桉树杂交种与其亲本的近红外光谱判别

研究桉树控制授粉后目标性状的基因作用方式是探索其基因重组规律的重要内容。常规的数量统计分析精度往往不高,而DNA分析的专业要求高,且费时费力。该研究利用近红外光谱(NIRs)研究不同基因型桉树杂交种、亲本及杂交种与亲本间近红外光谱信息的关系,探索NIRs用于桉树杂交种与其亲本判别的可行性和准确性。以控制授粉的桉树亲本及其杂交F1代材料为对象,每种基因型从各自田间试验分别选取10个单株,采集树冠中上部新鲜健康叶片。用手持式近红外仪Phazir Rx(1624)采集桉树杂交种与其亲本叶片的NIRs信息。每单株选10片完全生理成熟的健康叶片,避开叶脉扫描其正面光谱5次,以50条NIRs信息的均值代表单个叶片的NIRs信息,最终每个基因型获得10条NIRs信息。对原始NIRs采用二阶多项式S.G一阶导数预处理。预处理后的NIRs用于多元统计分析,首先对桉树杂交亲本和子代样本进行主成分分析(PCA),直观展示不同基因型的分类情况。然后运用簇类独立软模式(SIMCA)和偏最小二乘判别分析(PLS-DA)两种有监督的判别模式验证NIRs用于桉树杂交种与其亲本树种的分类判别效果。PCA结果显示,不同的亲本间、杂交种间及杂交种与亲本间样本的主因子得分可以清晰地将各基因型分开。SIMCA模式判别分析中,桉树杂交种样本到亲本PCA模型的样本距离显示,待判别样本能够形成单独的聚类,且能直观反映两者的遗传相似。PLS-DA判别结果显示,桉树杂交亲本的PLS模型能通过预测其杂交子代的响应变量将其与亲本准确分开。结果表明,桉树叶片的NIRs信息可以准确地反映桉树杂交子代遗传信息的传递规律,NIRs判别模型可以准确地将各种基因型予以区分。因此,NIRs信息不仅可用于桉树杂交种和纯种的定性判别,还可以分析桉树基因重组过程中加性遗传效应的大小,从而为桉树遗传基础分析及其育种改良研究提供理论支撑。     

企业自主研发与合作创新的风险测度及组合优化

企业在整合内部创新要素进行自主研发的同时,也会寻求外部创新资源进行合作创新,当前同时从事多个R&D项目已成为常见的企业经营活动,如何在不确定条件下分析多个R&D项目投资的策略选择及风险优化,对于企业的长期发展具有重要意义。根据企业是否采取合作创新策略,可将其R&D项目分为自主研发与合作创新两类,以项目的研发成功率和投资收益率代表技术风险和市场风险,分别测度自主研发与合作创新项目的风险特性,并在此基础上构建企业R&D项目投资组合优化模型,以在自主研发与合作创新项目之间进行权衡取舍。结果表明,企业对于自主研发与合作创新项目投资组合的最优投资权重,主要取决于这两类组合的期望收益率、收益率方差、期望成功率以及两组合之间的协方差。企业可基于关键参数制定出最优的R&D项目投资组合选择策略,合理分配资金以达到风险最小化的投资目标。     

Correlation‐assisted nearest shrunken centroid classifier with applications for high dimensional spectral data

High throughput data are frequently observed in contemporary chemical studies. Classification through spectral information is an important issue in chemometrics. Linear discriminant analysis (LDA) fails in the large‐p‐small‐n situation for two main reasons: (1) the sample covariance matrix is singular when p > n and (2) there is an accumulation of noise in the estimation of the class centroid in high dimensional feature space. The Independence Rule is a class of methods used to overcome these drawbacks by ignoring the correlation information between spectral variables. However, a strong correlation is an essential characteristic of spectral data. We proposed a new correlation‐assisted nearest shrunken centroid classifier (CA‐NSC) to incorporate correlation information into the classification. CA‐NSC combines two sources of information [class centroid (mean) and correlation structure (variance)] to generate the classification. We used two real data analyses and a simulation study to verify our CA‐NSC method. In addition to NSC, we also performed a comparison with the soft independent modeling of class analogy (SIMCA) approach, which uses only correlation structure information for classification. The results show that CA‐NSC consistently improves on NSC and SIMCA. The misclassification rate of CA‐NSC is reduced by almost half compared with NSC in one of the real data analyses. Generally, correlation among variables will worsen the performance of NSC, even though the discriminatory information contained in the class centroid remains unchanged. If only correlation structure information is used (as in the case of SIMCA), the result will be satisfactory only when the correlation structure alone can provide sufficient information for classification. Copyright © 2015 John Wiley & Sons, Ltd.     

Cause–effect analysis: improvement of a first year engineering students’ calculus teaching model

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause–effect analysis, often used for business improvement. The cause–effect analysis indicates that there are many factors that impact on secondary school teaching of mathematics, factors that the tertiary sector has no control over. The analysis also indicates the undesirable issues that are at the root of impeding success in the calculus module. Most important is that students are not encouraged to become independent thinkers from an early age. This triggers problems in follow-up courses where students are expected to have learned to deal with the work load and understanding of certain concepts. A new model was designed to lessen the impact of these undesirable issues.     

On the Number of k‐Dominating Independent Sets

We study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erd?s and Moser—is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of k‐dominating independent sets in n‐vertex graphs is between and if , moreover the maximum number of 2‐dominating independent sets in n‐vertex graphs is between and . Graph constructions containing a large number of k‐dominating independent sets are coming from product graphs, complete bipartite graphs, and finite geometries. The product graph construction is associated with the number of certain Maximum Distance Separable (MDS) codes.     

Nucleus Independent Chemical Shift (NICS) at Small Distances from the Molecular Plane: The Effect of Electron Density

When close to the molecular plane, the behavior of nucleus independent chemical shift (NICS) as a function of the distance from the molecular plane deviates from its behavior at larger distances. By using a dense grid of NICS-probes (BQs) it is shown that, when close to the molecular plane, maximal (absolute) NICS values are obtained above the atoms. These maxima move towards the center as the grid is elevated until the (absolute) maximum NICS is obtained at the center and stay there when the grid is further elevated. It is shown that this behavior is a result of the current density, which is influenced by the electron density, according to the Biot-Savart law, which, in turn, causes the induced magnetic field measured by the NICS. It is thus concluded that if magnetic aromaticity is studied, the NICS calculations should be carried out at a large enough distance so that only the π-ring current affects the NICS. At distances ≥2 Å, NICS(r)_π,zz=A+B*C^r. Using non-linear correlation for obtaining A, B and C and extrapolate to NICS(1)_π,zz and NICS(1.7)_π,zz is recommended as measures for aromaticity.     

关于一类电-力振动模型的建模与分析

从电学、力学的基本原理出发,通过数学方法建立和分析了一种电-力振动模型。这是一种较复杂的电力混合作用的线性振动系统,由模型的特殊结构(类扬声器结构)作者确立了两种磁场,即感生磁场和外磁场两者正交独立,并规定了电学、力学两种不同物理量的坐标取向关系。该模型需要求得三阶正系数常微分方程的收敛解,再求得包含暂态、稳态项的完整解。另外,文章从能量和做功的角度,通过对电压电流间的相位差分析,对所建模型的正确性作了论证,同时也为这类建模引荐了一种论证手段。