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q-bio.NC2022
Quantifying Extrinsic Curvature in Neural Manifolds
Francisco Acosta, Sophia Sanborn, Khanh Dao Duc +2
The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In…
math.CO2022
VC-Dimension and Distance Chains in
Ruben Ascoli, Livia Betti, Justin Cheigh +8
Given a domain and a collection of functions , the Vapnik-Chervonenkis (VC) dimension of measures its complexity in an appropriate s…
cs.CG2022
Distinct Angles and Angle Chains in Three Dimensions
Ruben Ascoli, Livia Betti, Jacob Lehmann Duke +6
In 1946, Erdős posed the distinct distance problem, which seeks to find the minimum number of distinct distances between pairs of points selected from any configuration of poin…