Kernel density estimators for random fields satisfying an interlaced mixing condition

For a sequence of strictly stationary random fields that are uniformly ρ′-mixing$\rho \prime \mathrm{-}\mathrm{mixing}$ and satisfy a Lindeberg condition, a central limit theorem is obtained for sequences of “rectangular” sums from the given random fields. The “Lindeberg CLT” is then used to prove a CLT for some kernel estimators of probability density for some strictly stationary random fields satisfying ρ′-mixing$\rho \prime \mathrm{-}\mathrm{mixing}$, and whose probability density and joint densities are absolutely continuous.     

Accelerated life test planning with independent lognormal competing risks

In accelerated life testing (ALT), products are exposed to stress levels higher than those at normal use in order to obtain information in a timely manner. Past work on planning ALT is predominantly on a single cause of failure. This article presents methods for planning ALT in the presence of k competing risks. Expressions for computing the Fisher information matrix are presented when risks are independently distributed lognormal. Optimal test plans are obtained under criteria that are based on determinants and maximum likelihood estimation. The proposed method is demonstrated on ALT of motor insulation.     

DT-optimum designs for model discrimination and parameter estimation

The paper introduces DT-optimum designs that provide a specified balance between model discrimination and parameter estimation. An equivalence theorem is presented for the case of two models and extended to an arbitrary number of models and of combinations of parameters. A numerical example shows the properties of the procedure. The relationship with other design procedures for parameter estimation and model discrimination is discussed.     

Pilot–pivotal trials for average bioequivalence

Before carrying out a full scale bioequivalence trial, it is desirable to conduct a pilot trial to decide if a generic drug product shows promise of bioequivalence. The purpose of a pilot trial is to screen test formulations, and hence small sample sizes can be used. Based on the outcome of the pilot trial, one can decide whether or not a full scale pivotal trial should be carried out to assess bioequivalence. This article deals with the design of a pivotal trial, based on the evidence from the pilot trial. A two-stage adaptive procedure is developed in order to determine the sample size and the decision rule for the pivotal trial, for testing average bioequivalence using the two one-sided test (TOST). Numerical implementation of the procedure is discussed in detail, and the required tables are provided. Numerical results indicate that the required sample sizes could be smaller than that recommended by the FDA for a single trial, especially when the pilot study provides strong evidence in favor of bioequivalence.     

Negative dependence and the Simes inequality

It is shown that the Simes inequality is reversed for a broad class of negatively dependent distributions.     

Precision parameter in the variable precision rough sets model: an application

Despite their diverse applications in many domains, the variable precision rough sets (VPRS) model lacks a feasible method to determine a precision parameter (β)$(\beta )$ value to control the choice of β$\beta$-reducts. In this study we propose an effective method to find the β$\beta$-reducts. First, we calculate a precision parameter value to find the subsets of information system that are based on the least upper bound of the data misclassification error. Next, we measure the quality of classification and remove redundant attributes from each subset. We use a simple example to explain this method and even a real-world example is analyzed. Comparing the implementation results from the proposed method with the neural network approach, our proposed method demonstrates a better performance.     

论文习作--课堂教学改革的一次有益尝试

介绍了在"离散数学"教学过程中开展的一次教改活动的概况.通过论文习作,激发了广大学生的学习热情,加深了对教学内容的理解,启发了学生的创造性思维,提高了运用数学工具解决实际问题的能力,锻炼了写作技能,同时也增强了学生间的团结互助和师生间的友谊.     

Gender and Mathematics Achievement in China and the United States

This study examines the relationship between gender and mathematics achievement among students in China and the United States, with an emphasis on the gender gap among mathematically talented students. The results show that in neither the US nor China are there gender differences in eighth grade math-achievement test scores. In China, there are no gender differences in mean college entrance examination math scores among high-school seniors, while in America, the mean SAT-Math score among male high-school seniors has been consistently higher than those of their female counterparts. In both the US and China, there are gender differences among the top math performers on college entrance examinations; boys are over-represented. The Chinese national mathematics curriculum, well-trained teachers, beliefs by students and their parents that academic achievement is more a product of effort than of natural ability, a gender-neutral parental expectation for children’s education, and generous family spending on the education of girls are suggested as possible factors underlying the comparable performance of the Chinese female and male students. The sorting system at Chinese secondary school level and a cultural stereotype favoring boys in mathematics are suggested as possible contributors to the math-achievement gender gap found among the top Chinese high school seniors.

The Effect of Mixing Events on the Dynamics of pH1N1 Outbreaks at Small Residential Colleges

Abstract

Objective: The authors examine the dynamics and the impact of all-campus events on pH1N1 spread at Bates College in fall 2009, with comparisons to 3 other campuses. Participants: Students (N = 285) presented or called in to the Bates Health Center with symptoms consistent with influenza-like illness. Methods: Health Center staff at Bates collected data on the outbreak; data from other colleges are from Web sites and journal articles. Data were analyzed using a mathematical model for influenza. Results: Bates held 2 vaccine clinics mid-outbreak. The data are consistent with the hypothesis that the vaccine clinics may have altered routine student interactions, facilitating transmission of pH1N1 among students who otherwise might not have encountered each other. Conclusion: The vaccine clinics, held when vaccine became available, were too late to halt transmission. The disruptions to campus rhythms due to the vaccine clinics may instead have contributed to pH1N1 spread.