Developing a new nonbinary SNP fluorescent multiplex detection system for forensic application in China

Nonbinary single‐nucleotide polymorphisms (SNPs) are potential forensic genetic markers because their discrimination power is greater than that of normal binary SNPs, and that they can detect highly degraded samples. We previously developed a nonbinary SNP multiplex typing assay. In this study, we selected additional 20 nonbinary SNPs from the NCBI SNP database and verified them through pyrosequencing. These 20 nonbinary SNPs were analyzed using the fluorescent‐labeled SNaPshot multiplex SNP typing method. The allele frequencies and genetic parameters of these 20 nonbinary SNPs were determined among 314 unrelated individuals from Han populations from China. The total power of discrimination was 0.9999999999994, and the cumulative probability of exclusion was 0.9986. Moreover, the result of the combination of this 20 nonbinary SNP assay with the 20 nonbinary SNP assay we previously developed demonstrated that the cumulative probability of exclusion of the 40 nonbinary SNPs was 0.999991 and that no significant linkage disequilibrium was observed in all 40 nonbinary SNPs. Thus, we concluded that this new system consisting of new 20 nonbinary SNPs could provide highly informative polymorphic data which would be further used in forensic application and would serve as a potentially valuable supplement to forensic DNA analysis.     

基于纹理特征的挠性印制电路板焊盘缺陷检测

纹理特征反应了物体表面微观几何形貌与颜色的波动程度。针对挠性印制电路(FPC)焊盘纹理特征的提取与检测,本文提出基于灰度与纹理梯度二维分布特征的方法建立描述纹理特征的熵统计量,该统计量能够灵敏地反映、量化焊盘金面正常或异常情况下的不同表面视觉特征,当用于缺陷检测时,可准确地识别出焊盘缺陷,检测准确率高达96.7%,50个焊盘的平均检测时间为300ms,满足在线检测的要求。     

基于主成分回归的杭州市PM2.5含量的综合分析

为探究杭州市PM2.5含量与其他指标之间的关系,搜集杭州市2019年的AQI指数和AQI 6项指标进行分析.首先通过相关分析揭示PM2.5与其余5项指标的相关性,发现各指标与PM2.5均呈线性关系,又因为其余5项指标之间存在显著的线性相关性,故自变量之间存在多重共线性.为了消除多重共线性的影响,对这5项指标提取主成分,再基于主成分分析做回归分析.最后对模型进行统计诊断,按照一定标准筛选出原始数据中的强影响点,删除强影响点后得到最终模型.     

The pinnacle set of a permutation

The peak set of a permutation records the indices of its peaks. These sets have been studied in a variety of contexts, including recent work by Billey, Burdzy, and Sagan, which enumerated permutations with prescribed peak sets. In this article, we look at a natural analogue of the peak set of a permutation, instead recording the values of the peaks. We define the “pinnacle set” of a permutation $w$ to be the set $\{w\left(i\right):i\text{ is a peak of}w\}$. Although peak sets and pinnacle sets mark the same phenomenon for a given permutation, the behaviors of these sets differ in notable ways as distributions over the symmetric group. In the work below, we characterize admissible pinnacle sets and study various enumerative questions related to these objects.     

基于直觉模糊集的多属性决策方法

对基于直觉模糊信息的多属性决策问题进行了研究,引入了直觉模糊数的得分函数、直觉模糊正理想点和负理想点,然后给出了基于TOPSIS的多属性决策方法,通过计算各备选方案的得分向量与直觉模糊负理想点得分向量之间的距离来确定各备选方案的综合评价指数,进而判断方案的优劣次序.最后,通过一个具体的实例分析说明了该方法的有效性与具体应用过程.     

A new uniform mapping algorithm for sample selection

A new algorithm for sample selection in the field of experimental design is presented. This method was designed for a multivariate data set of samples where the variables' levels are pre‐determined by the system instead of being determined by the practitioner and especially appropriate for non‐symmetrical multivariable space. Symmetrical experimental designs are not applicable in either of the cases. Anyway, this method is also applicable to symmetrical designs. Several tests have been made for symmetrical and non‐symmetrical cases and also about an already treated real case, comparing the new algorithm with others previously known in literature. Its performance has been checked considering several evaluation quality criteria like D‐optimal, A‐optimal, G‐optimal and models error prediction. Copyright © 2008 John Wiley & Sons, Ltd.     

Susceptibility of the rectangular Ising ferromagnet

The critical index values= 7/4 for the susceptibility and=15 for the critical isotherm are derived rigorously for the rectangular Ising ferromagnet with nearest neighbor interactions. The critical indices associated with the Fisher moment definition of the correlation length are obtained asTT _c+. The index of the fluctuation sum definition of critical correlations is obtained.Partially supported by grant PHY 76 17191.     

Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions

The Jeffreys divergence is a renown arithmetic symmetrization of the oriented Kullback–Leibler divergence broadly used in information sciences. Since the Jeffreys divergence between Gaussian mixture models is not available in closed-form, various techniques with advantages and disadvantages have been proposed in the literature to either estimate, approximate, or lower and upper bound this divergence. In this paper, we propose a simple yet fast heuristic to approximate the Jeffreys divergence between two univariate Gaussian mixtures with arbitrary number of components. Our heuristic relies on converting the mixtures into pairs of dually parameterized probability densities belonging to an exponential-polynomial family. To measure with a closed-form formula the goodness of fit between a Gaussian mixture and an exponential-polynomial density approximating it, we generalize the Hyvärinen divergence to α-Hyvärinen divergences. In particular, the 2-Hyvärinen divergence allows us to perform model selection by choosing the order of the exponential-polynomial densities used to approximate the mixtures. We experimentally demonstrate that our heuristic to approximate the Jeffreys divergence between mixtures improves over the computational time of stochastic Monte Carlo estimations by several orders of magnitude while approximating the Jeffreys divergence reasonably well, especially when the mixtures have a very small number of modes.     

最大最小次序统计量的联合分布

X1,X2,…,Xn是来自总体X的简单随机样本,Nk=min1≤i≤k{Xi},Mk=max1≤i≤k{Xi}(k=1,2,…,n),本文给出了最小次序统计量与最大次序统计量的联合分布函数.     

Sequentially Estimating the Approximate Conditional Mean Using Extreme Learning Machines

This study examined the extreme learning machine (ELM) applied to the Wald test statistic for the model specification of the conditional mean, which we call the WELM testing procedure. The omnibus test statistics available in the literature weakly converge to a Gaussian stochastic process under the null that the model is correct, and this makes their application inconvenient. By contrast, the WELM testing procedure is straightforwardly applicable when detecting model misspecification. We applied the WELM testing procedure to the sequential testing procedure formed by a set of polynomial models and estimate an approximate conditional expectation. We then conducted extensive Monte Carlo experiments to evaluate the performance of the sequential WELM testing procedure and verify that it consistently estimates the most parsimonious conditional mean when the set of polynomial models contains a correctly specified model. Otherwise, it consistently rejects all the models in the set.