## 3 Results  
The study methodology of the PPG signal to finally get the phase space reconstruction and draw interesting conclusions about the underlying physiological dynamics followed the next steps: first, we took 15,000 points, which corresponded to one minute of recorded signal. Obviously, the selected epoch was assumed stationary once the procedure, described in Section 2.2.2, was applied to the data. Then, we studied its graphical representation, considering different options for different graphic representations, as shown in Figures 11-13 (see Appendix A), to sustain the presence of a latent dynamic structure. Second, we tried to figure out the attractor more akin to the original, based on the optimal lag \(\tau\) (see Section 2.3.1), according to the autocorrelation function (AF) (Figure 9(a)) and the mutual information (MI) (Figure 9(b)), as well as on the optimal embedding dimension \(m\) (see Section 2.3.2), in accordance with the principal component analysis (PCA) (Figure 10(a)), the correlation dimension (D2) (Figure 10(b)), and the false nearest neighbors method (FNN) (Figure 10(c)). Figure 10: From a sample PPG signal (Subject Number 4): (**a**) autocorrelation function (AF), where the first zero crossing is when \(\tau=44\); and (**b**) mutual information (MI), where the first minimum is with \(\tau=54\). Figure 9: From the dynamic variable \(x\) of the Lorenz attractor: false nearest neighbors. From \(m=3\), the number of false nearest neighbors is almost zero. We applied the methodology to study 10 min of the PPG signal from each subject, and the results were similar to the ones shown in this paper. We saw in the Lorenz flow, according to the AF, that the criterion of \(1/e\) was approximately similar to the MI result because the attractor was chaotic and both linear and nonlinear correlations decayed rapidly, as illustrated in Figure 7. In the PPG signal, the criterion of the first zero crossing was closer to the MI result (see Figure 10) because the PPG signal was predominantly quasi-periodic on small timescales [22], while the correlations were stronger. Either way, the criterion of the first minimum of MI was adopted because it ensured statistical independence between the values, in linear and nonlinear terms. The parameters \(\tau\) and \(m\) calculated for five subjects, with results from each of the methods previously described, are in Table 1. The optimal \(\tau\) depended on the subject considered and on the time interval in which it estimated. Probably the range of optimal \(\tau\) values varied with each subject and could be a hallmark of each individual. It should make a careful study with all subjects and under changing conditions of the organism in its psychosomatic relationship with the surrounding environment. Figure 11: From a sample PPG signal (Subject Number 4): (**a**) Principal component analysis (PCA). The inner box clearly shows how the dynamic behavior of the attractor can be characterized with roughly seven directions. (**b**) Correlation dimension (\(D_{2}\)). It can be seen how from \(m=4\), the correlation dimension was confined to a constant value in an intermediate and reduced range of scales \(\varepsilon\). (**c**) False nearest neighbors. From \(m=5\), the number of false nearest neighbors is almost zero. Once we had the parameter \(\tau\) for each subject, calculated by the MI criterion, we proceeded to the calculation of parameter \(m\). Figure 11 visually depicts the results for a sample PPG signal, which corresponded to Subject Number 4 in Table 1. We saw that multivariate analysis, such as the PCA linear method, did not provide the ideal value of \(m\), although it was not unreasonable, mostly because physical systems do not usually have very high dimensions. The correlation dimension gave the value of \(m>2\) [\(D_{2}\)], which except for the first subject, amounted to a value of \(m=5\). For the FNN method, all calculations agreed with \(m=5\).