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Place cells in the hippocampus are active when an animal visits a certain location (referred to as a place field) within an environment. Grid cells in the medial entorhinal cortex (MEC) respond at multiple locations, with firing fields that…
Grid cells in the entorhinal cortex encode the position of an animal in its environment using spatially periodic tuning curves of varying periodicity. Recent experiments established that these cells are functionally organized in discrete…
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…
Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence…
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 medial entorhinal cortex (MEC) of the mammalian brain exhibit a strikingly regular hexagonal firing field over space. These cells are learned after birth and are thought to support spatial navigation but also more abstract…
Grid cells in medial entorhinal cortex are believed to play a key role in path integration. However, the relation between path integration and the grid-like arrangement of their firing field remains unclear. We provide theoretical evidence…
Grid cells in the medial entorhinal cortex and place cells in the hippocampus together support spatial navigation. The two regions are reciprocally connected, and there is a chicken-and-egg problem for how both arise and reinforce each…
High-dimensional neural activity often reside in a low-dimensional subspace, referred to as neural manifolds. Grid cells in the medial entorhinal cortex provide a periodic spatial code that are organized near a toroidal manifold,…
This paper investigates the conformal isometry hypothesis as a potential explanation for the hexagonal periodic patterns in grid cell response maps. We posit that grid cell activities form a high-dimensional vector in neural space, encoding…
Grid cells in the entorhinal cortex, together with head direction, place, speed and border cells, are major contributors to the organization of spatial representations in the brain. In this work we introduce a novel theoretical and…
We take the testing perspective to understand what the minimal discrimination time between two stimuli is for different types of rate coding neurons. Our main goal is to describe the testing abilities of two different encoding systems:…
Decades of research on the neural code underlying spatial navigation have revealed a diverse set of neural response properties. The Entorhinal Cortex (EC) of the mammalian brain contains a rich set of spatial correlates, including grid…
The ability of the organism to distinguish between various stimuli is limited by the structure and noise in the population code of its sensory neurons. Here we infer a distance measure on the stimulus space directly from the recorded…
The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cortex (mEC) show a triangular grid pattern, and once established might be based in part on path-integration mechanisms. Grid axes are tightly…
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…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Grid cells are believed to play an important role in both spatial and non-spatial cognition tasks. A recent study observed the emergence of grid cells in an LSTM for path integration. The connection between biological and artificial neural…
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…
Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…