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Mathis, Alexander; Stemmler, Martin B. and Herz, Andreas V. M. ORCID logoORCID: https://orcid.org/0000-0002-3836-565X (2015): Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns. In: eLife, Vol. 4, e05979 [PDF, 2MB]

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Lattices abound in nature-from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. These arrangements provide solutions for optimal packings, efficient resource distribution, and cryptographic protocols. Do lattices also play a role in how the brain represents information? We focus on higher-dimensional stimulus domains, with particular emphasis on neural representations of physical space, and derive which neuronal lattice codes maximize spatial resolution. For mammals navigating on a surface, we show that the hexagonal activity patterns of grid cells are optimal. For species that move freely in three dimensions, a face-centered cubic lattice is best. This prediction could be tested experimentally in flying bats, arboreal monkeys, or marine mammals. More generally, our theory suggests that the brain encodes higher-dimensional sensory or cognitive variables with populations of grid-cell-like neurons whose activity patterns exhibit lattice structures at multiple, nested scales.

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