Fig 1.
Synergy and redundancy values for the bivariate Gaussian system given by Eqs (3) and (4) for .
Line styles represent raw atoms (dashed), atoms normalised by total mutual information (NMI, dotted), and atoms normalised by our proposed null-model procedure (NuMIT, solid).
Fig 2.
(a) Distributions of redundancy, unique information, and synergy with MMI definition for TMI=1.0 nat and (b) TMI=3.0 nat.
(c) PID-atom averages for different values of mutual information over random Gaussian systems with 2 univariate sources and a univariate target. (d) Same as (c) but with NMI-normalised PID atoms.
Fig 3.
NuMIT- and NMI-normalised PID atoms for Gaussian models of Eq (6) for various choices of parameters.
(a) Normalised redundancy as a function of sources correlation (Eq (10)). (b) Normalised unique information and (c) normalised synergy for various cross-coupling values between one source and the target (Eq (11)). Shaded areas represent the standard deviation across various .
Fig 4.
PID-atom distributions for all subjects under different drugs and placebo effects using MMI definition.
From left to right, results refer to LSD, ketamine, and psilocybin drugs. Panel rows represent (a) the raw values of PID atoms, (b) the NMI-normalised PID atoms, and (c) the NuMIT-normalised PID atoms. The dashed black lines are drawn at zero. (P-values calculated with a one-sample t-test against the zero-mean null hypothesis. *: p<0.05; **: p<0.01; ***: p<0.001).
Table 1.
Pearson correlations increase from NMI to NuMIT, for synergy and redundancy and for all drugs (MMI-CCS comparison).
P-values refer to the coefficient of the interaction between PID measure and normalisation. ALL refers to the results obtained with the Linear Mixed Effect model (Eq (12)), whereas LSD, KET, PSIL refer to those obtained with the OLS (Eq (29)).
Fig 5.
Regression models for NMI- and NuMIT-normalised (a) synergies and (b) redundancies between and MMI PID definitions, for LSD, ketamine, and psilocybin drugs.
Δ indicates the differences between drug and placebo in PID atoms obtained with either PID (MMI or CCS).
Fig 6.
Raw values of PID atoms distribution for subject 1 under ketamine and placebo effects using the MMI PID.