Spatial Topology Rule Checking Algorithm of Linear Entity Based on Quadtree

Spatial topology rule is the primary method to insure the consistency and validity of spatial topology relation in GIS software. Topology rule can be divided into three categories according to geographic entity’s geometric shape: point topology rule, line topology rule and polygon topology rule. At first, this paper summarizes the various linear geographic entities’ topological relations which have practical application, then designs a series of linear entity topology rules detailedly. Based on these rules, this paper proposes a topology rule checking algorithm using quadtree, which is designed on the basis of MAPGIS7.4 spatial data model. The algorithm has already been applied to MAPGIS platform and gained good effects.

Rule Extraction in Transient Stability Study Using Linear Decision Trees

为了提高精细规则的性能,提出一种基于支持样本的线性决策树的规则提取方法。该方法筛选临近稳定边界的支持样本,作为决策树的输入样本,精简了样本数目;提出基于线性分类器的决策树方法,以得到基于组合属性的安全稳定运行规则。在单机无穷大系统和IEEE 39节点系统中的对比研究表明：由于考虑了支持样本的特殊性,用线性组合规则代替单属性规则,减少了计算时间,提高了泛化能力,丰富了规则的物理含义,得到的灵敏度信息可用于辅助决策,在安全稳定精细规则提取中具有应用潜力。

Energy analysis of stability on shallow tunnels based on non-associated flow rule and non-linear failure criterion

On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.

数据降维与K-均值聚类的质量评估

聚类分析在大数据时代应用广泛,但缺乏直观评价聚类质量的有效方法。为此,提出一种具有数据降维和搜寻数据固有聚类数量的处理模式。在数据散射矩阵基础上构造一个增广矩阵,利用线性辨别分析将高维数据变换到最具辨别性的低维特征子空间以实现数据降维。为解决分区聚类算法的随机初始化问题,提出最小-最大规则,避免出现空聚类并确保数据的可分性。对于聚类的结果,计算每个聚类的轮廓系数,通过比较轮廓的尺寸以评价不同聚类数量情况下的聚类质量。对K-均值算法的仿真结果说明,这种处理模式不仅能够可视化确定未知数据所固有的聚类数量,而且能为高维数据提供有效的分析方法。

考虑源-荷不确定性的微能源网日前鲁棒优化调度

微能源网集成园区/社区的分布式能量系统、多元荷载及控制装置,能够实现多能源联产联供功能,有利于提升各类能源网络运行灵活性和经济性。为有效应对微能源网内部负荷和新能源出力的不确定性,首先建立多面体不确定集刻画负荷和光伏出力波动情况,构建描述微能源网网络拓扑和能流耦合关系的能源集线器(energy hub,EH)耦合矩阵。然后,以最小化系统运行成本为目标建立微能源网在并网和孤岛运行模式下的两阶段鲁棒优化经济调度模型,并运用线性决策规则(linear decision rule,LDR)和对偶理论制定模型求解策略。最后,基于IEEE 33节点配电网改进设计的微能源网进行算例验证分析。结果表明,LDR能够在一定精度范围内通过线性仿射函数有效近似刻画决策变量和不确定变量间的关系,降低两阶段鲁棒优化经济调度模型的求解难度。

Use Chou’s 5-Steps Rule to Predict Remote Homology Proteins by Merging Grey Incidence Analysis and Domain Similarity Analysis

Detecting remote homology proteins is a challenging problem for both basic research and drug development. Although there are a couple of methods to deal with this problem, the benchmark datasets based on which the existing methods were trained and tested contain many high homologous samples as reflected by the fact that the cutoff threshold was set at 95%. In this study, we reconstructed the benchmark dataset by setting the threshold at 40%, meaning none of the proteins included in the benchmark dataset has more than 40% pairwise sequence identity with any other in the same subset. Using the new benchmark dataset, we proposed a new predictor called “dRHP-GreyFun” based on the grey modeling and functional domain approach. Rigorous cross-validations have indicated that the new predictor is superior to its counterparts in both enhancing success rates and reducing computational cost. The predictor can be downloaded from https://github.com/jcilwz/dRHP-GreyFun.

Solving Linear Programming Problems via Appending an Elastic Constraint

Despite it is often available in practice, information of optimal value of linear programming problems is ignored by conventional simplex algorithms. To speed up solution process, we propose in this paper some variants of the bisection algorithm, explo

A Modified Centered Climbing Algorithm for Linear Programming

In this paper, we propose a modified centered climbing algorithm (MCCA) for linear programs, which improves the centered climbing algorithm (CCA) developed for linear programs recently. MCCA implements a specific climbing scheme where a violated constraint is probed by means of the centered vector used by CCA. Computational comparison is made with CCA and the simplex method. Numerical tests show that, on average CPU time, MCCA runs faster than both CCA and the simplex method in terms of tested problems. In addition, a simple initialization technique is introduced.

A Generalization of Cramer’s Rule

In this paper, we find two formulas for the solutions of the following linear equation , where is a real matrix. This system has been well studied since the 1970s. It is known and simple proven that there is a solution for all if, and only if, the rows of A are linearly independent, and the minimum norm solution is given by the Moore-Penrose inverse formula, which is often denoted by;in this case, this solution is given by . Using this formula, Cramer’s Rule and Burgstahler’s Theorem (Theorem 2), we prove the following representation for this solution , where are the row vectors of the matrix A. To the best of our knowledge and looking in to many Linear Algebra books, there is not formula for this solution depending on determinants. Of course, this formula coincides with the one given by Cramer’s Rule when .

New Optimal Pivot Rule for the Simplex Algorithm

The purpose of this paper is to introduce a new pivot rule of the simplex algorithm. The simplex algorithm first presented by George B. Dantzig, is a widely used method for solving a linear programming problem (LP). One of the important steps of the simplex algorithm is applying an appropriate pivot rule to select the basis-entering variable corresponding to the maximum reduced cost. Unfortunately, this pivot rule not only can lead to a critical cycling (solved by Bland’s rules), but does not improve efficiently the objective function. Our new pivot rule 1) solves the cycling problem in the original Dantzig’s simplex pivot rule, and 2) leads to an optimal improvement of the objective function at each iteration. The new pivot rule can lead to the optimal solution of LP with a lower number of iterations. In a maximization problem, Dantzig’s pivot rule selects a basis-entering variable corresponding to the most positive reduced cost;in some problems, it is well-known that Dantzig’s pivot rule, before reaching the optimal solution, may visit a large number of extreme points. Our goal is to improve the simplex algorithm so that the number of extreme points to visit is reduced;we propose an optimal improvement in the objective value per unit step of the basis-entering variable. In this paper, we propose a pivot rule that can reduce the number of such iterations over the Dantzig’s pivot rule and prevent cycling in the simplex algorithm. The idea is to have the maximum improvement in the objective value function: from the set of basis-entering variables with positive reduced cost, the efficient basis-entering variable corresponds to an optimal improvement of the objective function. Using computational complexity arguments and some examples, we prove that our optimal pivot rule is very effective and solves the cycling problem in LP. We test and compare the efficiency of this new pivot rule with Dantzig’s original pivot rule and the simplex algorithm in MATLAB environment.

Solution Building for Arbitrary System of Linear Inequalities in an Explicit Form

The known Fourier-Chernikov algorithm of linear inequality system convolution is complemented with an original procedure of all dependent (redundant) inequalities deletion. The concept of “almost dependent” inequalities is defined and an algorithm for further reducing the system by deletion of these is considered. The concluding algorithm makes it possible to hold actual-time convolution of a general inequality system containing up to 50 variables with the rigorous method of dependent inequalities deletion and up to 100 variables with the approximate method of one. The main application of such an approach consists in solving linear inequality system in an explicit form. These results are illustrated with a series of computer experiments.

Fetal ECG Extraction Based on Adaptive Linear Neural Network

Fetal ECG extraction has the vital significance for fetal monitoring.This paper introduces a method of extracting fetal ECG based on adaptive linear neural network.The method can be realized by training a small quantity of data.In addition,a better result can be achieved by improving neural network structure.Thus,more easily identified fetal ECG can be extracted.Experimental results show that the adaptive linear neural network can be used to extract fetal ECG from maternal abdominal signal effectively.What's more,a clearer fetal ECG can be extracted by improving neural network structure.

基于鲁棒优化的微电网自调度模型研究

为了最小化微电网运行成本,提出了一个考虑微电网中分布式能源不确定性的两阶段半预期鲁棒优化模型。通过考虑未来部分时段的信息,半预期鲁棒优化模型尽可能地接近实际调度情况。分布式能源的不确定性被描述为由盒式约束和控制集合大小约束所结合产生的不确定集合。模型中的决策变量使用线性决策规则进行线性逼近,将两阶段鲁棒优化模型转换为多阶段鲁棒模型。最后使用约束生成算法有效地求解多阶段鲁棒模型。对微电网配电系统进行了仿真,证明所提出的半预期鲁棒优化模型的正确性和有效性。结果表明,充分考虑分布式能源不确定性的半预期鲁棒优化模型与传统的鲁棒优化模型相比,更具有经济性和鲁棒性。

High Accuracy Arithmetic Average Discretization for Non-Linear Two Point Boundary Value Problems with a Source Function in Integral Form

In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.

芝麻过敏原的生物信息学分析

通过DNAstar和IEDB等生物信息学软件对7种芝麻过敏原的生物学信息进行分析,采用多种方案对芝麻过敏原的抗原指数、亲水性、表面可及性、柔韧性等参数及其二级结构进行预测,并对预测的抗原表位综合分析.利用SWISS-MODEL进行同源建模并用拉氏图评价其结构稳定性.结果表明,7种芝麻过敏原蛋白均存在多个可能的抗原表位,采用同源建模的方式成功构建了芝麻过敏原蛋白的三级结构模型,拉氏图显示该模型的构象稳定.本研究为制备特异性抗体肽段和过敏原检测等提供了依据.

基于数据挖掘探讨药食同源类中药在治疗感冒后咳嗽中的用药规律

目的:探讨近10年来药食同源类中药防治感冒后咳嗽的应用及配伍规律。方法:检索4个中文数据库(CNKI、WANFANG DATA、VIP、CBM),筛选2012—2021年治疗感冒后咳嗽的临床文献,建立方药数据库。通过Microsoft Excel 2019、SPSS Modeler 18.0及SPSS Statistics 24.0软件对处方药物进行关联规则、复杂网络、系统聚类和因子分析。结果:纳入的417首处方涉及257味中药,较常见的药食同源中药为甘草、桔梗、苦杏仁、陈皮、茯苓、生姜等;关联规则分析得到34对核心药组;复杂网络核心处方由止嗽散组成;聚类分析得到8个药物组合;因子分析提取出14个公因子。结论:药食同源类中药的运用符合中医学“治未病”的思想,可以应用于预防感冒后咳嗽。

Optimal pivot path of the simplex method for linear programming based on reinforcement learning

Based on the existing pivot rules,the simplex method for linear programming is not polynomial in the worst case.Therefore,the optimal pivot of the simplex method is crucial.In this paper,we propose the optimal rule to find all the shortest pivot paths of the simplex method for linear programming problems based on Monte Carlo tree search.Specifically,we first propose the SimplexPseudoTree to transfer the simplex method into tree search mode while avoiding repeated basis variables.Secondly,we propose four reinforcement learning models with two actions and two rewards to make the Monte Carlo tree search suitable for the simplex method.Thirdly,we set a new action selection criterion to ameliorate the inaccurate evaluation in the initial exploration.It is proved that when the number of vertices in the feasible region is C_(n)^(m),our method can generate all the shortest pivot paths,which is the polynomial of the number of variables.In addition,we experimentally validate that the proposed schedule can avoid unnecessary search and provide the optimal pivot path.Furthermore,this method can provide the best pivot labels for all kinds of supervised learning methods to solve linear programming problems.

Combinations of Right Half-Plane Mappings and Vertical Strip Mappings Convex in the Vertical Direction

In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided they are locally univalent and sense-preserving. Furthermore, we extend this analysis to a more general case by setting specific conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic mappings, and prove the sufficient conditions that their combinations are locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.

On mathematical arbitrariness of some papers on the potential homologous linear rule investigation

The history of homologous linear rule investigation is reviewed simply. The author puts forward a problem worth paying attention to in the recent potential homologous linear rule investigation, especially some mistakes made in these investigations on mathematical foundations. The author also exposes the mathematical arbitrariness of some papers on their potential homologous linear rule investigation.