在超图形上的bootstrap泄露
Hao Peng1,2, Chenyi Wang1, Dandan Zhao1
1School of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, Zhejiang, China.
Chaos (Woodbury, N.Y.)
|April 10, 2025
概括
本研究介绍了对超图的通用化引导透模型,以了解网络在级联失效时的稳定性. 高阶相互作用显著影响网络行为,影响巨大的活跃组件.
科学领域:
- 网络科学 网络科学
- 统计物理 统计物理
- 复杂的系统复杂的系统.
背景情况:
- 引导透模型分析网络的稳定性,以防止级联失败.
- 现实世界的数据揭示了超越对对关系的更高阶交互,通常是通过超图建模的.
- 现有的模型往往忽略了这些高阶相互作用.
研究的目的:
- 提出和分析一个概括的引导透模型在超图上.
- 调查高阶相互作用对网络稳定性和相位转换的影响.
- 了解感染值和更高阶边缘的比例如何影响网络行为.
主要方法:
- 开发一个通用的引导式传递模型,通过超图集结合更高阶的交互.
- 数字模拟用于观察不同条件下的网络行为.
- 理论分析来推导透值和表征相位过渡.
主要成果:
- 引导透值和相位过渡类型取决于感染值和更高阶边缘的比例.
- 显著的感染值导致巨型活性成分 (GAC) 的持续增长,占用概率增加.
- 一个小的感染值导致GAC大小从连续增长转变为不连续增长,随着初始激活概率的增加.
- 增加更高阶边缘降低了透值,提高了网络的稳定性.
- 高阶边缘增加了激活机会,将 GAC 的增长从连续转变为不连续.
结论:
- 概括的超图启动透模型有效地捕捉了高阶交互对网络稳定性的影响.
- 通过增加更高阶边缘的比例来增强网络的稳定性.
- 感染值和更高阶边缘比例之间的相互作用决定了这些网络中相位过渡的性质.
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