大学数学基础课教学中融入数学建模思想的实践

数学建模不仅限于解决实际问题,也可以是数学发展过程中提出的理论问题。基于近年来在大学数学基础课教学中融入数学建模思想的教学实践,论述了其主要思路与做法。介绍了将数学建模思想融入数学基础课教学的两个教学案例,即微积分方法的本质和从方程组出发引入线性相关与线性无关概念。     

Modelling udder infection data using copula models for quadruples

We study copula models for correlated infection times in the four udder quarters of dairy cows. Both a semi-parametric and a nonparametric approach are considered to estimate the marginal survival functions, taking into account the effect of a binary udder quarter level covariate. We use a two-stage estimation approach and we briefly discuss the asymptotic behaviour of the estimators obtained in the first and the second stage of the estimation. A pseudo-likelihood ratio test is used to select an appropriate copula from the power variance copula family that describes the association between the outcomes in a cluster. We propose a new bootstrap algorithm to obtain the p-value for this test. This bootstrap algorithm also provides estimates for the standard errors of the estimated parameters in the copula. The proposed methods are applied to the udder infection data. A small simulation study for a setting similar to the setting of the udder infection data gives evidence that the proposed method provides a valid approach to select an appropriate copula within the power variance copula family.     

Estimation in capture–recapture models when covariates are subject to measurement errors and missing data

For capture–recapture models when covariates are subject to measurement errors and missing data, a set of estimating equations is constructed to estimate population size and relevant parameters. These estimating equations can be solved by an algorithm similar to the EM algorithm. The proposed method is also applicable to the situation when covariates with no measurement errors have missing data. Simulation studies are used to assess the performance of the proposed estimator. The estimator is also applied to a capture–recapture experiment on the bird species Prinia flaviventris in Hong Kong. The Canadian Journal of Statistics 37: 645–658; 2009 © 2009 Statistical Society of Canada     

Invariant co-ordinate selection

Summary.  A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue–eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection . By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given.     

ASSOCIATIONS BETWEEN AIR POLLUTION AND HOSPITAL VISITS FOR CARDIOVASCULAR DISEASES IN THE ELDERLY IN SYDNEY USING BAYESIAN STATISTICAL METHODS

Using generalized linear models (GLMs), Jalaludin  et al. (2006;  J. Exposure Analysis and Epidemiology   16 , 225–237) studied the association between the daily number of visits to emergency departments for cardiovascular disease by the elderly (65+) and five measures of ambient air pollution. Bayesian methods provide an alternative approach to classical time series modelling and are starting to be more widely used. This paper considers Bayesian methods using the dataset used by Jalaludin  et al.  (2006) , and compares the results from Bayesian methods with those obtained by Jalaludin  et al.  (2006) using GLM methods.     

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.     

Familial Patterning and Prevalence of Male Androphilia in Samoa

Previous research established that male androphilia (i.e., sexual arousal and attraction to adult males) clusters in families. Some studies find that male androphilia clusters in both the paternal and maternal lines, while others find that it clusters only in the latter. Most of the research investigating the familial nature of male androphilia has taken place in Western cultural contexts that are problematic for such research because they are characterized by low fertility. To address this, our previous work has examined familial patterning of male androphilia in Samoa, a high-fertility population in which androphilic males are readily identified due to their public status as fa’afafine (a third gender category). Building on this work, the present study replicated the familial nature of male androphilia in Samoa using a sample size that was ~122% larger than the one we previously employed (N = 382, M ±SD age: 29.72 years ±10.16). Samoan fa’afafine had significantly more fa’afafine relatives in their maternal and paternal lines compared to Samoan gynephilic males (p < .001). The prevalence of male androphilia was equivalent across both the paternal and maternal lines (all p > .15). The revised prevalence estimate of male androphilia in Samoa falls between 0.61% and 3.51%.     

“I Feel Like More of a Man”: A Mixed Methods Study of Masculinity,Sexual Performance,and Circumcision for HIV Prevention

Ethnographic studies from numerous societies have documented the central role of male circumcision in conferring masculinity and preparing boys for adult male sexuality. Despite this link between masculinity, sexuality, and circumcision, there has been little research on these dynamics among men who have been circumcised for HIV prevention. We employed a mixed methods approach with data collected from recently circumcised men in the Dominican Republic (DR) to explore this link. We analyzed survey data collected six to 12 months post-circumcision (N = 293) as well as in-depth interviews conducted with a subsample of those men (n = 30). We found that 42% of men felt more masculine post-circumcision. In multivariate analysis, feeling more masculine was associated with greater concern about being perceived as masculine (OR = 1.70, 95% CI: 1.25–2.32), feeling more potent erections post-circumcision (OR = 2.25, 95% CI: 1.26–4.03), and reporting increased ability to satisfy their partners post-circumcision (OR = 2.30, 95% CI: 1.11–4.77). In qualitative interviews, these factors were all related to masculine norms of sexually satisfying one’s partner, and men’s experiences of circumcision were shaped by social norms of masculinity. This study highlights that circumcision is not simply a biomedical intervention and that circumcision programs need to incorporate considerations of masculine norms and male sexuality into their programming.     

自由与责任:网络空间伦理诉求及其实现策略

习近平在世界互联网大会上的主旨讲话中指出,互联网把世界变成了“鸡犬相闻”的地球村,改变着人们的生产生活,有力推动了社会发展;同时,他又指出,网络空间不是“法外之地”,并明确提出了加强网络空间治理、规范网络空间行为等要求.网络的虚拟性、开放性和交互性,既给人们提供了自由的空间和舞台,又对人们的道德要求和责任担当提出了更高的要求.行为主体网络信息的自由表达有其必要的边界和限度,网络行为中的责任担当对规范网络空间和现实社会的有序发展存在着积极的应然价值,自由与责任构建了网络空间最基本的伦理诉求.