Matsunaga Tsutomu, Muramatsu Masaaki
Research and Development Headquarters, NTT DATA Corporation, 3-3-9, Toyosu, Koto-ku, Tokyo, 135-8671, Japan.
Medical Research Institute, Tokyo Medical and Dental University, 1-5-45, Yushima, Bunkyo-ku, Tokyo, 113-8510, Japan.
BMC Res Notes. 2019 Mar 5;12(1):122. doi: 10.1186/s13104-019-4149-8.
The regularity of scale-free patterns in rank-size relations has been observed in word frequency, city size distribution, firm size distribution, and gene expression. Because of the common emergence of this regularity, understanding its mechanisms has been of great interest. For obtaining the scale-free pattern regularity, various models based on the rich-get-richer mechanism have been proposed; however, the overarching procedure of searching for the "rich" is in disagreement with the locally interacting behaviors seen in the aforementioned natural and social phenomena.
We implemented a computational model of a resource distribution system inspired by observations of word connectivity, which is created by local constraints with periodic and phase modulatory features. Here, we empirically demonstrated that a phase-modulated periodic connecting system can reach a dynamic equilibrium state as the most probable case, with the self-organizing scale-free patterns. The regularity could be a result of the configurational balance in spatiotemporal inequity during the resource distribution process with an adaptive constrained connectivity. Our results suggest that investigations of interferences of oscillating fluctuations in the system will elucidate the autoregulatory dynamic behavior.
在词频、城市规模分布、企业规模分布和基因表达中均观察到了等级 - 规模关系中的无标度模式规律。由于这种规律普遍存在，理解其机制一直备受关注。为了获得无标度模式规律，已经提出了各种基于富者更富机制的模型；然而，寻找“富者”的总体过程与上述自然和社会现象中所观察到的局部相互作用行为不一致。
我们基于对词连通性的观察实现了一个资源分配系统的计算模型，该模型由具有周期性和相位调制特征的局部约束创建。在此，我们通过实验证明，一个相位调制的周期性连接系统作为最可能的情况，可以达到具有自组织无标度模式的动态平衡状态。这种规律可能是在具有自适应约束连通性的资源分配过程中时空不平等的构型平衡的结果。我们的结果表明，对系统中振荡波动干扰的研究将阐明自调节动态行为。
