The flat-maximum effect and generic linear scoring models: a test

Received on 1 July 1991. Predicting human behaviour patterns with linear correlationmodels has absorbed researchers for the past five decades. Althoughmost observers generally concede that humans are inferior tosuch models in combining information, linear scoring modelsare unfortunately, plagued by the flat-maximum effect or the‘curse of insensitivity’. As Lovie & Lovie(1986)observe: ‘The predictive ability of linear models is insensitiveto large variations in the size of regression weights and tothe number of predictors.’ In essence, seemingly differentscoringmodels tend to produce indistinguishable predictive outcomes. Since its demonstration by Dawes & Corrigan (1974), observershave cast the flat maximum in a decidedly negative light. Incontrast, Lovie & Lovie (1986) present a provocatively contrarianview of the flat maximum‘s positive potential. In thissame vein, we examine the predictive power of a generic credit-scoringmodel versus individual empirically derived systems. If, asWainer (1976) noted in regard to the flat maximum, ’itdon‘t make no nevermind’, generic credit-scoringmodels could provide cheaper alternatives to individual empiricallyderived models. During the period 1984–8, a series of linear credit-scoringmodels were developed for ten Southeastern U.S. credit unions.For each credit union, stepwise multiple regression was employedto select a subset of explanatory variables to be used in adiscriminant analysis. A generic credit-scoring equation wasdeveloped from the resulting discriminant analyses using weightedaverage coefficients from five systems. The predictive powerof the generic model was compared to the predictive power ofholdout sample of the five remaining credit-scoring models. In all cases, the generic model's performance was very closeto that of the empirically derived models. Thus, our findingssupport Lovie & Lovie's (1986) challenge to the conventionalwisdom that the flat maximum casts a pall on the successfulmodelling of judgement processes. Indeed, the flat maximum impliesa positive role for simpler, and hence cheaper, generic models.Although further research is needed, it should be possible todevelop hybrid models with generic cores that perform as wellas empirically derived linear models.     

A comparison of neural networks and linear scoring models in the credit union environment

The purpose of the present paper is to explore the ability of neural networks such as multilayer perceptrons and modular neural networks, and traditional techniques such as linear discriminant analysis and logistic regression, in building credit scoring models in the credit union environment. Also, since funding and small sample size often preclude the use of customized credit scoring models at small credit unions, we investigate the performance of generic models and compare them with customized models. Our results indicate that customized neural networks offer a very promising avenue if the measure of performance is percentage of bad loans correctly classified. However, if the measure of performance is percentage of good and bad loans correctly classified, logistic regression models are comparable to the neural networks approach. The performance of generic models was not as good as the customized models, particularly when it came to correctly classifying bad loans. Although we found significant differences in the results for the three credit unions, our modular neural network could not accommodate these differences, indicating that more innovative architectures might be necessary for building effective generic models.     

Dynamics of generic 2-dimensional linear differential systems

We prove that for a C⁰-generic (a dense Gδ) subset of all the 2-dimensional conservative nonautonomous linear differential systems, either Lyapunov exponents are zero or there is a dominated splitting μ almost every point.     

Normalizable linear orders and generic computations in finite models

Numerous results about capturing complexity classes of queries by means of logical languages work for ordered structures only, and deal with non-generic, or order-dependent, queries. Recent attempts to improve the situation by characterizing wide classes of finite models where linear order is definable by certain simple means have not been very promising, as certain commonly believed conjectures were recently refuted (Dawar's Conjecture). We take on another approach that has to do with normalization of a given order (rather than with defining a linear order from scratch). To this end, we show that normalizability of linear order is a strictly weaker condition than definability (say, in the least fixpoint logic), and still allows for extending Immerman-Vardi-style results to generic queries. It seems to be the weakest such condition. We then conjecture that linear order is normalizable in the least fixpoint logic for any finitely axiomatizable class of rigid structures. Truth of this conjecture, which is a strengthened version of Stolboushkin's conjecture, would have the same practical implications as Dawar's Conjecture. Finally, we suggest a series of reductions of the two conjectures to specialized classes of graphs, which we believe should simplify further work. Received: 13 July 1996     

美国的数学教育

本文是作者为意大利数学家写的一篇报告，作者是美国Center for Mathematical Education，Newton，MA的主任，鉴于其中对美国数学教育作了较全面的介绍，故摘译于此，希望有助于我们改进教学，作者还有另一篇文章讲中学数学教师的数学培训，因未找到，原文中涉及该文处，只好改写，又因为时间关系，没有逐句仔细翻译，但希望大意不错，请读者原谅。     

中美数学研究人员交流计划申请指南

为了加强中美青年科学家在数学领域交流,营造有利于中国科研人员参与国际(地区)合作与竞争的良好环境,鼓励基金承担者开展积极而富有成效的国际合作与交流.中国国家自然科学基金委员会和美国基金会就数学领域的合作签署合作备忘录,共同支持中美数学研究人员.     

国家自然科学基金数学动态报道 中美数学研究人员交流计划申请指南

为了加强中美青年科学家在数学领域交流，营造有利于中国科研人员参与国际（地区）合作与竞争的良好环境，鼓励基金承担者开展积极而富有成效的国际合作与交流。中国国家自然科学基金委员会和美国基金会签署合作协议，共同支持中美数学研究人员。     

A generic environment for modelling future launch operations—GEM-FLO: a success story in generic modelling

Several NASA programs have been established to study and improve the current launch capability to meet the need for more aggressive space exploration in the future. Numerous launch systems have been proposed by different government and commercial organizations with the potential goal of replacing the Space Shuttle. NASA must evaluate new designs and technologies with the objective of improving upon today's Shuttle cost, performance, and turnaround time, before the government or commercial organizations pursue the large undertaking of a new launch system. To address this issue, the Generic Simulation Environment for Modelling Future Launch Operations (GEM-FLO) was developed to accurately predict processing turnaround times and other effectiveness criteria and support making key business and program decisions. GEM-FLO utilizes a generic modelling paradigm to provide a single platform for modelling different designs, which helped significantly cut the cost of these studies. This paper documents a success story in generic simulation modelling.