## 2 Materials and Methods
### Data Analysis Method  
The postural control performance was evaluated from the CoP data while vibration stimulation was applied. Furthermore, the CoP data divided the Dur-section into three evaluation sections (ES\({}_{i}\), i = 1, 2, 3) determined according to the frequency of vibration stimulation and the response frequencies of the proprioceptors. Table 2 lists the names of each ES, the frequency of the vibration stimulus and the corresponding proprioceptors.  
Because the previous studies showed that a relationship existed between CoP displacement in an anteroposterior direction and the response of proprioceptors by vibration stimulus, the CoP displacement in the anteroposterior direction was only considered [10]. Previous studies used the relative proprioceptive weighting ratio (RPW) and the root mean square (RMS) of GS and LM as evaluation indexes to evaluate the proprioceptive predominance of body location and the magnitude of CoP in an anteroposterior direction [11; 15; 18]. The evaluation indexes applicable to the sweep frequency method were introduced as follows.  
To obtain information regarding the proprioceptive predominance of body locations, modified RPW was calculated using the following equation.  
\[RPW^{i}=\frac{RMS_{GS}^{i}}{RMS_{GS}^{i}+RMS_{LM}^{i}}\times 100\ [\%]\ \ \ (i=1,\ 2,\ 3) \tag{3}\]  
where the subscript \(i\) is used to distinguish the ESs. The higher is the value of \(RPW^{i}\) from 50% to 100%, the higher is the reliability of GS input. On the other hand, the lower is the value of \(RPW^{i}\) from 50% to 0%, the higher is the reliability of LM input [11; 15]. \(RMS_{*}^{i}\) means the effective value of the magnitude of CoP in an anteroposterior direction. In each ES in the Dur-section, the larger the RMS, the higher the amount of transition of postural sway in the anteroposterior direction compared to those in the Pre-section. \(RMS_{*}^{i}\) was calculated using the following equations.  
\[RMS_{*}^{1}=\sqrt{\frac{1}{N}\sum_{n=n_{1}}^{n_{2}}\left\{Y_{Dur(*)}(n)- \overline{Y}_{pre(*)}\right\}^{2}} \tag{4}\]  
\[RMS_{*}^{2}=\sqrt{\frac{1}{N}\sum_{n=n_{3}}^{n_{4}}\left\{Y_{Dur(*)}(n)- \overline{Y}_{pre(*)}\right\}^{2}} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**ES\({}_{i}\)** & **Frequency [Hz]** & **Corresponding Proprioceptors** \\ \hline ES\({}_{1}\) & 30–43 & Meissner corpuscle \\ ES\({}_{2}\) & 49–71 & Muscle spindles \\ ES\({}_{3}\) & 168–247 & Vater-Pacini corpuscle \\ \hline \hline \end{tabular} ES: Evaluation section.  
\end{table}
Table 2: Lists of names of each ES, frequency of vibration stimulus and corresponding proprioceptors.  
\[RMS_{*}^{3}=\sqrt{\frac{1}{N}\sum_{t=n_{5}}^{n_{6}}\left\{Y_{Dur(*)}(n)-\overline{Y} _{pre(*)}\right\}^{2}} \tag{6}\]  
where \(N\) is the total sampling number of each ES; \(n\) is the number of data series; \(Y_{Dur(*)}(n)\) is the CoP in the anteroposterior direction in the Dur-section; \(\overline{Y}_{pre(*)}\) is the mean value of CoP in the anteroposterior direction in the Pre-section; the superscript \"*\" is used to distinguish stimulation body locations, namely, the GS or LM; and subscript numbers are used to distinguish the ESs. In this case, \(N\) was equal to 1000 because all ESs were analyzed in 10 s and the sampling frequency was 100 Hz. Table 3 shows the numbers of data series corresponding to the start frequency and the end frequency of ES\({}_{i}\) in the case of frequency ascend mode and descend mode. In each of the ascend and descend modes, the numbers of sampling series \(n\) corresponding to measurement time \(t\) were calculated by Equations (1) and (2) in order to obtain the start and end frequencies of each ES, respectively, as shown in Table 2. To correct the CoP in the Dur-section based on the CoP in the Pre-section, the CoP in the Dur-section was subtracted from the mean value of the CoP in the Pre-section. These values were calculated using MATLAB (MathWorks, Inc., Natick, MA, USA).