在时间变化的复杂网络中检测相位过渡的统一方法
Mohamed Ridha Znaidi1, Jayson Sia1, Scott Ronquist2
1Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, 90089, USA.
Scientific reports
|October 20, 2023
概括
本研究引入了一种新的几何框架,以了解局部网络变化如何影响时间变化的复杂网络 (TVCN) 中的全球属性. 该方法使用福曼-里奇曲率来检测各种系统中的相位过渡,从人工网络到政治数据.
科学领域:
- 复杂系统科学 复杂系统科学
- 网络理论 网络理论
- 几何分析 几何分析
背景情况:
- 了解时间变化的复杂网络 (TVCN) 对于控制和预测至关重要.
- 当地网络变化对全球物业的影响仍然难以量化.
- 现有的方法缺乏统一的方法来将本地互动与全球网络动态联系起来.
研究的目的:
- 开发一个用于分析TVCNs的数学框架.
- 研究网络的几何性质及其在相变中的作用.
- 建立一个统一的方法,将本地网络交互与全球动力学联系起来.
主要方法:
- 提出了一个以几何学为灵感的框架来描述网络状态.
- 使用福曼-里奇曲率来定义和检测TVCN中的相位.
- 应用该框架来分析人工网络,神经网络训练,细胞重编程 (Hi-C数据) 和美国参议院投票数据.
主要成果:
- 在使用曲率形式主义的人工生成网络中成功检测到相位过渡.
- 证明了框架在人工神经网络培训和学习期间识别阶段过渡的有效性.
- 观察到细胞重编程动态曲率网络的奇点趋势.
- 在1994年大选后的美国参议院数据中使用拟议的曲率形式主义识别了政治变化.
结论:
- 提出的曲率形式主义为检测TVCN中的相变提供了一个强大的工具.
- 该框架提供了一种统一的方法,将本地网络互动与全球网络动态联系起来.
- 这种几何视角在各种科学领域具有广泛的适用性,包括机器学习,生物学和政治学.
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