浅谈矩阵特征值的估计

矩阵的特征值问题是矩阵计算的一个重要方向,在众多的领域中都得到了应用。在这样的大背景下,有必要深入地研究矩阵的特征值的估计问题。基于此,本文将结合国内外对于矩阵的特征值的估计方面的研究,以及一些具体的应用实例,来深入地探索矩阵的特征值的估计问题。     

Popularity breeds contempt: The evolution of reputational dislike relations and friendships in high school

In this study, we examined the dynamics of the perception of “dislike” ties (reputational dislike) among adolescents within the contexts of friendship, perceived popularity, substance use, and Facebook use. Survey data were collected from a longitudinal sample of 238 adolescents from the 11th and 12th grades in one California high school. We estimated stochastic actor-based network dynamic models, using reports of reputational dislike, friendships, and perceived popularity, to identify factors associated with the maintenance and generation reputational dislike ties. The results showed that high-status adolescents and more frequent Facebook users tended to become perceived as or stay disliked by their peers over time. There was a tendency for friendships to promote the creation and maintenance of reputational disliking but not vice versa. Adolescents tended to perceive others as disliked when their friends also perceived them as disliked. There was no evidence that either cigarette smoking or drinking alcohol affected reputational dislike dynamics. This study highlights the important role that the hierarchical peer system, online peer context, and friendships play in driving information diffusion of negative peer relations among adolescents.     

An integrated approach for water resources decision making under interactive and compound uncertainties

In recent years, the issue of water allocation among competing users has been of great concern for many countries due to increasing water demand from population growth and economic development. In water management systems, the inherent uncertainties and their potential interactions pose a significant challenge for water managers to identify optimal water-allocation schemes in a complex and uncertain environment. This paper thus proposes a methodology that incorporates optimization techniques and statistical experimental designs within a general framework to address the issues of uncertainty and risk as well as their correlations in a systematic manner. A water resources management problem is used to demonstrate the applicability of the proposed methodology. The results indicate that interval solutions can be generated for the objective function and decision variables, and a number of decision alternatives can be obtained under different policy scenarios. The solutions with different risk levels of constraint violation can help quantify the relationship between the economic objective and the system risk, which is meaningful for supporting risk management. The experimental data obtained from the Taguchi's orthogonal array design are useful for identifying the significant factors affecting the means of total net benefits. Then the findings from the mixed-level factorial experiment can help reveal the latent interactions between those significant factors at different levels and their effects on the modeling response.     

Estimation of odds ratios under order restrictions

A new method for estimating a set of odds ratios under an order restriction based on estimating equations is proposed. The method is applied to those of the conditional maximum likelihood estimators and the Mantel-Haenszel estimators. The estimators derived from the conditional likelihood estimating equations are shown to maximize the conditional likelihoods. It is also seen that the restricted estimators converge almost surely to the respective odds ratios when the respective sample sizes become large regularly. The restricted estimators are compared with the unrestricted maximum likelihood estimators by a Monte Carlo simulation. The simulation studies show that the restricted estimates improve the mean squared errors remarkably, while the Mantel-Haenszel type estimates are competitive with the conditional maximum likelihood estimates, being slightly worse.     

Selective Maintenance in System Reliability with Random Costs of Repairing and Replacing the Components

In this paper we consider the problem of determining the optimum number of repairable and replaceable components to maximize a system's reliability when both, the cost of repairing the components and the cost of replacement of components by new ones, are random. We formulate it as a problem of non-linear stochastic programming. The solution is obtained through Chance Constrained programming. We also consider the problem of finding the optimal maintenance cost for a given reliability requirement of the system. The solution is then obtained by using Modified E-model. A numerical example is solved for both the formulations.     

An additive subdistribution hazard model for competing risks data

The cumulative incidence function plays an important role in assessing its treatment and covariate effects with competing risks data. In this article, we consider an additive hazard model allowing the time-varying covariate effects for the subdistribution and propose the weighted estimating equation under the covariate-dependent censoring by fitting the Cox-type hazard model for the censoring distribution. When there exists some association between the censoring time and the covariates, the proposed coefficients’ estimations are unbiased and the large-sample properties are established. The finite-sample properties of the proposed estimators are examined in the simulation study. The proposed Cox-weighted method is applied to a competing risks dataset from a Hodgkin's disease study.     

Stochastic Bounds with a Low Rank Decomposition

We investigate how we can bound a discrete time Markov chain (DTMC) by a stochastic matrix with a low rank decomposition. In the first part of the article, we show the links with previous results for matrices with a decomposition of size 1 or 2. Then we show how the complexity of the analysis for steady-state and transient distributions can be simplified when we take into account the decomposition. Finally, we show how we can obtain a monotone stochastic upper bound with a low rank decomposition.     

Concept mapping as an approach for expert-guided model building: The example of health literacy

Concept mapping served as the starting point for the aim of capturing the comprehensive structure of the construct of ‘health literacy.’ Ideas about health literacy were generated by 99 experts and resulted in 105 statements that were subsequently organized by 27 experts in an unstructured card sorting. Multidimensional scaling was applied to the sorting data and a two and three-dimensional solution was computed. The three dimensional solution was used in subsequent cluster analysis and resulted in a concept map of nine “clusters”: (1) self-regulation, (2) self-perception, (3) proactive approach to health, (4) basic literacy and numeracy skills, (5) information appraisal, (6) information search, (7) health care system knowledge and acting, (8) communication and cooperation, and (9) beneficial personality traits. Subsequently, this concept map served as a starting point for developing a “qualitative” structural model of health literacy and a questionnaire for the measurement of health literacy. On the basis of questionnaire data, a “quantitative” structural model was created by first applying exploratory factor analyses (EFA) and then cross-validating the model with confirmatory factor analyses (CFA). Concept mapping proved to be a highly valuable tool for the process of model building up to translational research in the “real world”.     

Weighted Stochastic Restricted Estimation in Linear Measurement Error Models

This article discusses the consistent estimation of the parameters in a linear measurement error model when stochastic linear restrictions on regression coefficients are available. We propose some methodologies to obtain the consistent estimation when either the covariance matrix of the measurement errors or the reliability matrix of independent variables is known. Their finite- and large-sample properties are derived with not necessarily normal errors. A Monte Carlo simulation is carried out to study the the finite properties of the estimators.     

简论郑板桥的天道循环观

郑板桥的史论较多,他对历史的评价与他的喜怒哀乐是联系在一起的。但其历史观是相对稳定的。郑板桥历史评价的基点是他的天道循环观,他认为社会与人生都是一场大戏,世事总是翻来又复去的;同时在天道循环观的基础上郑板桥又出现了一种历史虚无主义的倾向,他认为人一切奋斗的结果都会因天道循环而走向缥缈;当然,他也认为,虽然天道循环是不可抗拒的,但人的因素不可忽视,只要人发挥积极的作用,人与社会就可以延缓这种循环的进程。