Multiscale neural dynamics and task-dependent states in human MEG via time-delay embedding

The brain's temporal organisation arises from the dynamic interplay between neural rhythms that supports cognition across timescales from milliseconds to minutes. Such a complex and flexible organisation poses fundamental representational challenges. Time-delay embedding (TDE) has emerged as a promising computational tool in the study of neural signals, yet it is employed in two fundamentally different ways: as a spectral estimator, via the singular-spectrum analysis framework and the TDE hidden Markov model (TDE-HMM), and as a phase-space reconstruction tool for attractor geometry, where it enables recurrence-based analyses. The consequences of this epistemological divide - what each TDE philosophy reveals about cognitive dynamics, and at what interpretive cost - remain poorly characterised. This thesis addresses that gap through three investigations, each conducted on magnetoencephalography (MEG) recordings of human subjects performing an N-back working-memory task. In the first study, we demonstrate that TDE-HMM recovers cognitively meaningful temporal structure across multiple timescales simultaneously, tracking both fast trial-level neural events and slow block-level contextual influences across three independent MEG cohorts â without prior specification of the timescales of interest. In the second study, we show that TDE-HMM realisations of statistically comparable free energy can produce non-equivalent posterior dynamics, such that recovered brain maps map differently to task conditions across models, revealing a potential gap between statistical model quality and scientific interpretability that motivates cross-methodological triangulation as a validity criterion. In the third study, we apply recurrence quantification analysis to the phase-space reconstruction of MEG signals and demonstrate that structured recurrent episodes become less frequent with increasing working-memory load while preserving their internal character - a pattern consistent with event-related desynchronisation and inconsistent with a gain change - providing interpretative specificity that spectral and entropy-based measures alone cannot supply. Taken together, these findings reveal the fundamental tradeoff between the two TDE philosophies: the spectral use of TDE can uncover multiscale cognitive dynamics with fine temporal precision, but at the apparent cost of initialisation instability; the geometric, phase-space reconstruction use disambiguates signal reorganisations that spectral approaches cannot, at the cost of temporal resolution. The analytical choice made on top of a time-delay embedding is not merely technical: it determines how the TDE parameters should be selected and what aspects of cognitive dynamics are visible.