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State space discovery in spatial representation circuits with persistent cohomology

View ORCID ProfileLouis Kang, Boyan Xu, View ORCID ProfileDmitriy Morozov
doi: https://doi.org/10.1101/2020.10.06.328773
Louis Kang
1Redwood Center for Theoretical Neuroscience, University of California, Berkeley
2Neural Circuits and Computations Unit, RIKEN Center for Brain Science
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  • For correspondence: louis.kang@riken.jp
Boyan Xu
3Department of Mathematics, University of California, Berkeley
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Dmitriy Morozov
4Computational Research Division, Lawrence Berkeley National Laboratory
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Abstract

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We explore the application of persistent cohomology to the brain’s spatial representation system. We simulate populations of grid cells, head direction cells, and conjunctive cells, each of which span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures and demonstrate its robustness to various forms of noise. We identify regimes under which mixtures of populations form product topologies can be detected. Our results suggest guidelines for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

Competing Interest Statement

The authors have declared no competing interest.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted October 08, 2020.
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State space discovery in spatial representation circuits with persistent cohomology
Louis Kang, Boyan Xu, Dmitriy Morozov
bioRxiv 2020.10.06.328773; doi: https://doi.org/10.1101/2020.10.06.328773
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State space discovery in spatial representation circuits with persistent cohomology
Louis Kang, Boyan Xu, Dmitriy Morozov
bioRxiv 2020.10.06.328773; doi: https://doi.org/10.1101/2020.10.06.328773

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