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CAP Delta-Phase Kuramoto Variants: An Honest Detector Panel

Abstract

The Kuramoto diagnostic showed that the simple mean-R delta-phase Kuramoto detector fails on CAP recordings such as brux2 because both N3 and Wake epochs carry a high mean order parameter — the mean discards the N3-vs-Wake separation of R(t), and a bruxism recording's Wake epochs produce artefact-driven coherence with little genuine slow-wave power. This study audits four new variants that each target that failure from a different angle, alongside the three established detectors, on the same four-recording CAP panel and at the same matched false-alarm operating point (target_false_alarm = 0.10, 10 000-permutation significance test, seed 42).

The headline result: coherent_sustained_kuramoto is the first Kuramoto-family detector to beat the normalized delta envelope on this panel (mean detection rate 0.552 vs 0.525), and the decisive lever is time-resolved amplitude gating, which raises the mean-R detector from 0.184 to 0.457 and repairs the brux2 failure (0.062 → 0.837).

Variants

Detector Definition
normalized_delta_envelope Delta-band Hilbert envelope / broadband envelope, averaged across channels (established baseline).
multi_channel_delta_kuramoto Mean of R(t), the across-channel delta-phase order parameter (established).
snr_weighted_delta_kuramoto Per-channel, per-epoch SNR-weighted R(t) (established; shown not to improve on mean-R).
amplitude_gated_delta_kuramoto Mean of R(t)·A(t), where A(t) is the instantaneous mean delta amplitude — coherence contributes only where genuine slow-wave power exists.
sustained_delta_kuramoto Lower quartile of R(t) within the epoch — the sustained coherence floor.
adaptive_channel_kuramoto Mean R(t) over channels whose whole-recording delta SNR is at or above the median.
coherent_sustained_kuramoto Lower quartile of R(t)·A(t) — sustained coherent slow-wave power (amplitude gate + sustained floor).

Results

Cross-subject mean detection rate (matched FA 0.10)

Detector mean DR std DR geo-mean p beats chance
coherent_sustained_kuramoto 0.552 0.339 0.0011 0.75
normalized_delta_envelope 0.525 0.360 0.0010 0.75
amplitude_gated_delta_kuramoto 0.457 0.287 0.0013 0.75
adaptive_channel_kuramoto 0.204 — — 0.75
multi_channel_delta_kuramoto 0.184 0.070 0.0149 0.75
snr_weighted_delta_kuramoto 0.175 — — 0.75
sustained_delta_kuramoto 0.173 — — 0.75

Per-recording detection rate

Recording Condition envelope mean-R amplitude-gated coherent-sustained
n1 control 0.380 0.231 0.386 0.377
n2 control 0.005 0.223 0.046 0.081
brux2 bruxism 0.913 0.062 0.837 0.893
narco2 narcolepsy 0.803 0.218 0.559 0.856

Interpretation

  • Amplitude gating is the decisive lever. Weighting R(t) by the instantaneous delta amplitude lifts the mean-R detector from 0.184 to 0.457. On brux2 — where mean-R catastrophically fails (0.062) because bruxism Wake epochs are spuriously coherent — the gate recovers 0.837, close to the envelope's 0.913. This confirms the diagnostic hypothesis: mean-R counts coherence that carries no genuine slow-wave power.
  • The sustained floor helps only on top of the gate. sustained_delta_kuramoto alone (0.173) is no better than mean-R (0.184); but the lower quartile of the gated series (coherent_sustained, 0.552) beats the amplitude gate alone (0.457) and the envelope (0.525). Requiring sustained coherent power, not a transient burst, is what pushes the Kuramoto family past the envelope.
  • coherent_sustained_kuramoto also beats the envelope on narco2 (0.856 vs 0.803), not only on average.
  • Honest trade-off on n2. n2 is the one recording where pure phase coherence uniquely wins: mean-R scores 0.223 while the envelope collapses to 0.005 and the gated variants score 0.046–0.081. n2 has low delta SNR but high phase coherence, so amplitude gating suppresses exactly the signal that discriminates there. No single detector dominates every regime — this points to a regime-adaptive ensemble (pure phase coherence for low-SNR/high-coherence recordings, amplitude-gated sustained coherence otherwise) as the next step.
  • Channel selection and per-epoch SNR weighting are not the levers. adaptive_channel_kuramoto (0.204) barely improves on mean-R, and snr_weighted_delta_kuramoto (0.175) does not improve at all. The discriminating structure is temporal (instantaneous amplitude, sustained floor), not which channels are used.

Reproduction

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

The script reads the four CAP recordings from scratchpad/cap_data/, 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_cap_kuramoto_variants_evidence.py.

Scope and limitations

  • Four recordings. Cross-subject statistics on four recordings are descriptive, not powered; the per-recording verdicts (each a 10 000-permutation test on hundreds of epochs) are the primary evidence.
  • Raw EDF files are citation-only. Only derived sealed records and the aggregate JSON are committed; the raw PhysioNet CAP recordings are not redistributed.
  • N3-vs-Wake only. The audit separates deep sleep from wakefulness; it does not attempt full multi-stage classification.