Strong approximations of the quantile process of the product-limit estimator

The quantile process of the product-limit estimator (PL-quantile process) in the random censorship model from the right is studied via strong approximation methods. Some almost sure fluctuation properties of the said process are studied. Sections 3 and 4 contain strong approximations of the PL-quantile process by a generalized Kiefer process. The PL and PL-quantile processes by the same appropriate Kiefer process are approximated and it is demonstrated that this simultaneous approximation cannot be improved in general. Section 5 contains functional LIL for the PL-quantile process and also three methods of constructing confidence bands for theoretical quantiles in the random censorship model from the right.     

Using two successive subgradients in the ellipsoid method for nonlinear programming

A variant of the ellipsoid method for nonlinear programming is introduced to enhance the speed of convergence. This variant is based on a new simple scheme to reduce the ellipsoid volume by using two center cuts generated in two consecutive iterations of the ellipsoid method. Computational tests show a significant improvement in computational efficiency. The tests show that the improvement is more significant for larger-size problems.     

Reduced-rank regression for the multivariate linear model

The problem of estimating the regression coefficient matrix having known (reduced) rank for the multivariate linear model when both sets of variates are jointly stochastic is discussed. We show that this problem is related to the problem of deciding how many principal components or pairs of canonical variates to use in any practical situation. Under the assumption of joint normality of the two sets of variates, we give the asymptotic (large-sample) distributions of the various estimated reduced-rank regression coefficient matrices that are of interest. Approximate confidence bounds on the elements of these matrices are then suggested using either the appropriate asymptotic expressions or the jackknife technique.     

Influence of ring position on the temporal dependence of charge movement in a switchable [2]rotaxane

Switchable mechanically interlocked molecular architectures (MIMAs) are promising candidates for the components of nanoscale devices. An example of a MIMA-based switch used in nanoscale devices is the electrochemically switchable Stoddart-Heath-type [2]rotaxane. This system's two coconformations differ in electrical conductance, a feature that has been harnessed for electronic and information storage applications. Herein we study the flow of charge in two coconformations of a bistable Stoddart-Heath-type [2]rotaxane and report statistical predictions of electron transfer times using a probabilistic approach for characterizing the timescale of quantum particle transit. The ratio of predicted transfer times for the two coconformations is consistent with the experimentally reported difference in electrical conductance. Path information offered by the probabilistic method gives insight into the influence of ring position on the mechanism of electron transit in this mechanically interlocked assembly.     

CONSENSUS FORMATION OF TWO-LEVEL OPINION DYNAMICS

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or(1- α)d, where α∈(0, 1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound dc = 1/(4α) for the two-level opinion dynamics on Z. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold dc increases with α but does not depend on p.     

星间激光比对GPS相对定位精度数据量确定方法

针对星间激光比对GPS相对定位精度结果的精确性和可信度问题,研究了星间激光比对GPS相对定位精度数据量的确定方法;运用数理统计方法推导了相对误差、置信水平和数据量之间的概率不等式;为实现激光比对结果的精确性、可信度和数据量选取的综合权衡提供了量化分析手段,仿真结果验证了该方法的正确性和有效性.     

关于洛伦兹曲线和基尼系数的统计推断

本文对于洛伦兹曲线的最一般定义,在无任何附加限制条件下,论证了基于样本数据所得到的洛仑兹曲线的通常估计量具有强相合性.在此基础上,证明了基尼系数和Schutz系数的通常估计量均具有强相合性.此外,导出了基尼系数估计量的渐进分布,并在此基础上给出了大样本情形下基尼系数的置信区间.     

20 Ne(34 Ne)原子与18 Na2(23 Na2,37 Na2)分子低温下冷碰撞的同位素效应研究

本文用多体刚性椭球模型计算了相对入射能量为190 meV时,氖的同位素原子²⁰Ne,³⁴Ne与钠的同位素分子¹⁸Na₂,²³Na₂,³⁷Na₂ 替代碰撞体系的态态转动激发积分散射截面和总转动激发积分散射截面,在此基础上计算并分析了相互作用势的不同区域对²⁰Ne-¹⁸Na_{2关键词： 多体刚性椭球模型 转动激发积分散射截面 钠同位素分子 椭球等势面}     

Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

The paper is devoted to solving the two‐stage problem of stochastic programming with quantile criterion. It is assumed that the loss function is bilinear in random parameters and strategies, and the random vector has a normal distribution. Two algorithms are suggested to solve the problem, and they are compared. The first algorithm is based on the reduction of the original stochastic problem to a mixed integer linear programming problem. The second algorithm is based on the reduction of the problem to a sequence of convex programming problems. Performance characteristics of both the algorithms are illustrated by an example. A modification of both the algorithms is suggested to reduce the computing time. The new algorithm uses the solution obtained by the second algorithm as a starting point for the first algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

旋转椭球形电容器的静电能

利用复数坐标系z上的儒可夫斯基变换,计算带电旋转椭球形电容器的静电能,并对结果进行了讨论.