# What grid cells convey about rat location

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By Ila Fiete, Caltech.

- Single neurons in a region (dMEC) of the entorhinal cortex of rats fire whenever the rat is on any vertex of a regular triangular lattice that tiles 2-d space. We observe that this periodic code is analogous to an advanced numeral system for the representation of rat position. Specifically, the firing of cells in dMEC represents position as a modulo remainder with respect to the periodicity of the neural response in space, and the neural code for position is a residue number system (RNS) code. The RNS code has many properties, including a combinatorially large capacity, parallelized representation, and parallelized and convenient arithmetic updating of the represented variable. These properties are uniquely useful in the in the biological context for the representation of variables that possess a large dynamic range (high accuracy and large range) that must be continuously updated through incremental addition steps as the quantity is continuously varied (e.g., the position estimate must be continuously updated as the rat moves about). At the same time, the RNS code has pathologies which make it difficult to invert, even though in principle the modulo representation is fully invertible.

- I'll discuss the neurobiological implications and experimental predictions of these insights into the dMEC code for rat position and consider other variables that might be well-suited to a modulo or RNS representation.

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