The smooth fractionator

A modification of the general fractionator sampling technique called the smooth fractionator is presented. It may be used in almost every situation in which sampling is performed from distinct items that are uniquely defined, often they are physically separated items or clusters like pieces, blocks, slabs, sections, etc. To each item is associated a ‘guesstimate’ or an associated variable with a more‐or‐less close – and possibly biased ? relationship to the content of the item. The smooth fractionator is systematic sampling among the items arranged according to the guesstimates in a unique, symmetric sequence with one peak and minimal jumps. The smooth fractionator is both very simple to implement and so efficient that it should probably always be used unless the natural sequence of the sampling items is equally smooth. So far, there is no theory for the prediction of the efficiency of smooth fractionator designs in general, and their properties are therefore illustrated with a range of real and simulated examples. At the cost of a slightly more elaborate sampling scheme, it is, however, always possible to obtain an unbiased estimate of the real precision and of some of the variance components. The only real practical problem for always obtaining a high precision with the smooth fractionator is specimen inhomogeneity, but that is detectable at almost no extra cost. With careful designs and for sample sizes of about 10, the sampling variation for the primary, smooth fractionator sampling step may in practice often be small enough to be ignored.     

A simple and efficient alternative to implementing systematic random sampling in stereological designs without a motorized microscope stage

When properly applied, stereology is a very robust and efficient method to quantify a variety of parameters from biological material. A common sampling strategy in stereology is systematic random sampling, which involves choosing a random sampling relevant objects start point outside the structure of interest, and sampling at sites that are placed at pre‐determined, equidistant intervals. This has proven to be a very efficient sampling strategy, and is used widely in stereological designs. At the microscopic level, this is most often achieved through the use of a motorized stage that facilitates the systematic random stepping across the structure of interest. Here, we report a simple, precise and cost‐effective software‐based alternative to accomplishing systematic random sampling under the microscope. We believe that this approach will facilitate the use of stereological designs that employ systematic random sampling in laboratories that lack the resources to acquire costly, fully automated systems.     

Non‐uniform systematic sampling in stereology*

Non‐uniform systematic sampling designs in stereology are studied. Various methods of constructing non‐uniform systematic sampling points from prior knowledge of the measurement function are presented. As an example, we consider area estimation from lengths of linear intercepts. The efficiency of two area estimators, based on non‐uniform sampling of parallel lines, is compared to that of the classical 2D Cavalieri estimator, based on uniform sampling, in a sample of planar profiles from transverse sections of 41 small myelinated axons. The comparison is based on simulations. It is concluded that for profiles of this type one of the non‐uniform sampling schemes is more efficient than the traditional uniform sampling scheme. Other examples where non‐uniform systematic sampling may be used are in area estimation from lines emanating from a fixed point, area estimation from concentric circles or spirals and curve length estimation from sweeping lines. It is shown that proportional‐to‐size sampling is a special case of non‐uniform systematic sampling. Finally, the effect of noise in the observations is discussed.     

A new fractionator principle with varying sampling fractions: exemplified by estimation of synapse number using electron microscopy

The quantification of ultrastructure has been permanently improved by the application of new stereological principles. Both precision and efficiency have been enhanced. Here we report for the first time a fractionator method that can be applied at the electron microscopy level. This new design incorporates a varying sampling fraction paradigm. The method allows for systematic random sampling from blocks of variable slab thickness, thereby eliminating the need for exhaustive serial sectioning through an entire containing space. This novel approach acknowledges the inaccuracy inherent in estimating the total object number using section sampling fractions based on the average thickness of sections of variable thicknesses. As an alternative, this approach estimates the correct particle section sampling probability based on an estimator of the Horvitz–Thompson type, resulting in a theoretically more satisfying and accurate estimate of the expected number of particles for the defined containing space.     

Evaluation of variance models for fractionator sampling of trees

We compared the performance of several models for predicting, from small samples, the precision of estimates of the total number of blossoms on fruit trees obtained using a three‐stage fractionator, in which the sampling units were defined by the tree structure: (1) primary branches and stem (2) secondary branches and shoots and (3) flowering buds. The models considered were the semiempirical models of Cruz‐Orive (1990, 2004 ) (CO), a random sample model (SR), a Poisson model (P), successive differences (D) and repeated systematic sampling (R). Procedures that relied upon a single sample and a model of the variance (SR, P, D) were not able to predict the estimator variance because the considered structures strongly violated model assumptions. The semiempirical CO model performed acceptably in some cases where model assumptions were violated to a moderate degree. The repeated systematic sampling procedure, which does not rely upon a model of the variance, usually provided very good predictions when the resampling terms were distributed appropriately across more than one sampling stage.     

A simple technique to measure the movements of the microscope stage along the x and y axes for stereological methods

Measurements of microscope stage movements in the x and y directions are of importance for some stereological methods such as the optical disector and optical fractionator. The length of stage movements can be measured with great precision and accuracy using a suitable motorized stage, which is generally a computer-assisted instrument. This type of equipment is generally too expensive for and not readily available in many laboratories. This paper describes a simple method to measure the movements of the microscope stage along the x and y directions, which can be used for purposes such as systematic uniform random sampling. It needs a microscope attachment consisting of two dial indicators; one of them is used to measure the amount of stage movement along the x -axis and the other measures the amount of movement along the y -axis. Movements of the stage on the micrometre-scale can be measured easily using this device.     

Automatic sampling for unbiased and efficient stereological estimation using the proportionator in biological studies

Quantification of tissue properties is improved using the general proportionator sampling and estimation procedure: automatic image analysis and non-uniform sampling with probability proportional to size (PPS). The complete region of interest is partitioned into fields of view, and every field of view is given a weight (the size) proportional to the total amount of requested image analysis features in it. The fields of view sampled with known probabilities proportional to individual weight are the only ones seen by the observer who provides the correct count. Even though the image analysis and feature detection is clearly biased, the estimator is strictly unbiased. The proportionator is compared to the commonly applied sampling technique (systematic uniform random sampling in 2D space or so-called meander sampling) using three biological examples: estimating total number of granule cells in rat cerebellum, total number of orexin positive neurons in transgenic mice brain, and estimating the absolute area and the areal fraction of β islet cells in dog pancreas. The proportionator was at least eight times more efficient (precision and time combined) than traditional computer controlled sampling.     

On the empirical variance of a fractionator estimate

The fractionator consists of several sampling stages with systematic sampling at each stage; data are collected only at the last stage. Therefore, predicting the error variance of a fractionator estimator is a non-trivial problem, because the observations are correlated in a complicated, unknown way. Gundersen proposed to split the material sampled at the first stage into two subsets, and to compute the variance of the pooled estimate empirically using the corresponding pair of observations made in these two subsets. The idea is very effective, but the estimator thus proposed needed some corrections. The purpose of this paper is to present an improved estimator of the coefficient of error of a fractionator estimator using Gundersen's design.     

Reliability-based design optimization via high order response surface method

To reduce the computational effort of reliability-based design optimization (RBDO), the response surface method (RSM) has been widely used to evaluate reliability constraints. We propose an efficient methodology for solving RBDO problems based on an improved high order response surface method (HORSM) that takes advantage of an efficient sampling method, Hermite polynomials and uncertainty contribution concept to construct a high order response surface function with cross terms for reliability analysis. The sampling method generates supporting points from Gauss-Hermite quadrature points, which can be used to approximate response surface function without cross terms, to identify the highest order of each random variable and to determine the significant variables connected with point estimate method. The cross terms between two significant random variables are added to the response surface function to improve the approximation accuracy. Integrating the nested strategy, the improved HORSM is explored in solving RBDO problems. Additionally, a sampling based reliability sensitivity analysis method is employed to reduce the computational effort further when design variables are distributional parameters of input random variables. The proposed methodology is applied on two test problems to validate its accuracy and efficiency. The proposed methodology is more efficient than first order reliability method based RBDO and Monte Carlo simulation based RBDO, and enables the use of RBDO as a practical design tool.     

Estimation of the number of stellate cells in a liver with the smooth fractionator

To better evaluate the activation and proliferative response of hepatic stellate cells (HSC) in hepatic fibrosis, it is essential to have sound quantitative data in non‐pathological conditions. Our aim was to obtain the first precise and unbiased estimate of the total number of HSC in the adult rat, by combining the optical fractionator, in a smooth sampling design, with immunocytochemistry against glial fibrillary acidic protein. Moreover, we wanted to verify whether there was sufficiently relevant specimen inhomogeneity that could jeopardize the high expected estimate precision when using the smooth fractionator design for HSC. Finally, we wanted to address the question of what sampling scheme would be advisable a priori for future studies. Microscopical observations and quantitative data provided no evidence for inhomogeneity of tissue distribution of HSC. Under this scenario, we implemented a baseline sampling strategy estimating the number (N?) of HSC as 207E⁰⁶ (CV = 0.17). The coefficient of error [CE(N?)] was 0.04, as calculated by two formerly proposed approaches. The biological difference among animals contributed ? 95% to the observed variability, whereas methodological variance comprised the remaining 5%. We then carried out a half reduction of sampling effort, at the level of both sections and fields. In either occasion, the CE(N?) values were low (? 0.05) and the biological variance continued to be far more important than methodological variance. We concluded that our baseline sampling (counting 650–1000 cells/rat) would be appropriate to assess the lobular distribution and the N? of HSC. However, if the latter is the only parameter to be estimated, around half of our baseline sampling (counting 250–600 cells/rat) would still generate precise estimates [CE(N?) < 0.1], being in this case more efficient to reduce the number of sections than to reduce the sampled fields.     

Global spatial sampling with isotropic virtual planes: estimators of length density and total length in thick, arbitrarily orientated sections

Existing design-based direct length estimators require random rotation around at least one axis of the tissue specimen prior to sectioning to ensure isotropy of test probes. In some tissue it is, however, difficult or even impossible to define the region of interest, unless the tissue is sectioned in a specific, nonrandom orientation. Spatial uniform sampling with isotropic virtual planes circumvents the use of physically isotropic or vertical sections. The structure that is contained in a thick physical section is investigated with software-randomized isotropic virtual planes in volume probes in systematically sampled microscope fields using computer-assisted stereological analysis. A fixed volume of 3D space in each uniformly sampled field is probed with systematic random, isotropic virtual planes by a line that moves across the computer screen showing live video images of the microscope field when the test volume is scanned with a focal plane. The intersections between the linear structure and the virtual probes are counted with columns of two dimensional disectors.
Global spatial sampling with sets of isotropic uniform random virtual planes provides a basis for length density estimates from a set of parallel physical sections of any orientation preferred by the investigator, i.e. the simplest sampling scheme in stereology. Additional virtues include optimal conditions for reducing the estimator variance, the possibility to estimate total length directly using a fractionator design and the potential to estimate efficiently the distribution of directions from a set of parallel physical sections with arbitrary orientation.
Other implementations of the basic idea, systematic uniform sampling using probes that have total 3D × 4π freedom inside the section, and therefore independent of the position and the orientation of the physical section, are briefly discussed.     

基于改进 RRT ∗ 算法的智能轮椅全局路径规划研究

现实环境中智能轮椅大多数处在复杂场景下工作,其自主导航时对路径安全性等要求较高。 渐进最优随机搜索树 RRT ∗ 算法 基本满足移动机器人最优路径规划,但由于智能轮椅本体较大,容易与环境较近接触,因此可对环境模型进行膨胀并定义不同搜索步 长,使其规划出的路径远离障碍物。 其次为保证用户在使用智能轮椅导航时能够获得更高的舒适性,更高效的到达目的地,而借用启 发式约束采样思想和人工势场中引力场思想修剪此算法规划时的冗余节点,从而减小系统运行内存,随后结合轮椅的最小转弯半径, 提出最小段路径曲率约束策略和三次 B 样条曲线算法对路径进行平滑处理,使其更加适合轮椅行驶。 最终在 MATLAB 和 Gazebo 仿真 平台对改进前后算法对比实验,并将本文算法应用与智能轮椅实体上,试验结果表明,该算法能够有效解决智能轮椅全局路径规划问 题,能够明显提升全局路径规划效率,具有一定安全性,可为其移动机器人领域提供有效参考。     

平稳噪声背景下周期信号基频初相位检测

给出了采用Ｍｏｒｌｅｔ小波变换并结合集合平均检测叠加有平稳随机噪声周期信号基频初相位的方法,为旋转机械故障定位提供新手段。数字仿真结果及实例表明,即使信噪比很小的,本方法仍能得到较好结果。     

随机加权法在可靠性参数评估中的应用研究

介绍了随机加权法的基本思想,并将其应用于正态分布小样本的参数置信限估计。采用MonteCarlo仿真方法,验证了估计准确度与样本量之间的关系,指出了随机加权法的适用范围。结果表明,对于样本均值的置信下限估计,在样本量大于一定值时,随机加权法的估计准确度能够达到置信度的要求,而对于样本方差的置信上限估计,准确度较低,因此随机加权法不适用于方差的置信上限估计。算例证明,随机加权法能够在满足置信度要求的基础上,得到更加合理的均值的置信下限估计,与传统方法相比,优势明显。     

Estimating the total number of lymphatic valves in infant lungs with the fractionator

The fractionator is illustrated by means of a biomedical example involving the estimation of the number of lymphatic valves in lungs of infants who had died from sudden infant death syndrome (SIDS) and other known causes. The method is unbiased irrespective of tissue deformations and it does not require external information such as section thickness. An upper bound of the coefficient of error of the estimate of the number of valves within one lung was 6.5%, despite the fact that the number of valves counted per lung at the last stage ranged between 11 and 37 only. The upper bound includes the biological variation of the number of valves among infant lungs. Some theoretical remarks are also made on the efficiency of the fractionator. It is suggested, for instance, that the initial sampling stages cause more impact on the precision of the final estimator than the subsequent stages, and that an optimal arrangement of fragments submitted to systematic sampling should have the smallest fragments at the ends, with fragment contents increasing smoothly toward the middle of the series.     

随机信号在路面不平度仿真中的应用

重点研究了随机信号在路面不平度仿真中的应用,分别使用AR法和伪白噪声法在空间域下对C级路面进行仿真。仿真使用Matlab语言,仿真步长为0.1m,路面长度为10km。结果表明:两种仿真方法的计算量与所仿真的路面长度成正比,AR法计算量小,而伪白噪声法算法稳定性好,提高仿真精度的措施灵活。     

基于连续扫描方式的激光共焦扫描显微镜的研制

研发了一套基于连续扫描的激光共焦扫描显微镜(laser confocal scanning microscopy,LCSM)系统。该系统采用工作台连续运动方式实现扫描,提出了利用单次采集的数据滤除随机噪声的方法,避免了多帧取平均对成像速度造成的影响。实现连续扫描的关键在于解决工作台运动与数据采集的同步问题,利用采集卡有限采集模式,合理匹配工作台参数和采集参数,成功解决了这一问题。详细介绍了影响分辨率的因素,通过合理选取探测器针孔直径,取样间隔,确保了实现高分辨率的要求。系统利用Visual C#开发的控制平台,成功地对生物细胞进行了扫描成像。实验结果表明:基于连续扫描的LCSM具有较高的分辨率,生成的显微图像没有任何畸变,并且成像速度有了大幅度提高。     

具有随机型和区间型干扰因素的产品健壮设计研究

针对随机型和区间型干扰因素共同作用条件下的产品健壮设计问题，在同时考虑设计目标健壮性和设计约束可行健壮性的基础上，提出了健壮设计的分位数型设计准则；在该设计准则的基础上，建立了产品健壮设计的分位数优化模型，保证了所设计产品的抗干扰能力和可靠度。通过汽车离合器膜片弹簧的健壮设计实例，验证了该方法的有效性和实用性。