Journal
PATTERNS
Volume 3, Issue 8, Pages -Publisher
CELL PRESS
DOI: 10.1016/j.patter.2022.100555
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Funding
- NIH [BRAIN R01EB026945, BRAIN R01EB026908]
- NSF [PHY 1734030, NCS-FO 2024364, 2019976]
- Swartz Center for Theoretical Neuroscience at the University of Washington
- Klingenstein-Simons Fellows and Pew Biomedical Scholars programs
- Simons Foundation [MMLS 400425]
- Santa Fe Institute
- Aspen Center for Physics (NSF) [PHY-1607611]
- Office Of Internatl Science &Engineering
- Office Of The Director [2019976] Funding Source: National Science Foundation
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This passage introduces a scale-dependent participation ratio method to determine the dimensionality of systems at different scales, which can be applied to various systems and studies of brain activity.
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 and brain states shows fundamental trends in the dimensionality of neural activity-for example, in behaviorally engaged versus spontaneous states. Our novel method unifies widely used measures of dimensionality and applies broadly to multivariate data across several fields of science.
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