在网络拓学中量化新兴效应的分类框架.
Johnny Jingze Li1, Sebastian Pardo-Guerra2, Kalyan Basu3
1Center for Engineered Natural Intelligence and Department of Mathematics, University of California San Diego, La Jolla, CA 92093, U.S.A. jil164@ucsd.edu.
Neural computation
|July 8, 2025
概括
我们引入了一个新的框架,使用同质代数来测量复杂系统中的新兴效应. 这种方法将系统属性与网络结构联系起来,使预测和理解出现成为可能.
科学领域:
- 复杂系统科学 复杂系统科学
- 网络理论 网络理论
- 计算数学 计算数学 计算数学
背景情况:
- 新兴效应是复杂系统的关键,但缺乏理论测量框架.
- 了解出现需要量化在单个组件中不存在的属性.
研究的目的:
- 开发一种计算方法来量化复杂系统中出现的效应.
- 建立一个理论框架,将出现与网络拓和结构联系起来.
主要方法:
- 使用同质代数来建模作为结构非线性出现的模型.
- 在cohomologies的数学结构中编码出现.
- 将框架应用于用于计算测量的网络模型.
主要成果:
- 开发了一种基于网络拓学的新型计算测量出现.
- 证明该措施与现有的信息理论措施相关.
- 展示了框架能够预测和解释新出现的影响的能力.
结论:
- 拟议的框架提供了一种可靠的方法来衡量和理解出现.
- 网络拓和局部结构是新兴潜力的关键决定因素.
- 这项工作为预测和分析各种复杂系统中新出现的现象提供了一条途径.
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