## 3 Results  
### Variability of Heart Rate and Oxygen Consumption at Aerobic Threshold across Participant Groups  
The final number of time series considered in this study was 111, since 12 time series did not meet the inclusion criteria introduced in the Materials and Methods section. Table 1 serves as a comprehensive overview of participant profiles and study parameters, allowing for a detailed comparison and analysis across different demographic and health-related categories within the study population.  
Figure 3 presents HR and VO2 values at the AerT for the study participants. It showcases a wide spectrum of HR values, ranging from 60 to 180 beats per minute (bpm), and VO2 values, spanning from 600 to 2500 mL/min at AerT. Notably, young athletes typically display lower VO2 values, which can be attributed to their smaller body sizes. Conversely, cardiac patients often exhibit both lower VO2 and HR values, reflecting their distinct physiological condition.  
Figure 4 illustrates two representative HR time series and outlines the key steps of the automatic detection process. These time series were analyzed using the Python script with our automatic detection algorithm. The series on the right pertains to a young athlete from group Y, while the series on the left is from a cardiac patient in group C. The blue graded lines vividly depict the incremental test's workload. As the intensity of physical exercise increases, so does the HR, as observed in panels (a) and (d). Panel (d) demonstrates how beta blockers effectively regulate the increase in HR. Through the RQA of HR, the determinism for each epoch and its second derivative were computed, as shown in panels (b) and (e). The colored points mark relative minima identified by our automatic algorithm. In panels (c) and (f), the most convex minimum, which aligns with the AerT value, is highlighted by a red vertical line.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & **Group A** & **Group O** & **Group C** & **Group Y** & **All** \\ \hline Name & Athletes & Obese & Cardiac & Young athletes & Athlete, obese \\  & & & & & \\  & & & & & \\ n & 27 & 19 & 16 & 49 & 111 \\ Age(years) & 15.30 \(\pm\) 1.87 & 42.90 \(\pm\) 12.67 & 52.80 \(\pm\) 10.09 & 15.20 \(\pm\) 2.02 & 25.35 \(\pm\) 16.62 \\ BMI (kg/m\({}^{2}\)) & 22.06 \(\pm\) 3.28 & 39.98 \(\pm\) 4.95 & 25.92 \(\pm\) 4.29 & 22.65 \(\pm\) 4.97 & 25.78 \(\pm\) 7.60 \\ Range (years) & 14-20 & 19–63 & 35–70 & 11–17 & 11–70 \\ Gender & 25/2 & 6/13 & 16/0 & 26/23 & 73/38 \\ (MW/OW) & 27/0 & 0/19 & 13/3 & 32/17 & 72 NW/39 OW \\ Hstatus & Healthy (H) & Disease (D) & Disease (D) & Healthy (H) & 76 H/35 D \\ Incremental & 20 or & 1 km/h every & 10 (Watts/min) & 10 (Watts/min) & 10, 15, 20 \\ protocol & 15 (Watts/min) & 3 min & & & (Watts/min) \\ Type & Cycle-ergometer (C) & Treadmill (T) & Cycle-ergometer (C) & Cycle-ergometer (C) & 90 C/19 T \\ \hline \hline \end{tabular}
\end{table}
Table 1: Overview of participant profiles and study parameters.  
Figure 4: Representative HR time series, panels (**a**,**d**), belong to groups C and Y, respectively. Panels (**b**,**e**) show DET(%), and the second derivative where the dashed red horizontal line corresponds to the cut-off; in panels (**c**,**f**), DET (%) (in black), and workload (in blue) are shown point by point, respectively. The red vertical line corresponds to AerT (the most convex minimum of DET (%), as explained in the Materials and Methods section).  
Figure 3: HR (bpm) vs. VO\({}_{2}\) (mL/min) at AerT from 111 CPET tests. The participants are divided into athletes (group A, blue cross), obese (group O, red circle), cardiac patients (group C, light-blue diamond), and young athletes (group Y, yellow circle), respectively.