**2. Methods and Experiments**

*2.1. DFA*

DFA is a variant of the correlation analysis of experimental datasets originally proposed by Peng et al. [14,15]. It is based on RMS analysis of signal profile and includes the following steps:

(1) Transition from signal *x*(*i*), *i* = 1, . . . , *N* to its profile *y*(*k*), *k* = 1, . . . , *N*

$$y(k) = \sum\_{i=1}^{k} [\mathbf{x}(i) - \langle \mathbf{x} \rangle], \qquad \langle \mathbf{x} \rangle = \sum\_{i=1}^{N} \mathbf{x}(i). \tag{1}$$

(2) Segmentation of the profile *y*(*k*) into parts of length *n* (*n*<*N*).

(3) Computation of the local trend *yn*(*k*) for each segment using a least-squares straightline fit.

(4) Estimation of the standard deviation,

$$F(n) = \sqrt{\frac{1}{N} \sum\_{k=1}^{N} \left[ y(k) - y\_n(k) \right]^2}. \tag{2}$$

(5) Implementation steps 2–4 over a wide range of *n*.

(6) Computation of the scaling exponent *α*,

$$F(n) \sim n^a. \tag{3}$$

Power-law dependence (3) is observed for various random processes, but many realworld datasets with an inhomogeneous structure often exhibit different local slopes of lg *F* vs. lg *n*, and *α* may differ for short-range and long-range correlations. DFA is usually applied to reveal the features of complex dynamics related to the region of long-range correlations. Specific values of *α*, associated with *α* < 0.5, *α* = 0.5, and 0.5 < *α* < 1, describe, respectively, anti-correlated behavior (alternation of large and small values of *x*(*i*)), lack of correlations (e.g., white noise), and positive power-law correlations (large values of *x*(*i*) tend to follow large values, and vice versa) [15]. Positive correlations, which may differ from power-law behavior, are associated with *α* > 1.
