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Grid cells in the medial entorhinal cortex provide a periodic spatial code that enables path integration. Theoretical models propose that grid cell activity forms a toroidal manifold, supporting continuous attractor dynamics. In this study, we introduce a novel decoding algorithm that reconstructs movement trajectories from grid cell activity using topological data analysis (TDA) and path listings in Topology. Our approach maps trajectories from the toroidal representation of grid cell activity back to R2, effectively recovering the original movement path. We validated the algorithm on both CAN-simulated and experimental grid cell recordings, demonstrating its ability to reconstruct movement paths while preserving topological structure. Additionally, we examined the impact of noise and data sparsity on decoding accuracy. Our findings reinforce the toroidal organization of grid cell activity and suggest a potential computational mechanism underlying the internal navigation system.</p>"},{"label":"Group","value":["Theses & Dissertations"]},{"label":"Digital Origin","value":["born digital"]},{"label":"Discipline","value":["Computer Science"]},{"label":"Date","value":"April 15, 2025"},{"label":"EDTF Date","value":"D:00 M:00 Y:2025"},{"label":"File Format","value":["application/pdf"]},{"label":"Digital Object Identifier (DOI)","value":"https://doi.org/10.14418/wes01.1.3202"},{"label":"Type","value":["Text"]}],"description":"Topological decoding of grid cell activity via path lifting to covering 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