to pass a proposal and modify the distribution of power among parties. The second objective of this paper is to show that this reform could have an impact in parliaments. This is illustrated by the case of the Basque Parliament from 1980 to 2016. At the theoretical level this paper provides some relations between measures of success.     

Qualified voting systems

Voting systems are defined by three components: the set of votes that individuals are allowed to cast (that is, the instructions voters receive on how to fill in the ballot), a support function (that transforms ballots into support or votes), and an outcome function (which states how to aggregate those votes). In this paper, we investigate how these components interact. To that end, we impose two requirements on the outcome functions, called support monotonicity and limited symmetry. We identify the family of outcome functions that satisfy both properties.     

An experimental study of voting rules and polls in three-candidate elections

We report the results of elections conducted in a laboratory setting, modelled on a threecandidate example due to Borda. By paying subjects conditionally on election outcomes, we create electorates with (publicly) known preferences. We compare the results of experiments with and without non-binding pre-election polls under plurality rule, approval voting, and Borda rule. We also refer to a theory of voting “equilibria,” which makes sharp predictions concerning individual voter behavior and election outcomes. We find that Condorcet losers occasionally win regardless of the voting rule or presence of polls. Duverger's law (which asserts the predominance of two candidates) appears to hold under plurality rule, but close three-way races often arise under approval voting and Borda rule. Voters appear to poll and vote strategically. In elections, voters usually cast votes that are consistent with some strategic equilibrium. By the end of an election series, most votes are consistent with a single equilibrium, although that equilibrium varies by experimental group and voting rule.     

A core of voting games with improved foresight

This paper considers voting situations in which the vote takes place iteratively. If a coalition replaces the status quo a with a contestant b, then b becomes the new status quo, and the vote goes on until a candidate is reached that no winning coalition is willing to replace. It is well known that the core, that is, the set of undominated alternatives, may be empty. To alleviate this problem, Rubinstein [Rubinstein, A., 1980. Stability of decision systems under majority rule. Journal of Economic Theory 23, 150–159] assumes that voters look forward one vote before deciding to replace an alternative by a new one. They will not do so if the new status quo is going to be replaced by a third that is less interesting than the first. The stability set, that is, the set of undominated alternatives under this behavior, is always non-empty when preferences are strict. However, this is not necessarily the case when voters’ indifference is allowed. Le Breton and Salles [Le Breton, M., Salles, M., 1990. The stability set of voting games: Classification and generecity results. International Journal of Game Theory 19, 111–127], Li [Li, S., 1993. Stability of voting games. Social Choice and Welfare 10, 51–56] and Martin [Martin, M., 1998. Quota games and stability set of order d. Economic Letters 59, 145–151] extend the sophistication of the voters by having them look d votes forward along the iterative process. For d sufficiently large, the resulting set of undominated alternatives is always non-empty even if indifference is allowed. We show that it may be unduly large. Next, by assuming that other voters along a chain of votes are also rational, that is, they also look forward to make sure that the votes taking place later on will not lead to a worst issue for them, we are able to reduce the size of this set while insuring its non-emptiness. Finally, we show that a vote with sufficient foresight satisfies a no-regret property, contrarily to the classical core and the stability set.     

The effect of ideology on policy outcomes in proportional representation systems

In this paper we propose a model in which there are ideological and strategic voters who vote under proportional rule. We prove that the behavior of ideological voters matters for the determination of the outcome. We show that a subset of strategic voters partially counteracts the votes of the ideological voters.     

A mathematical model for estimating the potential margin of state undecided voters for a candidate in a US Federal election

A US Federal election in which candidates from two major political parties compete for the votes of those undecided voters in a state who usually do not vote in US elections is considered. A mathematical model for evaluating the expectation of the margin of votes to be received from such voters by either candidate as a result of the election campaigns of all the competing candidates is proposed. On the basis of this model, finding the estimation under consideration is reducible to finding the minimum of the maximin function of the difference of two bilinear functions with one and the same first vector argument whose second vector arguments belong to a polyhedron of connected variables (strategies of the candidates), and this minimum is sought on another polyhedron.     

网页排序中的随机模型及算法

随着互联网规模的日益增长, 搜索引擎已经成为互联网上有效的信息获取工具. 而在众多搜索引擎的背后, 是信息检索技术, 也即网页排序算法在起作用. 网页排序包括重要性排序和相关性排序. 通过我们研究发现, 尽管这两类排序所依据的准则不同, 但是都可以通过建立适当的随机过程模型来研究. 对于网页重要性排序, 我们通过分析用户浏览网页的行为建立了Markov 骨架过程的框架. 基于该框架我们分析了三种不同的随机过程模型对用户行为模拟的合理程度, 并设计了名为BrowseRank 的一组新算法, 该算法可以根据用户上网行为来计算网页的重要性. 在网页相关性排序中, 我们主要针对排序结果联合问题建立了一个基于Markov 链的监督学习框架. 通过将传统方法的监督化, 使原来难于解决的问题变的易于学习, 将原来的NP- 难问题转化为一个半正定规划问题, 提高了效率.     

Parametric vs. divisor methods of apportionment

This paper formulates a new criterion that distinguishes the set of parametric methods within the set of all the divisor methods of apportionment. The criterion—that a method transfer seats as it “should”—asks that as population (or the votes of parties in a PR system) is shifted more and more from one state to another state (from one party to another party) at some point the first state (or party) is apportioned one less seat, the second state (or party) one more seat, and the remaining apportionments are as they were. It goes on to examine several properties of parametric methods.     

On the feasibility of applying capture–recapture experiments for web evolution estimations

This paper proposes a novel application for estimating the size and evolution of web page populations, based on the capture–recapture methodology, which is mainly used in wildlife biological studies. Firstly, we present the necessary modifications and amendments needed for the web capture–recapture paradigm, and then we discuss the limitations confronted. The paper provides the implementation details of the proposed web capture recapture model along with its initial assessment. The anticipated outcome was to examine whether we can conduct capture–recapture experiments on the web (or a web sub-universe such as an Internet search engine directory), in order to further estimate evolution rates in web page populations.