Related papers: Theta functions and optimal lattices for a grid ce…

Lattices abound in nature - from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. Such regular arrangements provide solutions for optimally dense packings, efficient resource…

Grid cells, discovered more than a decade ago [5], are neurons in the brain of mammals that fire when the animal is located near certain specific points in its familiar terrain. Intriguingly, these points form, for a single cell, a…

Grid cells in the brain respond when an animal occupies a periodic lattice of "grid fields" during spatial navigation. The grid scale varies along the dorso-ventral axis of the entorhinal cortex. We propose that the grid system minimizes…

We propose a mechanism enabling the appearance of border cells -- neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows…

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their…

Questions about information encoded by the brain demand statistical frameworks for inferring relationships between neural firing and features of the world. The landmark discovery of grid cells demonstrates that neurons can represent spatial…

Lattices with minimal normalized second moments are designed using a new numerical optimization algorithm. Starting from a random lower-triangular generator matrix and applying stochastic gradient descent, all elements are updated towards…

Representing and reasoning about physical space is fundamental to animal survival, and the mammalian lineage expresses a wealth of specialized neural representations that encode space. Grid cells, whose discovery earned a Nobel prize, are a…

We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a generalized linear model (kinetic Ising model), study their functional…

Grid cells play a principal role in enabling mammalian cognitive representations of ambient environments. The key property of these cells -- the regular arrangement of their firing fields -- is commonly viewed as means for establishing…

We study the local optimality of Simple Cubic, Body-Centred-Cubic and Face-Centred-Cubic lattices among Bravais lattices of fixed density for some finite energy per point. Following the work of Ennola [Math. Proc. Cambridge, 60:855--875,…

Research on network mechanisms and coding properties of grid cells assume that the firing rate of a grid cell in each of its fields is the same. Furthermore, proposed network models predict spatial regularities in the firing of inhibitory…

Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various wireless communication setups. However,…

Many recent models study the downstream projection from grid cells to place cells, while recent data has pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the…

About a decade ago grid cells were discovered in the medial entorhinal cortex of rat. Their peculiar firing patterns, which correlate with periodic locations in the environment, led to early hypothesis that grid cells may provide some form…

This work investigates linear precoding over non-singular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is…

We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate…

The grid firing patterns are thought to provide an efficient intrinsic metric capable of supporting universal spatial metric for mammalian spatial navigation in all environments. However, whether spatial representations of grid cells in the…

Since their Nobel Prize winning discovery in 2005, grid cells have been studied extensively by neuroscientists. Their multi-scale periodic firing rates tiling the environment as the animal moves around has been shown as critical for path…

To afford flexible behaviour, the brain must build internal representations that mirror the structure of variables in the external world. For example, 2D space obeys rules: the same set of actions combine in the same way everywhere (step…