A self‐adaptive intelligence gray prediction model with the optimal fractional order accumulating operator and its application

The self‐adaptive intelligence gray predictive model (SAIGM) has an alterable‐flexible model structure, and it can build a dynamic structure to fit different external environments by adjusting the parameter values of SAIGM. However, the order number of the raw SAIGM model is not optimal, which is an integer. For this, a new SAIGM model with the fractional order accumulating operator (SAIGM_FO) was proposed in this paper. Specifically, the final restored expression of SAIGM_FO was deduced in detail, and the parameter estimation method of SAIGM_FO was studied. After that, the Particle Swarm Optimization algorithm was used to optimize the order number of SAIGM_FO, and some steps were provided. Finally, the SAIGM_FO model was applied to simulate China's electricity consumption from 2001 to 2008 and forecast it during 2009 to 2015, and the mean relative simulation and prediction percentage errors of the new model were only 0.860% and 2.661%, in comparison with the ones obtained from the raw SAIGM model, the GM(1, 1) model with the optimal fractional order accumulating operator and the GM(1, 1) model, which were (1.201%, 5.321%), (1.356%, 3.324%), and (2.013%, 23.944%), respectively. The findings showed both the simulation and the prediction performance of the proposed SAIGM_FO model were the best among the 4 models.     

基于函数系数自回归模型的风速时间序列预测

准确预测风电场风速是解决风能对电力系统所造成的安全、稳定运行和电能质量等问题的有效途径之一.风速的难以预测是由于它的高度随机和非线性.基于一种非参数的非线性自回归随机模型来预测风速,模型的自回归系数随模型依赖变量的变化而变化,因而它有灵活的非线性结构.数值实验和比较结果表明了这种函数系数自回归模型在风电场风速预测中的有效性.     

基于模糊灰色新陈代谢FGM(1,1)模型预测及应用探讨

巷道围岩变形是煤矿开采普遍存在的问题,巷道开挖过程中围岩会出现破裂现象.主要探讨模糊灰色系统的深部巷道围岩变形预测模型及应用,通过分析模糊数学理论、灰色理论,给出模糊灰色系统预测新陈代谢模型.     

基于Leslie模型的北京市基础教育学龄人口分城乡预测

以2010年第六次人口普查数据为基点,考虑到已经开放的单独二胎政策以及全面放开的二胎政策等因素,对北京市2020—2030年基础教育学龄人口变动情况分城乡进行预测.研究发现:北京学龄人口总体上呈现先上升后下降趋势;城市学龄人口远远高于农村学龄人口;城市各个阶段学龄人口均出现了先升后降趋势;农村幼儿园学龄人口呈现快速下降趋势,小学、初中学龄人口均呈现了先升后降趋势,农村高中学龄人口呈现了"下降-上升-下降-上升"的反复波动.学龄人口的变化反映了未来教育需求的变动,在未来10-15年,北京市还需要加大教师队伍建设、加强基础设施建设,努力实现城乡教育资源均衡化,最大限度地实现教育公平.     

基于果蝇算法优化广义回归神经网络的矢量水听器的DOA估计

为了提高矢量水听器阵列对窄带信号的DOA估计精度,运用果蝇算法优化广义回归神经网络,通过对阵列协方差矩阵实值化,并提取信号子空间的基作为样本特征进行网络训练,构建了果蝇算法优化下的广义回归神经网络,实现了基于矢量水听器阵列的水下声源的DOA估计.仿真实验结果表明,方法泛化性能较好,能解决输入维数过大的问题,且运行时间短,DOA估计精度高,具有较强的工程应用价值.     

Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.     

张量鲁棒主成分分析的增广拉格朗日交替方向方法

张量的鲁棒主成分分析是将未知的一个低秩张量与一个稀疏张量从已知的它们的和中分离出来.因为在计算机视觉与模式识别中有着广阔的应用前景,该问题在近期成为学者们的研究热点.本文提出了一种针对张量鲁棒主成分分析的新的模型,并给出交替方向极小化的求解算法,在求解过程中给出了两种秩的调整策略.针对低秩分量本文对其全部各阶展开矩阵进行低秩矩阵分解,针对稀疏分量采用软阈值收缩的策略.无论目标低秩张量为精确低秩或近似低秩,本文所提方法均可适用.本文对算法给出了一定程度上的收敛性分析,即算法迭代过程中产生的任意收敛点均满足KKT条件.如果目标低秩张量为精确低秩,当迭代终止时可对输出结果进行基于高阶奇异值分解的修正.针对人工数据和真实视频数据的数值实验表明,与同类型算法相比,本文所提方法可以得到更好的结果.     

Insights into stretching ratio and velocity slip on MHD rotating flow of Maxwell nanofluid over a stretching sheet: Semi-analytical technique OHAM

Main core part of the research is to develop a novel mathematical model of MHD-Maxwell nanofluid over a stretching and shrinking surface. The stretching ratio, velocity slip and convective boundary conditions are also incorporated. The PDE's with associative boundary conditions are deduced into coupled highly non-linear ODE's by utilizing suitable transformations. The deduced dimensionless sets of Ordinary differential equations are solved by Optimal-Homotopy Analysis Method (OHAM). Behavior of pertinent parameters on the velocity, temperature and concentration fields as well as important aspects skin friction, Nusselt number and Sherwood number are recorded in Table 2. Outcomes declared that role of stretching ratio plays a prominent role in stretching surfaces its clearly recorded in Table 1(a & b).     

基于改进免疫遗传算法的近红外光谱变量选择方法

该文在免疫遗传算法（IGA）的基础上,提出一种改进免疫遗传算法（iIGA）用于近红外光谱波长变量的选择。该算法舍去了原算法中固定抗体相似度阈值的思想,取而代之的是抗体相似度阈值自适应,同时引入精英保留策略和贪心算法思想,使得算法朝着正确的方向进行局部性探优。将该算法在玉米的淀粉和蛋白质含量数据集上进行实验测试,建立偏最小二乘（PLS）分析模型,并与IGA、遗传算法（GA）以及全谱方法进行了对比。结果表明,在玉米淀粉含量的预测上,iIGA相较于原IGA算法,预测集均方根误差（RMSEP）从0.312 0降至0.298 0,预测集预测精度提升4.5%;在玉米蛋白质含量的预测上,RMSEP从0.124 4降至0.110 3,预测集预测精度提升11.3%。分别对预测淀粉和蛋白质模型的RMSEP值进行显著性检验,F值分别为165.22和182.05,P值分别为9.5 × 10－23和4.5 × 10－24,P值均小于0.05,因此,iIGA能显著提升模型预测精度。     

Heterocyclic Substitutions Greatly Improve Affinity and Stability of Folic Acid towards FRα. an In Silico Insight

Folate receptor alpha (FRα) is known as a biological marker for many cancers due to its overexpression in cancerous epithelial tissue. The folic acid (FA) binding affinity to the FRα active site provides a basis for designing more specific targets for FRα. Heterocyclic rings have been shown to interact with many receptors and are important to the metabolism and biological processes within the body. Nineteen FA analogs with substitution with various heterocyclic rings were designed to have higher affinity toward FRα. Molecular docking was used to study the binding affinity of designed analogs compared to FA, methotrexate (MTX), and pemetrexed (PTX). Out of 19 FA analogs, analogs with a tetrazole ring (FOL03) and benzothiophene ring (FOL08) showed the most negative binding energy and were able to interact with ASP81 and SER174 through hydrogen bonds and hydrophobic interactions with amino acids of the active site. Hence, 100 ns molecular dynamics (MD) simulations were carried out for FOL03, FOL08 compared to FA, MTX, and PTX. The root mean square deviation (RMSD) and root mean square fluctuation (RMSF) of FOL03 and FOL08 showed an apparent convergence similar to that of FA, and both of them entered the binding pocket (active site) from the pteridine part, while the glutamic part was stuck at the FRα pocket entrance during the MD simulations. Molecular mechanics Poisson-Boltzmann surface accessible (MM-PBSA) and H-bond analysis revealed that FOL03 and FOL08 created more negative free binding and electrostatic energy compared to FA and PTX, and both formed stronger H-bond interactions with ASP81 than FA with excellent H-bond profiles that led them to become bound tightly in the pocket. In addition, pocket volume calculations showed that the volumes of active site for FOL03 and FOL08 inside the FRα pocket were smaller than the FA–FRα system, indicating strong interactions between the protein active site residues with these new FA analogs compared to FA during the MD simulations.