大数据背景下基于社交网络的聚类随机游走抽样算法研究

数字经济时代,社交网络作为数字化平台经济的重要载体,受到了国内外学者的广泛关注。大数据背景下,社交网络的商业应用价值巨大,但由于其网络规模空前庞大,传统的网络分析方法 因计算成本过高而不再适用。而通过网络抽样算法获取样本网络,再推断整体网络,可节约计算资源, 因此抽样算法的好坏将直接影响社交网络分析结论的准确性。现有社交网络抽样算法存在忽略网络内部拓扑结构、容易陷入局部网络、抽样效率过低等缺陷。为了弥补现有社交网络抽样算法的缺陷,本文结合大数据社交网络的社区特征,提出了一种聚类随机游走抽样算法。该方法首先使用社区聚类算法将原始网络节点进行社区划分,得到多个社区网络,然后分别对每个社区进行随机游走抽样获取样本网 络。数值模拟和案例应用的结果均表明,聚类随机游走抽样算法克服了传统网络抽样算法的缺点,能够在降低网络规模的同时较好地保留原始网络的结构特征。此外,该抽样算法还可以并行运算,有效提升抽样效率,对于大数据背景下大规模社交网络的抽样实践具有重大现实意义。     

Measuring agreement between two statistics with applications to age standardization

Summary.  We detail a general method for measuring agreement between two statistics. An application is two ratios of directly standardized rates which differ only by the choice of the standard. If the statistics have a high value for the coefficient of agreement then the expected squared difference between the statistics is small relative to the variance of the average of the two statistics, and inferences vary little by changing statistics. The estimation of a coefficient of agreement between two statistics is not straightforward because there is only one pair of observed values, each statistic calculated from the data. We introduce estimators of the coefficient of agreement for two statistics and discuss their use, especially as applied to functions of standardized rates.     

A modified random-effect procedure for combining risk difference in sets of 2×2 tables from clinical trials

Summary Meta-analyses of sets of clinical trials often combine risk differences from several 2×2 tables according to a random-effects model. The DerSimonian-Laird random-effects procedure, widely used for estimating the populaton mean risk difference, weights the risk difference from each primary study inversely proportional to an estimate of its variance (the sum of the between-study variance and the conditional within-study variance). Because those weights are not independent of the risk differences, however, the procedure sometimes exhibits bias and unnatural behavior. The present paper proposes a modified weighting scheme that uses the unconditional within-study variance to avoid this source of bias. The modified procedure has variance closer to that available from weighting by ideal weights when such weights are known. We studied the modified procedure in extensive simulation experiments using situations whose parameters resemble those of actual studies in medical research. For comparison we also included two unbiased procedures, the unweighted mean and a sample-size-weighted mean; their relative variability depends on the extent of heterogeneity among the primary studies. An example illustrates the application of the procedures to actual data and the differences among the results. This research was supported by Grant HS 05936 from the Agency for Health Care Policy and Research to Harvard University.     

实数域及四元数除环上有平方根的方阵

给出了实数域及实四元数除环上方阵有平方根的充分必要条件．     

Generalized additive models for location, scale and shape

Summary.  A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y , as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton–Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.     

中国传统文化中的"尚三"理念对巴金《家·春·秋》创作的影响

巴金自称是受外国文学影响最多的作家之一,但是中国传统文化对他的创作在无形中的影响恐怕连他自己都没有意识到,在巴金的小说尤其是在长篇小说《家.春.秋》创作中就处处可见"尚三"传统的影响,形成了几种独特的创作现象:三事话语,三复情节,三变情节,三极建构,三而后成,传统文化与外来文化的相互渗透融合,是巴金能够成为文学大师的文化基础。     

几类循环图的分数染色数

通过构造几类图的最大独立集,给出了它们的分数染色数的下界;再通过构造具有该下界值的分数染色,给出了这几类循环图的分数染色数的上界,于是就确定了它们的分数染色数.     

关于广义Ramanujan-Nagell方程解数

设p是奇素数，D是适合p D是正奇数，证明了，当D≠Ap^r-1，其中r是正整数时，方程x^2 D=4p^n至多有1组正整数解（x,n）。     

上市公司综合评价研究

客观合理地评价上市公司,是投资者、上市公司以及监管机构都非常关注的问题,也是规范发展证券市场的一个重要方面。基于平衡记分卡的原理,提出了我国上市公司的评价指标体系。财务层面的评价采用因子分析法;客户层面、内部层面、学习与创新层面以及综合评价,则是根据模糊三角数的概念构造判断矩阵,利用模糊三角数比较大小的原理进行排序。     

k+l色k-饱和图

给出了一类具有较多边数的k+1色k-饱和图(不含K_k,但添加任一边都含K_k的图)的结构。导出了n点最大k+1色k-饱和图的边数的下界。