Nervous Activity of the Brain in Five Dimensions
| Autor: | Edward Bormashenko, Arturo Tozzi, Arjuna P. H. Don, Norbert Jaušovec, Sheela Ramanna, James F. Peters, Irina Legchenkova |
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| Rok vydání: | 2021 |
| Předmět: |
Surface (mathematics)
Matching (graph theory) Computer science brain Structure (category theory) Electroencephalography 03 medical and health sciences symbols.namesake 0302 clinical medicine Fractal fractal medicine Quaternion 030304 developmental biology General Environmental Science 0303 health sciences neurodata medicine.diagnostic_test business.industry Orthographic projection higher dimensions Pattern recognition Fourier analysis symbols General Earth and Planetary Sciences Artificial intelligence business 030217 neurology & neurosurgery |
| Zdroj: | Biophysica Volume 1 Issue 1 Pages 4-47 |
| ISSN: | 2673-4125 |
| DOI: | 10.3390/biophysica1010004 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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