Open puzzles for DMD analysis of brain networks: eigenvector phase bounds and data sufficiency
PTenigma · x · 2026-11-08
While preparing a lecture on DMD (Dynamic Mode Decomposition) analysis of brain networks, the author poses two open theoretical puzzles:
- A Davis-Kahan-like finite-sample law for the phase of a complex DMD eigenvector, where the spectral gap is replaced by a quantity accounting for non-normality.
- A data sufficiency law to predict a finite-sample phase-identifiability horizon for a specific pair of networks or brain regions.
He also offers a six-way-intersection analogy for multi-network interaction, speculating the third network may go up and down like 3D chess—the brain has at least three principal gradients, perhaps mirroring this structure.
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