Robust principal component analysis for compositional tables

A data table arranged according to two factors can often be considered a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant information consists of ratios between different cells of such a table. This is particularly useful when analyzing several compositional tables jointly, where the absolute numbers are in very different ranges, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and orthonormal coordinates can be assigned to these parts. However, these coordinates usually require some prior knowledge about the data, and they are not easy to handle for exploring the relationships between the given factors. Here we propose a special choice of coordinates with direct relation to centered logratio (clr) coefficients, which are particularly useful for an interpretation in terms of the original cells of the tables. With these coordinates, robust principal component analysis (rPCA) is performed for dimension reduction, allowing to investigate relationships between the factors. The link between orthonormal coordinates and clr coefficients enables to apply rPCA, which would otherwise suffer from the singularity of clr coefficients.     

On the Exact Hazard and Survival Functions of the MVK Stochastic Carcinogenesis Model

The MVK two-stage carcinogenesis model is one of the most widely accepted mechanistic models in carcinogenesis modeling. However, due to a perceived difficulty in obtaining analytic solutions for the hazard and survival functions, approximations and numerical methods have been used to calculate these two fundamental quantities. This paper focuses on a special case of the homogeneous MVK model where the number of normal cells is constant. The probability generating function (pgf) for the number of tumor cells is derived, and the exact analytic solutions to the hazard and survival functions are obtained from the pgf.     

非对称信息下网络广告价格均衡分布研究

网络广告正以迅雷不及掩耳的姿态席卷全球,成为当今最为热门的广告宣传形式。网络广告的传播形式尽管不一,但都是向消费者传递产品信息,消除厂商与消费者之间的信息不对称。网络广告价格和产品销售价格的均衡分析能为企业进行网络广告投资和从事电子商务等商业活动提供理论依据。     

C~n中单位多圆柱上一类强星形映射齐次展开式第四项的精确估计

本文主要在Cn中单位多圆柱上建立一类强星形映射齐次展开式第四项的精确估计,所得结果揭示多复变数中关于一类强星形映射齐次展开式第四项的Bieberbach猜想成立.从而深化了多复变数已有结果.     

中国内地动漫产业与港澳台未成年人关系研究

中国内地的动漫产业不仅对内地未成年人产生影响,同时也作用于港澳台未成年人。港澳台未成年人可分为三个层次,本文将针对港澳台未成年人同质文化圈这一层次进行研究,在与内地相比较的情况下,对港澳台地区未成年人的文化环境和文化心理结构进行分析。并结合港澳台动漫产业发展情况,探讨内地动漫产业对港澳台未成年人的影响。     

Some properties of clasical multi-dimesional scaling

The paper gives a new optimal property of the classical method of multi-dimensional scaling when the distance matrix is non-Euclidean. We also examine robustness of the method under a linear model. A technique to estimate missing values is also given.     

区间灰数序列的白化方法及其性质研究

由于灰代数运算体系尚不完善,难以有效构建基于灰数序列的灰色模型,而传统灰数序列的白化方法又将导致信息损失,故在不破坏区间灰数独立性及信息完整性的前提下,设计一种区间灰数序列白化处理的新方法,重点研究白化序列与原区间灰数序列在平移变换及倍乘变换过程中的数据特点;同时将白化序列成功地应用于区间灰数预测及关联分析模型的构建。这一研究成果对拓展灰色模型的适用范围具有重要意义。     

Computation of multivariate normal probabilities with polar coordinate systems

We consider the problem of evaluation of the probability that all elements of a multivariate normally distributed vector have non-negative coordinates; this probability is called the non-centred orthant probability. The necessity for the evaluation of this probability arises frequently in statistics. The probability is defined by the integral of the probability density function. However, direct numerical integration is not practical. In this article, a method is proposed for the computation of the probability. The method involves the evaluation of a measure on a unit sphere surface in p-dimensional space that satisfies conditions derived from a covariance matrix. The required computational time for the p-dimensional problem is proportional to p²·2^p?1, and it increases at a rate that is lower than that in the case of the existing method.     

广州市产业结构与就业结构的协调性分析

研究了高速列车与厦深铁路韩江大桥(48+2×80+88+48) m道岔连续梁的空间耦合振动中的桥梁响应问题。以模态坐标法形成结构的动力方程,适用SAP2000形成基本振型并由此获得振型参数,利用Matlab软件编写求解程序,得到了道岔连续梁动力响应的一些成果。