Relativistic conformal symmetry of neural field propagation in the brain
Juan M. Romero, Carlos Trenado, Berenice Aguilar, Miriam Tirradentro
arXiv Preprint Archive August 25, 2013 preprint
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper |
|---|---|
| Keywords | Hep-th Q-bio.nc |
| Key points | Derives exact solutions for a neural field propagation equation under the relativistic conformal group and shows that in four dimensions the pulse becomes a Yukawa potential at large distances. |
Abstract
In this paper, we address a neural field equation that characterizes spatio-temporal propagation of a neural population pulse. Due that the human brain is a complex system whose constituents interaction give rise to fundamental states of consciousness and behavior, it is crucial to gain insight into its functioning even at relativistic scales. To this end, we study the action of the relativistic conformal group on the accounted neural field propagation equation. In particular, we obtain an exact solution for the field propagation equation when the space-time is 3 or 4 dimensional. Furthermore, in the 4 dimensional case and the large distance limit, it is shown that the neural population pulse becomes a Yukawa potential.