## Materials and Methods
### Adjustment of Synchronization Analysis Algorithm Parameters  
For the initial adjustment of the methods and finding appropriate parameters of the synchronization analysis algorithm that fit to the typical blood pressure and heart rate variability characteristics, another set of 150 stationary records which were obtained independently from this study and already used in previously reported analysis [37] from subjects with various autonomic status under supine resting conditions (typical record duration around 10 min) have been used. First optimization of synchronization algorithm parameters \(\tau\), \(T\) and \(\delta\) was performed. The appropriate choice of these values depended on the specific experimental conditions and was not always universal for the given type of data. The parameters may be adjusted to optimize the sensitivity of the algorithm by avoiding the saturation at either very low or very high synchronization coefficients. The gliding window duration \(\tau\) determined the number of phase points in the window. It was connected with the parameter \(\delta\) used to calculate the threshold for the standard deviation of the instantaneous phase first differences since the standard deviation calculated for a finite data sample depended on the sample size. To choose the appropriate window size \(\tau\), first the boundary conditions that specify its possible range were determined. One of the common hypotheses of the Mayer waves origin is their baroreflex loop based nature, suggesting that their period of about 10 s corresponds to the full feedback loop cycle [38]. Accordingly, any internally or externally induced changes in blood pressure were followed by characteristic regulatory oscillations with the Mayer waves period. Thus, choosing the gliding window size that was comparable or above this 10 s period eliminated these short-term regulatory oscillations by averaging. Alternatively, to ensure that the observed variations in both blood pressure and pulse intervals were proper measurements not caused by single faulty measurements and do not appear artifacts of preliminary filtering procedures, one has to guarantee that at least several actual measurements have been performed in each window. Taking into account typical heart rate values, a 3 s gliding window will typically result in having 3-4 pulse measurements under resting conditions and even more under stress conditions with an increased heart rate. Accordingly, one has to restrict with \(\tau\) above 3 s, and preferably, not longer than half period of Mayer oscillations, that is 5 s. For a better temporal resolution of the analysis, choosing the lower bound of the appropriate range that was a 3 s gliding window seems plausible. Next the threshold for the standard deviation of the phase difference was chosen empirically as 2\(\pi\)/300, \(T=0.4\) s, the latter adjusted empirically to avoid saturation and this way increase the dynamic range of the Sync index. The graphic insets in Figure 2 exemplify the analysis results for a single tilt-test record. In addition to pre-processed data sequences and their Hilbert phases, the figure displays their first differences as well as the results of their standard deviation analysis in a gliding window (in the lower right panel). The dashed lines denote the 2\(\pi\)/8 threshold for the standard deviation of the phase difference. The bold solid curve denotes \(\Phi_{\text{PI}}\)-\(\Phi_{\text{SBP}}\) and curve fragments highlighted by red color denote the synchronization episodes where the standard deviation of the phase difference remains below the 2\(\pi\)/8 threshold. Finally, the fraction of such episodes within the total record duration determines the synchronization coefficient Sync. The figure shows that, while for the entire analysed fragment the synchronization coefficient Sync was somewhat around 50%, it exhibited considerable variations along the record.