Generating Replications of Chaotic Time Series

This paper addresses the problem of resampling chaotic time series. We propose a method based on resampling distances between nearest neighbours in phase space, so that the resampled time series present the original points differently positioned along the trajectory. This approach allows one to obtain time series with the same length of the original one, so that confidence intervals for Lyapunov exponents, correlation dimension and other invariants would be determined. For its generality this kind of resampling would be applicable to chaotic time series no matter the observations concern natural or life sciences. The method has been tested with common simulated chaotic systems with both clean and noisy data. Short and noisy time series, as the ones we simulated, typically occur in medicine, biology, and social sciences.     

Nonlinear and Non-Gaussian State Space Modeling Using Sampling Techniques

In this paper, the nonlinear non-Gaussian filters and smoothers are proposed using the joint density of the state variables, where the sampling techniques such as rejection sampling (RS), importance resampling (IR) and the Metropolis-Hastings independence sampling (MH) are utilized. Utilizing the random draws generated from the joint density, the density-based recursive algorithms on filtering and smoothing can be obtained. Furthermore, taking into account possibility of structural changes and outliers during the estimation period, the appropriately chosen sampling density is possibly introduced into the suggested nonlinear non-Gaussian filtering and smoothing procedures. Finally, through Monte Carlo simulation studies, the suggested filters and smoothers are examined.     

Free Energy Level Correction by Monte Carlo Resampling with Weighted Histogram Analysis Method

Free energy calculations may provide vital information for studying various chemical and biological processes. Quantum mechanical methods are required to accurately describe interaction energies, but their computations are often too demanding for conformational sampling. As a remedy, level correction schemes that allow calculating high level free energies based on conformations from lower level simulations have been developed. Here, we present a variation of a Monte Carlo (MC) resampling approach in relation to the weighted histogram analysis method (WHAM). We show that our scheme can generate free energy surfaces that can practically converge to the exact one with sufficient sampling, and that it treats cases with insufficient sampling in a more stable manner than the conventional WHAM-based level correction scheme. It can also provide a guide for checking the uncertainty of the level-corrected surface and a well-defined criterion for deciding the extent of smoothing on the free energy surface for its visual improvement. We demonstrate these aspects by obtaining the free energy maps associated with the alanine dipeptide and proton transfer network of the KillerRed protein in explicit water, and exemplify that the MC resampled WHAM scheme can be a practical tool for producing free energy surfaces of realistic systems.     

采用加权直方图分析和蒙特卡洛重采样法对自由能级的校正研究

本文采用加权直方图分析方法和蒙特卡洛重采样方法进行自由基校正研究. 生成的自由能表面几乎可以收敛到具有足够采样情况的精准表面,并且比常规的加权直方图分析校正方法能更稳定地处理采样不足的情况,为检测能级校正表面的不确定性提供指南,并且定义了明确的标准用以确定能改善其视觉效果的自由能表面平滑程度. 本文通过水中的丙氨酸二肽和KillerRed蛋白质子转移的自由能图证明该方法的优势,说明蒙特卡洛重采样法可以作为在产生自由能表面实际的系统中的实用工具.     

基于正则粒子重采样算法的红外成像消噪处理

 针对红外成像消噪的粒子滤波退化问题,提出正则粒子重采样算法。该算法从粒子群重采样获得粒子云(xjk,nj)mj=1,解决了粒子多样性消失的问题并克服粒子匮乏的现象;接着又通过添加辅助粒子v,将下一时刻观测值权值大的粒子进行标识,使粒子权值ωik∝p(xk｜yik-1)p(xk｜μik-1)更加稳定;给出了运动物体的红外成像消噪模型。实验仿真表明：正则粒子重采样算法通过添加辅助粒子使红外成像消噪效果好,成像清晰度在95%以上。     

Monte Carlo滤波新进展及其应用

非高斯、非线性的状态空间模型研究近年来有很多新的进展，在许多领域得到应用，其中用Monte Carlo方法进行滤波是一种简洁、方便的新方法，本文介绍这方面的新进展以及应用情况，包括本研究组的研究成果．     

Bootstrapping the Empirical Distribution Function of a Spatial Process

In this article, we consider a stationary α-mixing random field in IR ^d. Under a large-sample scheme that is a mixture of the so-called “infill” and “increasing domain” asymptotics, we establish a functional central limit theorem for the empirical processes of this random field. Further, we apply a blockwise bootstrap to the samples. Under the condition that the side length of the block for some 0 < β < 1, where λ _n is the growth rate in the increasing domain asymptotics, we show that the bootstrapped empirical process converges weakly to the same limiting Gaussian process almost surely. Extension to multivariate random fields and application to differentiable statistical functionals are also given. A spatial version of the Bernstein’s inequality is developed, which may be of some independent interest. In final form 13 December 2004     

Protein folding pathways extracted by OFLOOD: Outlier FLOODing method

The Outlier FLOODing method (OFLOOD) is proposed as an efficient conformational sampling method to extract biologically rare events such as protein folding. In OFLOOD, sparse distributions (outliers in the conformational space) were regarded as relevant states for the transitions. Then, the transitions were enhanced through conformational resampling from the outliers. This evidence indicates that the conformational resampling of the sparse distributions might increase chances for promoting the transitions from the outliers to other meta‐stable states, which resembles a conformational flooding from the outliers to the neighboring clusters. OFLOOD consists of (i) detections of outliers from conformational distributions and (ii) conformational resampling from the outliers by molecular dynamics (MD) simulations. Cycles of (i) and (ii) are simply repeated. As demonstrations, OFLOOD was applied to folding of Chignolin and HP35. In both cases, OFLOOD automatically extracted folding pathways from unfolded structures with ns‐order computational costs, although µs‐order canonical MD failed to extract them. © 2014 Wiley Periodicals, Inc.     

利用光谱指数反演植被叶绿素含量的精度及稳定性研究

农业遥感中,利用光谱指数方法反演作物叶绿素含量一直得到广泛地应用。利用PSR-3500光谱仪及SPAD-502叶绿素仪同步获取了冬小麦冠层光谱数据及对应叶片的叶绿素相对含量(SPAD值),并利用高斯光谱响应模型将PSR获取的地面连续光谱数据重采样为多光谱Landsat-TM7及高光谱Hyperion光谱数据,然后分别计算基于两种传感器的归一化差值植被指数(normalized difference vegetation index, NDVI)、综合叶绿素光谱指数(MCARI/OSAVI,the ratio of the modified transformed chlorophyll absorption ratio index (MCARI) to optimized soil adjusted vegetation index(OSAVI))、三角形植被指数(triangle vegetation index, TVI)及通用植被指数(vegetation index based on universal pattern decomposition method, VIUPD),再将四种光谱指数与叶绿素含量进行回归分析。结果表明,针对重采样后的TM和Hyperion两种传感器数据,VIUPD反演叶绿素含量精度(决定系数R2)最高,反演能力最稳定,这与其“不受传感器影响”的特性密不可分;MCARI/OSAVI反演精度和稳定性次之,是因为引入的OSAVI削弱了土壤背景的影响;宽波段指数NDVI和TVI对模拟TM数据有较好的反演精度,对Hyperion数据反演精度却很低,可能是因为两种指数的构成形式简单,考虑的影响因素较少。以冬小麦为例,对利用光谱指数反演植被叶绿素含量的精度和稳定性进行了研究并分析了其影响因素,经比较发现利用植被指数VIUPD进行植被叶绿素含量反演时,其精度和稳定性最好。