Identification of a Group's Physiological Synchronization with Earth's Magnetic Field

Abstract

A new analysis technique for the evaluation of the degree of synchronization between the physiological state of a group of people and changes in the Earth's magnetic field based on their cardiac inter-beat intervals was developed and validated. The new analysis method was then used to identify clusters of similar synchronization patterns in a group of 20 individuals over a two-week period. The algorithm for the identification of slow wave dynamics for every person was constructed in order to determine meaningful interrelationships between the participants and the local magnetic field data. The results support the hypothesis that the slow wave rhythms in heart rate variability can synchronize with changes in local magnetic field data, and that the degree of synchronization is affected by the quality of interpersonal relationships.

Keywords: earth’s magnetic field; geomagnetic field; heart rate variability; nonlinear dynamical systems; psychophysiology.

Figure 1

An example of the local magnetic field intensity data (measured in Lithuania during the time period between 2015/02/26 01:00:01 and 2015/02/26 03:00:01).

Figure 2

An example of the spectrogram for the magnetic field data presented in Figure 1. Frequency resolution is $\frac{1}{4096}$, $\mathsf{\Delta }\theta =4 \text{h}, \mathsf{\Delta }\omega =52 \mathrm{Hz}, \omega \in \left[0;52\right]\mathrm{Hz}$.

Figure 3

Time series $X=\left(X_1,\dots ,X_n\right)$ representing a numerical solution to Equation (4) with initial conditions $x\left(0\right)=0; x^{\prime }\left(0\right)=0.8$.

Figure 4

Examples of attractors for different time lag values. In (a) $\tau =4$; (b) $\tau =12$; (c) $\tau =23$; (d) $\tau =31$; (e) $\tau =43$; (f) $\tau =50$.

Figure 5

Shifting the origin to the center of mass of the attractor for $\tau =4$: (a) the original attractor; (b) the origin shifted to the center of the mass of the attractor.

Figure 6

Sliced diagrams of the attractors shown in Figure 4.

Figure 7

The identification of optimal time lag value ${\tau }_{*}$.

Figure 8

Time series $X$ (a) and $Y$ (b) and the difference $X-Y$ (c), obtained from numerical integration of the coupled nonlinear pendulum model (Equation (5)). Dotted lines separate time intervals with different values for the coupling parameters.

Figure 9

The sets of optimal time lags (a) ${\tau }_{*j}^{\left(X\right)}$ and (b) ${\tau }_{*j}^{\left(Y\right)}$ for the time series depicted in Figure 8. Circles in (c) denote the absolute differences ${\tau }_{*j}^{\left(X,Y\right)}$ between optimal time lags for $X$ and $Y$. The solid red line in (c) corresponds to the averaged absolute differences $A^{\left(X,Y\right)}=\left[{\overline{\tau }}_1^{\left(X,Y\right)}{\overline{\tau }}_2^{\left(X,Y\right)} \dots {\overline{\tau }}_{16}^{\left(X,Y\right)}\right]$.

Figure 10

The scheme of the application of Algorithm C on the experimental data. The horizontal axis of the depicted data corresponds to the indices of the time series.

Figure 11

Dendrogram plot for the two-day (2015/02/27 18:05:00 through 2015/03/01 18:05:00) data. Numbers on the X axis represent participants (numbered from 1 to 20).

Figure 12

The variation of the slow dynamics of the geometrical synchronization constructed from optimal time lags for participant 7 (red line) and participant 20 (blue line) for the time period between 2015/02/27 18:05:00–2015/03/01 18:05:00.

Figure 13

The variation of the slow dynamics of the geometrical synchronization constructed from optimal time lags for participant 7 (red line) and participant 15 (blue line) for the time period between 2015/02/27 18:05:00–2015/03/01 18:05:00.

Figure 14

Dendrogram plot for the two-week data. Numbers on the X axis represent participants (numbered from 1 to 20).

Figure 15

The graph of the evaluated interaction levels between participants. Nodes represent participants (numbered from 1 to 20). A line with an arrow pointing from person $a$ to $b$ ($a,b$), represents that person $a$ feels positive about person $b$. The width of the line is proportional to the overall ($a,b$) interaction value (sum of $a$’s ratings of the interaction with the $b$’s ratings over the 14 days).

Figure 16

Participant 15’s change of status during self-evaluation in points (max—10, min—0; Y axis) over the 14 days (X axis). The green, black, red, and blue lines correspond to the self-evaluation of social, general, physical, and emotional states, respectively.