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Efficient and flexible representation of higher-dimensional cognitive variables with grid cells

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(a) Firing fields and their hexagonal arrangement shown for two simulated grid cells from two modules of different scale. (b) Schematic picture of the origin of periodic firing fields. Left: a schematic environment (black line) with cell responses (green, blue) of two grid cells from two modules of different scale. Right: schematic picture of two grid modules depicted as 1-dimensional circular continuous attractors. The colored triangles symbolize recording devices whose responses are shown on the left. A positional change (small arrow on left-hand side) corresponds to a change in phase (small arrows on right-hand side) in each module. Both phase-changes are related by a fixed scalar factor resulting in different spatial periodicity. (c) Schematic picture of the coding space (gray box) spanned by multiple, here 2, grid modules (blue and green). The modulo-arithmetic nature of the grid code enables an extraordinarily huge coding range by tightly “packing/folding” an environment (black line) into code space (gray). The fixed ratio of module scales results in a linear embedding with fixed “slope”.

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doi: https://doi.org/10.1371/journal.pcbi.1007796.g001