## 4 Discussion
### SampEn RR at Rest and during Exercise  
The exercise experiment in a previous study was divided into three 30 min rest periods and three 20 min exercise periods [40]. However, the study differs from this study in that it was not an incremental exercise test.  
The SampEn RR results of this study are presented in Table 2; SampEn RR is higher during exercise than at rest. The results in this study had a similar trend; SampEn RR values at rest were significantly lower than in the sub-max stage and ACP stage.  
Some other studies have used SampEn to analyze human behavior during exercise. A study investigated low-intensity isometric and dynamic lower limb exercises and used SampEn to analyze differences between exercise and rest [41]. SampEn RR was significantly lower during low-intensity isometric exercise than at rest. However, SampEn RR increased during dynamic exercise, and SampEn RR values at rest and during exercise were not significantly different. By contrast with [41], the exercise in this study was dynamic, and SampEn RR increased more after exercise; this may be attributable to the negative load applied in this study. The authors of [41] also investigated the correlation between SampEn RR and HRV and reported that SampEn RR and RR were positively correlated (\(R=0.46\), \(p<0.01\)). This result is similar to our results, as SampEn RR was correlated with RR at rest (\(R=0.51\), \(p<0.01\)). This study is the first to investigate the association between SampEn SV and SVV, and the results revealed that SampEn RR at rest was associated with SVV nHF (\(R=0.46\), \(p<0.05\)). These results may indicate some correlation between cardiovascular variability and complexity.  
One study examined differences in RR complexity between young healthy trained and untrained boys [42]. Electrocardiograms were recorded during supine rest, standing, an incremental running exercise, and relaxation. SampEn RR was different between the trained and untrained groups; the overall SampEn RR distribution was saddle-like in the untrained group but more widely distributed in the trained group. In this study, the data of participants with different exercise habits were also investigated; the SampEn RR results were significantly different in the E group between rest, sub-max, and ACP. By contrast, no significant differences in SampEn RR between stages was observed for the S or N groups. Hence, our results are consistent with [41] in that SampEn RR appeared to change significantly in the trained group; hence, it could be an indicator for advanced assessment.  
In a study published in 2021, data on RR intervals were collected during treadmill exercise and recovery in young people with a maximum VO\({}_{2}\)[43]. Differences and the residual of SampEn RR were associated with VO\({}_{2}\). This result demonstrates that the SampEn assessment system is useful for assessing physical load. It also suggests that the direction of this study is promising.  
In 2018, Entropy of Entropy (EoE) was proposed for hybrid analysis applied to heartbeat interval time series, and disorder and complexity were analyzed separately [44]. Recently, a method has been proposed to measure instantaneous complexity, named intrinsic entropy (IE) [45]. The results of SampEn RR cannot effectively distinguish between ACP and sub-max, which is not consistent with the hypothesis, perhaps because conventional entropy may not explain the fact that complexity is different from irregularity. Alternatively, maybe it is because conventional entropy may not be able to calculate instantaneous changes. In the future, EoE and IE are methods that can be applied to the analysis of heartbeat interval time series to gather more advanced information.