Estimation of Symmetry-Constrained Gaussian Graphical Models: Application to Clustered Dense Networks

We propose a model selection algorithm for high-dimensional clustered data. Our algorithm combines a classical penalized likelihood method with a composite likelihood approach in the framework of colored graphical Gaussian models. Our method is designed to identify high-dimensional dense networks with a large number of edges but sparse edge classes. Its empirical performance is demonstrated through simulation studies and a network analysis of a gene expression dataset.     

Computational Aspects of Nonparametric Bayesian Analysis with Applications to the Modeling of Multiple Binary Sequences

Abstract

We consider Markov mixture models for multiple longitudinal binary sequences. Prior uncertainty in the mixing distribution is characterized by a Dirichlet process centered on a matrix beta measure. We use this setting to evaluate and compare the performance of three competing algorithms that arise more generally in Dirichlet process mixture calculations: sequential imputations, Gibbs sampling, and a predictive recursion, for which an extension of the sequential calculations is introduced. This facilitates the estimation of quantities related to clustering structure which is not available in the original formulation. A numerical comparison is carried out in three examples. Our findings suggest that the sequential imputations method is most useful for relatively small problems, and that the predictive recursion can be an efficient preliminary tool for more reliable, but computationally intensive, Gibbs sampling implementations.     

Spatial Lasso With Applications to GIS Model Selection

Geographic information systems (GIS) organize spatial data in multiple two-dimensional arrays called layers. In many applications, a response of interest is observed on a set of sites in the landscape, and it is of interest to build a regression model from the GIS layers to predict the response at unsampled sites. Model selection in this context then consists not only of selecting appropriate layers, but also of choosing appropriate neighborhoods within those layers. We formalize this problem as a linear model and propose the use of Lasso to simultaneously select variables, choose neighborhoods, and estimate parameters. Spatially dependent errors are accounted for using generalized least squares and spatial smoothness in selected coefficients is incorporated through use of a priori spatial covariance structure. This leads to a modification of the Lasso procedure, called spatial Lasso. The spatial Lasso can be implemented by a fast algorithm and it performs well in numerical examples, including an application to prediction of soil moisture. The methodology is also extended to generalized linear models. Supplemental materials including R computer code and data analyzed in this article are available online.     

Analysis of a Non-linear Partial Difference Equation,and Its Application to Cardiac Dynamics

A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on this equation, and it is shown that regular perturbations are inadequate due to the appearance of secular terms. A singular perturbation procedure known as the method of multiple scales is shown to provide good agreement with numerical simulation except in the neighborhood of a singularity of the slow flow. The perturbation analysis is supplemented by a local numerical simulation near this singularity. The resulting analysis is shown to predict a "spatial bifurcation" phenomenon in which parts of the chain may be oscillating in period-2 motion while other parts may be oscillating in higher periodic motion or even chaotic motion.     

Oscillation for a class of diffusive hematopoiesis model with several arguments

By considering solution curve's or surface's composition of the functions of several variables and constructing the suitable lower-upper solution pair for the following special diffusive Hematopoiesis model eP (t, x)/et= ΔP (t, x)- γP (t, x) +m Σi=1 βiP (t-τi,x)/1+Pn (t-τi,x) (0.1)under Neumann boundary condition, sufficient conditions are provided for the oscillation of the positive equilibrium for (0.1). Moreover, these results extend or complement existing results.     

拓扑度计算定理及其应用

利用半序方法和不动点指数理论,建立了一个非锥映射全连续算子拓扑度为1的新的计算定理.作为应用,考虑了Hammerstein积分方程的非平凡解存在性问题.     

应用近红外漫反射光谱对猪肉肉糜进行定性定量检测研究

利用傅里叶变换近红外漫反射光谱结合不同数学建模算法对不同部位取样的猪肉肉糜进行定性判别建模,并建立猪肉肉糜品质指标脂肪、蛋白质和水分含量的定量检测模型。结果表明:不同部位取样猪肉肉糜判别分析PLSDA模型性能良好,最优模型校正集判别正确率为100%,预测集判别正确率为96%;比较两种方法结合,不同光谱预处理建立各品质指标的定量模型,LS-SVM模型性能优于PLSR模型,脂肪和水分含量最佳预测模型校正及预测相关系数r均高于0.9,蛋白质含量最优模型校正及预测相关系数r,RMSEC,RMSEP和RMSECV分别为0.722,0.593,1.595,1.550和1.888,模型精度需进一步提高。研究表明利用傅里叶变换近红外漫反射光谱快速判别不同部位猪肉肉糜的方法是可行的,脂肪和水分含量定量分析模型从预测精度、稳定性及适应性考虑均具一定的通用性,具有良好的市场应用前景。     

基于高光谱的膜下滴灌小麦氮素营养评价研究

通过小麦氮素和品种对比试验,分析不同氮素和品种处理小麦生育期氮肥偏生产力与光谱参数的相关关系,建立小麦氮肥偏生产力的光谱参数估算模型,结果表明绿度植被指数(GREENNDVI)在拔节期与小麦氮肥偏生产力呈极显著相关,相关系数0.640 4。用GREENNDVI在拔节期建立小麦氮肥偏生产力的估算模型,均方根误差0.459 7。研究表明利用光谱参数可以有效地估算小麦氮肥偏生产力。     

氯化钠近红外光谱检测技术研究

氯化钠(NaCl)近红外光谱分析在生物医学上有着重要的意义。钠离子(Na+)是人体血液中电解质的主要成分,而电解质有助于维持身体的酸碱平衡。采用近红外光谱技术测量氯化钠浓度,在分析钠离子近红外光谱检测机理的基础上,选定波长建立了NaCl浓度线性回归预测模型,同时为了减小温度对水吸收的扰动,使用选定光谱区建立偏最小二乘(PLS)非线性回归模型。结果表明所建立的非线性校正模型决定系数(R2)=99.82%,交叉验证均方误差(RMSECV)=14.5,剩余预测偏差(RPD)=23.7。完全满足日常生化检测精度要求,该技术可以应用于医院实验室钠离子浓度定量分析。