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Degree-ordered percolation on a hierarchical scale-free network.
Lee, Hyun Keun,Shim, Pyoung-Seop,Noh, Jae Dong Published by the American Physical Society through 2014 Physical review. E, Statistical, nonlinear, and so Vol.89 No.6
<P>We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical (u,v) flower network with u ??? v. Highest degree nodes are linked directly without intermediate nodes for u=1, while this is not the case for u ??? 1. Using the renormalization-group-like procedure, we derive the recursion relations for the percolating probability and the percolation order parameter, from which the percolation threshold and the critical exponents are obtained. When u ??? 1, the DOP critical behavior turns out to be identical to that of the bond percolation with a shifted nonzero percolation threshold. When u=1, the DOP and the bond percolation have the same vanishing percolation threshold but the critical behaviors are different. Implication to an epidemic spreading phenomenon is discussed.</P>
Hwayeong Cheon,Young Je Son,Sung Bae Park,Pyoung-Seop Shim,Joo-Hiuk Son,Hee-Jin Yang 대한신경외과학회 2023 Journal of Korean neurosurgical society Vol.66 No.4
Objective : The use of indocyanine green videoangiography (ICG-VA) to assess blood flow in the brain during cerebrovascular surgery has been increasing. Clinical studies on ICG-VA have predominantly focused on qualitative analysis. However, quantitative analysis numerical modelling for time profiling enables a more accurate evaluation of blood flow kinetics. In this study, we established a multiple exponential modified Gaussian (multi-EMG) model for quantitative ICG-VA to understand accurately the status of cerebral hemodynamics. Methods : We obtained clinical data of cerebral blood flow acquired the quantitative analysis ICG-VA during cerebrovascular surgery. Varied asymmetric peak functions were compared to find the most matching function form with clinical data by using a nonlinear regression algorithm. To verify the result of the nonlinear regression, the mode function was applied to various types of data. Results : The proposed multi-EMG model is well fitted to the clinical data. Because the primary parameters—growth and decay rates, and peak center and heights—of the model are characteristics of model function, they provide accurate reference values for assessing cerebral hemodynamics in various conditions. In addition, the primary parameters can be estimated on the curves with partially missed data. The accuracy of the model estimation was verified by a repeated curve fitting method using manipulation of missing data. Conclusion : The multi-EMG model can possibly serve as a universal model for cerebral hemodynamics in a comparison with other asymmetric peak functions. According to the results, the model can be helpful for clinical research assessment of cerebrovascular hemodynamics in a clinical setting.