Controlling the Multifractal Generating Measures of Complex Networks
Controlling the Multifractal Generating Measures of Complex Networks
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DOI：
10.1038/s41598-020-62380-6
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发表时间：
2020-03
影响因子：
4.6
通讯作者：
Ruochen Yang;P. Bogdan
中科院分区：
文献类型：
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作者：
Ruochen Yang;P. Bogdan
真实复杂网络的数学建模旨在表征其结构并破译其基本原理。自我重复模式和多重分形存在于许多现实世界的复杂系统中，如大脑、遗传、地球科学和社会网络。为了更好地理解真实网络中的多重分形行为，我们提出了加权多重分形图模型来表征交互权重编码的时空复杂性和异质性。我们提供了分析工具来验证所提出模型的多重分形性质。通过改变初始单位方的参数，该模型可以再现具有不同对称程度、位置、支撑和形状的多种多重分形谱。我们估计并研究了对应于两个现实世界复杂系统的加权多重分形图模型，即(i)酵母细胞在静止状态和指数生长状态下的染色体相互作用，以及（ii）认知健康人群和表现出晚期轻度认知障碍导致阿尔茨海默病的患者的大脑网络。对恢复模型的分析表明，所提出的随机图模型为理解复杂网络的自相似结构和区分不同的网络结构提供了一种新的方法。此外，通过将真实的复杂网络映射到多重分形生成措施上，它允许我们开发新的网络设计和控制策略，例如在不同功能条件或状态下对真实系统的多重分形措施进行最小控制。
Mathematical modelling of real complex networks aims to characterize their architecture and decipher their underlying principles. Self-repeating patterns and multifractality exist in many real-world complex systems such as brain, genetic, geoscience, and social networks. To better comprehend the multifractal behavior in the real networks, we propose the weighted multifractal graph model to characterize the spatiotemporal complexity and heterogeneity encoded in the interaction weights. We provide analytical tools to verify the multifractal properties of the proposed model. By varying the parameters in the initial unit square, the model can reproduce a diverse range of multifractal spectrums with different degrees of symmetry, locations, support and shapes. We estimate and investigate the weighted multifractal graph model corresponding to two real-world complex systems, namely (i) the chromosome interactions of yeast cells in quiescence and in exponential growth, and (ii) the brain networks of cognitively healthy people and patients exhibiting late mild cognitive impairment leading to Alzheimer disease. The analysis of recovered models show that the proposed random graph model provides a novel way to understand the self-similar structure of complex networks and to discriminate different network structures. Additionally, by mapping real complex networks onto multifractal generating measures, it allows us to develop new network design and control strategies, such as the minimal control of multifractal measures of real systems under different functioning conditions or states.