A Graphical Method of Exploring the Mean Structure in Longitudinal Data Analysis

Abstract

In a longitudinal study, individuals are observed over some period of time. The investigator wishes to model the responses over this time as a function of various covariates measured on these individuals. The times of measurement may be sparse and not coincident across individuals. When the covariate values are not extensively replicated, it is very difficult to propose a parametric model linking the response to the covariates because plots of the raw data are of little help. Although the response curve may only be observed at a few points, we consider the underlying curve y(t). We fit a regression model y(t) = x ^Tβ(t) + ε(t) and use the coefficient functions β(t) to suggest a suitable parametric form. Estimates of y(t) are constructed by simple interpolation, and appropriate weighting is used in the regression. We demonstrate the method on simulated data to show its ability to recover the true structure and illustrate its application to some longitudinal data from the Panel Study of Income Dynamics.     

浙江大学求是化学班人才培养的多层次科研实践体系

浙江大学化学系在求是化学班的培养过程中,以基础学科拔尖创新人才为培养目标,注重提升本科生科研能力,依托学科优势,从科研基础知识体系构建、科研思维模式拓展和科研创新实践能力强化等方面构筑分阶段、分层次、多平台、多模式的科研实践培养体系。该体系总体上以科研训练为主线,从广度科研认知到深度科研实践,融通校内第一、二课堂和校外第三、四课堂,贯穿整个拔尖人才培养过程。经过多年的探索与实践,该科研实践体系在培养学生的科研能力、创新思维和国际视野等方面已经初见成效。     

以问题为导向的点-面式教学法在药剂学教学中的应用——以“手性”知识的教学为例

在药剂学课程教学中,为讲解传授“手性”相关的知识和概念,设计了一种新的教学法,并进行了实践应用。通过对该教学方法的总结和提炼,将以上教学法命名为“以问题为导向的点-面式教学法”。该教学法是以“反应停”具体事例为问题引导,提出和确定问题后,引出知识点,从药学相关领域知识面展开教学活动后,进行知识点总结,最后达成最终的教学目标。该教学法对教学实践工作有一定的参考价值。     

Repeated Interaction Quantum Systems: Van Hove Limits and Asymptotic States

We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively). This generalizes known results (Attal and Joye in J. Stat. Phys. 126:1241–1283, 2007) in that the von Neumann algebras describing the system and the chain element may not be of finite type. Then (but now assuming that the small system is of finite type), we prove that both effective dynamics capture the long-term behavior of the system: existence of a unique asymptotic state for them implies the same property for the respective exact dynamics—provided that the perturbation parameter is sufficiently small. The zero-th order term in a power series expansion in the perturbation parameter of such an asymptotic state is given by the asymptotic state of the effective dynamics. We conclude by working out the case in which the small system and the chain element are spins. Dedicated to Mariana Huerta. This work was partially funded by Nucleus Millennium Information and Randomness P04-069-F.     

Conceptual metaphors for isomorphism and homomorphism: Instructors’ descriptions for themselves and when teaching

Group isomorphism and homomorphism are topics central to abstract algebra, yet research on instructors’ views of these concepts is limited. Based on interviews from two instructors as well as classroom video from eight class periods, this paper examines the language used to discuss isomorphism and homomorphism. Language used by instructors in interviews and classroom settings are identified and classified into four main categories: formal definition, mapping, sameness, and combinations of sameness and mapping language. How the two instructors drew on language classified into those four categories in the interview and instruction settings are examined for isomorphism and homomorphism. Similarities and differences between the interview and instruction contexts reveal the wide variety of ways of understanding isomorphism and homomorphism as well as a research need to examine mathematicians’ content knowledge in more than one context.     

How do we understand mathematical practices in non-mathematical fields? Reflections inspired by cases from 12th and 13th century China

Recent studies of the history of mathematics have shed light on the diversity of mathematical practices in the ancient world. In this article, I address this issue from two perspectives. First, I analyze different mathematical instruments used in different domains in 12^th and 13^th century China. Second, by analyzing how the text is related to the problems written down in the same period, I argue that there existed two categories of mathematical problems. As a result, I suggest that problems, textual procedures, and material operations should be considered together when regarding various mathematical practices in mathematical and non-mathematical fields.     

THE COURSE OF “STRUCTURAL MODEL DESIGN AND FABRICATION”

“知行统一” 的观念在教育界已深入人心,但是要做到切实履行却非易事。经过为期九年的精心打造,上海交通大学开设的创新型实践课程“结构模型设计与制作” 初步实现了“学与行” 的有机融合,教学效果显著,深受学生欢迎。本文是对该课程的总结与反思,希望对我国相关工科教学改革起到有益的借鉴作用。     

物理化学实验研究型教学改革与实践

针对不同专业学科发展需要,设计体现具有我校学科特色的物理化学实验教学内容和教学模式。培养学生以科研的状态进入到实验中,鼓励学生独立设计方案,提出问题,分析问题并解决问题,充分激发学生主动性和积极性,改进考核机制,有利于创新思维培养。以科研论文的形式总结实验,体现物理化学实验课程对实际应用和科研工作的指导作用。通过以上实践,实现从实践中来到实践中去的能力培养目标,充分发挥物理化学实验教学在培养一流创新性研究型专业人才中的重要作用。     

分析化学课程网上实践教学的组织与实施

针对当前在远程教育平台开展实验实训教学中存在的矛盾,以分析化学为例,充分利用现代通信技术和教育的结合,在实验教学中设计多媒体、视频、虚拟仿真实验室、实验拓展设计等4大资源模块。并从网上平台设计、组织与实施、教学质量保障、效果评价等方面进行论述,探索如何构建高效的分析化学网上实践教学课堂,以满足远程教育实验教学发展的需要,为广大的自学者学习技能建立良好的学习平台。     

以“科学和工程实践”视角分析高中化学教科书

以“科学和工程实践”的8大环节和学习者主体性2个维度建立模型,分析上海科学技术出版社出版的高中化学教科书中的实践活动。发现此教科书中的实践十分注重分析环节,能较好发挥学生主体性的环节有：科学实践中的分析解释数据环节;工程实践中的建模、计划、实施调查等环节。但总体上工程实践不足,无论科学实践还是工程实践,在提出问题、设计步骤这2个环节上学生过于被动。据此认为,在化学教科书实践活动的修改或教学优化上,应增强学生的主动性,除了要开展科学探究活动,也要适当增加工程设计等活动。