Figures and data
Diagram of a state-space process.
CSER discriminates between states of consciousness.
That is, it preserves the key empirical properties of LZ: entropy increases under the effects of psychedelics (left), and decreases in NREM sleep (middle) and general anaesthesia (right). Top row shows subject-level averages, bottom row shows spatial distributions of LZ and CSER. Given the different locations of ECoG sensors in each subject of the anaesthesia dataset, we show only one subject (Chibi) and use Cohen’s d instead of t-scores.
Spectral decomposition of CSER differences across states of consciousness reveals largest contribution from γ frequencies.
Plots show mean and standard deviation of subject-level differences in CSER decomposed into frequency bands. Note that in each plot the sum of complexity in all bands equals the total (or broadband) complexity. In all three cases, the largest contribution to the difference is high-frequency neural activity. Frequency bands used are δ: 1–4 Hz, θ: 4–8 Hz, α: 8–14 Hz, β: 14–25 Hz, γ: >25 Hz.
Time-resolved entropy estimates differentiate between time courses of standard and deviant percepts.
(top left) Layout of ECoG electrodes overlaid on the monkey’s cortex, with the selected electrode in red. (bottom left) Schematic diagram of experimental paradigm, in which the subject listens to a tone train composed of ‘standard’ and ‘deviant’ tones (see text for details). (right) Event-related potentials of standard and deviant trials (top), and the instantaneous entropy rate difference computed via CSER (bottom). Stars represent a significant cluster with p < 0.001. Note that the entropy difference precedes the ERP by approximately 20 ms. Original data from Komatsu et al. (2015) and the Neurotycho database.
LZ and CSER approximate entropy rate, but CSER converges faster.
(left) LZ-estimated entropy rates of discrete signals with different lengths (x-axis) and memory order q. Except for low values of q, LZ shows a slow convergence to the true entropy rate (black line). (right) Similar analysis using CSER and synthetic real-valued signals. CSER converges to the true entropy rate for all values of q within approximately 1000 samples, within the range of typical M/EEG datasets. Note the logarithmic scale of the x-axis
State-space models accurately estimate entropy rate and power spectrum, and are robust to model order selection.
Synthetic data was generated from a known state-space model of order 
Subject-level differences in broadband CSER and LZ across states of consciousness.
Subject-level differences in spectral CSER across states of consciousness. Frequency bands used are δ: 1–4 Hz, θ: 4–8 Hz, α: 8–14 Hz, β: 14–25 Hz, γ: >25 Hz.
Subject-level differences in spectral CSER across states of consciousness, controlled for gamma coherence. Results correspond to the regression coefficients for conscious state in the linear model ‘CSER State + Coherence’. Coherence was calculated using the Fieldtrip toolbox (Oostenveld et al., 2011) with a multitaper Fourier transform method, and averaged across all pairs of channels. Effect size d here was calculated as suggested by Feingold (2013), taking the regression coefficient divided by the residual standard deviation of the full model. Frequency bands used are δ: 1–4 Hz, θ: 4–8 Hz, α: 8–14 Hz, β: 14–25 Hz, γ: >25 Hz.
Sliding-window CSER estimates show no signi1cant differences between standard and deviant tones.
Results are shown before (left) and after (right) applying a 150 Hz lowpass filter to the data and downsampling it to 300 Hz. A standard cluster test found no significant differences between conditions in either case.
