## 4 Discussion
### Fractal Analysis  
The DFA method enables the assessment of the fractal structure in the time series of the RR intervals, providing information on short-term and long-term correlations in cardiac dynamics, as well as information on the adaptability and regulation of the autonomic nervous system. Based on the results obtained from the analysis using the DFA method, the following findings can be made:  
* Under mental stress, the value of \(\alpha_{1}\) (\(p<0.0001\)), determining short-term dependencies, decreases, which means that the short-term dynamics of the RR interval series become more chaotic and less correlated, which is an indicator of a stress response. This dynamic is due to a disturbed balance between sympathetic and parasympathetic activity, i.e., stress causes activation of the sympathetic nervous system, which leads to a more chaotic rhythm and reduced HRV. This information can be helpful in developing stress management strategies that include relaxation techniques and increasing parasympathetic activity;
* The value of the parameter \(\alpha_{2}\) (\(p=0.076\)), which reflects the long-term correlations in the heart rate, shows weaker changes under the influence of stress compared to \(\alpha 1\). This can be explained by the fact that long-term correlations are more resistant to short-term stressful stimuli. This result is consistent with studies [45,46] that also show that \(\alpha_{2}\) is primarily affected by long-term changes in cardiac function associated with stress or disease;
* The summary value of the \(\alpha_{\text{all}}\) parameter (\(p<0.0001\)) also decreased under stress. The value of this parameter reflects the overall decrease in autocorrelation and increase in irregularity in the RR interval series. This parameter is related to the Hurst exponent by the following equation: \(\alpha_{\text{all}}=\text{H}\). This relationship reflects the key concept that the two quantities measure the fractal properties of time series. The Hurst parameter is a measure of the long-term correlation in data and is widely used in time series analysis, particularly in the context of the statistical properties of cardiac variability. Higher  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Group 1-Rest** & **Group 2-Stress** & **\(p\)-Value** \\  & **[Mean \(\pm\) SD]** & **[Mean \(\pm\) SD]** & **\(p\)-Value** \\ \hline \(\alpha_{1}\) (DFA) & 1.167 \(\pm\) 0.09 & 0.753 \(\pm\) 0.14 & \textless{}0.0001 \\ \(\alpha_{2}\) (DFA) & 0.945 \(\pm\) 0.18 & 0.861 \(\pm\) 0.10 & 0.0760 \\ \(\alpha_{\text{all}}\) (DFA) & 0.981 \(\pm\) 0.08 & 0.847 \(\pm\) 0.02 & \textless{}0.0001 \\ H\({}_{\text{ap}}\)\({}_{2}\) (MFDA) & 0.979 \(\pm\) 0.02 & 0.851 \(\pm\) 0.09 & \textless{}0.0001 \\ \(\alpha_{\text{min}}\) (MFDA) & 1.45 \(\pm\) 0.16 & 1.08 \(\pm\) 0.11 & \textless{}0.0001 \\ \(\alpha_{\text{max}}\) (MFDFA & 0.63 \(\pm\) 0.06 & 0.79 \(\pm\) 0.04 & \textless{}0.0001 \\ \(\Delta\alpha=\alpha_{\text{max}}-\alpha_{\text{min}}\) (MFDFA) & 0.82 \(\pm\) 0.11 & 0.28 \(\pm\) 0.18 & \textless{}0.0001 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparative analysis of DFA and MFDFA-derived parameters at rest and under stress.  
values of H (or \(\alpha_{\text{all}}\)) indicate better adaptability of the organism to stressful situations and higher resistance to stress. The relationship between \(\alpha\) and H is particularly useful in the context of DFA, as the method is designed to assess the fractality of time series, allowing us to identify and analyze complex dependencies that cannot be revealed by the application of standard statistical methods. Similar results were reported in publication [46].