On Approximate Graph Colouring and MAX-k-CUT Algorithms Based on the θ-Function

The problem of colouring a k-colourable graph is well-known to be NP-complete, for k 3. The MAX-k-CUT approach to approximate k-colouring is to assign k colours to all of the vertices in polynomial time such that the fraction of `defect edges' (with endpoints of the same colour) is provably small. The best known approximation was obtained by Frieze and Jerrum (1997), using a semidefinite programming (SDP) relaxation which is related to the Lovász -function. In a related work, Karger et al. (1998) devised approximation algorithms for colouring k-colourable graphs exactly in polynomial time with as few colours as possible. They also used an SDP relaxation related to the -function.In this paper we further explore semidefinite programming relaxations where graph colouring is viewed as a satisfiability problem, as considered in De Klerk et al. (2000). We first show that the approximation to the chromatic number suggested in De Klerk et al. (2000) is bounded from above by the Lovász -function. The underlying semidefinite programming relaxation in De Klerk et al. (2000) involves a lifting of the approximation space, which in turn suggests a provably good MAX-k-CUT algorithm. We show that of our algorithm is closely related to that of Frieze and Jerrum; thus we can sharpen their approximation guarantees for MAX-k-CUT for small fixed values of k. For example, if k = 3 we can improve their bound from 0.832718 to 0.836008, and for k = 4 from 0.850301 to 0.857487. We also give a new asymptotic analysis of the Frieze-Jerrum rounding scheme, that provides a unifying proof of the main results of both Frieze and Jerrum (1997) and Karger et al. (1998) for k 0.     

Cohabitation and Marriage in a Risky World

Different couples are analyzed in presence of income uncertainty and precautionary saving. Married couples have legal restrictions on their relationship that force them to act cooperatively, while cohabitants with limited commitment act non-cooperatively. This makes risk sharing different for different couples; married couples share risk completely, while cohabitants share risk to a lesser extent due to their lack of commitment and cooperation. This makes precautionary savings greater for cohabitants than for married couples. However, cohabitants also tend to undersave to possibly increase assistance from their partner. However, mutual altruism mitigates the inefficiencies and enforces time consistent risk sharing among cohabitants.I am thankful to Jonas Agell, Sophia Grahn-Voorneveld, Peter Kooreman and to Mats Persson for valuable comments on an earlier version. I have also received useful comments from the editor and from two anonymous referees. Generous financial support from the Jan Wallander and Tom Hedelius Foundation and from Knut and Alice Wallenbergs Foundation is gratefully acknowledged.     

关于亚纯p叶函数的新子类

引进和研究亚纯ｐ叶函数的新子类Ｔｎ,ｐ（Ａ,Ｂ）和Ｔ＊ｎ,ｐ（Ａ,Ｂ）,建立了包含关系,讨论了类中函数的积分变换等性质,对类Ｔ＊ｎ,ｐ（Ａ,Ｂ）确定了系数不等式、偏差定理、亚纯凸性半径与卷积性质     

交易量和交易量驱动的股价动力学分析方法

近20 年来, 理论界开始更加注重交易量在研究中的重要作用, 特别是从信息的角度出发, 研究者相信交易量能提供独立于股票价格之外的信息. 但是如何将交易量合适地融入价格序列中仍然是一个争论的话题. 本文系统地回顾了国内外有关交易量的研究现状, 指出由于累计交易量是时间的单调增函数, 与时间相比, 交易量不仅包含有时间价值因素, 而且还包含了交易成本等信息价值因素. 随后本文提出了交易量驱动的价格变化的研究思想. 在此基础上给出了基于交易量进程的股价动力学分析方法以及两种构造交易量进程的股价序列方法, 指出在日历时间假设下的时间序列和在交易时间假设下的时间序列是交易量进程假设的特例. 通过随机选择18 个股票的实证研究初步表明, 在更低的阶数或更少的参数情况下, 本模型具有更高的拟合精度和解释能力.     

无外部市场条件下中间产品转移价格的研究

系统地讨论了不存在外部市场条件下中间产品最优转移价格的确定方法. 首先在各分厂 成本函数和最终产品需求函数已知条件下, 分别讨论了各分厂产量相同和产量不同情形下中 间产品最优转移价格的确定问题. 接着讨论了各分厂成本函数和最终产品需求函数未知条件 下中间产品转移价格的确定问题. 本文提出的三种确定中间产品转移价格的方法均给出了具 体的计算公式, 具有较大的理论价值和应用价值.     

基于流程图及过程代数的流程表达方法

提出一种新的用于BPR 的业务流程表达方法. 首先用基于活动属性的流程图来描述业 务流程; 再利用图论的矩阵分析方法描述流程图; 然后结合过程代数的方法, 由流程图的矩阵 推导出一个能全面反映流程情况的代数表达式——过程代数式; 最后通过对过程代数式的分 析, 提出流程的评价指标.     

信息技术项目产权结构及其管理模式的研究

基于Hart 产权理论, 应用两阶段博弈模型分析信息技术外包过程, 研究信息技术资产属 性、投资效用、人力资本属性对信息技术项目产权结构的影响. 公司根据资源重要性选择信息 技术外包的组织形式和产权结构, 控制被忽略的资产及其属性的负面作用, 特别是在外包过程 中应当充分考虑外包商人力资源管理和人力资源的稳定性. 证明了任何一方都应将投资用于 自己擅长的专业上, 任何信息技术项目产权结构都导致专用性投资不足, 产权结构选择是各种 产权结构的平衡, 关键问题是如何改进双边治理的低投资边际效益.     

A Three‐step Method for Choosing the Number of Bootstrap Repetitions

This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests, p‐values, and bias correction. For each of these problems, the paper provides a three‐step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval length, test's critical value, test's p‐value, or bias‐corrected estimate based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B=∞. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals. Monte Carlo simulations show that the proposed methods work very well.     

A Simple Analysis of the Exact Probability Matching Prior in the Location-Scale Model

It has long been asserted that in univariate location-scale models, when concerned with inference for either the location or scale parameter, the use of the inverse of the scale parameter as a Bayesian prior yields posterior credible sets that have exactly the correct frequentist confidence set interpretation. This claim dates to at least Peers, and has subsequently been noted by various authors, with varying degrees of justification. We present a simple, direct demonstration of the exact matching property of the posterior credible sets derived under use of this prior in the univariate location-scale model. This is done by establishing an equivalence between the conditional frequentist and posterior densities of the pivotal quantities on which conditional frequentist inferences are based.     

清代虞山诗派的创作气局

虞山诗派是清代的一个重要的诗歌创作群体。诗人们继承杜甫诗史传统,具有忧世意识。创作上或出入宋元,以博学为宗,表现出学人气度;或法乳温李,以西昆体为理想范式。虽各树法幢,不遵一轨,但无论钱、冯,亦或流裔,都能在诗学观念和审美取向上异中求同,交互兼容,从而形成了特有的诗派创作气局。