Title: On multifractals: a non-linear study of actigraphy data,
Abstract: This work aimed, to determine the characteristics of activity series from
fractal geometry concepts application, in addition to evaluate the possibility
of identifying individuals with fibromyalgia. Activity level data were
collected from 27 healthy subjects and 27 fibromyalgia patients, with the use
of clock-like devices equipped with accelerometers, for about four weeks, all
day long. The activity series were evaluated through fractal and multifractal
methods. Hurst exponent analysis exhibited values according to other studies
($H>0.5$) for both groups ($H=0.98\pm0.04$ for healthy subjects and
$H=0.97\pm0.03$ for fibromyalgia patients), however, it is not possible to
distinguish between the two groups by such analysis. Activity time series also
exhibited a multifractal pattern. A paired analysis of the spectra indices for
the sleep and awake states revealed differences between healthy subjects and
fibromyalgia patients. The individuals feature differences between awake and
sleep states, having statistically significant differences for $\alpha_{q-} -
\alpha_{0}$ in healthy subjects ($p = 0.014$) and $D_{0}$ for patients with
fibromyalgia ($p = 0.013$). The approach has proven to be an option on the
characterisation of such kind of signals and was able to differ between both
healthy and fibromyalgia groups. This outcome suggests changes in the
physiologic mechanisms of movement control.