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Fig. 1 The relationship between the geometric properties of the neural activity space and the size of neural assemblies. (A) Illustration of how dimensionality of neural activity (DPR ) changes with the number of recorded neurons. (B) The eigenvalues of the neural covariance matrix dictate the geometrical configuration of the neural activity space with λ−−√i being the distribution width along a principal axis. (C) Examples of two neural populations with identical dimensionality (DPR=25/11≈2.27 ) but different spatial configurations, as revealed by the eigenvalue spectrum (green: {λi}={7,7,1} , blue: {λi}={9,3,3} ).