ADAPTIVE MESHLESS METHOD BASED ON LOCAL FIT TECHNOLOGY

An h-adaptive meshless method is proposed in this paper. The error estimation is based on local fit technology, usually confined to Voronoi Cells. The error is achieved by comparison of the computational results with smoothed ones, which are projected with Taylor series. Voronoi Cells are introduced not only for integration of potential energy but also for guidance of refinement. New nodes are placed within those cells with high estimated error. At the end of the paper, two numerical examples with severe stress gradient are analyzed. Through adaptive analysis accurate results are obtained at critical subdomains, which validates the efficiency of the method.

Automatic image segmentation method for cotton leaves with disease under natural environment

In order to improve the image segmentation performance of cotton leaves in natural environment, an automatic segmentation model of diseased leaf with active gradient and local information is proposed. Firstly, a segmented monotone decreasing edge composite function is proposed to accelerate the evolution of the level set curve in the gradient smooth region. Secondly, canny edge detection operator gradient is introduced into the model as the global information. In the process of the evolution of the level set function, the guidance information of the energy function is used to guide the curve evolution according to the local information of the image, and the smooth contour curve is obtained. And the main direction of the evolution of the level set curve is controlled according to the global gradient information, which effectively overcomes the local minima in the process of the evolution of the level set function. Finally, the Heaviside function is introduced into the energy function to smooth the contours of the motion and to increase the penalty function Φ(x) to calibrate the deviation of the level set function so that the level set is smooth and closed. The results showed that the model of cotton leaf edge profile curve could be obtained in the model of cotton leaf covered by bare soil, straw mulching and plastic film mulching, and the ideal edge of the ROI could be realized when the light was not uniform. In the complex background, the model can segment the leaves of the cotton with uneven illumination, shadow and weed background, and it is better to realize the ideal extraction of the edge of the blade. Compared with the Geodesic Active Contour(GAC) algorithm, Chan-Vese(C-V) algorithm and Local Binary Fitting(LBF) algorithm, it is found that the model has the advantages of segmentation accuracy and running time when processing seven kinds of cotton disease leaves images, including uneven lighting, leaf disease spot blur, adhesive diseased leaf, shadow, complex background, unclear diseased leaf edges, and staggered condition. This model can not only conduct image segmentation of cotton leaves under natural conditions, but also provide technical support for the accurate identification and diagnosis of cotton diseases.

Q-Band X-Mode Reflectometry and Density Profile Reconstruction

By installing an X-mode polarized Q-band（32-56 GHz） reflectometry at the low field side on EAST,the zero density cutoff layer was determined and the edge density profile was measured in normally operating plasmas.A Monte Carlo procedure has been developed to analyze the density profiles by considering the error of time delay measured by reflectometry.By combining this Q-band and previously developed V- and W-band reflectometries,the density profiles from edge to core can be measured in most EAST experiments.The line integrated densities deduced from density profiles measured by reflectometry are consistent with those directly measured by a horizontal interferometer.The density pedestal measured by reflectometry shows a clear crash during an ELM（edge localized mode） event,after which the pedestal gradually increases and recovers in 10 ms and then remains little changed up to the next ELM.

A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship

Recently, Gijbels and Rousson[6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth. As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson’s approach. Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory.

Numerical Discretization-Based Kernel Type Estimation Methods for Ordinary Differential Equation Models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation（ODE） models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method（kernel smoothing or local polynomial fitting） in the first stage, and a numerical discretization method（Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method） in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.

Confidence Intervals of Variance Functions in Generalized Linear Model

In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.

Base pair distance analysis in single DNA molecule by direct stochastic optical reconstruction microscopy

Precise fluorescence imaging of single l-DNA molecules for base pair distance analysis requires a superresolution technique, as these distances are on the order of diffraction limit. Individual l-DNA molecules intercalated with the fluorescent dye YOYO-1 were investigated at subdiffraction spatial resolution by direct stochastic optical reconstruction microscopy（d STORM）. Various dye-to-DNA base pair ratios were imaged by photoswitching YOYO-1 between the fluorescent state and the dark state using two laser sources. The acquired images were reconstructed into a super-resolution image by applying Gaussian fitting to the centroid of the point spread function. By measuring the distances between localized fluorophores, the base pair distances in single DNA molecules for dye-to-DNA base pair ratios of 1：50,1：100, and 1：500 were calculated to be 17.1 0.8 nm, 34.3 2.2 nm, and 170.3 8.1 nm[17_TD$IF], respectively,which were in agreement with theoretical values. These results demonstrate that intercalating dye in a single DNA molecule can be photoswitched without the use of an activator fluorophore, and that super-localization precision at a spatial resolution of 17 nm was experimentally achieved.