多分形非线性是乘法级联动态的可靠估计器
Madhur Mangalam1, Aaron D Likens1, Damian G Kelty-Stephen2
1University of Nebraska at Omaha, Division of Biomechanics and Research Development, Department of Biomechanics, and Center for Research in Human Movement Variability, Nebraska 68182, USA.
Physical review. E
|April 18, 2025
概括
一个新的统计数据,tMF,可靠地识别了自然和行为科学中的乘法级联. 它量化了跨度互动性和ergodicity断裂,独立于序列长度或噪声类型.
科学领域:
- 自然和行为科学 自然和行为科学
- 复杂系统分析 复杂系统分析
- 时间序列建模时间序列建模
背景情况:
- 测量时间序列越来越多地被建模为随机乘法级联.
- 多分体形式主义研究这些级联,但没有替代比较,多分体性可能是模两可的.
- 现有的方法对序列长度,线性相关性或加法动态敏感.
研究的目的:
- 开发一种强大的方法来识别随机的乘法级联.
- 量化这些过程中的跨度互动性和ergodicity破坏.
- 为了解决时间序列分析中的多分位的模两可.
主要方法:
- 构建随机级联,其长度变化,噪声类型 (添加式白色高斯噪声,分数高斯噪声) 和噪声操作 (加法与乘法).
- 开发并应用一个t-统计,tMF,比较原始多分体光谱宽度与替代光谱宽度.
- 分析了tMF对序列长度,噪声类型和代数的敏感性.
主要成果:
- 该tMF统计可靠地识别随机的乘法级联,无论序列长度或噪声类型.
- tMF对交互性和代数比对序列长度更敏感.
- 倍增级联表现出比添加级联更强的ergodicity打破,与相关的噪音和代数增加.
结论:
- tMF是一个强大的指标,用于识别乘数级联过程和量化ergodicity破坏.
- 这一指标促进了对自然科学和行为科学中的级联机制的理解.
- tMF显示了将团队级发现扩展到个人级分析的潜力.
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