多层玻璃窗隔声效果的数学模型分析

借助物理学声波传播理论,研究单层玻璃隔声的衡量方法,推导出双层窗户比单层窗户隔声效果好的数学模型为I4″/I2=(1-α1)(l-α2)/e2α11,并探讨在有限的建筑材料规定下实现隔声效果最佳的方法.     

成分数据路径分析模型

路径分析是一种探索和验证系统内部各个因素之间因果关系的多元统计方法.本文针对现实中大量存在的成分数据变量,提出成分数据路径分析模型,给出模型的方程表达形式和图形表达形式.在成分数据多元线性回归的基础上,提出模型的参数估计方法,并利用Bootstrap分析技术,给出路径系数显著性检验办法.在某公司官方网站的用户满意度与推荐意愿影响因素应用研究中,成分数据路径分析建模结果表明,满意度主要受到易用性的影响,而推荐意愿主要受到有用性的影响.这一结论为网站原型设计与营销推广提供了新的启示.     

Mixture Modeling for Longitudinal Data

In this article, we propose an unbiased estimating equation approach for a two-component mixture model with correlated response data. We adapt the mixture-of-experts model and a generalized linear model for component distribution and mixing proportion, respectively. The new approach only requires marginal distributions of both component densities and latent variables. We use serial correlations from subjects’ subgroup memberships, which improves estimation efficiency and classification accuracy, and show that estimation consistency does not depend on the choice of the working correlation matrix. The proposed estimating equation is solved by an expectation-estimating-equation (EEE) algorithm. In the E-step of the EEE algorithm, we propose a joint imputation based on the conditional linear property for the multivariate Bernoulli distribution. In addition, we establish asymptotic properties for the proposed estimators and the convergence property using the EEE algorithm. Our method is compared to an existing competitive mixture model approach in both simulation studies and an election data application. Supplementary materials for this article are available online.     

Geometric Fourier Analysis for Computational Vision

Projective Fourier analysis — geometric Fourier analysis of the group SL(2,), the group identified in the conformal camera that provides image perspective transformations—is discussed in the framework of representation theory of semisimple Lie groups. The compact model of projective Fourier analysis is constructed, complementing the noncompact model proposed before. Detailed mathematical formulation of both models is presented. It is demonstrated that the projective Fourier analysis provides the data model for efficient perspectively covariant digital image representation well adapted to the retino-cortical mapping of biological visual system, and therefore, explicitly designed for the foveated sensors of a silicon retina, the use of which in active vision systems is presently limited due to the lack of such a model.     

Analysis of Data from a Series of Events by a Geometric Process Model

Geometric process was first introduced by Lam.A stochastic process {X_i,i=1,2,...} iscalled a geometric process (GP) if,for some a>0,{a~(i-1)X_i,i=1,2,...} forms a renewal process.In thispaper,the GP is used to analyze the data from a series of events.A nonparametric method is introduced forthe estimation of the three parameters in the GP.The limiting distributions of the three estimators are studied.Through the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous Poisson models.It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.     

A Geometric Framework for Stochastic Shape Analysis

We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is introduced in the vector field which transports the data in the large deformation diffeomorphic metric mapping framework for shape analysis and image registration. The stochasticity thereby models errors or uncertainties of the flow in following the prescribed deformation velocity. The approach is illustrated in the example of finite-dimensional landmark manifolds, whose stochastic evolution is studied both via the Fokker–Planck equation and by numerical simulations. We derive two approaches for inferring parameters of the stochastic model from landmark configurations observed at discrete time points. The first of the two approaches matches moments of the Fokker–Planck equation to sample moments of the data, while the second approach employs an expectation-maximization based algorithm using a Monte Carlo bridge sampling scheme to optimise the data likelihood. We derive and numerically test the ability of the two approaches to infer the spatial correlation length of the underlying noise.

     

Nonparametric Bayesian Modeling for Multivariate Ordinal Data

This article proposes a probability model for k-dimensional ordinal outcomes, that is, it considers inference for data recorded in k-dimensional contingency tables with ordinal factors. The proposed approach is based on full posterior inference, assuming a flexible underlying prior probability model for the contingency table cell probabilities. We use a variation of the traditional multivariate probit model, with latent scores that determine the observed data. In our model, a mixture of normals prior replaces the usual single multivariate normal model for the latent variables. By augmenting the prior model to a mixture of normals we generalize inference in two important ways. First, we allow for varying local dependence structure across the contingency table. Second, inference in ordinal multivariate probit models is plagued by problems related to the choice and resampling of cutoffs defined for these latent variables. We show how the proposed mixture model approach entirely removes these problems. We illustrate the methodology with two examples, one simulated dataset and one dataset of interrater agreement.     

Tree-Structured Mixed-Effects Regression Modeling for Longitudinal Data

Tree-structured models have been widely used because they function as interpretable prediction models that offer easy data visualization. A number of tree algorithms have been developed for univariate response data and can be extended to analyze multivariate response data. We propose a tree algorithm by combining the merits of a tree-based model and a mixed-effects model for longitudinal data. We alleviate variable selection bias through residual analysis, which is used to solve problems that exhaustive search approaches suffer from, such as undue preference to split variables with more possible splits, expensive computational cost, and end-cut preference. Most importantly, our tree algorithm discovers trends over time on each of the subspaces from recursive partitioning, while other tree algorithms predict responses. We investigate the performance of our algorithm with both simulation and real data studies. We also develop an R package melt that can be used conveniently and freely. Additional results are provided as online supplementary material.     

Dictionary Learning and Non-Asymptotic Bounds for Geometric Multi-Resolution Analysis

Data sets in high-dimensional spaces are often concentrated near low-dimensional sets. Geometric Multi-Resolution Analysis (Allard, Chen, Maggioni, 2012) was introduced as a method for approximating (in a robust, multiscale fashion) a low-dimensional set around which data may concentrated and also providing dictionary for sparse representation of the data. Moreover, the procedure is very computationally efficient. We introduce an estimator for low-dimensional sets supporting the data constructed from the GMRA approximations. We exhibit (near optimal) finite sample bounds on its performance, and demonstrate the robustness of this estimator with respect to noise and model error. In particular, our results imply that, if the data is supported on a low-dimensional manifold, the proposed sparse representations result in an error which depends only on the intrinsic dimension of the manifold. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

合成氨煤气炉DCS数据建模与统计分析

利用相关系数阵的条件数研究影响煤气炉上部温度的各影响因素之间的复共线性,利用对数回归方法建立煤气炉上部温度与各影响因素之间的线性回归模型。经检验回归方程与回归系数均具有良好的显著性.所建模型对改善炉况,保持生产过程持续稳定具有现实指导意义。     

用于几何非线性分析的增量形式的虚功方程

本文导出了适用于几何非线性有限元分析的增量形式的虚功方程。在这个增量形式的虚功方程中,考虑了积累误差的影响。     

随机缺失数据下的时间序列分析建模

在时间序列建模过程中,数据的缺失会极大地影响模型的准确性,因此对缺失数据的填补尤为重要.选取北京市空气质量指数(AQI)数据。将其随机缺失10%.分别利用EM算法和polyfit直线拟合的方法对缺失值插补,补全数据后建立ARMA模型并作预测分析.结果表明,利用polyfit函数插补法具有较好的结果.     

基于海南省旅游人数的数学建模

使用两种不同的建模方法,研究了海南省2002～2009年的月度旅游人数,并建立了相应的数学模型.方法一利用微分方程结合传统时间序列分解法和自回归分布滞后模型;方法二利用ARIMA(p,d,q)(P,D,Q)~s模型.通过比较两种不同的方法,最终选出最优预测模型.     

Ramsey-Type Results for Geometric Graphs, II

We show that for any two-coloring of the segments determined by n points in the plane, one of the color classes contains noncrossing cycles of lengths . This result is tight up to a multiplicative constant. Under the same assumptions, we also prove that there is a noncrossing path of length Ω(n ^2/3 ) , all of whose edges are of the same color. In the special case when the n points are in convex position, we find longer monochromatic noncrossing paths, of length . This bound cannot be improved. We also discuss some related problems and generalizations. In particular, we give sharp estimates for the largest number of disjoint monochromatic triangles that can always be selected from our segments. Received March 25, 1997, and in revised form March 5, 1998.     

Ramsey-Type Results for Geometric Graphs, I

For any 2-coloring of the segments determined by n points in general position in the plane, at least one of the color classes contains a non-self-intersecting spanning tree. Under the same assumptions, we also prove that there exist pairwise disjoint segments of the same color, and this bound is tight. The above theorems were conjectured by Bialostocki and Dierker. Furthermore, improving an earlier result of Larman et al., we construct a family of m segments in the plane, which has no more than members that are either pairwise disjoint or pairwise crossing. Finally, we discuss some related problems and generalizations. Received October 17, 1995, and in revised form February 10, 1996.     

多标度数据几何轮廓相似性的度量与应用

在多标度数据的分类问题中,对于分布特征不清或小样本下的数据的相似性度量仍是研究的热点.对此,建立了基于样本几何轮廓相似度的判别分析模型,并应用于采动沉陷建筑物损坏等级的评价,结果表明该模型简洁、有效,无需数据预处理,较少依赖先验信息,具有推广应用的价值.