%0 Journal Article %A Eugenio Urdapilleta %A Francesca Troiani %A Federico Stella %A Alessandro Treves %T Can rodents conceive hyperbolic spaces? %D 2015 %R 10.1101/015057 %J bioRxiv %P 015057 %X The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal has adapted. We show that, according to self-organizing models, if raised in a non-Euclidean hyperbolic cage rats should be able to form hyperbolic grids. For a given range of grid spacing relative to the radius of negative curvature of the hyperbolic surface, such grids are predicted to appear as multi-peaked firing maps, in which each peak has seven neighbours instead of the Euclidean six, a prediction that can be tested in experiments. We thus demonstrate that a useful universal neuronal metric, in the sense of a multi-scale ruler and compass that remain unaltered when changing environments, can be extended to other than the standard Euclidean plane.mECmedial entorhinal cortexPSpseudosphere %U https://www.biorxiv.org/content/biorxiv/early/2015/02/09/015057.full.pdf