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首页> 外文期刊>Journal of Basic and Applied Physics >Fluctuation Scaling and 1/f Noise
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Fluctuation Scaling and 1/f Noise

机译：波动比例和1 / f噪声

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A power law relationship between the variance and the mean, when derived from sequential data using expanding enumerative bins, implies 1/f noise. This relationship, called fluctuation scaling by physicists and Taylor’s law by ecologists, is found within diverse physical, econometric and biological systems. Its origin remains controversial. Both fluctuation scaling and 1/f noise are proposed to manifest consequent to a central limit-like effect specified by the Tweedie convergence theorem that has as its foci of convergence a family of statistical distributions, the Tweedie exponential dispersion models. An example of fluctuation scaling and 1/f noise is provided here based on deviations in position of the prime numbers; the Tweedie compound Poisson distribution is shown to correspond to these deviations. Whereas many different physical and biological mechanisms have been proposed to explain fluctuation scaling, Taylor’s law and 1/f noise, such mechanisms are inapplicable to a number theoretic example like this. The Tweedie convergence theorem provides a generally applicable explanation for the origin of these scaling relationships, and can provide insight into processes like self-organized criticality and multifractality.
机译：当使用扩展的枚举仓从顺序数据中得出方差和均值之间的幂律关系时，就意味着1 / f噪声。这种关系在物理学家，计量经济学和生物系统中都有发现，被物理学家称为波动定标，被生态学家称为泰勒定律。其起源仍然有争议。提出波动定标和1 / f噪声都是由于Tweedie收敛定理所指定的类似中心极限的效应而表现出来的，该定理具有作为统计收敛点的Tweedie指数色散模型作为其收敛的焦点。这里基于素数位置的偏差提供了波动比例缩放和1 / f噪声的示例。 Tweedie复合泊松分布表明与这些偏差相对应。尽管已经提出了许多不同的物理和生物学机制来解释波动标度，泰勒定律和1 / f噪声，但是这种机制不适用于像这样的数个理论示例。 Tweedie收敛定理为这些比例关系的起源提供了一个普遍适用的解释，并且可以提供对自组织临界和多重分数等过程的洞察力。

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