## 2 Materials and Methods
### Data Analysis  
EEG analysis was carried out separately for each stage of the experiment, namely R1, S1, R2, and S2. The successive stages of rest and stress test were compared: R1 and S1, and R2 and S2. EEG signals were analyzed in the frequency range from 0.05 to 18 Hz. Particular attention was paid to the \(\delta_{1}\)-range (0.05-0.15 Hz), which is associated mainly with the processes of sympathetic control, and the \(\delta_{2}\)-range (0.15-0.50 Hz), which is associated mainly with the processes of parasympathetic control and respiratory influences [1]. We also analyzed \(\delta\) (0.5-3.0 Hz), \(\theta\) (4.0-7.0 Hz), \(\alpha\) (11.0-12.0 Hz), and \(\beta\) (15.0-18.0 Hz) rhythms. The frequency components in the corresponding ranges were extracted using a bandpass filter. For each EEG signal, the periodogram was evaluated in 6-min windows using the fast Fourier transform [47]. Then, the average powers of EEG oscillations were calculated in the corresponding frequency ranges. The obtained indices are denoted in the paper by the word \"activity\": \(\delta_{1}\)-activity, \(\delta_{2}\)-activity, and \(\alpha\)-activity. The ratio of average powers in \(\beta\)- and \(\alpha\)-ranges was also calculated and denoted as \(\beta\)/\(\alpha\)-activity. For each EEG lead, the individual values of the spectral indices were averaged over the ensemble of all subjects and presented as topographic maps of values linearly interpolated around the EEG leads. The median values of the spectral indices for each EEG lead were marked in color on the maps. Figure 1: (**a**) Protocol for the stress test. (**b**) Stroop Color Word Test. (**c**) Mental arithmetic test. To compare the stages of the experiment, the difference between the spectral indices at stages S1 and R1, and stages S2 and R2 was calculated for each subject and normalized to the value of the spectral index at R1 or R2, respectively. The obtained relative values of index differences were denoted by the symbol \(\Delta\): \(\Delta\delta_{1}\)-activity, \(\Delta\delta_{2}\)-activity, \(\Delta\alpha\)-activity, and \(\Delta\beta\)/\(\alpha\)-activity. For each pair of EEG leads, the phase coherence coefficient \(\gamma\)[48] was calculated:  
\[\gamma=\sqrt{\left\langle\cos\Delta\varphi(t)\right\rangle^{2}+\left\langle \sin\Delta\varphi(t)\right\rangle^{2}}, \tag{1}\]  
where \(\Delta\phi(t)\) is the difference in instantaneous phases of oscillations in the signals of analyzed EEG leads and angular brackets denote averaging over time. The instantaneous phases of oscillations in the analyzed frequency ranges were calculated using the Hilbert transform [49]. The obtained indices are denoted in the paper by the word \"coherence\": \(\delta_{1}\)-coherence, \(\delta_{2}\)-coherence, \(\delta\)-coherence, and \(\theta\)-coherence. If the phases of the analyzed signals are coherent, the phase difference \(\Delta\phi(t)\) will remain constant and its distribution density will be delta peak, resulting in \(\gamma=1\). Otherwise, \(\gamma\) is close to 0. When analyzing experimental signals, noise, non-stationarity, and the finite length of realizations affect the value of \(\gamma\), thus it takes intermediate values between 0 and 1. For each EEG lead, the values of its coherence coefficients with the other leads were averaged over the leads and presented as topographic maps of values interpolated around the EEG leads. For each lead, the median values of the coherence coefficients calculated over the ensemble of all subjects were shown on the maps in color. To compare the stages of the experiment, the difference between the coherence coefficients at stages S1 and R1, and stages S2 and R2 was calculated for each subject and normalized to the value of the coherence coefficient at R1 or R2, respectively. The obtained relative values of coefficient differences were denoted by the symbol \(\Delta\): \(\Delta\delta_{1}\)-coherence, \(\Delta\delta_{2}\)-coherence, \(\Delta\delta\)-coherence, and \(\Delta\theta\)-coherence.