A Gray Code model for the encoding of grid cells in the Entorhinal Cortex - Monteiro, Jânio (2021)
In the brains of humans and mammals, the formation of episodic memories results from the association between objects, space and time. Both the hippocampus and the entorhinal cortex have shown to play an essential role in the formation of these memories. The hippocampus may be considered as an indexer of the pattern of neocortical activity produced by an episode, while the entorhinal cortex is characterized as performing time and space integration, conveying that information to the hippocampus, in the form of grid cells. Although these grid cells are biological based, non-biological grid cells are used in discrete global grid systems that currently support the indexing of assets across the globe, allowing a more adequate partitioning of the Earth into logical structures that take into account the heterogeneity of the scales of the associated geospatial data. The reasons that led to the definition of these grid systems at macro-levels may have led to the formation of similar structures inside our brains. In this paper, we investigate a representation that unifies these views, creating new types of Gray encodings for both one- and two-dimensional spaces. We start by defining a multilayer ternary encoder based on an equilateral triangular coordinate system. After defining a space filling method for this two-dimensional architecture, two Gray codes for one-dimensional signals are defined, for both circular/periodic and non-circular representations of signals. An algorithm is defined to build the two-dimensional Gray encoding of grid cells, which is then successfully applied in a navigation system of a robot, generating patterns of grid cells similar with the ones observed in neuroscience.