To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的...目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的REPEATED语句实现修正poisson回归。此外,采用不同的统计方法对5个虚拟的研究数据进行了分析比较。结果以分层的Mantel-Haenszel法为标准参照,修正poisson回归对aRR点和区间估计均较为理想,普通poisson回归的aRR区间估计偏于保守。而logistic回归得到的aOR值明显偏离真实的RR值。结论修正poisson回归模型适合于处理常见结局事件的前瞻性研究资料。展开更多
为了度量E-Bayes估计的误差,该文基于E-Bayes估计的定义,引入了E-Bayes估计的E-MSE(expected mean square error)的定义.对Poisson分布的参数,在不同损失函数(包括:平方损失,K-损失,加权平方损失)下分别给出了E-Bayes估计及其E-MSE的表...为了度量E-Bayes估计的误差,该文基于E-Bayes估计的定义,引入了E-Bayes估计的E-MSE(expected mean square error)的定义.对Poisson分布的参数,在不同损失函数(包括:平方损失,K-损失,加权平方损失)下分别给出了E-Bayes估计及其E-MSE的表达式.用MonteCarlo方法进行模拟比较提出的估计方法的性能,分析了一个真实数据集并进行了比较,所得结果比较基于E-MSE,结果表明该文提出的方法可行且便于应用.展开更多
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
文摘目的介绍应用修正poisson回归模型计算常见结局事件的前瞻性研究中暴露因素的调整相对危险度的精确区间估计值。方法应用稳健误差方差估计法(sandwich variance esti mator)来校正相对危险度(RR)的估计方差,并通过SAS程序中GENMOD过程的REPEATED语句实现修正poisson回归。此外,采用不同的统计方法对5个虚拟的研究数据进行了分析比较。结果以分层的Mantel-Haenszel法为标准参照,修正poisson回归对aRR点和区间估计均较为理想,普通poisson回归的aRR区间估计偏于保守。而logistic回归得到的aOR值明显偏离真实的RR值。结论修正poisson回归模型适合于处理常见结局事件的前瞻性研究资料。
文摘为了度量E-Bayes估计的误差,该文基于E-Bayes估计的定义,引入了E-Bayes估计的E-MSE(expected mean square error)的定义.对Poisson分布的参数,在不同损失函数(包括:平方损失,K-损失,加权平方损失)下分别给出了E-Bayes估计及其E-MSE的表达式.用MonteCarlo方法进行模拟比较提出的估计方法的性能,分析了一个真实数据集并进行了比较,所得结果比较基于E-MSE,结果表明该文提出的方法可行且便于应用.
