Generalized discrete discrepancy and its applications in experimental designs

In recent years, there has been increasing interest in the study of discrete discrepancy. In this paper, the popular discrete discrepancy is extended to the so-called generalized discrete discrepancy. Connections among generalized discrete discrepancy and other optimality criteria, such as orthogonality, generalized minimum aberration and minimum moment aberration, are investigated. These connections provide strong statistical justification of generalized discrete discrepancy. A lower bound of generalized discrete discrepancy is also obtained, which serves as an important benchmark of design uniformity.     

再论语素融合说问题

语素融合说长期流行,但至今无人为它寻得可靠的证据。持语素融合说者多以孤立的观点看问题,不计成词信息;偏执共时论,割断历史;趋从现行理论,误解语言事实。上述事实均表明语素融合说不成立。     

Column generation with free replicability in DEA

The evaluation of efficiency scores in data envelopment analysis is based on the construction of artificial decision making units subject to some assumptions, usually requiring convexity of the production possibility set. This demands divisibility in input and output, which is not always possible. The so-called free replicability model, proposed by Henry Tulkens, permits input and output to enter in only discrete amounts. The model is of a mixed integer programming type, for which the number of variables, here corresponding to the decision making units, may be critical in order to reach an optimal solution.     

基于词素构词规律的大学英语词汇教学研究

以传授词汇知识为重心的传统的词汇教学方式是造成大学生记忆词汇无方的主要原因,这已经引起了众多英语教师的关注,成为一个亟待解决的问题。词素构词是一种全新的构词理念,指的是所有单词都是由一个或一个以上的词素构成的,探讨词素构词规律及其在大学英语词汇教学中的作用能为词汇教学改革提供新的视角与启示。     

汉字性质研究综述

关于汉字的性质历来说法各异,概括起来,大体分为表意文字、语素文字和表音节的表音文字三大类。依据汉字发展到现阶段的实际情况,可将其归结为一种表意性的记号文字。     

释“铜斤”

“铜斤”一词多数词典未收,《汉语大词典》虽作了收录但释义错误,且仅有孤证。结合书证的上下文及其他相关书证,从构词法角度对“铜斤”一词进行深入分析可知：“铜斤”是一个名量式复音词,意为“一定数量的铜”,表示的是复数或者集体的概念,属于泛称。其中,“斤”只是一个量词语素做词缀,没有实际的词汇意义。这一用法最晚产生于宋代,在清代很常见,一直延用到民国时期才消失。     

A Lagrangian relaxation approach for the multiple sequence alignment problem

We present a branch-and-bound (bb) algorithm for the multiple sequence alignment problem (MSA), one of the most important problems in computational biology. The upper bound at each bb node is based on a Lagrangian relaxation of an integer linear programming formulation for MSA. Dualizing certain inequalities, the Lagrangian subproblem becomes a pairwise alignment problem, which can be solved efficiently by a dynamic programming approach. Due to a reformulation w.r.t. additionally introduced variables prior to relaxation we improve the convergence rate dramatically while at the same time being able to solve the Lagrangian problem efficiently. Our experiments show that our implementation, although preliminary, outperforms all exact algorithms for the multiple sequence alignment problem. Furthermore, the quality of the alignments is among the best computed so far.     

Optimal Berry–Esseen bound for parameter estimation of SPDE with small noise

We investigate a rate of convergence on asymptotic normality of the maximum likelihood estimator (MLE) for parameter $\theta$ appearing in parabolic SPDEs of the form

$d{u}^{?}(t,x)=(A_0+\theta A_1)u^{?}(t,x)dt+?dW(t,x),$

where $A_0$ and$A_1$ are partial differential operators, $W$ is a cylindrical Brownian motion (CBM) and $?\downarrow 0$. We find an optimal Berry–Esseen bound for central limit theorem (CLT) of the MLE. It is proved by developing techniques based on combining Malliavin calculus and Stein’s method.     

Computing the conditional stationary distribution in Markov chains of level-dependent M/G/1-type

This paper considers the computation of the conditional stationary distribution in Markov chains of level-dependent M/G/1-type, given that the level is not greater than a predefined threshold. This problem has been studied recently and a computational algorithm is proposed under the assumption that matrices representing downward jumps are nonsingular. We first show that this assumption can be eliminated in a general setting of Markov chains of level-dependent G/G/1-type. Next we develop a computational algorithm for the conditional stationary distribution in Markov chains of level-dependent M/G/1-type, by modifying the above-mentioned algorithm slightly. In principle, our algorithm is applicable to any Markov chain of level-dependent M/G/1-type, if the Markov chain is irreducible and positive-recurrent. Furthermore, as an input to the algorithm, we can set an error bound for the computed conditional distribution, which is a notable feature of our algorithm. Some numerical examples are also provided.