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In this paper, we present the implementation of Velocity Controlled (or tuned) Oscillators (VCO) to model spatial coding and navigation in the mammalian hippocampus. Specifically, we demonstrate these spatial cells by representing a spatial firing map of grid, place, and border cells. Since the VCO is the basis for Oscillatory Interference (OI) models based on the Spatial Envelope Synthesis (SES) approach of hippocampal and entorhinal navigation, we use these models in our hardware implementation to construct more complex spatial cells from simple interference between VCOs. We develop the design of a VCO ASIC chip containing up to 128 independently tuned VCOs.
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Grid cells, border cells, and discrete complex analysis
We propose a mechanism enabling the appearance of border cells—neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity toward the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.
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- Award ID(s):
- 1901338
- PAR ID:
- 10554725
- Editor(s):
- Wu, Si
- Publisher / Repository:
- Frontiers in Computational Neuroscience
- Date Published:
- Journal Name:
- Frontiers in Computational Neuroscience
- Volume:
- 17
- ISSN:
- 1662-5188
- Subject(s) / Keyword(s):
- grid cells, border cells, percolation, discrete complex analysis, learning and memory, hippocampo-cortical network
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fncom.2023.1242300
