Accuracy and CPU time of JE-TLM,PLRC-TLM and CRC-TLM methods for plasma medium

The current density (JE), the piecewise linear recursive convolution (PLRC) and the constant convolution recursive (CRC) techniques are developed and integrated into the transmission line matrix (TLM) algorithm. A comparison of these three schemes according to the criteria of accuracy and CPU time is presented. Numerical experiments show that JE provides the most accurate solution and requires the least CPU time; PLRC is nearly as accurate but consumes more CPU time than CRC.     

含中介值ξ-η-ζ等式的证明方法

介绍含三个中介值ξ-η-ζ等式的几种证明方法,并结合实例加以说明.     

Imperialist competitive algorithm combined with chaos for global optimization

A novel chaotic improved imperialist competitive algorithm (CICA) is presented for global optimization. The ICA is a new meta-heuristic optimization developed based on a socio-politically motivated strategy and contains two main steps: the movement of the colonies and the imperialistic competition. Here different chaotic maps are utilized to improve the movement step of the algorithm. Seven different chaotic maps are investigated and the Logistic and Sinusoidal maps are found as the best choices. Comparing the new algorithm with the other ICA-based methods demonstrates the superiority of the CICA for the benchmark functions.     

A thermodynamic and dynamic subgrid closure model for two‐material cells

A general and robust subgrid closure model for two‐material cells is proposed. The conservative quantities of the entire cell are apportioned between two materials, and then, pressure and velocity are fully or partially equilibrated by modeling subgrid wave interactions. An unconditionally stable and entropy‐satisfying solution of the processes has been successfully found. The solution is valid for arbitrary level of relaxation. The model is numerically designed with care for general materials and is computationally efficient without recourse to subgrid iterations or subcycling in time. The model is implemented and tested in the Lagrange‐remap framework. Two interesting results are observed in 1D tests. First, on the basis of the closure model without any pressure and velocity relaxation, a material interface can be resolved without creating numerical oscillations and/or large nonphysical jumps in the problem of the modified Sod shock tube. Second, the overheating problem seen near the wall surface can be solved by the present entropy‐satisfying closure model. The generality, robustness, and efficiency of the model make it useful in principle in algorithms, such as ALE methods, volume of fluid methods, and even some mixture models, for compressible two‐phase flow computations. Copyright © 2013 John Wiley & Sons, Ltd.     

基于RBM的神经网络时间序列预测

为了克服神经网络依赖初始化结果,泛化能力不强的缺点,提出一种基于受限玻尔兹曼机(RBM)的神经网络模型.利用无监督学习方法优化神经网络的初始权值和阈值,将RBM与神经网络融合起来,模型与时间序列神经网络做实验对比,结果表明,基于受限的玻尔兹曼机的神经网络模型优于神经网络预测模型,模型可以提高预测的精准度,具有一定的应用意义.     

Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm

The trust region method which originated from the Levenberg–Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.     

Approximating exponential and logarithmic functions using polynomial interpolation

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.     

Gauss–Seidel Estimation of Generalized Linear Mixed Models With Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) are often fit by computational procedures such as penalized quasi-likelihood (PQL). Special cases of GLMMs are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints make it difficult to apply these iterative procedures to datasets having a very large number of records.

We propose a computationally efficient strategy based on the Gauss–Seidel algorithm that iteratively fits submodels of the GLMM to collapsed versions of the data. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status, and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. For Poisson and binomial regression models, the Gauss–Seidel approach is found to substantially outperform existing methods in terms of maximum analyzable sample size. Remarkably, for both models, the average time per iteration and the total time until convergence of the Gauss–Seidel procedure are less than 0.3% of the corresponding times for the IWLS algorithm. Platform-independent pseudo-code for fitting GLMS, as well as the source code used to generate and analyze the datasets in the simulation studies, are available online as supplemental materials.     

北海航道班轮运输排班模型的构建与求解

首先,以拟开通的大连港至鹿特丹港北海航道班轮航线为研究对象,以油耗和运营成本最小化为优化目标,将官方已有记载的北海航道通过的货船航速数据输入Eureqa软件,得到航行最高速度f(x)与进入北海航道时间t的拟合度最好的函数公式.在此基础上,构建了北海航道班轮运输排班的数学模型;其次,在仿真实例分析中,选用了5000TEU的集装箱船作为计算参数,将捕食搜索算法运用到数学模型求解之中,并且运用MATLAB软件进行求解,在最快航速受限的前提下,得到单艘班轮最佳往返时间和相同型号班轮的最低配置数目以及在服务周期内班轮公司所要付出的最低运营成本;最后,通过比较研究,得出结论是:最快航速的提高,对于降低北海航线班轮运输的运营成本将起较大作用.