Light Affine Set Theory: A Naive Set Theory of Polynomial Time

In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL.In this paper, we consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in LAST.     

Identifying a Reordering of Rows and Columns for Multiple Proximity Matrices Using Multiobjective Programming

This paper is concerned with a problem where K (n×n) proximity matrices are available for a set of n objects. The goal is to identify a single permutation of the n objects that provides an adequate structural fit, as measured by an appropriate index, for each of the K matrices. A multiobjective programming approach for this problem, which seeks to optimize a weighted function of the K indices, is proposed, and illustrative examples are provided using a set of proximity matrices from the psychological literature. These examples show that, by solving the multiobjective programming model under different weighting schemes, the quantitative analyst can uncover information about the relationships among the matrices and often identify one or more permutations that provide good to excellent index values for all matrices.     

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.     

情绪状态对不同年龄儿童定势转换的影响

采用情绪影片引发情绪的方法,考察64名8~12岁儿童在正负情绪状态下定势转换能力的表现。研究为4(年龄)×2(情绪)×3(重复转换条件:重复、短时转换、长时转换)3因素重复测量混合设计。结果表明,情绪状态对任务转换产生了影响,可能是积极情绪比消极情绪对任务定势的长时转换削弱更大。不同年龄的儿童在这两种任务转换条件中没有出现显著的年龄差异,说明8~12岁儿童均已具备在两个任务之间进行即时转换的能力。     

内隐的可接近信息对FOK判断等级和准确性的影响

该研究使用RJR研究范式,探讨内隐的可接近信息对FOK判断等级和判断准确性的影响。结果发现：FOK判断等级受内隐的可接近信息量的影响,二者呈非单调递增、递减的关系;FOK判断等级随内隐的可接近信息强度的增强而增高;FOK判断准确性随内隐的可接近信息量的增多而降低,并随内隐的可接近信息强度的增强而增高。     

Constructing robust crew schedules with bicriteria optimization

Optimization‐based computer systems are used by many airlines to solve crew planning problems by constructing minimal cost tours of duty. However, today airlines do not only require cost effective solutions, but are also very interested in robust solutions. A more robust solution is understood to be one where disruptions in the schedule (due to delays) are less likely to be propagated into the future, causing delays of subsequent flights. Current scheduling systems based solely on cost do not automatically provide robust solutions. These considerations lead to a multiobjective framework, as the maximization of robustness will be in conflict with the minimization of cost. For example crew changing aircraft within a duty period is discouraged if inadequate ground time is provided. We develop a bicriteria optimization framework to generate Pareto optimal schedules for the domestic airline. A Pareto optimal schedule is one which does not allow an improvement in cost and robustness at the same time. We developed a method to solve the bicriteria problem, implemented it and tested it with actual airline data. Our results show that considerable gain in robustness can be achieved with a small increase in cost. The additional cost is mainly due to an increase in overnights, which allows for a reduction of the number of aircraft changes. Copyright © 2003 John Wiley & Sons, Ltd.     

心理定势现象的认知神经机制

问题解决活动中的心理定势,是指人们固执地沿用熟悉方案、忽略其他方案的反应倾向。它可能源于人们已经掌握的陈述性知识,也可能源于程序性知识,两类不同来源的心理定势的发生条件和影响效果都不尽相同。然而,过往的研究都没有做出严格区分。本文通过梳理相关研究,描述心理定势现象,解释心理定势是怎么发生的,分析心理定势是在什么条件下发生的、会对心理与行为活动造成什么样的影响,从而评述两种来源的心理定势的认知神经机制,指出尚未解决的科学问题。     

Constructing Cantorian counterexamples

Cantors diagonal argument provides an indirect proof that there is no one-one function from the power set of a set A into A. This paper provides a somewhat more constructive proof of Cantors theorem, showing how, given a function f from the power set of A into A, one can explicitly define a counterexample to the thesis that f is one-one.     

Effects of Performance-Based Pay Systems on Quantity and Quality in Computer Programming

This experiment was conducted to investigate the effects of quality-contingent pay systems on quantity and quality. Three computer science students were paid to create simple computer programs across 25 sessions. A multiple-baseline across subjects design was used to compare the effects of three kinds of pay systems; pay-for-hour, pay-for-quantity, and pay-for-quality systems. The quantity was higher when pay was based on the quantity of the programs produced, and the quality was highest when pay was based on the quality of the programs. The production cost including quality inspection costs was highest when pay was based on the time worked.     

题库智能化组卷的心理计量理论与方法

现代教育成就测验的广泛应用,促使题库技术迅速发展。现代教育测量理论与计算机技术的结合,更使智能化组卷成为可能。本文报告了以项目反应理论为指导,并改进一般线性规划法为分步离差加权模型法,编制程序在高等教育自学考试“逻辑学”题库上,成功实现智能化组卷的研究成果,从而为计算机技术在题库建设中的应用作了新的探讨。