Approximation algorithms for connected facility location problems

We study Connected Facility Location problems. We are given a connected graph G=(V,E) with nonnegative edge cost c _e for each edge e∈E, a set of clients D⊆V such that each client j∈D has positive demand d _j and a set of facilities F⊆V each has nonnegative opening cost f _i and capacity to serve all client demands. The objective is to open a subset of facilities, say , to assign each client j∈D to exactly one open facility i(j) and to connect all open facilities by a Steiner tree T such that the cost is minimized for a given input parameter M≥1. We propose a LP-rounding based 8.29 approximation algorithm which improves the previous bound 8.55 (Swamy and Kumar in Algorithmica, 40:245–269, 2004). We also consider the problem when opening cost of all facilities are equal. In this case we give a 7.0 approximation algorithm.     

The power functions of the likelihood ratio tests for a simple tree ordering in normal means: unequal weights

Likelihood ratio tests are considered for two testing situations; testing for the homogeneity of k normal means against the alternative restricted by a simple tree ordering trend and testing the null hypothesis that the means satisfy the trend against all alternatives. Exact expressions are given for the power functions for k = 3 and 4 and unequal sample sizes, both for the case of known and unknown population variances, and approximations are discussed for larger k. Also, Bartholomew’s conjectures concerning minimal and maximal powers are investigated for the case of equal and unequal sample sizes. The power formulas are used to compute powers for a numerical example.     

The Rise of Statistical Phylogenetics

This paper provides a review of the many applications of statistics within the field of phylogenetics, that is, the study of evolutionary history. The reader is assumed to be a statistician rather than a phylogeneticist, so some background is given on what phylogenetics is, along with a brief history of different approaches to phylogenetic inference. The latter half of the paper focuses on a series of open statistical problems in the field with the aim of encouraging more statisticians to engage with this fascinating area of research.     

Hip fracture prediction from a new classification algorithm based on recursive partitioning methods

Classification and regression tree has been useful in medical research to construct algorithms for disease diagnosis or prognostic prediction. Jin et al. 7 Jin, H., Lu, Y., Harris, R. T., Black, D., Stone, K., Hochberg, M. and Genant, H. 2004. Classification algorithms for hip fracture prediction base on recursive partitioning methods. Med. Decis. Mak., 24: 386–398. (doi:10.1177/0272989X04267009)[Crossref], [PubMed], [Web of Science ®] , [Google Scholar] developed a robust and cost-saving tree (RACT) algorithm with application in classification of hip fracture risk after 5-year follow-up based on the data from the Study of Osteoporotic Fractures (SOF). Although conventional recursive partitioning algorithms have been well developed, they still have some limitations. Binary splits may generate a big tree with many layers, but trinary splits may produce too many nodes. In this paper, we propose a classification approach combining trinary splits and binary splits to generate a trinary–binary tree. A new non-inferiority test of entropy is used to select the binary or trinary splits. We apply the modified method in SOF to construct a trinary–binary classification rule for predicting risk of osteoporotic hip fracture. Our new classification tree has good statistical utility: it is statistically non-inferior to the optimum binary tree and the RACT based on the testing sample and is also cost-saving. It may be useful in clinical applications: femoral neck bone mineral density, age, height loss and weight gain since age 25 can identify subjects with elevated 5-year hip fracture risk without loss of statistical efficiency.     

独立学院人才失效的故障树分析

将人才培养作为一项系统工程,学生不能完成学业视作故障或者失效.应用可靠性理论,从故障树的分析入手,利用布尔代数运算,从独立学院学生、教师、家庭和学校四个方面进行剖析,找出学生不能完成学业的原因,提出促进独立学院学生完成学习任务一系列措施.     

从芭蕉图像看佛教艺术与文人情结

本文以南宋陆信忠《十六罗汉图》中的芭蕉湖石与芭蕉为纸的两个图像为引,分三个侧面论述芭蕉在中国文化史和艺术史上的意义传递,以及这种传递过程中所展现的佛教寓意与文人情怀、文字与图像的互动关系。芭蕉湖石和芭蕉为纸书的典故,经由佛典的隐喻转入文人书写,最终回归到佛教题材的《十六罗汉图》的图像中,在这一流传的脉络中,芭蕉的意义被复制、更变和选择,但不变的,是文人对于生命真义的诉求。     

“桐枝·桐孙·疏桐”意象考论

桐枝是凤凰、禽鸟的栖息之所。秋冬之际,桐枝高耸,与风雪摩戛、抗争。梧桐易生速长,树围逐年而增,桐枝也不断叉生,梧桐与桐枝是岁月流年的标记。桐孙是桐枝的别名。梧桐在古代被冠以柔木、阳木等美名,桐枝挺秀、孳蕃,桐孙成为子嗣之美称：桐孙木质坚实,是上佳的琴材。梧桐阔叶疏枝,从六朝到宋朝,疏桐寒井、疏桐寒鸟、疏桐缺月的意象组合模式递相出现。     

用于分类的随机森林和Bagging分类树比较

借助试验数据,从两种理论分析角度解释随机森林算法优于Bagging分类树算法的原因。将两种算法表述在两种不同的框架下,消除了这两种算法分析中的一些模糊之处。尤其在第二种分析框架下,更能清楚的看出,之所以随机森林算法优于Bagging分类树算法,是因为随机森林算法对应更小的偏差。     

Multi-step quantile regression tree

Quantile regression (QR) proposed by Koenker and Bassett [Regression quantiles, Econometrica 46(1) (1978), pp. 33–50] is a statistical technique that estimates conditional quantiles. It has been widely studied and applied to economics. Meinshausen [Quantile regression forests, J. Mach. Learn. Res. 7 (2006), pp. 983–999] proposed quantile regression forests (QRF), a non-parametric way based on random forest. QRF performs well in terms of prediction accuracy, but it struggles with noisy data sets. This motivates us to propose a multi-step QR tree method using GUIDE (Generalized, Unbiased, Interaction Detection and Estimation) made by Loh [Regression trees with unbiased variable selection and interaction detection, Statist. Sinica 12 (2002), pp. 361–386]. Our simulation study shows that the multi-step QR tree performs better than a single tree or QRF especially when it deals with data sets having many irrelevant variables.     

决策树优化研究

提出用新的极值点禁忌搜索算法构造分类问题的全局优化决策树,该算法呆用于不可微分的目标函数。全局树优化方法是非贪婪的,用于构造具有固定结构的多变量决策树,将多变量决策树表示成析取线性不等式集合,全局树优化就是使析取线性不等式中的分类误差最小化。