A contribution of the multiquadric method: Interpolation of potential inside the earth

The multiquadric (MQ) method, when converted into a proper integral equation, is a potential function. As a numerical method, it is capable of interpolation without the usual reciprocal distance singularities. An unusual result of a more detailed study is that the Newtonian attraction generated by each volume element inside a material body is a constant, proportional to the product of G and the density. Consequently, potential at the boundary is identical, whether computed internally with a proper integral for material space, or externally by the approach of unit masses from infinity in free space to the boundary points of a sphere. The capability of the proper integral form, and the corresponding MQ numerical approximation provides a basis for interpolation of potential and its functionals inside and on the boundary of the Earth.     

Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary

The multiquadric radial basis function (MQ) method is a recent meshless collocation method with global basis functions. It was introduced for discretizing partial differential equations (PDEs) by Kansa in the early 1990s. The MQ method was originally used for interpolation of scattered data, and it was shown to have exponential convergence for interpolation problems.In [1], we have extended the Kansa-MQ method to numerical solution and detection of bifurcations in 1D and 2D parameterized nonlinear elliptic PDEs. We have found there that the modest size nonlinear systems resulting from the MQ discretization can be efficiently continued by a standard continuation software, such as auto. We have observed high accuracy with a small number of unknowns, as compared with most known results from the literature.In this paper, we formulate an improved Kansa-MQ method with PDE collocation on the boundary (MQ PDECB): we add an additional set of nodes (which can lie inside or outside of the domain) adjacent to the boundary and, correspondingly, add an additional set of collocation equations obtained via collocation of the PDE on the boundary. Numerical results are given that show a considerable improvement in accuracy of the MQ PDECB method over the Kansa-MQ method, with both methods having exponential convergence with essentially the same rates.     

数学进化中的知识发现方法

从数学历史发展过程中去发现数学的进化规律,从创造数学符号和包容对立的概念中获得了最早的数学知识.将数学符号组合而成的表达式和方程,使问题变换成了形式化表示,当表达式和方程通过推演和求证,判断其正确性时,就形成了公式和定理,它们是数学中的基础理论.推演和求证过程是采用了等价变换.数学进化中更重要的知识发现方法是利用进化变换(对变量、函数、方程、方法等的变换)来拓展数学的新概念和解决不能求解的问题(可拓变换),从而建立了数学的理论体系.创造、包容、形式化变换、等价变换和进化变换都是数学进化中的知识发现方法.     

Topic discovery and evolution in scientific literature based on content and citations

Researchers across the globe have been increasingly interested in the manner in which important research topics evolve over time within the corpus of scientific literature. In a dataset of scientific articles, each document can be considered to comprise both the words of the document itself and its citations of other documents. In this paper, we propose a citation- content-latent Dirichlet allocation (LDA) topic discovery method that accounts for both document citation relations and the con-tent of the document itself via a probabilistic generative model. The citation-content-LDA topic model exploits a two-level topic model that includes the citation information for ‘father’ topics and text information for sub-topics. The model parameters are estimated by a collapsed Gibbs sampling algorithm. We also propose a topic evolution algorithm that runs in two steps: topic segmentation and topic dependency relation calculation. We have tested the proposed citation-content-LDA model and topic evolution algorithm on two online datasets, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI) and IEEE Computer Society (CS), to demonstrate that our algorithm effectively discovers important topics and reflects the topic evolution of important research themes. According to our evaluation metrics, citation-content-LDA outperforms both content-LDA and citation-LDA.     

符合动态演变特性的网格资源发现机制研究

近年来人们对如何提高网格资源发现效率做了大量的研究,但却忽略了适应网格资源动态演变特性的重要性.针对这一问题,结合小世界理论的网络特征,提出了一种新的基于P2P分布式结构化的网格资源发现机制.通过计算资源节点间属性相似度的方法,将网格资源分类组织在不同的虚拟组织中,结合P2P技术构建出两层覆盖式资源发现模型,并设计出相应的资源查找算法DSRD (distributed structure grid resource discovery).仿真实验结果表明,DSRD算法既能够适应资源的动态特性,同时又可有效地提高资源发现效率.     

Miscellaneous error bounds for multiquadric and related interpolators

We establish several types of a a priori error bounds for multiquadric and related interpolators. The results are stated and proven in the general multivariate case. These estimates show, for example, that in many cases such interpolators converge very quickly and can be used in the recovery of band limited functions from discrete data. We also include numerical experiments which illustrate the theoretical results.     

A framework for knowledge discovery and evolution in databases

A concept for knowledge discovery and evolution in databases is described. The key issues include: using a database query to discover new rules; using not only positive examples (answer to a query), but also negative examples to discover new rules; and harmonizing existing rules with the new rules. A tool for characterizing the exceptions in databases and evolving knowledge as a database evolves is developed     

Comments on "A computer-aided root-locus method"

This note generalizes the result given by C. T. Pan and K. S. Chao in the above paper to the case where the gain is negative, and emphasizes the use of Newton-Raphson for correcting starting points originated from complex multiple poles. Finally, it proposes the use of mixed scales in plotting RL's with this methodology.     

Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme

This paper discusses the application of the multizone decomposition technique with multiquadric scheme for the numerical solutions of a time-dependent problem. The construction of the multizone algorithm is based on a domain decomposition technique to subdivide the global region into a number of finite subdomains. The reduction of ill-conditioning and the improvement of the computational efficiency can be achieved with a smaller resulting matrix on each subdomain. The proposed scheme is applied to a hypothetical linear two-dimensional hydrodynamic model as well as a real-life nonlinear two-dimensional hydrodynamic model in the Tolo Harbour of Hong Kong to simulate the water flow circulation patterns. To illustrate the computational efficiency and accuracy of the technique, the numerical results are compared with those solutions obtained from the same problem using a single domain multiquadric scheme. The computational efficiency of the multizone technique is improved substantially with faster convergence without significant degradation in accuracy.     

Identification of non-linear processes using reciprocal multiquadric functions

In this paper radial basis function (RBF) networks are used to model general non-linear discrete-time systems. In particular, reciprocal multiquadric functions are used as activation functions for the RBF networks. A stepwise regression algorithm based on orthogonalization and a series of statistical tests is employed for designing and training of the network. The identification method yields non-linear models, which are stable and linear in the model parameters. The advantages of the proposed method compared to other radial basis function methods and backpropagation neural networks are described. Finally, the effectiveness of the identification method is demonstrated by the identification of two non-linear chemical processes, a simulated continuous stirred tank reactor and an experimental pH neutralization process.     

Improved accuracy of multiquadric interpolation using variable shape parameters

Given N scattered data points, we examined the problem of finding N variable Multiquadric (MQ) shape-parameters, or R² values. Because the problem of finding the optimal R² values is a nonlinear one, we optimized these parameters numerically by minimizing the root-mean-square (RMS) errors. The resulting R² values varied over many orders of magnitude. We have tested this approach on a number of univariate and bivariate (Franke's) problems, and found that the RMS error reduction was substantial.     

Enhancing knowledge discovery via association-based evolution of neural logic networks

The comprehensibility aspect of rule discovery is of emerging interest in the realm of knowledge discovery in databases. Of the many cognitive and psychological factors relating the comprehensibility of knowledge, we focus on the use of human amenable concepts as a representation language in expressing classification rules. Existing work in neural logic networks (or neulonets) provides impetus for our research; its strength lies in its ability to learn and represent complex human logic in decision-making using symbolic-interpretable net rules. A novel technique is developed for neulonet learning by composing net rules using genetic programming. Coupled with a sequential covering approach for generating a list of neulonets, the straightforward extraction of human-like logic rules from each neulonet provides an alternate perspective to the greater extent of knowledge that can potentially be expressed and discovered, while the entire list of neulonets together constitute an effective classifier. We show how the sequential covering approach is analogous to association-based classification, leading to the development of an association-based neulonet classifier. Empirical study shows that associative classification integrated with the genetic construction of neulonets performs better than general association-based classifiers in terms of higher accuracies and smaller rule sets. This is due to the richness in logic expression inherent in the neulonet learning paradigm.     

Comments on a numerical method for solving Boolean equations

A recent paper in this journal, by Abdel-Gawad, Atiya, and Darwish, presents a method of solving a system Boolean equations using the polynomial algebra invented by George Boole in 1854. The authors do not mention Boole, however, or the modern applications of this algebra. Their method entails reduction of the given system to a triangular system, which is solved by back-substitution. We show that the solutions of the triangular system include all those of the given system, but may include others that do not satisfy the given system.     

基于5G毫米波的小区发现方法研究

5G毫米波技术提供了丰富的频率资源和高吞吐量,但由于其严重的路径损耗和穿透损耗,在完成小区搜索和同步过程时,毫米微波蜂窝系统必须引入高定向波束赋形传输技术。基于改善定向传输过程中的时延问题,采用了一种基于传统算法的改进小区发现算法,该算法通过控制面与用户面平面分割的混合网络架构,利用背景信息改进小区发现过程,有效降低时延。通过MATLAB模拟仿真试验得出实验结果 :通过改进算法的传输时延比传统算法降低40%。     

LDPC码密度进化方法与门限研究

详细描述了密度进化(DE)方法的基本原理,比较和分析了离散密度进化(DDE)、对称傅立叶变换(SFT)和高斯近似(GA)等三种具体算法的特点,并求出AWGN信道下一些度分布的门限值。这对LDPC码理论分析和应用研究具有重要指导作用。     

Comments on "Comments on the Routh-Hurwitz criterion"

It is shown that the algorithm given by Shamash for determining the number of roots of polynomial in the right half plane via the Routh table in the presence of purely imaginary roots and a left column zero is not complete and can give erroneous results. Modification for getting correct results is suggested.     

基于进化策略的广义积分计算方法研究

提出了一种基于进化策略算法的广义积分计算新方法,该方法根据被积函数的变量区间任意选取分割点,作为进化策略的初始的群体,通过进化策略算法来优化这些分割点,最终可得到一些最优的分割点,然后再求和,再根据和函数定义适应度函数,在给定的终止条件下,可获的精度较高的积分值.最后,以广义积分(无穷积分),二重广义积分(瑕积分)为例,仿真结果表明,该算法相比传统的一些方法,具有计算精度高,自适应性强等特点.     

2种社团发现算法对工业共生网络演化过程描述的比较

针对工业共生网络特点,分别应用改进后的谱平分算法和凝聚算法2种典型的社团发现算法对卡伦堡及鲁北工业共生网络进行社团划分,并对其集聚性程度进行定量的比较和评价,从而对卡伦堡及鲁北工业共生网络演化过程做出定量描述,并与其实际工业共生网络的演化发展过程做出对比。结果表明,采用复杂网络社团划分算法可以实现对工业共生网络发展演化过程的定量描述,而改进后的谱平分算法比凝聚算法对工业共生网络演化过程的描述更接近其实际的发展状况。