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This expansion is especially useful when the fluctuation scales Tσ of the modulating functions are large in comparison with the fluctuation scales Tz of the modulated processes.
The bubble size, of the order of millimeter, is relatively large compared to the smallest liquid fluctuation scales.
The DLB group had a statistically significantly higher mean depression score at baseline and higher scores on the NPI, NPI carer distress and clinical assessment of cognitive fluctuation scales at both baseline and 12-month follow-up (p<0.001).
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The solid line represents Taylor's power law of fluctuation scaling.
We define an aggregate fluctuation scale, σr(t|fc), using a frequency cutoff fc ∝ 1/Min[Nu(t)] to eliminate infrequently used words.
The exponent of fluctuation scaling in the skewness kurtosis plane depends on the cardinal directions, L*, a*, and b*.
This power function corresponds to a wide spread phenomenon known as fluctuation scaling in many engineering process.
We observe β < 1/2, which indicates that the fluctuation scale decreases more slowly with increasing corpora size than would be expected from the Yule-Simon urn model prediction, deducible via the "delta method" for determining the approximate scaling of a distribution and its standard deviation σ43. Figure 7: Growth fluctuation of word use scale with the size of the corpora.
We also found that the sample skewness and the sample kurtosis of L*, a*, and b* follow a U-shaped pattern and a generalized version of fluctuation scaling.
Yet, it is shown that this is a poor choice for unsteady processes where the sample step size is significantly larger than the fluctuation scale.
Moreover, the fluctuation scale σr(t|fc) is positively influenced by adverse conditions such as wars and revolutions, since a decrease in Nu(t) may decrease the competitive advantage that old words have over new words, allowing new words to break through.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com