Estimation of Generalized DINA Model with Order Restrictions

Cognitive diagnostic models provide valuable information on whether a student has mastered each of the attributes a test intends to evaluate. Despite its generality, the generalized DINA model allows for the possibility of lower correct rates for students who master more attributes than those who know less. This paper considers the use of order-constrained parameter space of the G-DINA model to avoid such a counter-intuitive phenomenon and proposes two algorithms, the upward and downward methods, for parameter estimation. Through simulation studies, we compare the accuracy in parameter estimation and in classification of attribute patterns obtained from the proposed two algorithms and the current approach when the restricted parameter space is true. Our results show that the upward method performs the best among the three, and therefore it is recommended for estimation, regardless of the distribution of respondents’ attribute patterns, types of test items, and the sample size of the data.     

Using Neural Network Analysis to Define Methods of DINA Model Estimation for Small Sample Sizes

The DINA model is a commonly used model for obtaining diagnostic information. Like many other Diagnostic Classification Models (DCMs), it can require a large sample size to obtain reliable item and examinee parameter estimation. Neural Network (NN) analysis is a classification method that uses a training dataset for calibration. As a result, if this training dataset is determined theoretically, as was the case in Gierl’s attribute hierarchical method (AHM), the NN analysis does not have any sample size requirements. However, a NN approach does not provide traditional item parameters of a DCM or allow for item responses to influence test calibration. In this paper, the NN approach will be implemented for the DINA model estimation to explore its effectiveness as a classification method beyond its use in AHM. The accuracy of the NN approach across different sample sizes, item quality and Q-matrix complexity is described in the DINA model context. Then, a Markov Chain Monte Carlo (MCMC) estimation algorithm and Joint Maximum Likelihood Estimation is used to extend the NN approach so that item parameters associated with the DINA model are obtained while allowing examinee responses to influence the test calibration. The results derived by the NN, the combination of MCMC and NN (NN MCMC) and the combination of JMLE and NN are compared with that of the well-established Hierarchical MCMC procedure and JMLE with a uniform prior on the attribute profile to illustrate their strength and weakness.     

基因科技的二重性及其社会意义

本文首先论述基因科技整体上具有线性与非线性的二重性本质，是线性科学与非线性科学的一种中介。接着，它进一步阐明基因科技所揭示的生命机制中基因的遗传与变异二重性、对于性状确定与不确定的二重性、生命基因网络系统简单与复杂的二重性。进而，它揭示出基因科技二重性的社会意义。     

Evolution of Mathematical Proof

The authors present the main ideas of the computer-assisted proof of Mischaikow and Mrozek that chaos is really present in the Lorenz equations. Methodological consequences of this proof are examined. It is shown that numerical calculations can constitute an essential part of mathematical proof not only in the discrete mathematics but also in the mathematics of continua.     

知觉二元论:二元化的另一种方式

从隐私论题出发,本文将精神事件定义为从内在的观点所得到的知觉,把物理事件定义为从外在的观点所得到的知觉,并以此为起点发展出一个关于心灵的知觉二元论。本文还试图以此理论来说明心灵哲学领域长期存在的心-物互动问题,试图恢复并证明笛卡尔和莱布尼兹曾经达到的某些观察和结论。知觉是心灵最本质的特征,本文在用知觉来定义精神事件和物理事件的同时也发展出一个关于知觉的新理论。     

卡拉比猜想及其证明

卡拉比猜想的证明,引出了许多重要结果,对于后来数学和物理的发展做出了基础性贡献.文章依据原始文献,详细考察了卡拉比提出猜想,丘成桐解决卡拉比猜想的工作;同时讨论了卡拉比猜想与凯勒-爱因斯坦度量的密切关系以及丘成桐和奥宾在这两个问题上的工作.     

A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions

A simple proof of the identification of a mixture of two univariate normal distributions is given. The proof is based on the equivalence of local identification with positive definiteness of the information matrix and the equivalence of the latter to a condition on the score vector that is easily checked for this model. Two extensions using the same line of proof are also given. We would like to thank Tom Wansbeek, Michel Wedel, Arie Kapteyn, and two anonymous reviewers for helpful comments on earlier versions of this paper.     

反证法与归谬法的现代分析

本文以现代命题逻辑为分析工具,证明了:在正命题逻辑系统的基础上,反证法的证明能力强于归谬法,它们之间相差一个双重否定律;归谬律与不矛盾律加上充分条件否定后件律相等价;反证律与不矛盾律、排中律、充分条件否定后件律加上选言推理否定肯定律相等价.     

矩阵力学与波动力学等价性证明的历史分析

矩阵力学和波动力学是量子力学的两种早期形态.前者由海森堡、约当、玻恩提出,后者由薛定谔提出.1926年,薛定谔给出二者之间等价性的证明.随后,泡利、狄拉克、约当、冯·诺伊曼等人或是为等价性证明给出新的版本,或是给出了间接的论证.这两种力学现在已被表述为海森堡绘景和薛定谔绘景,而数学家近来又从量子化问题出发对其等价性做出...     

古巴比伦正四棱台体积公式古证复原

在古巴比伦数学中,正四棱台体积公式的表现形式和现代形式相比十分复杂.奎内斯(Ivor Grattan-Guinness)在解释该公式时,对分割图形的拼合方法不太合理.有鉴于此,基于平面情形与空间情形类比的思想对该公式进行了古证复原,这一方面能加深对古巴比伦几何学思想的理解,另一方面也为正四棱台体积公式的教学提供了有益的借鉴.     

苏颂水运仪象台的“尺寸”论证

考察从东汉至明代的现存六座历史天文文物,得出其天文尺值为1尺=24.5cm,这便是中国历代八尺高表测影和制造天文仪器的长度标准,该值从东汉至明末基本保持不变.从而把北宋苏颂水运仪象台的高度(35.65-36尺)定为873-882cm之间,宽度(21尺)为514.5cm,其他部件的尺寸也依此类推.这是对王振铎及后来国内外许多研制者把水运仪象台的高度和宽度分别定为11-12米和7米的重大校正和更改.     

数学证明严格性之相对意义与综合评判标准

数学命题的证明在结构上必然存在某种预设性,在其论证过程中必然存在逻辑空隙。数学推理在所采用的逻辑工具和方法上并非无懈可击,加之数学形式体系的非完整性与非封闭性,这些都充分表明数学知识无论是在其原初形式上、形成过程中和构成方式三个维度上都无法获得完全意义上的可靠性。即使在元层面的证明论诉求亦复如此。数学证明的标准是一个综合评判的动态体系。     

A Comparison of Two Methods for Fitting the INDCLUS Model

Chaturvedi and Carroll have proposed the SINDCLUS method for fitting the INDCLUS model. It is based on splitting the two appearances of the cluster matrix in the least squares fit function and relying on convergence to a solution where both cluster matrices coincide. Kiers has proposed an alternative method which preserves equality of the cluster matrices throughout. This paper shows that the latter method is generally to be preferred. However, because the method has a serious local minimum problem, alternative approaches should be contemplated.     

科学发展模式的生物进化论类比研究

科学发展的多元进化模式是科学哲学关于科学进步问题的成果之一。与其相对应的生物进化论类比则是近年来国际学术界争议的焦点。我们将从当代生物进化论出发,论证科学发展作为增生式的非目的性过程,其生物进化类比是恰当的。     

A Computational Model of the Belief System Under the Scope of Social Communication

This paper presents an approach to the belief system based on a computational framework in three levels: first, the logic level with the definition of binary local rules, second, the arithmetic level with the definition of recursive functions and finally the behavioural level with the definition of a recursive construction pattern. Social communication is achieved when different beliefs are expressed, modified, propagated and shared through social nets. This approach is useful to mimic the belief system because the defined functions provide different ways to process the same incoming information as well as a means to propagate it. Our model also provides a means to cross different beliefs so, any incoming information can be processed many times by the same or different functions as it occurs is social nets.     

GRB060614伽马射线暴的潮汐瓦解吸积模型

GRB060614是一个非常特殊的γ-射线暴,它具有长的持续时间但并没有与之相伴的超新星爆发,这有别于目前确定的两类γ-射线暴（一类是长而软的γ-射线暴,对应于大质量恒星的塌缩爆发;另一类是短而硬的γ-射线暴,对应于两个致密星体的并合）。这个暴的出现使人们重新思考关于γ-射线暴的分类和中心引擎问题。我们提出这个异常的γ-射线暴产生于一个中等质量黑洞对恒星的吞噬过程。该模型能成功地解释此次γ-射线暴的能量、子暴和周期性子结构等主要观测特征。同时,模型可对中等质量黑洞的性质给出一些重要限制。因此,本研究提供了理解这一新类型γ-射线暴和稀有的中等质量黑洞的新途径。     

整体与部分之和--一种整体论的心理学模式

整体与部分之和代表了西方心理学在理解人性方面的两种取向,即融洽化与机械论、还原论的取向。严格说来,个体身上只存在整体的心理两面是不存在部分的心理。西方正弦的心理学割裂整体人的做法不仅背离了心理学的初衷,而且与学科的目标－理解并把握人性背道而驰,因为作为分子的人与作为整体的人有着根本性的区别。与机械论和还原论相比,整体论的模式更有可能揭示人性的本质。     

析亚里士多德：前提为必然、前提为实然的模态三段论

本文主要从亚里士多德关于—前提为必然—前提为实然的模态三段论原文出发，对其思想进行分析和整理，指出了亚里士多德主张的十三个模态有效式，并提炼出其公理化思想。在此基础上，对亚里士多德的思想加以补充，提出了第十四个模态有效式并给予证明。     

西部开发模式与发展绿色经济研究

文章分析了西部传统的发展模式及其不足,这种模式在西部的开发中必须突破。论证了绿色经济和西部发展绿色经济的优势,指出了西部发展绿色经济的路径。