scholarly journals Complete coverage of space favors modularity of the grid system in the brain

2016 ◽  
Author(s):  
A. Sanzeni ◽  
V. Balasubramanian ◽  
G. Tiana ◽  
M. Vergassola
Keyword(s):  
Statistical Physics ◽  
Physical Space ◽  
Grid Cell ◽  
Triangular Grid ◽  
Grid System ◽  
Grid Cells ◽  
Scaling Relation ◽  
Complete Coverage ◽  
Space Experiments ◽  
The Brain

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 properties of periodicity, orientation and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e. there are groups of neurons which have grids with similar periodicity, orientation and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e. without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed co-modularity of grid cell periodicity, orientation and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.

scholarly journals Modeling grid fields instead of modeling grid cells

2018 ◽  
Author(s):  
Sophie Rosay ◽  
Simon N. Weber ◽  
Marcello Mulas
Keyword(s):  
Cell Activity ◽  
Physical Space ◽  
Grid Cell ◽  
Macroscopic Model ◽  
Grid Cells ◽  
Colloidal Systems ◽  
Cell Network ◽  
Microscopic Models ◽  
The Relationship ◽  
The Brain

A neuron’s firing correlates are defined as the features of the external world to which its activity is correlated. In many parts of the brain, neurons have quite simple such firing correlates. A striking example are grid cells in the rodent medial entorhinal cortex: their activity correlates with the animal’s position in space, defining ‘grid fields’ arranged with a remarkable periodicity. Here, we show that the organization and evolution of grid fields relate very simply to physical space. To do so, we use an effective model and consider grid fields as point objects (particles) moving around in space under the influence of forces. We are able to reproduce most observations on the geometry of grid patterns. This particle-like behavior is particularly salient in a recent experiment where two separate grid patterns merge. We discuss pattern formation in the light of known results from physics of two-dimensional colloidal systems. Finally, we draw the relationship between our ‘macroscopic’ model for grid fields and existing ‘microscopic’ models of grid cell activity and discuss how a description at the level of grid fields allows to put constraints on the underlying grid cell network.

scholarly journals Optimal configurations of spatial scale for grid cell firing under noise and uncertainty

2014 ◽  
Vol 369 (1635) ◽  
pp. 20130290 ◽  
Author(s):  
Benjamin W. Towse ◽  
Caswell Barry ◽  
Daniel Bush ◽  
Neil Burgess
Keyword(s):  
Spatial Scale ◽  
Spatial Scales ◽  
Grid Cell ◽  
Spatial Uncertainty ◽  
Grid System ◽  
Grid Cells ◽  
Spatial Cues ◽  
Firing Patterns ◽  
Wide Range ◽  
Spatial Noise

We examined the accuracy with which the location of an agent moving within an environment could be decoded from the simulated firing of systems of grid cells. Grid cells were modelled with Poisson spiking dynamics and organized into multiple ‘modules’ of cells, with firing patterns of similar spatial scale within modules and a wide range of spatial scales across modules. The number of grid cells per module, the spatial scaling factor between modules and the size of the environment were varied. Errors in decoded location can take two forms: small errors of precision and larger errors resulting from ambiguity in decoding periodic firing patterns. With enough cells per module (e.g. eight modules of 100 cells each) grid systems are highly robust to ambiguity errors, even over ranges much larger than the largest grid scale (e.g. over a 500 m range when the maximum grid scale is 264 cm). Results did not depend strongly on the precise organization of scales across modules (geometric, co-prime or random). However, independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues.

scholarly journals Complete coverage of space favors modularity of the grid system in the brain

2016 ◽  
Vol 94 (6) ◽  
Author(s):  
A. Sanzeni ◽  
V. Balasubramanian ◽  
G. Tiana ◽  
M. Vergassola
Keyword(s):  
Grid System ◽  
Complete Coverage ◽  
The Brain

scholarly journals A principle of economy predicts the functional architecture of grid cells

eLife ◽  
2015 ◽  
Vol 4 ◽  
Author(s):  
Xue-Xin Wei ◽  
Jason Prentice ◽  
Vijay Balasubramanian
Keyword(s):  
Three Dimensions ◽  
Periodic Lattice ◽  
Grid System ◽  
Grid Cells ◽  
Grid Structure ◽  
Functional Architecture ◽  
Optimal Organization ◽  
Scale Ratio ◽  
Hierarchical Code ◽  
The Brain

Grid cells in the brain respond when an animal occupies a periodic lattice of ‘grid fields’ during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 for realistic neurons, (iv) the scale ratio should vary modestly within and between animals. These results explain the measured grid structure in rodents. We also predict optimal organization in one and three dimensions, the number of modules, and, with added assumptions, the ratio between grid periods and field widths.

scholarly journals The effect of boundaries on grid cell patterns

2020 ◽  
Author(s):  
Mauro M. Monsalve-Mercado ◽  
Christian Leibold
Keyword(s):  
Feedback Inhibition ◽  
Physical Space ◽  
Grid Cell ◽  
Field Size ◽  
Grid Cells ◽  
Neuronal Populations ◽  
Cell Patterns ◽  
Biological Substrate ◽  
Efficient Code ◽  
Natural Result

Mammalian grid cells represent spatial locations in the brain via triangular firing patterns that tessellate the environment. They are regarded as the biological substrate for path integration thereby generating an efficient code for space. However, grid cell patterns are strongly influenced by environmental manipulations, in particular exhibiting local geometrical deformations and defects tied to the shape of the recording enclosure, challenging the view that grid cells constitute a universal code for space. We show that the observed responses to environmental manipulations arise as a natural result under the general framework of feedforward models with spatially unstructured feedback inhibition, which puts the development of triangular patterns in the context of a Turing pattern formation process over physical space. The model produces coherent neuronal populations with equal grid spacing, field size, and orientation.PACS numbers87.19.lv,87.10.Ed,02.30.Jr

scholarly journals Correlation structure of grid cells is preserved during sleep

2017 ◽  
Author(s):  
Richard J. Gardner ◽  
Li Lu ◽  
Tanja Wernle ◽  
May-Britt Moser ◽  
Edvard I. Moser
Keyword(s):  
Cell Activity ◽  
Physical Space ◽  
Grid Cell ◽  
Correlation Structure ◽  
Head Direction ◽  
Grid Cells ◽  
Cell Network ◽  
Fixed Reference ◽  
Network States ◽  
Direction Tuning

AbstractThe network of grid cells in the medial entorhinal cortex forms a fixed reference frame for mapping physical space. The mechanistic origin of the grid representation is unknown, but continuous attractor network (CAN) models explain multiple fundamental features of grid-cell activity. An untested prediction of CAN grid models is that the grid-cell network should exhibit an activity correlation structure that transcends behavioural or brain states. By recording from MEC cell ensembles during navigation and sleep, we found that spatial phase offsets of grid cells predict arousal-state-independent spike rate correlations. Similarly, state-invariant correlations between conjunctive grid-head-direction and pure head-direction cells were predicted by their head-direction tuning offsets. Spike rates of grid cells were only weakly correlated across modules, and module scale relationships disintegrated during slow-save sleep, suggesting that modules function as independent attractor networks. Collectively, our observations suggest that network states in MEC are expressed universally across brain and behaviour states.

scholarly journals Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns

eLife ◽  
2015 ◽  
Vol 4 ◽  
Author(s):  
Alexander Mathis ◽  
Martin B Stemmler ◽  
Andreas VM Herz
Keyword(s):  
Marine Mammals ◽  
Compound Eye ◽  
Activity Patterns ◽  
Cell Activity ◽  
Physical Space ◽  
Grid Cell ◽  
Three Dimensions ◽  
Face Centered Cubic ◽  
Higher Dimensional ◽  
The Brain

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.

scholarly journals A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication

2019 ◽  
Vol 8 (3) ◽  
pp. 146 ◽  
Author(s):  
Li Meng ◽  
Xiaochong Tong ◽  
Shuaibo Fan ◽  
Chengqi Cheng ◽  
Bo Chen ◽  
...  
Keyword(s):  
Coordinate System ◽  
Grid Cell ◽  
Triangular Grid ◽  
Grid System ◽  
Rectangular Coordinate System ◽  
Factors Affecting ◽  
Grid Systems ◽  
Starting Point ◽  
Rectangular Coordinates ◽  
Discrete Grid

Based on the analysis of the problems in the generation algorithm of discrete grid systems domestically and abroad, a new universal algorithm for the unit duplication of a polyhedral discrete grid is proposed, and its core is “simple unit replication + effective region restriction”. First, the grid coordinate system and the corresponding spatial rectangular coordinate system are established to determine the rectangular coordinates of any grid cell node. Then, the type of the subdivision grid system to be calculated is determined to identify the three key factors affecting the grid types, which are the position of the starting point, the length of the starting edge, and the direction of the starting edge. On this basis, the effective boundary of a multiscale grid can be determined and the grid coordinates of a multiscale grid can be obtained. A one-to-one correspondence between the multiscale grids and subdivision types can be established. Through the appropriate rotation, translation and scaling of the multiscale grid, the node coordinates of a single triangular grid system are calculated, and the relationships between the nodes of different levels are established. Finally, this paper takes a hexagonal grid as an example to carry out the experiment verifications by converting a single triangular grid system (plane) directly to a single triangular grid with a positive icosahedral surface to generate a positive icosahedral surface grid. The experimental results show that the algorithm has good universality and can generate the multiscale grid of an arbitrary grid configuration by adjusting the corresponding starting transformation parameters.

scholarly journals Description and Analysis of a 20-Year (1960-79) Digital Ice-Concentration Database for the Great Lakes of North America

1983 ◽  
Vol 4 ◽  
pp. 14-18 ◽  
Author(s):  
Raymond A. Assel
Keyword(s):  
North America ◽  
Great Lakes ◽  
Surface Area ◽  
Information Service ◽  
Grid Cell ◽  
Ice Cover ◽  
Unit Surface Area ◽  
Grid Cells ◽  
Data Set ◽  
Ice Concentration

A digital ice-concentration database spanning 20 years (1960 to 1979) was established for the Great Lakes of North America. Data on ice concentration, i.e. the percentage of a unit surface area of the lake that is ice-covered, were abstracted from over 2 800 historic ice charts produced by United States and Canadian government agencies. The database consists of ice concentrations ranging from zero to 100% in 10% increments for individual grid cells of size 5 × 5 km constituting the surface area of each Great Lake. The data set for each of the Great Lakes was divided into half-month periods for statistical analysis. Maxinium, minimum, median, mode, and average ice-concentrations statistics were calculated for each grid cell and half-month period. A lakewide average value was then calculated for each of the half-month ice-concentration statistics for all grid cells for a given lake. Ice-cover variability and the normal extent and progression of the ice cover is discussed within the context of the lakewide averaged value of the minimum and maximum ice concentrations and the lakewide averaged value of the median ice concentrations, respectively. Differences in ice-cover variability among the five Great Lakes are related to mean lake depth and accumulated freezing degree-days. A Great Lakes ice atlas presenting a series of ice charts which depict the maximum, minimum, and median icecover concentrations for each of the Great Lakes for nine half-monthly periods, starting the last half of December and continuing through the last half of April will be published in 1983 by the National Oceanic and Atmospheric Administration (NOAA). The database will be archived at the National Snow and Ice Data Center of the National Environmental Satellite Data and Information Service (NESDIS) in Boulder, Colorado, USA, also in 1983.

scholarly journals A new discrete multiplicative random cascade model for downscaling intermittent rainfall fields

2019 ◽  
Author(s):  
Marc Schleiss
Keyword(s):  
Classical Method ◽  
Mathematical Problem ◽  
Grid Cell ◽  
Cascade Model ◽  
Small Scale ◽  
Grid Cells ◽  
Cascade Generator ◽  
Cascade Models ◽  
First Results ◽  
Original Amount

Abstract. Spatial downscaling of rainfall fields is a challenging mathematical problem for which many different types of methods have been proposed. One popular solution consists in redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRC). This works well for slowly varying, homogeneous rainfall fields but often fails in the presence of intermittency (i.e., large amounts of zero rainfall values). The most common workaround in this case is to use two separate cascade models, one for the occurrence and another for the intensity. In this paper, a new and simpler approach based on the notion of equal-volume areas (EVAs) is proposed. Unlike classical cascades where rainfall amounts are redistributed over grid cells of equal size, the EVA cascade splits grid cells into areas of different sizes, each of them containing exactly half of the original amount of water. The relative areas of the sub-grid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity dependent standard deviation. The process ends when the amount of water in each sub-grid cell is smaller than a fixed bucket capacity, at which point the output of the cascade can be re-sampled over a regular Cartesian mesh. The present paper describes the implementation of the EVA cascade model and gives some first results for 100 selected events in the Netherlands. Performance is assessed by comparing the outputs of the EVA model to bilinear interpolation and to a classical DMRC model based on fixed grid cell sizes. Results show that on average, the EVA cascade outperforms the classical method, producing fields with more realistic distributions, small-scale extremes and spatial structures. Improvements are mostly credited to the higher robustness of the EVA model to the presence of intermittency and to the lower variance of its generator. However, improvements are not systematic and both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale extremes and variability, the EVA model tends to produce fields that are slightly too smooth and blocky compared with observations.

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