Bayesian Multiscale Smoothing for Making Inferences About Features in Scatterplots

A rather common problem of data analysis is to find interesting features, such as local minima, maxima, and trends in a scatterplot. Variance in the data can then be a problem and inferences about features must be made at some selected level of significance. The recently introduced SiZer technique uses a family of nonparametric smooths of the data to uncover features in a whole range of scales. To aid the analysis, a color map is generated that visualizes the inferences made about the significance of the features. The purpose of this article is to present Bayesian versions of SiZer methodology. Both an analytically solvable regression model and a fully Bayesian approach that uses Gibbs sampling are presented. The prior distributions of the smooths are based on a roughness penalty. Simulation based algorithms are proposed for making simultaneous inferences about the features in the data.     

拟矩形剖分上的样条空间的维数

矩形剖分~(记为$\Delta_{QR}$)~是指在矩形剖分~(记为$\Delta_{R}$)的基础上进行局部修改后得到的剖分,通常包括T-剖分~(记为$\Delta_{T}$)~和L-剖分~(记为$\Delta_{L}$).本文利用光滑余因子协调方法讨论了该剖分上的二元样条空间$S^\mu_k(\Delta_{QR})$的维数.在满足一定约束条件下, 得到了仅依赖于样条空间的次数,光滑度和剖分拓扑结构的显式维数公式.     

Information theory of optimization in chromatography: Analytical structure of optimization

Summary The analytical roles of chromatographic variables (column length, etc.) can be soundly comprehended and compared in terms of the precision (Φ) of measurements and efficiency (ϑ) of analysis which are described as Shannon information and information flow, respectively. The φϑ plots of the optimization process and the information Φ transmitted by a single peak are useful to understand the analytical structure of optimization. Variables treated here are mobile phase composition (X), column length (L), mobile phase velocity rate (u), detection wavelength (λ) and plate number (N).     

Log-Sigmoid Multipliers Method in Constrained Optimization

In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for constrained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augmented Lagrangian techniques.We established convergence of the LS type penalty method under very mild assumptions on the input data and estimated the rate of convergence of the LS multipliers method under the standard second order optimality condition for both exact and nonexact minimization.Some important properties of the dual function and the dual problem, which are based on the LS Lagrangian, were discovered and the primal–dual LS method was introduced.     

An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems

We present a new active-set strategy which can be used in conjunction with exponential (entropic) smoothing for solving large-scale minimax problems arising from the discretization of semi-infinite minimax problems. The main effect of the active-set strategy is to dramatically reduce the number of gradient calculations needed in the optimization. Discretization of multidimensional domains gives rise to minimax problems with thousands of component functions. We present an application to minimizing the sum of squares of the Lagrange polynomials to find good points for polynomial interpolation on the unit sphere in ℝ³. Our numerical results show that the active-set strategy results in a modified Armijo gradient or Gauss-Newton like methods requiring less than a quarter of the gradients, as compared to the use of these methods without our active-set strategy. Finally, we show how this strategy can be incorporated in an algorithm for solving semi-infinite minimax problems.     

气体团簇离子束两步能量修形法的平坦化效应

本文提出采用气体团簇离子束的两步能量修形法来改善4H-SiC(1000)晶片表面形貌.先用15 keV的高能Ar团簇离子进行整体修形,再用5 keV的低能团簇离子优化表面.结果表明,在相同的团簇离子剂量下,与单一15 keV的高能团簇处理相比,两步法修形后的表面具有更低的均方根粗糙度,两者分别为1.05 nm和0.78 nm.本文还以原子级平坦表面为研究对象,揭示了载能团簇引起的半球形离子损伤(弧坑)与团簇能量的关系,及两步能量修形法在弧坑修复中的优势.在原子力显微镜表征的基础上,引入了二维功率谱密度函数,以直观全面地给出材料的表面形貌特征及其随波长(频率)的分布.结果表明,经任何能量的团簇离子轰击的表面,在0.05—0.20μm波长范围内,团簇轰击都能有效地降低粗糙度,而在0.02—0.05μm范围内,则出现了粗化效应,这是由于形成了半球形离子损伤,但第二步更低能量的团簇离子处理可以削弱这种粗化效应.     

捷联惯导系统的空中标定方法

从工程实用和维护的角度出发,提出了一种针对机载捷联式系统的空中标定方法。该方法依据捷联惯导系统级标定的基本原理,使用卡尔曼滤波作为估计手段,惯性器件常值漂移、刻度系数误差及惯导系统基本误差项作为状态量,依据外部GPS信息作为观测基准,通过设定的飞行机动动作对各待标定误差项进行激励。仿真卡尔曼滤波结果表明,依据飞机实际运动过程设计的简单飞行轨迹即可以实现对所有误差项的有效激励,各误差项随飞行过程进行逐步收敛。这种系统级空中标定方法不需要飞机作特殊的机动动作,在实际工程中易于实现,且经过一个架次的飞行就可以对惯导系统进行一次标定补偿。     

降阶扩展卡尔曼滤波算法在船用INS/GPS组合导航系统中的应用

TNNS(真航向导航系统)由MS860接收机、INS及处理数据的PC/104架构的嵌入式工控机构成。针对TNNS推导了INS(惯性导航系统)的误差模型,提出了适合于TNNS的降阶扩展卡尔曼滤波算法组合GPS和INS。系统在东海作了三次海试,软件及滤波算法平台由C/C 编制。海上试验表明,组合滤波后,INS的位置误差由100m降低到40m以下;进行最优化滤波后的航向误差σ由原来的0.105°减小为0.034°,纵横摇的误差也大幅减小。整个海试结果表明,在TNNS中组合GPS/INS采用的降阶扩展卡尔曼滤波算法,大幅提高了系统精度和可靠性。     

利用差分GPS提高惯性导航系统飞行测试基准的精度

—本文研究用增广卡尔曼滤器（ＥＫＦ），把高精度ＩＮＳ、差分ＧＰＳ（ＤＧＰＳ）和测距／测距率无线电应答器系统（ＲＲＳ）及气压高度计进行最优组合，构成ＩＮＳ测试基准的方法；重点讨论ＩＮＳ／ＲＲＳ／ＤＧＰＳ卡尔曼滤波器误差模型。计算机仿真结果表明，基准导航系统的高度精度为１．２５ｍ（１σ），水平位置精度可达０．５９ｍ（１σ），速度精度为０．０１５ｍ／ｓ（１σ）。