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On Path Integration of Grid Cells: Group Representation and Isotropic Scaling [article]

Ruiqi Gao, Jianwen Xie, Xue-Xin Wei, Song-Chun Zhu, Ying Nian Wu
2021 arXiv   pre-print
We identify two conditions on the transformation. One is a group representation condition that is necessary for path integration.  ...  In this paper, we conduct theoretical analysis of a general representation model of path integration by grid cells, where the 2D self-position is encoded as a higher dimensional vector, and the 2D self-motion  ...  We thank Yaxuan Zhu from UCLA Department of Statistics for his help with experiments on egocentric vision. We thank Dr.  ... 
arXiv:2006.10259v6 fatcat:beai27vihbfwlkfon6ntfbyp7i

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

S. Grossberg, P. K. Pilly
2013 Philosophical Transactions of the Royal Society of London. Biological Sciences  
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  ...  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  ...  This article focuses upon a model of how path integration information is represented by MEC grid cells and HC place cells.  ... 
doi:10.1098/rstb.2012.0524 pmid:24366136 pmcid:PMC3866446 fatcat:2icdnof7hzhcbbwzpardmn4mfi

A unified theory for the computational and mechanistic origins of grid cells [article]

Ben Sorscher, Gabriel C. Mel, Samuel A Ocko, Lisa Giocomo, Surya Ganguli
2020 bioRxiv   pre-print
Here we forge an intimate link between the computational problem of path-integration and the existence of hexagonal grids, by demonstrating that such grids arise generically in biologically plausible neural  ...  The discovery of entorhinal grid cells has generated considerable interest in how and why hexagonal firing fields might mechanistically emerge in a generic manner from neural circuits, and what their computational  ...  ., the Office of Naval Research N00141812690, Simons Foundation SCGB 542987SPI, NIMH MH106475, and the James S McDonnell Foundation for L.M.G., and the Simons and James S McDonnell foundations, and an  ... 
doi:10.1101/2020.12.29.424583 fatcat:f3irtvi2trao5pi44plwomeybm

Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis

Yedidyah Dordek, Daniel Soudry, Ron Meir, Dori Derdikman
2016 eLife  
We thus asked how grid cells are affected by the nature of the input from the place cells.  ...  Consistent with experiments, grid spacing ratio between the first two consecutive modules is −1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.  ...  Acknowledgements We would like to thank Alexander Mathis and Omri Barak for comments on the manuscript, and Gilad Tocker and Matan Sela for helpful discussions and advice.  ... 
doi:10.7554/elife.10094 pmid:26952211 pmcid:PMC4841785 fatcat:lrxpqe4oevd7lihb6i2f32q4re

Grid-cell representations in mental simulation

Jacob LS Bellmund, Lorena Deuker, Tobias Navarro Schröder, Christian F Doeller
2016 eLife  
Furthermore, we capitalize on the six-fold rotational symmetry of grid-cell firing to demonstrate a 60° periodic pattern-similarity structure in the entorhinal cortex.  ...  Grid-like representations have been observed in the human entorhinal cortex during virtual and imagined navigation.  ...  The authors would like to thank S Collin and B Milivojevic for comments on the manuscript and A Backus for helpful discussions.  ... 
doi:10.7554/elife.17089 pmid:27572056 pmcid:PMC5005038 fatcat:wcobvp4gybbrfjkbxpje6gv7qi

Probabilistic Learning by Rodent Grid Cells

Allen Cheung, Daniel Bush
2016 PLoS Computational Biology  
No plausible model exists which explains stable grids in darkness for twenty minutes or longer, despite being one of the first results ever published on grid cells.  ...  Of the known spatial cells, grid cells form strikingly regular and stable patterns of activity, even in darkness.  ...  Barry Author Contributions Conceived and designed the experiments: A.C. Performed the experiments: A.C. Analyzed the data: A.C. Contributed reagents/materials/analysis tools: A.C.  ... 
doi:10.1371/journal.pcbi.1005165 pmid:27792723 pmcid:PMC5085080 fatcat:wnhsi6a4g5h25ioq4fmwr5j6yy

An Efficient Coding Theory for a Dynamic Trajectory Predicts non-Uniform Allocation of Grid Cells to Modules in the Entorhinal Cortex [article]

Noga Weiss Mosheiff, Haggai Agmon, Avraham Moriel, Yoram Burak
2016 arXiv   pre-print
This readout scheme requires persistence over varying timescales, ranging from ~1ms to ~1s, depending on the grid cell module.  ...  Grid cells in the entorhinal cortex encode the position of an animal in its environment using spatially periodic tuning curves of varying periodicity.  ...  An earlier version of this work appeared in abstract form (Weiss et al., 2015) .  ... 
arXiv:1601.02948v1 fatcat:5n7iiv4xffecnntxjzixck5rde

Mesoscale Theory of Grains and Cells: Crystal Plasticity and Coarsening

Surachate Limkumnerd, James P. Sethna
2006 Physical Review Letters  
While both the microscopic laws of dislocation motion and the macroscopic laws of coarsening and plastic deformation are well studied, we hitherto have had no simple, continuum explanation for the evolution  ...  At low temperatures under shear the dislocations (which allow only glide) form into cell structures.  ...  We seek to count the number of times the isotropic representations of the rotation group occurs within the products.  ... 
doi:10.1103/physrevlett.96.095503 pmid:16606276 fatcat:ucxo2ppqhzfeboegbmhrhp25xe

Evidence for grid cells in a human memory network

Christian F. Doeller, Caswell Barry, Neil Burgess
2010 Nature  
Jeffery and J. O'Keefe for providing help and facilities for single-unit recording; the Wellcome Trust Centre for Neuroimaging at UCL for providing help and scanning facilities; J. Krupic and R.  ...  King for help with virtual reality programming; and useful discussions with P. Dayan, K. Friston, U.  ...  may provide a neural substrate for path integration [1] [2] [3] 6 .  ... 
doi:10.1038/nature08704 pmid:20090680 pmcid:PMC3173857 fatcat:iwuojvemafdlxntnxedbe5jhmu


H. Chang, K. Andarawewa, J. Han, M. Barcellos-Hoff, B. Parvin
2007 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro  
Their intensity distributions are often heterogeneous and may lack specificity. Grouping of these linear structures can aid in segmentation and quantitative representation of protein localization.  ...  Application of this technique to quantitative analysis of cell-cell adhesion mediated by integral cell membrane proteins is demonstrated.  ...  Both monolayers and complex structures require cell-cell adhesion mediated by integral cell membrane proteins.  ... 
doi:10.1109/isbi.2007.356906 dblp:conf/isbi/ChangAHBP07 fatcat:clxjeuz5k5bbxlcbv7fcsanpcy

Combining cell-based hydrodynamics with hybrid particle-field simulations: efficient and realistic simulation of structuring dynamics

G. J. A. Sevink, F. Schmid, T. Kawakatsu, G. Milano
2017 Soft Matter  
We additionally implemented and tested an alternative and more isotropic finite difference gradient.  ...  Merging MD-SCF with multi-particle collision dynamics (MPCD), we mimic particle collisions at the level of computational cells and at the same time properly account for the momentum transfer that is important  ...  GJAS and FS acknowledge funding by the VW foundation in the context of an international project Multiscale hybrid modeling of (bio)membranes.  ... 
doi:10.1039/c6sm02252a pmid:28128838 fatcat:t4tuwxswajfgdbvy4laeuo63j4


W. David Arnett, Casey Meakin
2011 Astrophysical Journal  
We examine some implications of this simplest approximation, and suggest paths for improvement.  ...  Using the Lorenz model as representative of a convective cell, a multiple-cell model of a convective layer gives total luminosity fluctuations which are suggestive of irregular variables (red giants and  ...  This work was supported in part by NSF Grant 0708871 and NASA Grant NNX08AH19G at the University of Arizona. One of us (DA) wishes to thank Fr. Jose Fuñes and the Specalo Vaticano, Prof.  ... 
doi:10.1088/0004-637x/741/1/33 fatcat:fowvt6xdqffwjbg4x5pr2cv67y

Realism of Lagrangian large eddy simulations driven by renalysis meteorology: Tracking a pocket of open cells under a biomass burning aerosol layer

J. Kazil, M. Christensen, S. J. Abel, T. Yamaguchi, G. Feingold
2021 Journal of Advances in Modeling Earth Systems  
A boundary layer cold and dry bias occurring in LES can be counteracted by reducing the grid aspect ratio and by tightening the large scale wind speed nudging towards the surface.  ...  to open cells seen in the satellite imagery on the three considered trajectories.  ...  Acknowledgments We thank Tom Goren, Wayne Angevine, and Ryuji Yoshida, Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, and Chemical Sciences Laboratory, National  ... 
doi:10.1029/2021ms002664 pmid:35865715 pmcid:PMC9287006 fatcat:tlzeemkfjnd5vasqaedqgae6gu

Modelling cell migration strategies in the extracellular matrix

K. J. Painter
2008 Journal of Mathematical Biology  
Amoeboid cell populations migrate in the ECM by making frequent shape changes and have minimal impact on its structure.  ...  the pattern and rate of cell infiltration, including the formation of characteristic "fingering" patterns.  ...  Acknowledgments The author would like to express his gratitude to Thomas Hillen, who has provided the stimulant for much of this work as well as a number of highly constructive suggestions.  ... 
doi:10.1007/s00285-008-0217-8 pmid:18787826 fatcat:brq5cl4i75dhlgdpghdndqv6qy

Apar-T: code, validation, and physical interpretation of particle-in-cell results

Mickaël Melzani, Christophe Winisdoerffer, Rolf Walder, Doris Folini, Jean M. Favre, Stefan Krastanov, Peter Messmer
2013 Astronomy and Astrophysics  
One is that PIC collision- and fluctuation-induced thermalization times are expected to scale with the number of superparticles per grid cell, and thus to be a factor p 10^10 smaller than in real plasmas  ...  These models rely on two building blocks: coarse-graining, i.e., grouping of the order of p 10^10 real particles into a single computer superparticle, and field storage on a grid with its subsequent finite  ...  Some of the simulations have been performed at pôle scientifique de modélisation numérique, PSMN, at ENS-Lyon, whose staff we thank for their steady technical support.  ... 
doi:10.1051/0004-6361/201321557 fatcat:42vd5eyprzdcflaaflfwwiuzeq
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