The Backup 2-Median Problem on Block Graphs

The backup 2-median problem is a location problem to locate two facilities at vertices with the minimum expected cost where each facility may fail with a given probability. Once a facility fails, the other one takes full responsibility for the services. Here we assume that the facilities do not fail simultaneously. In this paper, we consider the backup 2-median problem on block graphs where any two edges in one block have the same length and the lengths of edges on different blocks may be different. By constructing a tree-shaped skeleton of a block graph, we devise an O（n log n q- m）-time algorithm to solve this problem where n and m are the number of vertices and edges, respectively, in the given block graph.  

基于185例肺小结节CT图像灰度共生矩阵纹理特征的多水平模型研究

为探讨基于肺小结节CT图像灰度共生矩阵纹理特征的多水平模型,对北京友谊医院和宣武医院提供的185例2137张肺小结节CT图像提取4种灰度共生矩阵纹理特征。根据该类资料具有层次结构的特点,拟合多水平统计模型。结果表明,能量,熵和惯性矩,在患者水平上具有聚集性,且在良恶性肺小结节间的差异有统计学意义(P值均小于0.001),提示多水平模型可以灵活有效地处理肺小结节CT图像这类具有层次结构的数据,在一定程度上有利于早期肺癌的鉴别诊断。  

医学数字化CT图像压缩效果的统计分析与评价

为探讨医学数字化CT图像的压缩效果,选取具有重要临床意义的肺部CT数字化图像2186张,基于小波变换进行无视觉损失压缩,对压缩效果进行统计分析与评价。经肺部影像学专家肉眼进行盲法评判,压缩后与病理诊断结果符合率为91.89(95%C I为:79%-98%),压缩前后综合评分差别无统计学意义。小波变换较好地实现了对肺部患者数字化CT图像的无视觉损失压缩。  

基于方向数据的核密度估计的对称检验的大偏差

设$f_n$是基于核函数$K$和取值于$d$-维单位球面${\mathbb{S}}^{d-1}$的独立同分布随机变量列的非参数核密度估计. 我们证明了若核函数是有界变差函数, 随机变量的密度函数$f$是连续的和对称的, $\{\sup_{x\in {\mathbb{SS}}^{d-1}}|f_n(x)-f_n(-x)|,n\ge 1\}$的大偏差原理成立.  

Sign-changing solutions for the stationary Kirchhoff problems involving the fractional Laplacian in RN

In this paper, we study the existence of least energy sign-changing solutions for a Kirchhoff-type problem involving the fractional Laplacian operator. By using the constraint variation method and quantitative deformation lemma, we obtain a least energy nodal solution u_b for the given problem. Moreover, we show that the energy of u_b is strictly larger than twice the ground state energy. We also give a convergence property of u_b as b ↘ 0, where b is regarded as a positive parameter.