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Xingwei T.,Beijing Normal University | Xingwei T.,Laboratory of Mathematics and Complex Systems | Tao H.,Beijing Normal University | Tao H.,Laboratory of Mathematics and Complex Systems | And 2 more authors.
Acta Mathematica Scientia | Year: 2010

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure. © 2010 Wuhan Institute of Physics and Mathematics.

Liu Q.,Beijing Normal University | Liu Q.,Laboratory of Mathematics and Complex Systems | Liu Q.,Beijing Information Teconology College | Wang H.,Beijing Normal University | And 4 more authors.
Surface and Interface Analysis | Year: 2011

This article presents the method of computer automatic recognition and measurement of the number and volume of nanoparticles formed on a rough surface by smoothing, enhancement and segmentation of image processing. The grafted grains (nanoparticles) on polyethylene surface are taken as the example. This method uses shock filter enhancement and globally convex segmentation to separate the nanoparticles from the polymer substrate surface. Then the nanoparticles are extracted from the rough surface, and the number and volume of nanoparticles on the rough surface are determined. By applying this method to analyze the surfaces irradiated for different time, the number and volume of grafted grains are obtained and they are consistent with the results obtained manually. Copyright © 2010 John Wiley & Sons, Ltd.

Zhiyun C.,Beijing Normal University | Hongzhu G.,Laboratory of Mathematics and Complex Systems
Acta Mathematica Scientia | Year: 2012

The relationship between a link diagram and its corresponding planar graph is briefly reviewed. A necessary and sufficient condition is given to detect when a planar graph corresponds to a knot. The relationship between planar graph and almost planar Seifert surface is discussed. Using planar graph, we construct an alternating amphicheiral prime knot with crossing number n for any even number n ≥ 4. This gives an affirmative answer to problem 1.66(B) on Kirby's problem list. © 2012 Wuhan Institute of Physics and Mathematics.

Wu Z.,Worcester Polytechnic Institute | Yang C.,Worcester Polytechnic Institute | Yang C.,Laboratory of Mathematics and Complex Systems | Tang D.,Worcester Polytechnic Institute
Journal of Biomechanical Engineering | Year: 2011

It has been hypothesized that mechanical risk factors may be used to predict future atherosclerotic plaque rupture. Truly predictive methods for plaque rupture and methods to identify the best predictor(s) from all the candidates are lacking in the literature. A novel combination of computational and statistical models based on serial magnetic resonance imaging (MRI) was introduced to quantify sensitivity and specificity of mechanical predictors to identify the best candidate for plaque rupture site prediction. Serial in vivo MRI data of carotid plaque from one patient was acquired with follow-up scan showing ulceration. 3D computational fluid-structure interaction (FSI) models using both baseline and follow-up data were constructed and plaque wall stress (PWS) and strain (PWSn) and flow maximum shear stress (FSS) were extracted from all 600 matched nodal points (100 points per matched slice, baseline matching follow-up) on the lumen surface for analysis. Each of the 600 points was marked ulcer or nonulcer using follow-up scan. Predictive statistical models for each of the seven combinations of PWS, PWSn, and FSS were trained using the follow-up data and applied to the baseline data to assess their sensitivity and specificity using the 600 data points for ulcer predictions. Sensitivity of prediction is defined as the proportion of the true positive outcomes that are predicted to be positive. Specificity of prediction is defined as the proportion of the true negative outcomes that are correctly predicted to be negative. Using probability 0.3 as a threshold to infer ulcer occurrence at the prediction stage, the combination of PWS and PWSn provided the best predictive accuracy with (sensitivity, specificity) (0.97, 0.958). Sensitivity and specificity given by PWS, PWSn, and FSS individually were (0.788, 0.968), (0.515, 0.968), and (0.758, 0.928), respectively. The proposed computational-statistical process provides a novel method and a framework to assess the sensitivity and specificity of various risk indicators and offers the potential to identify the optimized predictor for plaque rupture using serial MRI with follow-up scan showing ulceration as the gold standard for method validation. While serial MRI data with actual rupture are hard to acquire, this single-case study suggests that combination of multiple predictors may provide potential improvement to existing plaque assessment schemes. With large-scale patient studies, this predictive modeling process may provide more solid ground for rupture predictor selection strategies and methods for image-based plaque vulnerability assessment. © 2011 American Society of Mechanical Engineers.

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