Recovering Hidden Neural Oscillatory Modes from Partial Observations through Delay Embedding and Perturbation
Characterising the oscillatory behaviour generated by neural interactions is central to systems neuroscience because these dynamical properties are linked to brain function. However, inferring latent neural dynamics is challenging because recordings sample only part of the system. Time-delay embedding allows dynamical modes to be estimated from partial recordings, using methods such as Hankel…
Understanding brain function relies on deciphering the oscillatory behaviour of neural interactions. However, capturing the full picture is difficult, as recordings only glimpse a fraction of the system. Time-delay embedding offers a path to estimate dynamic patterns, but its limits and improvements remain unclear. To clarify these issues, researchers applied control theory to factorise the Hankel matrix of delay-embedded data into an observability matrix and a trajectory matrix resembling a controllability matrix.
By analysing their ranks, they demonstrated that delay embedding enhances observability, while perturbation augments trajectory rank by activating dormant modes. This framework was tested using Hankel DMD on simulations and human electrocorticography (ECoG) recordings. The findings reveal that perturbation boosts the estimation of fast-decaying modes, while deeper delay depths yield more reliable mode estimates and broaden their frequency range.
These insights clarify the potential of partial recordings to unlock neural dynamics and highlight strategies to extract more information.
Written by urgent.news from bioRxiv's reporting — not their text. Machine-written — may contain errors; check the original before relying on it.
