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 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 Trzy wymiary użytecznego miasta

1970 ◽  
Vol 42 ◽  
pp. 219-231
Author(s):  
Maciej Błaszak Maciej Błaszak ◽  
Artur Fojud Artur Fojud
Keyword(s):  
Neural Networks ◽  
Brain Networks ◽  
Physical Space ◽  
Central Executive ◽  
Three Dimensions ◽  
Default Mode ◽  
The City ◽  
The Brain

The paper analyzes three dimensions of the usable city: experiential, functional and rational. These dimensions are connected with three types of mental experiences, respectively, sensational, perceptional and conceptual, and with three neural networks: salience, central executive and default mode. It is argued that sensations refer to the physical space of the city, perceptions to the functional niche of the city, and concepts to the values implemented in the brain and recognized in the urban objects during their usage. The notion of the usable city is tightly connected with the notion of the happy city: three brain networks computing the information about dimensions of the usable city generate three parameters of happiness: pleasure, satisfaction, and one’s potential realization.

scholarly journals Quaternionic Assessment of EEG Traces on Nervous Multidimensional Hyperspheres

2020 ◽  
Author(s):  
Arturo Tozzi ◽  
James F. Peters ◽  
Norbert Jausovec ◽  
Irina Legchenkova ◽  
Edward Bormashenko
Keyword(s):  
Nervous Activity ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Data Sets ◽  
Operational Procedure ◽  
Higher Dimensional ◽  
Spatial Dimensions ◽  
The Brain ◽  
Real Experimental Data ◽  
Operational Assessment

The nervous activity of the brain takes place in higher-dimensional functional spaces. Indeed, recent claims advocate that the brain might be equipped with a phase space displaying four spatial dimensions plus time, instead of the classical three plus time. This suggests the possibility to investigate global visualization methods for exploiting four-dimensional maps of real experimental data sets. Here we asked whether, starting from the conventional neuro-data available in three dimensions plus time, it is feasible to find an operational procedure to describe the corresponding four-dimensional trajectories. In particular, we used quaternion orthographic projections for the assessment of electroencephalographic traces (EEG) from scalp locations. This approach makes it possible to map three-dimensional EEG traces to the surface of a four-dimensional hypersphere, which has an important advantage, since quaternionic networks make it feasible to enlighten temporally far apart nervous trajectories equipped with the same features, such as the same frequency or amplitude of electric oscillations. This leads to an incisive operational assessment of symmetries, dualities and matching descriptions hidden in the very structure of complex neuro-data signals.

scholarly journals Grid cell co-activity patterns during sleep reflect spatial overlap of grid fields during active behaviors

2017 ◽  
Author(s):  
Sean G. Trettel ◽  
John B. Trimper ◽  
Ernie Hwaun ◽  
Ila R. Fiete ◽  
Laura Lee Colgin
Keyword(s):  
Activity Patterns ◽  
Cell Activity ◽  
Grid Cell ◽  
Network Models ◽  
Grid Cells ◽  
Tuning Curves ◽  
Sensory Inputs ◽  
Cell Network ◽  
Spatial Tuning ◽  
Cell Cell

ABSTRACTContinuous attractor network models of grid formation posit that recurrent connectivity between grid cells controls their patterns of co-activation. Grid cells from a common module exhibit stable offsets in their periodic spatial tuning curves across environments, which may reflect recurrent connectivity or correlated sensory inputs. Here we explore whether cell-cell relationships predicted by attractor models persist during sleep states in which spatially informative sensory inputs are absent. We recorded ensembles of grid cells in superficial layers of medial entorhinal cortex during active exploratory behaviors and overnight sleep. Per pair and collectively, we found preserved patterns of spike-time correlations across waking, REM, and non-REM sleep, which reflected the spatial tuning offsets between these cells during active exploration. The preservation of cell-cell relationships across states was not explained by theta oscillations or CA1 activity. These results suggest that recurrent connectivity within the grid cell network drives grid cell activity across behavioral states.

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 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.

Advantages of Complementary Stereo Images as Viewed with the Low-Temperature Field-Emission SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1314-1315
Author(s):  
William P. Wergin ◽  
Eric F. Erbe
Keyword(s):  
Fold Increase ◽  
Horizontal Displacement ◽  
Three Dimensions ◽  
Stereo Image ◽  
Stereo Pair ◽  
Sem Micrograph ◽  
Left And Right ◽  
The Common ◽  
The Brain ◽  
Pair Analysis

The eye-brain complex allows those of us with normal vision to perceive and evaluate our surroundings in three-dimensions (3-D). The principle factor that makes this possible is parallax - the horizontal displacement of objects that results from the independent views that the left and right eyes detect and simultaneously transmit to the brain for superimposition. The common SEM micrograph is a 2-D representation of a 3-D specimen. Depriving the brain of the 3-D view can lead to erroneous conclusions about the relative sizes, positions and convergence of structures within a specimen. In addition, Walter has suggested that the stereo image contains information equivalent to a two-fold increase in magnification over that found in a 2-D image. Because of these factors, stereo pair analysis should be routinely employed when studying specimens.Imaging complementary faces of a fractured specimen is a second method by which the topography of a specimen can be more accurately evaluated.

Differences in the brain stem terminations of large- and small-diameter vestibular primary afferents

1995 ◽  
Vol 74 (3) ◽  
pp. 1362-1366 ◽  
Author(s):  
J. A. Huwe ◽  
E. H. Peterson
Keyword(s):  
Brain Stem ◽  
Large Diameter ◽  
Small Diameter ◽  
Movement Control ◽  
Three Dimensions ◽  
Significant Shift ◽  
Axon Diameter ◽  
Vestibular Complex ◽  
The Brain ◽  
Adjacent Brain

1. We visualized the central axons of 32 vestibular afferents from the posterior canal by extracellular application of horseradish peroxidase, reconstructed them in three dimensions, and quantified their morphology. Here we compare the descending limbs of central axons that differ in parent axon diameter. 2. The brain stem distribution of descending limb terminals (collaterals and associated varicosities) varies systematically with parent axon diameter. Large-diameter afferents concentrate their terminals in rostral regions of the medial/descending nuclei. As axon diameter decreases, there is a significant shift of terminal concentration toward the caudal vestibular complex and adjacent brain stem. 3. Rostral and caudal regions of the medial/descending nuclei have different labyrinthine, cerebellar, intrinsic, commissural, and spinal connections; they are believed to play different roles in head movement control. Our data help clarify the functions of large- and small-diameter afferents by showing that they contribute differentially to rostral and caudal vestibular complex.

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