A new concept, called the row-column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Eucli...A new concept, called the row-column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Euclidean lattice. Graphs mapped from fractals generated with the probability redistribution model behave scale-free. They have pattern-induced hierarchical organizations and comparatively much more extensive structures. The scale-free exponent has a negative correlation with the Hurst exponent, however, there is no deterministic relation between them. Graphs for fractals generated with the midpoint displacement model are exponential networks. When the Hurst exponent is large enough （e.g., H 〉 0.5）, the degree distribution decays much more slowly, the average coverage becomes significant large, and the initially hierarchical structure at H 〈 0.5 is destroyed completely. Hence, the row-column visibility graph can be used to detect the pattern-related new characteristics of two-dimensional landscapes.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10975099)the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learning,China+2 种基金the Innovation Program of Shanghai Municipal Education Commission,China(GrantNo.13YZ072)the Shanghai Leading Discipline Project,China(Grant No.XTKX2012)the Innovation Fund Project for Graduate Students of Shanghai,China(Grant No.JWCXSL1302)
文摘A new concept, called the row-column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Euclidean lattice. Graphs mapped from fractals generated with the probability redistribution model behave scale-free. They have pattern-induced hierarchical organizations and comparatively much more extensive structures. The scale-free exponent has a negative correlation with the Hurst exponent, however, there is no deterministic relation between them. Graphs for fractals generated with the midpoint displacement model are exponential networks. When the Hurst exponent is large enough （e.g., H 〉 0.5）, the degree distribution decays much more slowly, the average coverage becomes significant large, and the initially hierarchical structure at H 〈 0.5 is destroyed completely. Hence, the row-column visibility graph can be used to detect the pattern-related new characteristics of two-dimensional landscapes.
文摘三维超快成像是超声技术发展的重要方向.基于二维全采样阵列的传统三维成像方法需要较多成像阵元和采样通道,其紧密的阵元排列设计也客观上限制了阵列孔径大小和成像分辨率.行列寻址(row-column addressing,RCA)探头以行列检索的方式将通道数自N×N减少为N+N,从而极大地降低了阵列的硬件实现成本.本文仿真了中心频率为6MHz的128行+128列的RCA阵列,结合多角度平面波正交复合成像方法,通过延时叠加(delay and sum,DAS)波束合成、基于特征值分解(singular value decomposition,SVD)的杂波滤除和自相关多普勒速度求解算法,实现了血流仿体的多普勒成像,并分析了不同复合角度序列对成像效果的影响.定量分析表明,当角度数从5个增至33个时,-6 dB分辨率从0.986 mm提升至0.493 mm;当复合角度为17个时,功率多普勒图像的SNR可达30 dB,彩色多普勒沿直径方向的速度分布和真实值的平均误差约为26.0%.以上结果表明,基于RCA阵列的三维成像技术能够获得三维B-mode、功率多普勒和彩色多普勒图像,增大复合平面波角度数和角度范围可显著提高成像质量.本研究对于三维超快超声多普勒成像技术发展具有借鉴意义,相关方法有应用于血流血管成像,并进一步实现基于神经-血管耦合的组织功能监测与成像的潜力和前景.
