Identification of a Group’s Physiological Synchronization with Earth’s Magnetic Field
Abstract
:1. Introduction
2. Methods and Procedures
2.1. Participants
2.2. Ethics Statement
2.3. Computational Estimation of the Synchronization of a Group’s HRV Time Series with Earth’s Magnetic Field Data
2.3.1. Magnetic Field Data
2.4. Computation of the Power of Local Magnetic Field
- (1)
- Compute the spectrogram (as described previously).
- (2)
- Crop the spectrogram in order to eliminate intermittent chaotic outbreaks in the measured data due to manmade noise, lightening, etc.
- (3)
- Apply the Gaussian median filter of dimensions to for the reduction of noise.
- (4)
- Compute the signal power as .
2.4.1. Example: Computation of the Local Magnetic Field Power
2.5. Algorithm for the Computation of Geometrical Synchronization between Two Time Series
2.5.1. Computation of the Area of an Attractor in the State Space
- (1)
- Compute the center of the mass of the points comprising the attractor. Move the origin of the state space to the center of the mass.
- (2)
- Divide the state space of the attractor into the slices with equal central angles of a circle centered on the origin. The number of slices depends on the number of points in the observation window of the time series.
- (3)
- Set the radius of each slice to the maximal distance between a point belonging to that slice and the origin.
- (4)
- Compute the area of the attractor as the sum of areas of all slices.
2.5.2. Example 1: Identification of the Optimal Time Lag
2.5.3. Construction of the Algorithm for the Estimation of the Geometrical Synchronization between Two Time Series
- (1)
- Divide signals and into observation windows of size ( should be large enough to enable the reconstruction of a meaningful attractor in the state space):
- (2)
- Compute optimal time lags for each observation window for both time series using Algorithm B. Such computations result in two vectors of optimal time lags: . This information reduction algorithm allows the identification of similarities between attractors reconstructed from different time series from the geometrical point of view. The variation of optimal time lags reconstructed for a pair of time series is used for the quantification of the generalized geometrical synchronization between those time series.
- (3)
- Calculate the vector of absolute differences between obtained optimal time lags for each observation window: . The differences between the optimal time lags are used as the metric of geometrical similarity between the analyzed time series.
- (4)
- In order to identify the slow dynamics reflecting averaged changes in absolute differences between optimal time lags for each data signal, divide the vector of absolute differences into segments: . The number of points in each segment should be large enough to produce a meaningful averaging.
- (5)
- Calculate the mean absolute difference between optimal time lags for each segment. The obtained vector of mean absolute differences is defined as a measure representing the geometrical synchronization between data signals .
2.5.4. Computational Validation of the Geometrical Synchronization Algorithm
2.6. Clusterization of Multivariate Time Series Based and Their Synchronization with a Master Time Series
- (1)
- Compute the vector of mean absolute differences , describing the relationship between and as described in Algorithm C, for each .
- (2)
- Calculate the Euclidean distance (the measure used to estimate the geometrical similarity of two data vectors) which represents the similarity between all data signals, using the following formula:The above equation yields the symmetric matrix of Euclidean distances.
- (3)
- Construct a dendrogram plot (UPGMA) [37] using the obtained matrix. The main goal of the dendrogram is to identify the clusters of similar time series, i.e., the clustering process involves grouping the analyzed time series based on the similarity of the slower rhythm dynamics of their synchronization with master time series .
3. Results
3.1. The Application of the New Analysis Technique on HRV and Magnetic Field Data
3.1.1. Obtaining the Power of Local Magnetic Field during the Experiment
3.1.2. Identification of Clusters in the Groups Based on the Similarity/Synchronization between Participants’ HRV and Magnetic Field Activity
- (1)
- One of the steps of Algorithm C is splitting the participants’ HRV and local magnetic field power time series into segments. The standard length of analysis for HRV is five minutes [38]. Thus, inter-beat (RR) interval and magnetometer data was split into five-minute segments for analysis. Note that since HRV data consists of time intervals between each pair of heartbeats, the number of samples in the data vectors corresponding to each five-minute segment varies due to changes in the participants heart rate and other factors that influence HRV, such as stress and emotional states [39]. Since the power of the local magnetic field was computed for one-second time intervals, the resulting five-minute segments consisted of the same number of elements (300 data points). However, the difference in the size of the segments of HRV and the power of the local magnetic field time series did not impact the overall result of the study, since all of the segments represented the same concurrent five-minute time intervals.
- (2)
- We selected the number of slices in Algorithm B to be 60 because it was empirically observed that a higher number would result in some empty slices.
- (3)
- The maximal value of in Algorithm B was set to 50. Higher values of would generate too short trajectory matrices, because the five-minute segments consisted of approximately 300 elements.
- (4)
- The value of the parameter in Algorithm C, used for identification of slow dynamics of the synchronization between the two time series, was set to 48. This corresponded to a four-hour averaging of the difference of the optimal time lags. It was observed that this value of produced the most meaningful averaging.
- (5)
- As noted in Section 3.2 the magnetometer data contained one minute-long periods of missing data at the end of each hour. Since these periods in the time series did not contain any information, it was necessary to remove those periods in such a way that would not disrupt the timing between the HRV and magnetic field time series. The solution we implemented was to remove the missing data segments from both the five-minute magnetometer data and from the five-minute RR interval series. Since the cropped series obtained after this procedure fully defined the five-minute series, they were used in the data reduction step.
3.2. The Relation between Synchnorization Results and the Psychological Interactions between Participants
3.2.1. Psychological Survey Data
3.2.2. Comparison of Survey Data and the HRV/Magnetic Field Synchronization Results
4. Discussion
5. Conclusions
Supplementary Materials
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
EEG | Electroencephalogram |
HRV | Heart rate variability |
IBI | Inter-beat-interval |
Pc | pulsations continuous |
Pi | pulsations irregular |
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N | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
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1 | −1 | −1 | 2 | 2 | 1 | −1 | ||||||||||||||
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3 | ||||||||||||||||||||
4 | −1 | 4 | ||||||||||||||||||
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8 | ||||||||||||||||||||
9 | 2 | 1 | 6 | |||||||||||||||||
10 | 4 | 1 | 1 | 1 | 4 | 1 | ||||||||||||||
11 | 1 | |||||||||||||||||||
12 | 2 | 1 | 1 | −1 | ||||||||||||||||
13 | 1 | 4 | 2 | 8 | 1 | 3 | ||||||||||||||
14 | 2 | |||||||||||||||||||
15 | 2 | |||||||||||||||||||
16 | 2 | |||||||||||||||||||
17 | ||||||||||||||||||||
18 | ||||||||||||||||||||
19 | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | |||||||||
20 | 1 | 1 | 3 | 1 |
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Timofejeva, I.; McCraty, R.; Atkinson, M.; Joffe, R.; Vainoras, A.; Alabdulgader, A.A.; Ragulskis, M. Identification of a Group’s Physiological Synchronization with Earth’s Magnetic Field. Int. J. Environ. Res. Public Health 2017, 14, 998. https://doi.org/10.3390/ijerph14090998
Timofejeva I, McCraty R, Atkinson M, Joffe R, Vainoras A, Alabdulgader AA, Ragulskis M. Identification of a Group’s Physiological Synchronization with Earth’s Magnetic Field. International Journal of Environmental Research and Public Health. 2017; 14(9):998. https://doi.org/10.3390/ijerph14090998
Chicago/Turabian StyleTimofejeva, Inga, Rollin McCraty, Mike Atkinson, Roza Joffe, Alfonsas Vainoras, Abdullah A. Alabdulgader, and Minvydas Ragulskis. 2017. "Identification of a Group’s Physiological Synchronization with Earth’s Magnetic Field" International Journal of Environmental Research and Public Health 14, no. 9: 998. https://doi.org/10.3390/ijerph14090998