Figure 1

Behavior of time series examined in this paper: Both (a) and (b) show irregular fluctuations and long-term trends. (a) is human postural data (measured during quiet standing) of mediolateral and anteroposterior directions. The data were measured at $100\mathrm{Hz}$. The subject was healthy, stood barefoot, and had opened eyes. (b) is healthy human electroencephalography (EEG) data, where $S_1$ and $S_2$ are the subject identifiers and the third letter, $O$ and $C$, identifies the condition: $O=\text{eyes}$ open and resting, and $C=\text{eyes}$ closed and resting. The measurement point is $C_Z$ of the unipolor 10–20 Jasper registration scheme [3]. Measurements were not simultaneous and the data were digitized at $1024\mathrm{Hz}$ using a $12\text{−}\text{bit}$ A/D converter. The EEG impedances were less than $5\mathrm{K}\Omega$. The data were amplified, $\text{gain}=18000$, and amplifier frequency cut-off settings of $0.03\mathrm{Hz}$ and $200\mathrm{Hz}$ were used. The ordinate axis in (a) and (b) is arbitrary.Reuse & Permissions

Figure 2

(Color online) Behavior of our numerical data, irregular fluctuations with no trend, those with trends, and those with other trends. In this panel, the irregular fluctuations are Gaussian random numbers and both the long-term trends are artificial.Reuse & Permissions

Figure 3

(Color online) A plot of (a), (c), (e), (g), and (i) cross correlation (CC), and (b), (d), (f), (h), and (j) the average mutual information (AMI), where data have no trend and we use 99 SSS data. (a) and (b) are the coupled linear ARMA model, (c) and (d) are the Ikeda map, (e) and (f) are a chaotic neural network (CNN), (g) and (h) are Gaussian random numbers (GRN), and (i) and (j) are the $x$ component of the coupled linear ARMA model and that of the Ikeda map. The solid line is the original data and the dotted lines are the SSS data.Reuse & Permissions

Figure 4

(Color online) A plot of CC and AMI, where data have different long-term trends and we use 99 SSS data. The notation is the same as in Fig. 3.Reuse & Permissions

Figure 5

(Color online) A plot of the CC and AMI for the postural data: (a) CC and (b) AMI. The solid line is the original data and the dotted lines are the SSS data.Reuse & Permissions

Figure 6

(Color online) A plot of (a) and (c) CC, and (b) and (d) AMI for the EEG data: (a) and (b) $S_{1}C$ and $S_{1}O$ (the same subject and different conditions), and (c) and (d) $S_{1}C$ and $S_{2}C$ (different subjects and the same condition). For the explanation of this notation, see Fig. 1. The solid line is the original data and the dotted lines are the SSS data.Reuse & Permissions