非均匀的有限信息扩散函数的探索及应用

小样本的信息处理和分析一直是金融、信息、地震灾害等众多领域中的热点问题．本文运用一维非均匀的有限信息扩散函数（GIDM）方法对小样本问题进行处理，并通过应用于一个实际问题来进行验证，首先根据非均匀信息扩散选取扩散函数，并利用McCormack方法求得其数值解。进而按照优化的准则优化后与大样本进行比较，取得了较理想的结果．     

二维非均匀信息扩散及其应用

在风险分析和评估过程中,经常会遇到信息不充分、数据不完备的情况,即小样本问题.本文提出了二维的非均匀信息扩散方法,对小样本进行分析处理,并用于实际项目加以印证.其中非均匀信息扩散方程取(N)/(t)=(N 1)·((~2N)/(x~2) (~2N)/(y~2)),用MacCormack方法进行求解,在两个优化准则下建立优化模型,利用MATLAB编程实现,结果与大样本是一致的.     

小样本信息的研究和应用

基于现实研究中遇到的信息不完备、数据有残缺的情况,利用信息扩散原理进行二维小样本信息的处理、分析并应用于实际项目.采用均匀信息扩散优化处理方法和非均匀信息扩散方法对二维小样本进行探索,结果与大样本处理的结论是一致的;同时对样本点数影响信息扩散结果进行了理论推导.研究表明,小样本数量不会大幅度影响预测结果.     

比估计的两个常用的方差估计量的小样本比较

本文利用冯士雍和邹国华［１］或Ｓｕｎｄｂｅｒｇ［２］提出的比较方差估计量的新准则对比估计的两个常用的方差估计量进行了小样本比较．这是Ｃｏｃｈｒａｎ［３］提出的一个公开问题．我们的结果在一定的意义下回答了该问题．     

短期趋势判断与投资组合优选

针对股市非常有限的可预测性和投资组合优化时间窗口的选择问题,本文从股指趋势和个股收益率趋势类别两个层次上进行前瞻分析,并依据股指趋势判断和不同时间窗口对应的边际风险收益,提出投资组合优化计算的时间窗口选择规则,动态地进行资产组合优化。通过沪深A股及沪深300成份股两个样本集合的应用研究表明,考虑多层次短期趋势预测的动态投资组合选择方法能有效地改善资产组合绩效,是股市资产风险管理的有效方法之一。     

删失分位数变系数回归模型的FIC模型平均估计（英文）

考虑了删失分位数变系数回归模型的FIC准则,并基于FIC准则给出了兴趣参数的模型选择和平均估计.为了全面反映响应变量的分布信息,克服异常值和重尾模型误差,文章对响应变量的不同分位数水平进行建模,因此与普通最小二乘方法相比更为稳健.在较为一般的条件下,证明了所提估计的渐近性质,通过模拟实验研究了估计的有限样本性质,用所提方法分析了手机用户的游戏时间数据.     

信息复杂性准则的深入探讨

介绍联系拟合优度与模型复杂性测度的一种模型选择准则一信息复杂性(ICOMP)准则的基本原理.由Bozdogan提出的信息复杂性(ICOMP)准则可以视为两个Kullback-Leibler距离之和的一种近似.首先研究了所考虑模型中有真实模型的情况下,ICOMP准则类的渐近相容性;然后又介绍并完成了所考虑模型中没有真实模型的情况下,ICOMP准则类的渐近相容性.在有限样本容量的情况下,用ICOMP准则选择的估计模型,比用其他通用的准则选择的估计模型,更接近于真实模型.     

消除毛细管电泳槽道中弯道导致的扩散效应的新方法

首先分析了毛细管通道中流动的弯道效应及其产生的原因，接着在建立电渗流场数学模型的基础上，用有限差分法对弯道处内外壁面上不同电荷分布时的扩散进行了数值模拟．根据计算结果，提出了一种基于改变弯道处内外壁面上电荷分布的新方法，以此使流场的弯道效应最弱．同时还建立了分析和确定弯道处最佳电荷分布的优化方法．结果表明，该方法能极大地消除毛细管通道中的流动弯道效应．     

区间直觉模糊环境下公共文化设施建设方案选择研究

针对公共文化服务设施建设方案的选择问题,提出基于区间直觉模糊数(IVIFN)的多准则决策优化方法.首先给出全面考虑IVIFN模糊信息,可衡量两个不同IVIFNs的差异度的计算公式,据此构造带均衡系数的评价准则权重确定模型;然后给出考虑正负理想的相对距离计算公式,据此进行最终排序;最后以某省会城市的公共文化服务设施建设方案的选择问题为例,对决策结果进行多维度数值分析,设置不同的均衡系数值,并与不同的评价方法进行排序结果的比较,综合说明所提优化模型和决策方法的合理性和有效性.     

子空间聚类的重建模型及其快速算法

有限样本的子空间数据聚类建模及其大规模计算是子空间学习面临的主要问题.现有的大多数模型都不适合大规模计算.本文提出了一个新的优化模型,结合谱投影反馈和辅助信息优化.在提升模型的学习能力的同时,采用高效的分片符号更新算法,可以适合大规模计算.我们用较大规模的模拟例子和实际例子,分析检验了新的优化模型及其快速算法的优于现有其他模型与算法的有效性.     

Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems

The paper describes new results in the field of multiobjective optimization techniques. The Interactive Decision Maps (IDM) technique is based on approximation of Feasible Criterion Set (FCS) and subsequent visualization of the Pareto frontier of FCS by interactive displaying the bi-criteria slices of FCS. The Estimation Refinement (ER) method is now the main method for approximating convex FCS in the framework of IDM. The properties of the ER method are studied. We prove that the number of facets of the approximation constructed by ER and the number of the support function calculations of an approximated set are asymptotically optimal. These results are important from the point of view of real-life applications of ER.     

整数偶序列为蕴含强连通的Beineke－Harary判准

一个由ｎ个非负整数有序对构造的序列是有向可图的,如果它是某个有向图的度序列．一个有向可图序列是蕴含强连通的,如果它是某个强连通有向图的度序列．Ｂｅｉｎｅｋｅ和Ｈａｒａｒｙ给出了一个有向可图序列为蕴含强连通的判准．Ｂｅｉｎｅｋｅ－Ｈａｒａｒｙ判准的充分性证明是“相当长”的（见［１］）．本文的目的是给出Ｂｅｉｎｅｋｅ－Ｈａｒａｒｙ判准的充分性的一个简短证明．     

Model selection of copulas: AIC versus a cross validation copula information criterion

Akaike Information Criterion (AIC) is frequently employed in the semiparametric setting of selection of copula models, even though as a model selection tool it was developed in a parametric setting. Recently a Copula Information Criterion (CIC) has been especially designed for copula model selection. In this paper we examine the two approaches and present a simulation study where the performance of a cross-validated version of CIC is compared with the AIC criterion. Only minor differences are observed.     

Dynamic responses of the impact drive mechanism modeled by the distributed parameter system

The piezoelectric actuator has been used for precision positioning from micro-meter down to nano-meter scale. In this paper, the impact drive mechanism (IDM) is designed to achieve a high accuracy and ability in precision positioning motion, where the frictional force is described by the Leuven model combined with the Bounc–Wen model of the hysteresis. The frictional model allows accurate dynamic modeling both in the sliding and the presliding regimes without using switching functions. The governing equations with the hysteresis effects of the distributed parameter system are formulated to obtain the dynamic responses. By using the finite element formulation, numerical solutions due to effects of the piezoelectric element (PE) are provided to compare between the distributed and lumped parameter systems of the IDM. It is shown that the neglect in the mass of the PE will cause the precision errors in the scale of tens nano-meters.     

Banach空间中一类扰动优化问题最优解的特征与存在性

设(X,‖·‖)是Banach空间,x∈X,Z是X的非空子集,J是Z→R的下半连续下有界函数．本文研究扰动优化问题min_(z∈Z)(J(z)+‖x-z‖)(记作(J,x)-inf)的最优解的特征和最优解的存在性等问题．我们引入J－太阳集的概念,同时在Z是J-太阳集的情形下,给出了扰动优化问题(J,x)-inf的最优解的“Kolmogorov”型特征刻画．并借助于集合的若干紧性概念和最优值函数的方向导数研究了扰动优化问题(J,x)-inf的最优解的存在性．     

Horizontal coordinating contracts in the semiconductor industry

Integrated device manufacturers (IDMs) and foundries are two types of manufacturers in the semiconductor industry. IDMs integrate both design and manufacturing functions whereas foundries solely focus on manufacturing. Since foundries often have cost advantage over IDMs due to their specialization and economies of scale, IDMs have incentives to source from foundries for the purpose of avoiding excessive capacity investment risk. As the IDM is also a potential capacity source, the IDM and foundry are in a horizontal setting rather than a purely vertical setting. In the absence of sophisticated contracts, the benchmark contract for the IDM and foundry is a wholesale price contract. We define “coordinating” contracts as those that improve both the IDM’s and foundry’s expected profits over the benchmark wholesale price contract and also lead to the maximum system profit. This paper examines if there exist coordinating capacity reservation contracts. It is found that wholesale price contracts in the horizontal setting cannot achieve the maximum system profit due to either double marginalization effect, or “misalignment of capacity-usage-priority”. In contrast, if the IDM’s capacity investment risk is not too low, there always exist coordinating capacity reservation contracts. Furthermore, under coordinating contracts, the IDM’s sourcing structure, either sole sourcing from the foundry or dual sourcing, is contingent on the firms’ cost structures.     

New prior near-ignorance models on the simplex

The aim of this paper is to derive new near-ignorance models on the probability simplex, which do not directly involve the Dirichlet distribution and, thus, are alternative to the Imprecise Dirichlet Model (IDM). We focus our investigation on a particular class of distributions on the simplex which is known as the class of Normalized Infinitely Divisible (NID) distributions; it includes the Dirichlet distribution as a particular case. For this class it is possible to derive general formulae for prior and posterior predictive inferences, by exploiting the Lévy–Khintchine representation theorem. This allows us to generally characterize the near-ignorance properties of the NID class. After deriving these general properties, we focus our attention on three members of this class. We will show that one of these near-ignorance models satisfies the representation invariance principle and, for a given value of the prior strength, always provides inferences that encompass those of the IDM. The other two models do not satisfy this principle, but their imprecision depends linearly or almost linearly on the number of observed categories; we argue that this is sometimes a desirable property for a predictive model.     

Causal analysis of futures sugar prices in Zhengzhou

In this paper, we are interested in investigating the causal relationships among futures sugar prices in the Zhengzhou futures exchange market (ZF), the spot sugar prices in Zhengzhou (ZS) and the futures sugar prices in New York futures exchange market (NF). A useful tool called Bayesian network is introduced to analyze the problem. Since there are only three variables in our Bayesian network, the algorithm is straightforward: we display all the 25 possible network structures and adopt certain scoring metrics to evaluate them. We applied five different scoring metrics in total. Firstly, for each metric, we obtained 24 scores, each calculated from one of the 24 possible structures i.e. a Directed Acyclic Graph (DAG). Then we eliminated the network structure which represents the independence of the three variables according to our prior knowledge concerning the futures sugar market. After that, the optimal network structure which implies the causal relationships was selected according to the corresponding scoring metric. Finally, after comparing the results from different scoring metrics, we obtained the relatively affirmative conclusion that ZS causes ZF from both the Bayesian Dirichlet (BD) metric, Bayesian Dirichlet-Akaike Information Criterion (BD-AIC) metric, Bayesian Dirichlet-Bayesian Information Criterion (BD-BIC) metric and Bayesian Information Criterion (BIC) metric. The conclusions that NF causes ZF and ZF causes ZS from the Akaike Information Criterion (AIC) metric and ZF causes ZS from the BIC metric were useful and significant to our investigation.     

最优预测与因果关系检验

本文从信息论角度出发 ,给出了一个新的准则 ,并且证明在正态假设条件下 ,此时的最优预测与最小二乘意义下的最优预测相同 .最后 ,将此准则应用到因果关系的检验     

The pure virtual braid group is quadratic

If an augmented algebra $K$ over $\mathbb Q $ is filtered by powers of its augmentation ideal $I$ , the associated graded algebra $gr_I K$ need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper, we give a sufficient criterion (called the PVH Criterion) for $gr_I K$ to be quadratic. When $K$ is the group algebra of a group $G$ , quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for $G$ . Thus, the PVH Criterion also implies the existence of such a universal finite type invariant for the group $G$ . We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a universal finite type invariant.