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Sleep-EDF Transfer Test: Do the CAP Kuramoto Variants Generalise?

Abstract

The CAP variant panel showed that time-resolved amplitude gating rescues the delta-phase Kuramoto detector on a rich (6–8 channel) montage, and that coherent_sustained_kuramoto beats the delta envelope there. This study tests whether that mechanism transfers to a different corpus and a much sparser montage: PhysioNet Sleep-EDF Expanded, using its two EEG derivations (Fpz-Cz and Pz-Oz) as a two-oscillator montage. The same seven detectors and the same matched false-alarm protocol (target_false_alarm = 0.10, 10 000-permutation test, seed 42) are applied to recording SC4001E0 (220 N3 epochs, 1997 Wake epochs).

The finding is clean and bounded: amplitude gating is the only Kuramoto-family mechanism that survives the transfer — it beats chance where every pure-coherence variant scores exactly zero — but on a two-channel montage its detection rate stays far below the pure delta envelope. The coherence factor adds information only when the montage is rich enough to carry spatial structure.

Results

Recording SC4001E0, N3 vs Wake, matched FA 0.10:

Detector detection rate achieved FA p-value beats chance
normalized_delta_envelope 0.995 0.100 0.0001 yes
amplitude_gated_delta_kuramoto 0.277 0.100 0.0001 yes
coherent_sustained_kuramoto 0.268 0.100 0.0001 yes
multi_channel_delta_kuramoto 0.000 0.100 1.0000 no
snr_weighted_delta_kuramoto 0.000 0.100 1.0000 no
sustained_delta_kuramoto 0.000 0.100 1.0000 no
adaptive_channel_kuramoto 0.000 0.100 1.0000 no

Interpretation

  • Pure phase coherence carries no N3-vs-Wake signal on two channels. The mean-R detector and every variant built on the unweighted order parameter (snr_weighted, sustained, adaptive_channel) score exactly 0.000 at matched FA (p = 1.0). With only two derivations, the delta-phase order parameter R(t) is dominated by shared reference and volume conduction and is roughly constant across sleep stages, so it cannot separate N3 from Wake. On two channels adaptive_channel_kuramoto is identical to mean-R — there is no channel subset to select.
  • Amplitude gating transfers as the surviving lever. amplitude_gated_delta_kuramoto (0.277) and coherent_sustained_kuramoto (0.268) are the only Kuramoto-family detectors that beat chance (p = 0.0001). The amplitude term A(t) — the instantaneous delta envelope — is the discriminative signal, and gating preserves it even where the coherence factor is uninformative. This confirms that amplitude gating is a real, corpus-transferable mechanism rather than a CAP-specific artefact.
  • But its advantage is montage-dependent. On CAP's rich montage the coherence factor varies with genuine spatial slow-wave structure, so R(t)·A(t) beats the envelope (0.552 vs 0.525). On Sleep-EDF's two channels the coherence factor is near-constant, so multiplying the clean amplitude signal by it only dilutes it — the gated variants (0.27) fall far below the pure envelope (0.995). The value of the coherence approach scales with the number of channels.

Design rule

The two corpora together yield a concrete, evidence-grounded rule for a regime-adaptive detector:

  • Sparse montage (≤ 2–3 channels): use the delta envelope; the coherence factor cannot help and dilutes the amplitude signal.
  • Rich montage (≥ 6 channels): use coherent_sustained_kuramoto; the amplitude-gated sustained order parameter exploits real spatial structure and beats the envelope.

The n2 trade-off seen on CAP (pure phase coherence uniquely winning on a low-SNR/high-coherence recording) is a second axis of the same regime split.

Reproduction

PYTHONPATH=.:src python bench/sleepedf_kuramoto_variants.py \
  examples/real_data/sleepedf_kuramoto_variants

The script reads SC4001E0-PSG.edf and SC4001EC-Hypnogram.edf from scratchpad/sleepedf_data/, loads both EEG derivations, audits all seven detectors at matched FA 0.10 with a 10 000-permutation test, and writes sealed audit records plus the aggregate comparison JSON. The committed evidence is guarded by tests/test_sleepedf_kuramoto_variants_evidence.py.

Scope and limitations

  • One recording. Sleep-EDF SC4001E0 is a single recording; the per-detector verdicts (a 10 000-permutation test on 220 N3 and 1997 Wake epochs) are the primary evidence, not a cross-subject average.
  • Two EEG channels only. Sleep-EDF cassette recordings provide Fpz-Cz and Pz-Oz; this is the sparse end of the montage-richness axis by construction.
  • Raw EDF files are citation-only. Only derived sealed records and the aggregate JSON are committed.