![]() Thus, the aim of this paper is to promote and facilitate investigations of the scale-free amplitude modulation of ongoing neuronal oscillations with the use of DFA ( Linkenkaer-Hansen et al., 2001). We believe, however, that DFA could prove valuable to a wider community of neuroscientists than its current users. Detrended fluctuation analysis (DFA Peng et al., 1994), a method for analyzing scaling behavior in time series, has played a critical role in this success. There is growing evidence that physiological processes can exhibit fluctuations without characteristic scales and that this scale-free dynamics is important for their function ( Bassingthwaighte et al., 1994 Bak, 1996 Goldberger et al., 2002 Stam, 2005 Ghosh et al., 2008 He et al., 2010 West, 2010). ![]() Such systems are broadly referred to as “scale-free” ( Bassingthwaighte et al., 1994). For some objects or processes, however, the average value is a poor description, because they do not have a typical or “characteristic” scale. When investigating nature we often discard the observed variation and describe its properties in terms of an average, such as the mean or median ( Gilden, 2001). Finally, we provide a brief overview of insights derived from the application of DFA to ongoing oscillations in health and disease, and discuss the putative relevance of criticality for understanding the mechanism underlying scale-free modulation of oscillations. Practical advice on applying DFA to oscillations is supported by MATLAB scripts from the Neurophysiological Biomarker Toolbox (NBT) and links to the NBT tutorial website. To facilitate understanding and encourage wider use of scaling analysis of neuronal oscillations, we provide a pedagogical explanation of the DFA algorithm and its underlying theory. Furthermore, amplitude dynamics is remarkably independent of the time-averaged oscillation power, indicating that the DFA provides unique insights into the functional organization of neuronal systems. Detrended fluctuation analysis (DFA) has proven particularly useful, revealing that genetic variation, normal development, or disease can lead to differences in the scale-free amplitude modulation of oscillations. Recent years of research have shown that the complex temporal structure of ongoing oscillations is scale-free and characterized by long-range temporal correlations. ![]()
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