scholarly journals Connecting multiple spatial scales to decode the population activity of grid cells

2015 ◽  
Vol 1 (11) ◽  
pp. e1500816 ◽  
Author(s):  
Martin Stemmler ◽  
Alexander Mathis ◽  
Andreas V. M. Herz
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Cell Activity ◽  
Dead Reckoning ◽  
Grid Cell ◽  
Grid Cells ◽  
Population Vector ◽  
Population Activity ◽  
Multiple Spatial Scales ◽  
Scale Ratio

Mammalian grid cells fire when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. We show how animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales, even though neural activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into discrete modules within which all cells have the same lattice scale and orientation. The lattice scale changes from module to module and should form a geometric progression with a scale ratio of around 3/2 to minimize the risk of making large-scale errors in spatial localization. Such errors should also occur if intermediate-scale modules are silenced, whereas knocking out the module at the smallest scale will only affect spatial precision. For goal-directed navigation, the allocentric grid cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. The goal location is set by nonlinear gain fields that act on goal vector cells. This theory predicts neural and behavioral correlates of grid cell readout that transcend the known link between grid cells of the medial entorhinal cortex and place cells of the hippocampus.

scholarly journals Decoding the Population Activity of Grid Cells for Spatial Localization and Goal-Directed Navigation

2015 ◽  
Author(s):  
Martin Stemmler ◽  
Alexander Mathis ◽  
Andreas VM Herz
Keyword(s):  
Multiple Scales ◽  
Cell Activity ◽  
Dead Reckoning ◽  
Grid Cell ◽  
Spatial Localization ◽  
Grid Cells ◽  
Population Vector ◽  
Nonlinear Gain ◽  
Population Activity ◽  
Homing Vector

Mammalian grid cells fire whenever an animal crosses the points of an imaginary, hexagonal grid tessellating the environment. Here, we show how animals can localize themselves and navigate by reading-out a simple population vector of grid cell activity across multiple scales, even though this activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into modules with equal lattice scale and orientation. Computing the homing vector is least error-prone when the ratio of successive grid scales is around 3/2. Silencing intermediate-scale modules should cause systematic errors in navigation, while knocking out the module at the smallest scale will only affect navigational precision. Read-out neurons should behave like goal-vector cells subject to nonlinear gain fields.

scholarly journals Multi-Scale Extension in an Entorhinal-Hippocampal Model for Cognitive Map Building

2021 ◽  
Vol 14 ◽  
Author(s):  
Jiru Wang ◽  
Rui Yan ◽  
Huajin Tang
Keyword(s):  
Path Integration ◽  
Spatial Scales ◽  
Cell Activity ◽  
Grid Cell ◽  
Cognitive Maps ◽  
Map Building ◽  
Grid Cells ◽  
Multi Scale ◽  
Vision Processing ◽  
Neuroscience Research

Neuroscience research shows that, by relying on internal spatial representations provided by the hippocampus and entorhinal cortex, mammals are able to build topological maps of environments and navigate. Taking inspiration from mammals' spatial cognition mechanism, entorhinal-hippocampal cognitive systems have been proposed for robots to build cognitive maps. However, path integration and vision processing are time-consuming, and the existing model of grid cells is hard to achieve in terms of adaptive multi-scale extension for different environments, resulting in the lack of viability for real environments. In this work, an optimized dynamical model of grid cells is built for path integration in which recurrent weight connections between grid cells are parameterized in a more optimized way and the non-linearity of sigmoidal neural transfer function is utilized to enhance grid cell activity packets. Grid firing patterns with specific spatial scales can thus be accurately achieved for the multi-scale extension of grid cells. In addition, a hierarchical vision processing mechanism is proposed for speeding up loop closure detection. Experiment results on the robotic platform demonstrate that our proposed entorhinal-hippocampal model can successfully build cognitive maps, reflecting the robot's spatial experience and environmental topological structures.

scholarly journals Global assessment of how averaging over land-surface heterogeneity affects modeled evapotranspiration rates

2019 ◽  
Author(s):  
Elham Rouholahnejad Freund ◽  
Ying Fan ◽  
James W. Kirchner
Keyword(s):  
Spatial Heterogeneity ◽  
Land Surface ◽  
Large Scale ◽  
Potential Evapotranspiration ◽  
Spatial Scales ◽  
Grid Cell ◽  
Heat Fluxes ◽  
Mechanistic Modeling ◽  
Grid Cells ◽  
Heterogeneity Bias

Abstract. The major goal of large-scale Earth System Models (ESMs) is to understand and predict global change. However, computational constraints require ESMs to operate on relatively large spatial grids (typically ~1 degree or ~100 km in size) with the result that the heterogeneity in land surface properties and processes at smaller spatial scales cannot be explicitly represented. Averaging over this spatial heterogeneity may lead to biased estimates of energy and water fluxes in ESMs. For example, evapotranspiration rates and the properties that regulate them are spatially heterogeneous at scales orders of magnitude smaller than typical ESM grid cells. Here we quantify the effects of spatial heterogeneity on grid-cell-averaged evapotranspiration (ET) rates, as seen from the atmosphere over heterogeneous landscapes across the globe. In an earlier study, we used a Budyko framework to functionally relate ET to precipitation (P) and potential evapotranspiration (PET), and used a sub-grid closure relation to quantify the effects of sub-grid heterogeneity on average ET at 1° by 1° grid cells- the scale of typical ESM. We showed that because the relationships driving ET are nonlinear, averaging over sub-grid heterogeneity in P and PET leads to overestimation of average ET. In this study, we extend that work to the globe and examine the global distribution of this bias, its scale dependence, and the underlying mechanisms. Our analysis shows that this heterogeneity bias is more pronounced in mountainous terrain, in landscapes where P is inversely correlated with PET, and in regions with temperate climates and dry summers. We also show that the magnitude of this heterogeneity bias grows on average, and expands over larger areas, as the size of the grid cell increases. Correcting for this overestimation of ET in ESMs is important for modeling the water cycle, as well as for future temperature predictions, since current overestimations of ET rates imply smaller sensible heat fluxes, and potential underestimation of dry and warm conditions in the context of climate change. Our work provides a basis for translating the heterogeneity bias into correction factors in large-scale ESMs, and highlights the regions where more detailed mechanistic modeling is needed.

scholarly journals An isomorphic mapping hypothesis of the grid representation

2014 ◽  
Vol 369 (1635) ◽  
pp. 20120521 ◽  
Author(s):  
Michael Brecht ◽  
Saikat Ray ◽  
Andrea Burgalossi ◽  
Qiusong Tang ◽  
Helene Schmidt ◽  
...  
Keyword(s):  
Pyramidal Neurons ◽  
Dimensional Space ◽  
Grid Cell ◽  
Propagation Speed ◽  
Connectivity Matrix ◽  
Two Dimensional ◽  
Grid Cells ◽  
Population Activity ◽  
Medial Entorhinal Cortex ◽  
Mapping Hypothesis

We introduce a grid cell microcircuit hypothesis. We propose the ‘grid in the world’ (evident in grid cell discharges) is generated by a ‘grid in the cortex’. This cortical grid is formed by patches of calbindin-positive pyramidal neurons in layer 2 of medial entorhinal cortex (MEC). Our isomorphic mapping hypothesis assumes three types of isomorphism: (i) metric correspondence of neural space (the two-dimensional cortical sheet) and the external two-dimensional space within patches; (ii) isomorphism between cellular connectivity matrix and firing field; (iii) isomorphism between single cell and population activity. Each patch is a grid cell lattice arranged in a two-dimensional map of space with a neural : external scale of approximately 1 : 2000 in the dorsal part of rat MEC. The lattice behaves like an excitable medium with neighbouring grid cells exciting each other. Spatial scale is implemented as an intrinsic scaling factor for neural propagation speed. This factor varies along the dorsoventral cortical axis. A connectivity scheme of the grid system is described. Head direction input specifies the direction of activity propagation. We extend the theory to neurons between grid patches and predict a rare discharge pattern (inverted grid cells) and the relative location and proportion of grid cells and spatial band cells.

scholarly journals Home, head direction stability, and grid cell distortion

2020 ◽  
Vol 123 (4) ◽  
pp. 1392-1406 ◽  
Author(s):  
Juan Ignacio Sanguinetti-Scheck ◽  
Michael Brecht
Keyword(s):  
Entorhinal Cortex ◽  
Home Cage ◽  
Cell Activity ◽  
Grid Cell ◽  
Head Direction ◽  
Grid Cells ◽  
Head Direction Cells ◽  
Medial Entorhinal Cortex ◽  
Abstract Approach ◽  
Globally Stable

The home is a unique location in the life of humans and animals. In rats, home presents itself as a multicompartmental space that involves integrating navigation through subspaces. Here we embedded the laboratory rat’s home cage in the arena, while recording neurons in the animal’s parasubiculum and medial entorhinal cortex, two brain areas encoding the animal’s location and head direction. We found that head direction signals were unaffected by home cage presence or translocation. Head direction cells remain globally stable and have similar properties inside and outside the embedded home. We did not observe egocentric bearing encoding of the home cage. However, grid cells were distorted in the presence of the home cage. While they did not globally remap, single firing fields were translocated toward the home. These effects appeared to be geometrical in nature rather than a home-specific distortion and were not dependent on explicit behavioral use of the home cage during a hoarding task. Our work suggests that medial entorhinal cortex and parasubiculum do not remap after embedding the home, but local changes in grid cell activity overrepresent the embedded space location and might contribute to navigation in complex environments. NEW & NOTEWORTHY Neural findings in the field of spatial navigation come mostly from an abstract approach that separates the animal from even a minimally biological context. In this article we embed the home cage of the rat in the environment to address some of the complexities of natural navigation. We find no explicit home cage representation. While both head direction cells and grid cells remain globally stable, we find that embedded spaces locally distort grid cells.

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 Entorhinal cortex receptive fields are modulated by spatial attention, even without movement

eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Niklas Wilming ◽  
Peter König ◽  
Seth König ◽  
Elizabeth A Buffalo
Keyword(s):  
Entorhinal Cortex ◽  
Cell Activity ◽  
Receptive Fields ◽  
Grid Cell ◽  
Covert Attention ◽  
Grid Cells ◽  
Physical Movement ◽  
Mental Operations ◽  
Triangular Tiling ◽  
Central Fixation

Grid cells in the entorhinal cortex allow for the precise decoding of position in space. Along with potentially playing an important role in navigation, grid cells have recently been hypothesized to make a general contribution to mental operations. A prerequisite for this hypothesis is that grid cell activity does not critically depend on physical movement. Here, we show that movement of covert attention, without any physical movement, also elicits spatial receptive fields with a triangular tiling of space. In monkeys trained to maintain central fixation while covertly attending to a stimulus moving in the periphery we identified a significant population (20/141, 14% neurons at a FDR <5%) of entorhinal cells with spatially structured receptive fields. This contrasts with recordings obtained in the hippocampus, where grid-like representations were not observed. Our results provide evidence that neurons in macaque entorhinal cortex do not rely on physical movement.

scholarly journals A proposed method for assessing the extent of the seabed significantly affected by demersal fishing in the Greater North Sea

2013 ◽  
Vol 70 (6) ◽  
pp. 1085-1096 ◽  
Author(s):  
Markus Diesing ◽  
David Stephens ◽  
John Aldridge
Keyword(s):  
North Sea ◽  
Large Scale ◽  
Spatial Scales ◽  
Grid Cell ◽  
Natural Disturbance ◽  
Sea Floor ◽  
Natural Processes ◽  
Environmental Status ◽  
Waves And Currents ◽  
Fishing Disturbance

Abstract Diesing, M., Stephens, D., and Aldridge, J. 2013. A proposed method for assessing the extent of the seabed significantly affected by demersal fishing in the Greater North Sea. – ICES Journal of Marine Science, 70: 1085–1096. The widespread impact of bottom towed fishing gear on benthic species and communities has long been recognized. The responses to a given intensity of fishing disturbance can be influenced by the extent to which these species and communities are preconditioned to disturbance by natural processes, in particular waves and currents. The advent of vessel monitoring system (VMS) and models of natural disturbance enable high-resolution and large-scale comparisons of fishing and natural disturbance. VMS data were employed to estimate the trawled area per 12 km by 12 km grid cell. We then quantified natural disturbance by estimating the number of days in a year the seabed was disturbed by tides and waves. As natural disturbance acts on large spatial scales, we assumed that each natural disturbance event affects whole grid cells. Frequencies could thus be translated into an area of impact, allowing us to compare fishing with natural disturbance. We show how such comparisons can be used to estimate the extent of different seabed substrate types significantly affected by demersal fishing. A measure of the probability that fishing disturbance exceeds natural disturbance provides one metric for identifying areas of significant trawling impact on seabed habitats and might be used to measure progress towards achieving good environmental status for sea-floor integrity within the context of the European Union's Marine Strategy Framework Directive. For more than half the seabed in the English sector of the Greater North Sea, the results suggest that disturbance attributable to demersal fishing exceeds natural disturbance based on data from the years 2006 to 2008. The imbalance between natural and fishing disturbance is greatest in muddy substrates and deep circalittoral habitats.

scholarly journals StableClim, continuous projections of climate stability from 21000 BP to 2100 CE at multiple spatial scales

2020 ◽  
Author(s):  
Stuart C Brown ◽  
Tom M. L. Wigley ◽  
Bette L. Otto-Bliesner ◽  
Damien Fordham
Keyword(s):  
Spatial Scales ◽  
Grid Cell ◽  
Climatic Conditions ◽  
Multiple Spatial Scales ◽  
Global Mean Temperature ◽  
Temperature And Precipitation ◽  
Climate Stability ◽  
Biodiversity Change ◽  
Biogeographic Regions ◽  
Global Mean

Paleoclimatic data are used in eco-evolutionary models to improve knowledge of biogeographical processes that drive patterns of biodiversity through time, opening windows into past climate–biodiversity dynamics. Applying these models to harmonised simulations of past and future climatic change can strengthen forecasts of biodiversity change. StableClim provides continuous estimates of climate stability from 21,000 years ago to 2100 C.E. for ocean and terrestrial realms at spatial scales that include biogeographic regions and climate zones. Climate stability is quantified using annual trends and variabilities in air temperature and precipitation, and associated signal-to-noise ratios. Thresholds of natural variability in trends in regional- and global-mean temperature allow periods in Earth’s history when climatic conditions were warming and cooling rapidly (or slowly) to be identified and climate stability to be estimated locally (grid-cell) during these periods of accelerated change. Model simulations are validated against independent paleoclimate and observational data. Projections of climatic stability, accessed through StableClim, will improve understanding of the roles of climate in shaping past, present-day and future patterns of biodiversity.

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