论文标题
分层沉积和无规模网络：可见性算法方法
Hierarchical deposition and scale-free networks: a visibility algorithm approach
论文作者
论文摘要
通过水平可见性算法生成的动态网络的框架研究了由不等尺寸颗粒的层次分层沉积形成的界面的生长。对于沉积过程的确定性模型，所得网络不扩展，主要指数指数$γ_e= \ ln {3}/\ ln {2} $和瞬态指数$γ_O= 1 $。网络直径和聚类系数的确切计算表明，网络是规模不变的，并继承了沉积过程的模块化层次结构。对于随机过程，网络保持不含规模，其中学位指数渐近地收敛到$γ= 3 $，与系统参数无关。该结果表明该模型通过学位指数与系列的Hurst指数$ H $之间的关系中的分数高斯噪声（FGN）类别。最后，我们通过模块化在系统中仍然存在的依赖度依赖性聚类系数$ c（k）$。
The growth of an interface formed by the hierarchical deposition of particles of unequal size is studied in the framework of a dynamical network generated by a horizontal visibility algorithm. For a deterministic model of the deposition process, the resulting network is scale-free with dominant degree exponent $γ_e = \ln{3}/\ln{2}$ and transient exponent $γ_o = 1$. An exact calculation of the network diameter and clustering coefficient reveals that the network is scale invariant and inherits the modular hierarchical nature of the deposition process. For the random process, the network remains scale free, where the degree exponent asymptotically converges to $γ=3$, independent of the system parameters. This result shows that the model is in the class of fractional Gaussian noise (fGn) through the relation between the degree exponent and the series' Hurst exponent $H$. Finally, we show through the degree-dependent clustering coefficient $C(k)$ that the modularity remains present in the system.
