Representation Theorems for the Sequences of the Classes CRc and ERc

We prove two representation theorems in the Bojanic–Seneta sense for the classes CR _c and ER _c of O-regularly varying sequences.     

An Algorithm for a Letter-Based Representation of All-Pairwise Comparisons

All-pairwise comparisons among a set of t treatments or groups are one of the most frequent tasks in applied statistics. Users of statistical software are accustomed to the familiar lines display, in which treatments that do not differ significantly, are connected by a common line or letter. Availability of the lines display is restricted mainly to the balanced analysis of variance setup. This limited availability is at stark variance with the diversity of statistical methods and models, which call for multiple comparisons. This article describes a general method for graphically representing any set of t(t?1)/2 all-pairwise significance statements (p values) for t treatments by a familiar letter display, which is applicable regardless of the underlying data structure or the statistical method used for comparisons. The method reproduces the familiar lines display in case of the balanced analysis of variance. Its broad applicability is demonstrated using data from an international multienvironment wheat yield trial and from a fish catching survey.     

Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems

Let m ≥ 1 be an integer and N > 2m. Let μ be a positive Radon measure on . We study necessary and sufficient conditions on possible distributional solutions of , that guarantee the validity of the representation formula a.e. on , where and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities and weighted form of Hardy-Littlewood-Sobolev systems of integral equations. Received: March 2008     

A Tale of Two Airports: Exploring Flight Traffic at SFO and OAK

Tackling the airline on-time performance data from the Data Expo 2009 can be intimidating due to its unwieldy size. This paper demonstrates that concentrating on small subsets of the data can still reveal interesting stories. I explore flight traffic at two of the San Francisco Bay Area’s major airports. Simple graphical methods raise questions about differences between San Francisco International (SFO) and Oakland International (OAK) airport. Oakland International airport suffers a much lesser drop in traffic after September 11, 2001. This is found to be a consequence of Southwest Airlines accounting for most of the traffic out of OAK, the only carrier to maintain its flight volume after September 11. This article has supplementary material online.     

A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data

In this paper we consider the TJW product-limit estimatorF_n(x) of an unknown distribution functionFwhen the data are subject to random left truncation and right censorship. An almost sure representation of PL-estimatorF_n(x) is derived with an improved error bound under some weaker assumptions. We obtain the strong approximation ofF_n(x)−F(x) by Gaussian processes and the functional law of the iterated logarithm is proved for maximal derivation of the product-limit estimator toF. A sharp rate of convergence theorem concerning the smoothed TJW product-limit estimator is obtained. Asymptotic properties of kernel estimators of density function based on TJW product-limit estimator is given.     

Multiple Stable Stochastic Integrals: Series Representation and Absolute Continuity of Their Law

We study multiple stable stochastic integrals. We begin with a definition of these integrals using a generalization of the LePage representation as Samorodnitsky et al. in Ref. 15 but with a simplified probabilistic background and for general stable measure when 0<<1 and for symmetric stable measure when 1<2. This representation allows to study the law of multiple stable integrals. We prove they are absolutely continuous using a stratification method on the Skorokhod space on which we have previously taken back the problem.     

Simple Formulae for the Number of Quadrics and Symmetric Forms of Modules Over Local Rings

Simple formulae of similar type for the number of quadrics and symmetric forms of modules over local rings are found analytically. This simplification of known formulae of Levchuk and Starikova is achieved using integral representation method of combinatorial summation and leads to number-theoretical identities of new type. The problem of algebraic interpretation of new formulae is posed.     

Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems

This paper is devoted to the study ofthe existence of single and multiple positive solutions forthe first order boundary value problem x′= f(t,x),x(0)=x(T),where f ∈ C([0,T]×R).In addition,weapply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at theorigin.Our proofs are based on a fixed point theorem in cones.Our results improve some recent results in theliteratures.     

Superheat: An R Package for Creating Beautiful and Extendable Heatmaps for Visualizing Complex Data

The technological advancements of the modern era have enabled the collection of huge amounts of data in science and beyond. Extracting useful information from such massive datasets is an ongoing challenge as traditional data visualization tools typically do not scale well in high-dimensional settings. An existing visualization technique that is particularly well suited to visualizing large datasets is the heatmap. Although heatmaps are extremely popular in fields such as bioinformatics, they remain a severely underutilized visualization tool in modern data analysis. This article introduces superheat, a new R package that provides an extremely flexible and customizable platform for visualizing complex datasets. Superheat produces attractive and extendable heatmaps to which the user can add a response variable as a scatterplot, model results as boxplots, correlation information as barplots, and more. The goal of this article is two-fold: (1) to demonstrate the potential of the heatmap as a core visualization method for a range of data types, and (2) to highlight the customizability and ease of implementation of the superheat R package for creating beautiful and extendable heatmaps. The capabilities and fundamental applicability of the superheat package will be explored via three reproducible case studies, each based on publicly available data sources.     

单输入多时滞离散系统的线性二次调节问题

研究了单输入多时滞的离散时间系统的线性二次调节问题(LQR问题),给出了求解最优控制输入序列的一种简单有效而又新颖的方法.将该动态的离散时滞系统的LQR最优控制问题最终转化成了一个静态的、不带时滞的数学规划模型——带等式线性约束的严格凸二次规划问题,并利用两种方法解这个二次规划问题,均成功地导出了系统的最优控制输入序列.仿真结果验证了我们的方法的正确有效性.     

Polyharmonic splines: An approximation method for noisy scattered data of extra-large size

The aim of this paper is to provide a fast method, with a good quality of reproduction, to recover functions from very large and irregularly scattered samples of noisy data, which may present outliers. To the given sample of size N, we associate a uniform grid and, around each grid point, we condense the local information given by the noisy data by a suitable estimator. The recovering is then performed by a stable interpolation based on isotropic polyharmonic B-splines. Due to the good approximation rate, we need only M?N degrees of freedom to recover the phenomenon faithfully.     

财经新闻与股市预测——基于数据挖掘技术的实证分析

本研究深度挖掘了财经新闻主题内容与股市市场的相关性,并提出了一种基于理解当日新闻主题分布来分析中国股市涨跌的预测模型。具体来说,我们使用自动文本分析技术与机器学习技术,首先通过概率主题模型对财经新闻文档进行聚类得到其中的主题分布,再结合实际股票市场的交易数据分析其与市场之间的关联程度,最后引入支持向量机算法对股市走势进行预测。实验部分我们抽取了近三个月的新闻数据与沪深股市数据进行分析,结果表明:新闻中国际贸易以及城市化相关主题与股市变动关系密切,通过本文提出的算法能较准确得预测当日股市涨跌,而建立在其上的股指期货策略也取得了很好的效果。     

大学生就业扶持政策的有效性分析及改进:基于DEA方法的实证分析

鉴于数据包络分析(DEA)方法在评价多输入、多输出系统相对有效性方面所具有的优越性,基于DEA方法构建了C2R模型及相应投影分析模型和评价指标体系,对1999-2008年中国所实行的大学生就业扶持政策的有效性进行了评价分析,实证分析结果表明1999-2002年的大学生就业扶持政策在促进和解决大学生就业方面的效果显著,而2003年以后的大学生就业扶持政策在解决大学生就业问题上存在明显的效率损失,且政策效果逐年下降.为了提高大学生就业扶持政策的实施效果,就业扶持政策在未来的改进重点应着力从财政补贴、高等教育经费投入和贷款补助等政策内容入手,并提高政策的执行力度.     

Iteratively Reweighted Generalized Least Squares for Estimation and Testing With Correlated Data: An Inference Function Framework

The focus of this article is on fitting regression models and testing of general linear hypotheses for correlated data using quasi-likelihood based techniques. The class of generalized method of moments or GMMs provides an elegant approach for estimating a vector of regression parameters from a set of score functions. Extending the principle of the GMMs, in the generalized estimating equation framework, leads to a quadratic inference function or QIF approach for the analysis of correlated data. We derive an iteratively reweighted generalized least squares or IRGLS algorithm for finding the QIF estimator and establish its convergence properties. A software library implementing the techniques is demonstrated through several datasets.     

A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications

The system of partial differential equations

人口、资源、环境对经济发展的影响——基于我国省区面板数据的实证分析

基于我国30个省区12年的面板数据,构建了包含人口、资源、环境等多个自然、社会因素在内的个体固定效应模型,以研究人口、资源、环境对经济发展的影响.实证分析结果表明,高素质健康人口、节约型发展方式有助于推动经济发展.现阶段我国的经济增长伴随着环境污染的持续恶化,是以破坏环境为代价的,因此必须重视调控环境与经济之间的平衡.解决好人口资源环境与经济发展的矛盾,坚持可持续发展道路是我国经济健康稳定发展的必然要求.     

Asymptotic Properties of a Class of Mixture Models for Failure Data: The Interior and Boundary Cases

We analyse an exponential family of distributions which generalises the exponential distribution for censored failure time data, analogous to the way in which the class of generalised linear models generalises the normal distribution. The parameter of the distribution depends on a linear combination of covariates via a possibly nonlinear link function, and we allow another level of heterogeneity: the data may contain "immune" individuals who are not subject to failure. Thus the data is modelled by a mixture of a distribution from the exponential family and a "mass at infinity" representing individuals who never fail. Our results include large sample distributions for parameter estimators and for hypothesis test statistics obtained by maximising the likelihood of a sample. The asymptotic distribution of the likelihood ratio test statistic for the hypothesis that there are no immunes present in the population is shown to be "non-standard"; it is a 50-50 mixture of a chi-squared distribution on 1 degree of freedom and a point mass at 0. Our analysis clearly shows how "negligibility" of individual covariate values and "sufficient followup" conditions are required for the asymptotic properties.     

Optimal policies for inventory systems with two types of product sharing common hardware platforms: Single period and finite horizon

In this paper, we consider an inventory system whose products share a common hardware platform but are differentiated by two types of software. Choice of different software results in different installation cost and different selling price of the whole product. Product with different software also faces different customer demand. We investigate the optimal proportion of an order to be installed with software 1 or 2, that maximizes expected profit in the single and multiple period scenarios, respectively. The optimal policy is analytically obtained and proved to be an order-up-to policy in each scenario. Our investigation reveals that whether to replenish, and how much to replenish each product depend not only on its own initial inventory level, and system parameters, but also the initial inventory level of the other product. We perform numerical experiments using the optimal policies we have derived in the paper.     

A joint measurement of efficiency and effectiveness for non-storable commodities: Integrated data envelopment analysis approaches

Efficiency and effectiveness for non-storable commodities represent two distinct dimensions and a joint measurement of both is necessary to fully capture the overall performance. This paper proposes two novel integrated data envelopment analysis (IDEA) approaches, the integrated Charnes, Cooper and Rhodes (ICCR) and integrated Banker, Charnes and Cooper (IBCC) models, to jointly analyze the overall performance of non-storable commodities under constant and variable returns to scale technologies. The core logic of the proposed models is simultaneously determining the virtual multipliers associated with inputs, outputs, and consumption by additive specifications for technical efficiency and service effectiveness terms with equal weights. We show that both ICCR and IBCC models possess the essential properties of rationality, uniqueness, and benchmarking power. A case analysis also demonstrates that the proposed novel IDEA approaches have higher benchmarking power than the conventional separate DEA approaches. More generalized specifications of IDEA models with unequal weights are also elaborated.     

Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: An Orlicz-Sobolev space setting

We study the boundary value problem −div(log(1+q|∇u|)|∇u|^p−2∇u)=f(u) in Ω, u=0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary. We distinguish the cases where either f(u)=−λ|u|^p−2u+|u|^r−2u or f(u)=λ|u|^p−2u−|u|^r−2u, with p, q>1, p+q<min{N,r}, and r<(Np−N+p)/(N−p). In the first case we show the existence of infinitely many weak solutions for any λ>0. In the second case we prove the existence of a nontrivial weak solution if λ is sufficiently large. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces.