A scale-dependent measure of system dimensionality.

ABSTRACT: A fundamental problem in science is uncovering the effective number of degrees of freedom in a complex system: its dimensionality. A system's dimensionality depends on its spatiotemporal scale. Here, we introduce a scale-dependent generalization of a classic enumeration of latent variables, the participation ratio. We demonstrate how the scale-dependent participation ratio identifies the appropriate dimension at local, intermediate, and global scales in several systems such as the Lorenz attractor, hidden Markov models, and switching linear dynamical systems. We show analytically how, at different limiting scales, the scale-dependent participation ratio relates to well-established measures of dimensionality. This measure applied in neural population recordings across multiple brain areas a

SUBMITTER: Recanatesi S 

PROVIDER: S-EPMC9403367 | biostudies-literature | 2022 Aug

REPOSITORIES: biostudies-literature