statistical boundary

There was statistical significance of moist rales 、 tubbiness thorax 、 lung boundary descend ( P < 0.05);

双肺湿啰音、桶状胸、肺界下移、肺心病体征2组差异有统计学意义（P<0.05）；

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There was statistical significance of moist rales 、 tubbiness thorax 、 lung boundary descend ( P < 0.05); Results: ( 1) Clinical characteristics of PF-COPD were between COPD and pulmonary fibrosis.

结果：（1）PF-COPD的临床表现介于上述两种疾病之间。双肺湿罗音、桶状胸、肺界下移、肺心病体征2组差异有统计学意义（p<0.05）；

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Lattice Gas Automata ( LGA), based on micros statistical mechanics, is a way to simulate fluid different to the way of solving partial difference equations. It has the advantages of simple rule and the better adaptability of the complex boundary.

格子气方法是流体力学的一种基于微观统计力学的模拟方法，具有规律简单，对复杂边界具有较好的适应性等优点。

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To avoid deforming contours directly in a vector-valued space, a Gaussian mixture model ( GMM) is used to describe the statistical distribution of the space and get the boundary and region probabilities.

为了避免直接在多维空间中应用曲线演化模型，采用高斯混合模型（Gaussian mixture model，简称GMM）来描述该特征图像的概率分布，再从分布模型中计算得到每个像素点的区域信息和边界信息。

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Finally, we show that when the boundary modification is comparable to the thermodynamic quantities obtained under the thermodynamic limit approximation, the result of the standard statistical mechanics will be invalid.

最后借助边界效应得取值范围分析了标准统计物理的适用范围：当边界的影响与热力学极限结果可比时，标准统计的结果将会失效。

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