2026-09-29
Ugail and Howard combine DFA, theta-gamma coupling and alpha metastability into Ψ. Synthetic classes do not overlap; Sleep-EDF wake-vs-REM AUC is 0.996, N2 vs REM near chance.
Reading conscious level off EEG keeps hitting the same wall: one feature works on some contrasts and fails on others. Lempel-Ziv complexity, the spectral slope, and TMS-evoked perturbational complexity can split wake from anaesthesia in the right setting. Swap the states and the ranking flips. The spectral slope is essentially perfect on wake versus N2, then ranks REM above N2, which is the wrong order if the construct is vigilance.
Hassan Ugail at Bradford's Centre for Visual Computing and Intelligent Systems and Newton Howard at Rochester Institute of Technology do not offer another scalar that "measures consciousness." They combine three dynamical properties that recur across theories: scale-free temporal organisation, cross-frequency organisation, and metastable flexibility of large-scale synchrony. The composite Ψ is not a phenomenal meter. It tracks neural organisation associated with conscious-level processing. The paper does not pick Integrated Information Theory or global workspace, and it notes that the same operators could, in principle, run on artificial systems given suitable time series.
Three estimates, min-max normalised against a reference ensemble, then a weighted sum.
Weights are 0.40 / 0.35 / 0.25, chosen before seeing evaluation numbers. The synthetic side is a 16-channel, 250 Hz Kuramoto generator with nine planted states, 30 runs each. The empirical side is Sleep-EDF: 30 adults, Fpz-Cz and Pz-Oz, 1,078 artefact-free 30-second epochs, with subject-level means as the unit of analysis.
On the simulator, high-consciousness states (wake, task, psychedelic) sit at Ψ 0.76-0.90, low-vigilance (NREM-like sleep, minimally conscious) at 0.43-0.49, non-conscious and seizure at 0.05-0.10. Wake is about 0.89, psychedelic about 0.76. Pooling wake, task and psychedelic against anaesthesia plus non-conscious gives AUC=1.000 with no overlap across 150 draws. Ablating phase-amplitude coupling, metastability, or fractal scaling from a wake-like baseline of 0.79 drops Ψ to 0.59, 0.57 and 0.47. On Sleep to minimally conscious, Heff alone has AUC=0.00, M alone 1.00, and the composite recovers 0.98.
Real EEG is the test that counts.
| Contrast | Ψ | Spectral slope | LZC | Alpha power |
| Wake vs N2 | 0.973 | 1.000 | 0.946 | 0.938 |
| Wake vs REM | 0.996 | 0.993 | 0.783 | 0.780 |
| N2 vs REM | 0.584 | 0.317 | 0.274 | 0.204 |
Subject-level means: wake 0.640±0.005, N2 0.520±0.010, REM 0.502±0.010. All 30 subjects rank wake above both sleep stages (rank-biserial +1.00; Friedman χ²=45.27). N2 versus REM is Wilcoxon p=0.058, short of Bonferroni. Spectral slope takes wake vs N2 at 1.000; Ψ does not beat that single marker. On wake vs REM, Ψ is 0.996 against the slope's 0.993.
At two channels, PAC surrogate z-scores sit between -0.03 and 0.15: theta-gamma coupling is not actually detectable. D's discrimination is a between-subject ranking of the raw Tort index (wake about 0.0043, N2 about 0.0020). M collapses to a pairwise phase lag, with wake-versus-sleep AUC around 0.60. Heff supplies about half of Ψ's value and is peaked at each subject's own wake median.
For people scoring vigilance, anaesthesia, or disorders of consciousness, this is a reproducible recipe: organised complexity, not "more entropy means more conscious." The simulator makes a clean case that a single component misses some step on the state ladder. The sleep data only show that the index can separate wake from sleep at the subject level.
The sentence AI readers will notice sits in the positioning section: the operators are defined on time series, not on biology. There is no model or robot experiment. Reading this as a recipe for building consciousness in machines overclaims the paper.
This is a pipeline paper. DFA, phase-amplitude coupling and metastability are old tools. The contribution is the composite plus a head-to-head AUC table on Sleep-EDF.
The generator is stylised EEG with no microcircuitry and no receptor pharmacology for the "psychedelic" state. It plants the features the index is built to recover. Internal consistency is not evidence of phenomenal consciousness.
The real data are two-channel polysomnography. No anaesthesia, no disorders of consciousness, no dense EEG. The perfect wake-versus-sleep ranking is partly designed in: Heff peaks at each subject's wake median by construction. N2 versus REM does not use that anchor and falls near chance. Weights were not searched on the evaluation set. Synthetic and real operators differ in gamma band, H tuner and channel count, so the Ψ numbers are not interchangeable.
Volume conduction inflates zero-lag synchrony on scalp EEG. Two-channel M absorbs that confound; the paper does not apply a phase-lag correction.