## 2 Materials and Methods
### Multivariate Multiscale Entropy (MMSE)  
Entropy is particularly useful as a measure of the structure of time series, as it reflects the degree of regularity or irregularity of a sequence of data [28]. As mentioned previously, the physiological signals from the human body are dynamic, irregular, and non-linear. Therefore, to assess the structure dynamics across the different time series, [PERSON] et al. introduced the multiscale entropy (MSE) to measure complexity by calculating sample entropy (SampEn) as the following function of scale, converting the original time series into coarse-grain data, computing the entropy for every scale, and mapping its dependence on the scale [29].  
\[\begin{array}{c}\text{SampEn}(\text{m},\ \text{r},\ \text{N})=-\text{ln}\ ( \frac{\text{A}}{\text{B}})\\ \\ yj^{(\tau)}=\frac{1}{\tau}\sum_{i=(j-1)\tau=1}^{j\tau}xi,\ \text{where},\tau=\text{scale factor} \end{array}\]  
Although the MSE method only considers data channels separately, it can be effectively utilized for the evaluation of signal complexities over a variety of time scales, and previous studies effectively utilized it for analyses of biological, geoscientific, and physiological data [19]. [PERSON] and [PERSON] proposed that the MMSE algorithm could rigorously incorporate multivariate sample entropy in order to take both cross-channel and within-channel dependencies in numerous data channels into account, and then be used to evaluate the effects of said entropy over numerous temporal scales. In comparison to standard MSE, the MMSE algorithm allows for more degrees of freedom to be applied in any analysis, and the algorithm has been demonstrated to yield reliable assessments of the dynamic richness underlying multichannel observations [20; 28].  
The MMSE method assesses the relative complexity of normalized multichannel temporal data by plotting multivariate sample entropy as a function of the scale factor [28]. [PERSON] and [PERSON] analyzed the COP signals from quiet standing for both young and elderly subjects using the MMSE and MSE approaches. Both the MSE and MMSE analyses showed awareness differences [20; 30]. Moreover, the MMSE approach provides complexity analyses of real world biological and physical systems, which are typically of multivariate, correlated, and noisy natures. Since [PERSON] et al. first proposed empirical mode decomposition (EMD) method [31], it has been broadly applied for analyses of non-linear, non-stationary data based on the intrinsic characteristics of time series. Meanwhile, multivariate empirical mode decomposition (MEMD) solves the challenge of mode mixing through the addition of white noise to different channels and also overcomes the single input limitation of EMD. [PERSON] et al. found MEMD-enhanced MMSE can distinguish the smaller differences between before and after the use of vibration shoes in both two directions, which is more powerful than the EMD-enhanced MSE in each individual direction [32]. [PERSON] and [PERSON] applied the MSE and MMSE approaches to analyze the gait function of 24 elderly, chronically ill patients with cardiovascular disease, diabetes mellitus, or osteoporosis [33]. [PERSON] and [PERSON] based on COP-Based MMSE measures, further analysis to make a comparison of postural stability during upright standing between normal and flatfooted Individuals of 54 healthy young adults [34]. Their results showed that the MSE algorithms used to identify the sense of balance in young adults and elderly individuals were inferior to the MMSE algorithms utilized for the calculation of the CI of COP data.