BP网络的一种改进学习方法

章分析了传统BP学习方法的缺陷，给出了一种改进的学习方法，并用非线性函数tg△x和(e^△x-1)代替传统的线性函数△x进行网络学习和参数调整．仿真表明，该算法能有效克服网络陷入局部极小的困境，并大大提高收敛速度．     

On a Strategy to Develop Robust and Simple Tariffs from Motor Vehicle Insurance Data

The goals of this paper are twofold: we describe common features in data sets from motor vehicle insurance companies and we investigate a general strategy which exploits the knowledge of such features. The results of the strategy are a basis to develop insurance tariffs. We use a nonparametric approach based on a combination of kernel logistic regression and ε-support vector regression which both have good robustness properties. The strategy is applied to a data set from motor vehicle insurance companies.     

用柯西准则证明几个相关命题

以方法为中心探索性教学。可以提高学生的数学创新思维能力．本利用柯西准则证明了无穷级数与广义积分中的几个相关命题。     

具有学习效应和加工时间可控的平行机排序问题

本文研究了一类不相关平行机的排序问题,在该问题中工件的加工时间既具有学习效应,又资源可控,也就是说在该问题模型中,工件的实际加工时间为其正常的加工时间、加工过程中工件所处位置以及加工时间可控这些变量的函数。该研究的目的是为使得总机器负载和总的控制费用的加权和最小以及总的完工时间和总的控制费用的加权和最小。文章通过对问题的相关性质的分析和证明找到了一个解决问题的最优化算法,并且也证明了在处理机的数量给定的条件下,该问题的时间复杂性为O(n^m+2),最后也给出了相应的数值例子来阐述该问题。     

Solving a classification task by spiking neural network with STDP based on rate and temporal input encoding

This paper develops local learning algorithms to solve a classification task with the help of biologically inspired mathematical models of spiking neural networks involving the mechanism of spike-timing-dependent plasticity (STDP). The advantages of the models are their simplicity and, hence, the potential ability to be hardware-implemented in low-energy-consuming biomorphic computing devices. The methods developed are based on two key effects observed in neurons with STDP: mean firing rate stabilization and memorizing repeating spike patterns. As the result, two algorithms to solve a classification task with a spiking neural network are proposed: the first based on rate encoding of the input data and the second based on temporal encoding. The accuracy of the algorithms is tested on the benchmark classification tasks of Fisher's Iris and Wisconsin breast cancer, with several combinations of input data normalization and preprocessing. The respective accuracies are 99% and 94% by F1-score.     

Examining and developing fourth grade children’s area estimation performance

This study explored children’s area estimation performance. Two groups of fourth grade children completed area estimation tasks with rectangles ranging from 5 to 200 square units. A randomly assigned treatment group completed instructional sessions that involved a conceptual area measurement strategy along with numerical feedback. Children tended to underestimate areas of rectangles. Furthermore, rectangle size was related to performance such that estimation error and variability increased as rectangle size increased. The treatment group exhibited significantly improved area estimation performance in terms of accuracy, as well as reduced variability and instances of extreme responses. Area measurement estimation findings are related to a Hypothetical Learning Trajectory for area measurement.     

Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities

We investigated not only the effects of schema-based instruction (SBI) on the mathematical outcomes of seventh-grade students with mathematical learning disabilities (MLD), but also extended prior work to analyze students’ written explanations on open-ended items involving ratio and proportion situations—ratio, proportion, and percent of change problems— to understand the ability to reason about proportions and identify misconceptions. The sample of 338 students with MLD [scored below the 25th percentile on a proportional problem solving (PPS) pretest] was taken from Jitendra, Harwell, Im, et al. (2019), which randomly assigned classrooms to either the SBI or control condition. Students with MLD in SBI classrooms outperformed their counterparts in control classrooms on proportional problem solving and general mathematics problem solving. Similar results, favoring the SBI condition, were found on the open-ended items; however, overall mean scores across pretest, posttest, and delayed posttest were low. Findings provide evidence for the limited understanding of fractional representations of ratios and highlight students’ persistent use of numerical and additive reasoning in explaining their low performance on the open-ended items.     

通过数学建模竞赛培养研究生创新思维的探索与实践

全国研究生数学建模竞赛是教育部研究生教育创新计划项目,旨在通过举办竞赛不断增强研究生数学建模创新能力,为提高研究生培养质量奠定重要的知识和能力基础.本文介绍了我院在组织研究生参加大赛并取得较好成绩的成功经验和做法.     

Students’ whole number multiplicative concepts: A critical constructive resource for fraction composition schemes

This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students’ construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in relation to the whole. Students’ whole number multiplicative concepts were found to be critical constructive resources for students’ fraction composition schemes. Specifically, the interiorization of two levels of units, a particular multiplicative concept, was found to be necessary for the construction of a unit fraction composition scheme, while the interiorization of three levels of units was necessary for the construction of a general fraction composition scheme. These findings contribute to previous research on students’ construction of fraction multiplication that has emphasized partitioning and conceptualizing quantitative units. Implications of the findings for teaching are considered.     

基于子空间多核学习的企业财务困境预测方法

财务指标的异构性是影响企业财务困境预测精度的重要因素,现有多核学习方法能够用于解决异构数据学习问题。本文首先介绍了子空间多核学习财务困境预测理论框架,在此基础上根据子空间学习的最大化方差准则、类别可分性最大化准则、非线性子空间映射原理,提出了三种子空间多核学习方法,分别为最大化方差投影子空间多核学习、类别可分性最大化子空间多核学习、非线性子空间多核学习。利用采集的我国上市公司数据进行实验,对比所提出的方法同现有代表性财务困境预测方法,并对实验结果进行分析。实验结果表明,本文提出的子空间多核学习财务困境预测框架行之有效,该框架下所构造的子空间多核学习预测方法能够有效地提升财务困境预测精度。