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 Spatial scale-dependent land–atmospheric methane exchanges in the northern high latitudes from 1993 to 2004

2014 ◽  
Vol 11 (7) ◽  
pp. 1693-1704 ◽  
Author(s):  
X. Zhu ◽  
Q. Zhuang ◽  
X. Lu ◽  
L. Song
Keyword(s):  
Spatial Heterogeneity ◽  
Spatial Scale ◽  
Water Table ◽  
Spatial Scales ◽  
Grid Cell ◽  
High Latitudes ◽  
Atmospheric Methane ◽  
Ch4 Emissions ◽  
Biogeochemical Models ◽  
Macro Scale

Abstract. Effects of various spatial scales of water table dynamics on land–atmospheric methane (CH4) exchanges have not yet been assessed for large regions. Here we used a coupled hydrology–biogeochemistry model to quantify daily CH4 exchanges over the pan-Arctic from 1993 to 2004 at two spatial scales of 100 km and 5 km. The effects of sub-grid spatial variability of the water table depth (WTD) on CH4 emissions were examined with a TOPMODEL-based parameterization scheme for the northern high latitudes. We found that both WTD and CH4 emissions are better simulated at a 5 km spatial resolution. By considering the spatial heterogeneity of WTD, net regional CH4 emissions at a 5 km resolution are 38.1–55.4 Tg CH4 yr−1 from 1993 to 2004, which are on average 42% larger than those simulated at a 100 km resolution using a grid-cell-mean WTD scheme. The difference in annual CH4 emissions is attributed to the increased emitting area and enhanced flux density with finer resolution for WTD. Further, the inclusion of sub-grid WTD spatial heterogeneity also influences the inter-annual variability of CH4 emissions. Soil temperature plays an important role in the 100 km estimates, while the 5 km estimates are mainly influenced by WTD. This study suggests that previous macro-scale biogeochemical models using a grid-cell-mean WTD scheme might have underestimated the regional CH4 emissions. The spatial scale-dependent effects of WTD should be considered in future quantification of regional CH4 emissions.

scholarly journals seNorge_2018, daily precipitation and temperature datasets over Norway

2019 ◽  
Author(s):  
Cristian Lussana ◽  
Ole Einar Tveito ◽  
Andreas Dobler ◽  
Ketil Tunheim
Keyword(s):  
Spatial Scale ◽  
Climate Model ◽  
Spatial Scales ◽  
Small Scale ◽  
Total Precipitation ◽  
Climate Data ◽  
Wide Range ◽  
Analysis Quality ◽  
Station Density ◽  
Daily Total

Abstract. seNorge_2018 is a collection of observational gridded datasets over Norway for: daily total precipitation; daily mean, maximum and minimum temperatures. The time period covers 1957 to 2017, and the data are presented over a high-resolution terrain-following grid with 1 km spacing in both meridional and zonal directions. The seNorge family of observational gridded datasets developed at the Norwegian Meteorological Institute (MET Norway) has a twenty-year long history and seNorge_2018 is its newest member, the first providing daily minimum and maximum temperatures. seNorge datasets are used for a wide range of applications in climatology, hydrology and meteorology. The observational dataset is based on MET Norway's climate data, which has been integrated by the European Climate Assessment and Dataset database. Two distinct statistical interpolation methods have been developed, one for temperature and the other for precipitation. They are both based on a spatial scale-separation approach where, at first, the analysis (i.e., predictions) at larger spatial scales are estimated. Subsequently they are used to infer the small-scale details down to a spatial scale comparable to the local observation density. Mean, maximum and minimum temperatures are interpolated separately, then physical consistency among them is enforced. For precipitation, in addition to observational data, the spatial interpolation makes use of information provided by a climate model. The analysis evaluation is based on cross-validation statistics and comparison with a previous seNorge version. The analysis quality is presented as a function of the local station density. We show that the occurrence of large errors in the analyses decays at an exponential rate with the increase in the station density. Temperature analyses over most of the domain are generally not affected by significant biases. However, during wintertime in data-sparse regions the analyzed minimum temperatures do have a bias between 2 °C and 3 °C. Minimum temperatures are more challenging to represent and large errors are more frequent than for maximum and mean temperatures. The precipitation analysis quality depends crucially on station density: the frequency of occurrence of large errors for intense precipitation is less than 5 % in data-dense regions, while it is approximately 30 % in data-sparse regions. he open-access datasets are available20for public download at: daily total precipitation (DOI: https://doi.org/10.5281/zenodo.2082320, Lussana, 2018b); daily mean (DOI: https://doi.org/10.5281/zenodo.2023997, Lussana, 2018c) , maximum (DOI: https://doi.org/10.5281/zenodo.2559372, Lussana, 2018e) and minimum (DOI: https://doi.org/10.5281/zenodo.2559354, Lussana, 2018d) temperatures.

scholarly journals Environmental anchoring of grid-like representations minimizes spatial uncertainty during navigation

2017 ◽  
Author(s):  
Tobias Navarro Schröder ◽  
Benjamin W. Towse ◽  
Matthias Nau ◽  
Neil Burgess ◽  
Caswell Barry ◽  
...  
Keyword(s):  
Virtual Reality ◽  
Motion Parallax ◽  
Grid Cell ◽  
Cell System ◽  
Neural Mechanisms ◽  
Spatial Uncertainty ◽  
Grid System ◽  
Virtual Navigation ◽  
Human Participants

SummaryMinimizing spatial uncertainty is essential for navigation, but the neural mechanisms remain elusive. Here we combine predictions of a simulated grid cell system with behavioural and fMRI measures in humans during virtual navigation. First, we showed that polarising cues produce anisotropy in motion parallax. Secondly, we simulated entorhinal grid cells in an environment with anisotropic information and found that self-location is decoded best when grid-patterns are aligned with the axis of greatest information. Thirdly, when exposing human participants to polarised virtual reality environments, we found that navigation performance is anisotropic, in line with the use of parallax. Eye movements showed that participants preferentially viewed polarising cues, which correlated with navigation performance. Finally, using fMRI we found that the orientation of grid-cell-like representations in entorhinal cortex anchored to the environmental axis of greatest parallax information, orthogonal to the polarisation axis. In sum, we demonstrate a crucial role of the entorhinal grid system in reducing uncertainty in representations of self-location and find evidence for adaptive spatial computations underlying entorhinal representations in service of optimal navigation.

scholarly journals Spatial scale-dependent land-atmospheric methane exchange in the northern high latitudes from 1993 to 2004

2013 ◽  
Vol 10 (11) ◽  
pp. 18455-18478 ◽  
Author(s):  
X. Zhu ◽  
Q. Zhuang ◽  
X. Lu ◽  
L. Song
Keyword(s):  
Spatial Heterogeneity ◽  
Spatial Scale ◽  
Water Table ◽  
Spatial Scales ◽  
Grid Cell ◽  
High Latitudes ◽  
Atmospheric Methane ◽  
Ch4 Emissions ◽  
Biogeochemical Models ◽  
Macro Scale

Abstract. Effects of various spatial scales of water table dynamics on the land-atmospheric methane (CH4) exchange have not yet been assessed for large regions. Here we used a coupled hydrology-biogeochemistry model to quantify daily CH4 exchange over the pan-Arctic from 1993 to 2004 at two spatial scales (100 km and 5 km). The effects of sub-grid spatial variability of the water table depth (WTD) on CH4 emissions were examined with a TOPMODEL-based parameterization scheme for northern high latitudes regions. Our results indicate that 5 km CH4 emissions (38.1–55.4 Tg CH4 yr−1, considering the spatial heterogeneity of WTD) were 42% larger than 100 km CH4 emissions (using grid-cell-mean WTD) and the differences in annual CH4 emissions were due to increased emitting area and enhanced flux density after WTD redistribution. Further, the inclusion of sub-grid WTD spatial heterogeneity also influences the inter-annual variability of CH4 emissions. Soil temperature plays a more important role in the 100 km estimates, while the 5 km estimates are more influenced by WTD. This study suggests that previous macro-scale biogeochemical models using grid-cell-mean WTD might have underestimated the regional CH4 budget. The spatial scale-dependent effects of WTD should be considered in future quantifications of regional CH4 emissions.

scholarly journals A Local Measure of Symmetry and Orientation for Individual Spikes of Grid Cells

2018 ◽  
Author(s):  
Simon N. Weber ◽  
Henning Sprekeler
Keyword(s):  
Cell Activity ◽  
Grid Cell ◽  
Local Order ◽  
Global Symmetry ◽  
Grid Cells ◽  
Lighting Condition ◽  
Firing Patterns ◽  
Space And Time ◽  
Local Defects ◽  
Local Distortions

ABSTRACTGrid cells have attracted broad attention because of their highly symmetric hexagonal firing patterns. Recently, research has shifted its focus from the global symmetry of grid cell activity to local distortions both in space and time, such as drifts in orientation, local defects of the hexagonal symmetry, and the decay and reappearance of grid patterns after changes in lighting condition. Here, we introduce a method that allows to visualize and quantify such local distortions, by assigning both a local grid score and a local orientation to each individual spike of a neuronal recording. The score is inspired by a standard measure from crystallography, which has been introduced to quantify local order in crystals. By averaging over spikes recorded within arbitrary regions or time periods, we can quantify local variations in symmetry and orientation of firing patterns in both space and time.

scholarly journals A computational model that explores the effect of environmental geometries on grid cell representations

2017 ◽  
Author(s):  
Samyukta Jayakumar ◽  
Rukhmani Narayanamurthy ◽  
Reshma Ramesh ◽  
Karthik Soman ◽  
Vignesh Muralidharan ◽  
...  
Keyword(s):  
Cell Activity ◽  
Grid Cell ◽  
Point Of View ◽  
Experimental Results ◽  
Grid Cells ◽  
Computational Point ◽  
Model Code ◽  
Wide Range ◽  
Environmental Geometry ◽  
Geometry Analysis

AbstractGrid cells are a special class of spatial cells found in the medial entorhinal cortex (MEC) characterized by their strikingly regular hexagonal firing fields. This spatially periodic firing pattern was originally considered to be invariant to the geometric properties of the environment. However, this notion was contested by examining the grid cell periodicity in environments with different polarity (Krupic et al 2015) and in connected environments (Carpenter et al 2015). Aforementioned experimental results demonstrated the dependence of grid cell activity on environmental geometry. Analysis of grid cell periodicity on practically infinite variations of environmental geometry imposes a limitation on the experimental study. Hence we analyze the grid cell periodicity from a computational point of view using a model that was successful in generating a wide range of spatial cells, including grid cells, place cells, head direction cells and border cells. We simulated the model in four types of environmental geometries such as: 1) connected environments, 2) convex shapes, 3) concave shapes and 4) regular polygons with varying number of sides. Simulation results point to a greater function for grid cells than what was believed hitherto. Grid cells in the model code not just for local position but also for more global information like the shape of the environment. The proposed model is interesting not only because it was able to capture the aforementioned experimental results but, more importantly, it was able to make many important predictions on the effect of the environmental geometry on the grid cell periodicity.

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.

Learning Maps to Navigate Space

2021 ◽  
pp. 572-617
Author(s):  
Stephen Grossberg
Keyword(s):  
Entorhinal Cortex ◽  
Spatial Scales ◽  
Grid Cell ◽  
Gamma Oscillations ◽  
Place Cells ◽  
Self Organizing Map ◽  
Grid Cells ◽  
Map Learning ◽  
Neurophysiological Data ◽  
Self Organizing

This chapter explains how humans and other animals learn to learn to navigate in space. Both reaching and route-based navigation use difference vector computations. Route navigation learns a labeled graph of angles and distances moved. Spatial navigation requires neurons to learn navigable spaces that can be many meters in size. This is again accomplished by a spectrum of cells. Such spectral spacing supports learning of medial entorhinal grid cells and hippocampal place cells. The model responds to realistic rat navigational trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells develop in a hierarchy of self-organizing maps by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. Model parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same self-organizing map mechanisms can learn both grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple grid cell modules through medial entorhinal cortex to hippocampus uses a gradient of rates that is homologous to a rate gradient that drives adaptively timed learning at multiple rates through lateral entorhinal cortex to hippocampus (‘neural relativity’). The model clarifies how top-down hippocampal-to-entorhinal ART attentional mechanisms stabilize map learning, simulates how hippocampal, septal, or acetylcholine inactivation disrupts grid cells, and explains data about theta, beta and gamma oscillations.

scholarly journals seNorge_2018, daily precipitation, and temperature datasets over Norway

2019 ◽  
Vol 11 (4) ◽  
pp. 1531-1551 ◽  
Author(s):  
Cristian Lussana ◽  
Ole Einar Tveito ◽  
Andreas Dobler ◽  
Ketil Tunheim
Keyword(s):  
Spatial Scale ◽  
Climate Model ◽  
Spatial Scales ◽  
Small Scale ◽  
Total Precipitation ◽  
Climate Data ◽  
Wide Range ◽  
Analysis Quality ◽  
Station Density ◽  
Daily Total

Abstract. seNorge_2018 is a collection of observational gridded datasets over Norway for daily total precipitation: daily mean, maximum, and minimum temperatures. The time period covers 1957 to 2017, and the data are presented over a high-resolution terrain-following grid with 1 km spacing in both meridional and zonal directions. The seNorge family of observational gridded datasets developed at the Norwegian Meteorological Institute (MET Norway) has a 20-year-long history and seNorge_2018 is its newest member, the first providing daily minimum and maximum temperatures. seNorge datasets are used for a wide range of applications in climatology, hydrology, and meteorology. The observational dataset is based on MET Norway's climate data, which have been integrated by the “European Climate Assessment and Dataset” database. Two distinct statistical interpolation methods have been developed, one for temperature and the other for precipitation. They are both based on a spatial scale-separation approach where, at first, the analysis (i.e., predictions) at larger spatial scales is estimated. Subsequently they are used to infer the small-scale details down to a spatial scale comparable to the local observation density. Mean, maximum, and minimum temperatures are interpolated separately; then physical consistency among them is enforced. For precipitation, in addition to observational data, the spatial interpolation makes use of information provided by a climate model. The analysis evaluation is based on cross-validation statistics and comparison with a previous seNorge version. The analysis quality is presented as a function of the local station density. We show that the occurrence of large errors in the analyses decays at an exponential rate with the increase in the station density. Temperature analyses over most of the domain are generally not affected by significant biases. However, during wintertime in data-sparse regions the analyzed minimum temperatures do have a bias between 2 ∘C and 3 ∘C. Minimum temperatures are more challenging to represent and large errors are more frequent than for maximum and mean temperatures. The precipitation analysis quality depends crucially on station density: the frequency of occurrence of large errors for intense precipitation is less than 5% in data-dense regions, while it is approximately 30 % in data-sparse regions. The open-access datasets are available for public download at daily total precipitation (https://doi.org/10.5281/zenodo.2082320, Lussana, 2018b); and daily mean (https://doi.org/10.5281/zenodo.2023997, Lussana, 2018c), maximum (https://doi.org/10.5281/zenodo.2559372, Lussana, 2018e), and minimum (https://doi.org/10.5281/zenodo.2559354, Lussana, 2018d) temperatures.

scholarly journals Coordinated learning of grid cell and place cell spatial and temporal properties: multiple scales, attention and oscillations

2014 ◽  
Vol 369 (1635) ◽  
pp. 20120524 ◽  
Author(s):  
Stephen Grossberg ◽  
Praveen K. Pilly
Keyword(s):  
Entorhinal Cortex ◽  
Multiple Scales ◽  
Spatial Scales ◽  
Grid Cell ◽  
Neural Model ◽  
Gamma Oscillations ◽  
Place Cell ◽  
Place Cells ◽  
Grid Cells ◽  
Map Learning

A neural model proposes how entorhinal grid cells and hippocampal place cells may develop as spatial categories in a hierarchy of self-organizing maps (SOMs). The model responds to realistic rat navigational trajectories by learning both grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells can develop by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. The model's parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same SOM mechanisms can learn grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple spatial scale modules through medial entorhinal cortex to hippocampus (HC) may use mechanisms homologous to those for temporal learning through lateral entorhinal cortex to HC (‘neural relativity’). The model clarifies how top-down HC-to-entorhinal attentional mechanisms may stabilize map learning, simulates how hippocampal inactivation may disrupt grid cells, and explains data about theta, beta and gamma oscillations. The article also compares the three main types of grid cell models in the light of recent data.

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