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Nervous Activity of the Brain in Five Dimensions

Center for Nonlinear Science, Department of Physics, University of North Texas, Denton, TX 76203, USA
Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor’s Circle, Winnipeg, MB R3T 5V6, Canada
Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040 Adıyaman, Turkey
Ruperce 46, 2229 Malecnik, Slovenia
Computational Intelligence Laboratory, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
Applied Computer Science, University of Winnipeg, Winnipeg, MB R3B 2E9, Canada
Chemical Engineering Department, Engineering Faculty, Ariel University, P.O. Box 3, Ariel 407000, Israel
Author to whom correspondence should be addressed.
Received: 11 January 2021 / Revised: 9 February 2021 / Accepted: 18 February 2021 / Published: 22 February 2021
The nervous activity of the brain takes place in higher-dimensional functional spaces. It has been proposed that the brain might be equipped with phase spaces characterized by four spatial dimensions plus time, instead of the classical three plus time. This suggests that global visualization methods for exploiting four-dimensional maps of three-dimensional experimental data sets might be used in neuroscience. We asked whether it is feasible to describe the four-dimensional trajectories (plus time) of two-dimensional (plus time) electroencephalographic traces (EEG). We made use of quaternion orthographic projections to map to the surface of four-dimensional hyperspheres EEG signal patches treated with Fourier analysis. Once achieved the proper quaternion maps, we show that this multi-dimensional procedure brings undoubted benefits. The treatment of EEG traces with Fourier analysis allows the investigation the scale-free activity of the brain in terms of trajectories on hyperspheres and quaternionic networks. Repetitive spatial and temporal patterns undetectable in three dimensions (plus time) are easily enlightened in four dimensions (plus time). Further, a quaternionic approach makes it feasible to identify spatially far apart and temporally distant periodic trajectories with the same features, such as, e.g., the same oscillatory frequency or amplitude. This leads to an incisive operational assessment of global or broken symmetries, domains of attraction inside three-dimensional projections and matching descriptions between the apparently random paths hidden in the very structure of nervous fractal signals. View Full-Text
Keywords: higher dimensions; brain; neurodata; Fourier analysis; fractal higher dimensions; brain; neurodata; Fourier analysis; fractal
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MDPI and ACS Style

Tozzi, A.; Peters, J.F.; Jausovec, N.; Don, A.P.H.; Ramanna, S.; Legchenkova, I.; Bormashenko, E. Nervous Activity of the Brain in Five Dimensions. Biophysica 2021, 1, 38-47.

AMA Style

Tozzi A, Peters JF, Jausovec N, Don APH, Ramanna S, Legchenkova I, Bormashenko E. Nervous Activity of the Brain in Five Dimensions. Biophysica. 2021; 1(1):38-47.

Chicago/Turabian Style

Tozzi, Arturo, James F. Peters, Norbert Jausovec, Arjuna P.H. Don, Sheela Ramanna, Irina Legchenkova, and Edward Bormashenko. 2021. "Nervous Activity of the Brain in Five Dimensions" Biophysica 1, no. 1: 38-47.

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