EEG DYNAMICS ON HYPERBOLIC MANIFOLDS

 

Arturo Tozzi

Center for Nonlinear Science, Department of Physics, University of North Texas, Denton, Texas 76203, USA

1155 Union Circle, #311427, Denton, TX 76203-5017 USA

Computational Intelligence Laboratory, University of Manitoba, Winnipeg R3T 5V6 Manitoba, Canada

tozziarturo@libero.it

 

 

James F. Peters

Computational Intelligence Laboratory, University of Manitoba, Winnipeg R3T 5V6 Manitoba, Canada

Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor’s Circle, Winnipeg MB R3T 5V6, Canada

Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey

Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040 Adıyaman, Turkey

james.peters3@umanitoba.ca

Norbert Jaušovec

Department of Psychology, University of Maribor, Koroska Cesta 160, 2000 Maribor, Slovenia

norbert.jausovec@um.si

 

© Neuroscience Letters, 2018.  https://doi.org/10.1016/j.neulet.2018.07.035

 

 

Biological activities, including cellular metabolic pathways, protein folding and brain function, can be described in terms of curved trajectories in hyperbolic spaces which are constrained by energetic requirements.  Here, starting from theorems recently-developed by a deceased Field Medal young mathematician, we show how it is feasible to find and quantify the shortest, energy-sparing functional trajectories taking place in nervous systems’ concave phase spaces extracted from real EEG traces.  This allows neuroscientists to focus their studies on the few, most prominent functional EEG’s paths and loops able to explain, elucidate and experimentally assess the rather elusive mental activity. 

 
 
 
 

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