在网络上使用远程内存的随机步行
Ana Gabriela Guerrero-Estrada1, Alejandro P Riascos2, Denis Boyer1
1Instituto de Física, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico.
Chaos (Woodbury, N.Y.)
|January 9, 2025
概括
这项研究介绍了一个可解决的随机步行模型,在网络上使用内存. 它表明,步行者优先重新访问节点,导致权力规律衰减,而不是占用概率的指数衰减.
科学领域:
- 复杂的系统复杂的系统.
- 统计物理 统计物理
- 网络科学 网络科学
背景情况:
- 随机步行是交通现象的基本模型.
- 网络上的标准随机走路显示出职业概率的指数式衰减.
- 记忆效应可以改变随机散步的动态.
研究的目的:
- 介绍和分析一个完全可解决的随机步行模型,在任意网络上使用远程内存.
- 调查优先节点复习对步行者动态的影响.
- 探索这种记忆赋予的随机散步的放松动态和静止状态.
主要方法:
- 开发一个完全可解决的模型随机步行与偏好的记忆.
- 将职位概率表示为网络随机步行矩阵的 eigenmodes 之和.
- 分析晚期的放松动态和关键的自我组织.
主要成果:
- 占用概率幅度在很长时间内衰减为功率定律,偏离指数衰减.
- 与没有内存的随机步行相比,静止状态保持不变,实现详细平衡.
- 晚期放松被单一的权力规律所支配,批判性地自我组织,并依赖于网络固有值和重置概率.
结论:
- 带有优先记忆的随机步行模型为研究运输现象提供了一个新的框架.
- 职业概率的权力定律衰退意味着由于记忆而偏离了标准的随机步行行为.
- 这些发现适用于各种现实世界的复杂网络和现象,如人类流动性和流行病传播.
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