HyperSimulations

Simulating EEG hyperscanning data using coupled Kuramoto oscillators following stochastic delay differential dynamics and using connectome data. Benchmarking information-theoretic measures against standard connectivity measures.

Preparation and Finding Best Phenomenological Model of Single-Brain Dynamics

A. Brain Criticality Dynamics (criticality.py)

• Plot criticality dynamics of Kuramoto model of simulated source signals. Varying $C_{\text{intra}}$ [0,1] in 50 steps, 20 iterations, and three noise conditions (none, medium, high).

B. Finding Best Cintra (best_cintra.py, mahalanobis_distance.py)

• Calculating the Mahalanobis distance between the MI Gaussian connectivity matrices of various single-brain simulations — $C_{\text{intra}}$ [0.45,7], 25steps — and real resting-state EEG datasets (Gifford, Pérez).

Simulating Brain-to-Brain Interaction and Evaluating Various Connectivity Measures

1. Simulating source neural dynamics (simulations.py)

• Calculate the phases of each oscillator (N=180) in a large Kuramoto model which follows stochastic delayed differential dynamics.
• Convert all the phases into simulated EEG data using forward gain model (N=64).
• Plotting extensive parameter space, varying inter-brain connectivity ($C_{\text{inter}}$), biological noise (phase_noise, freq_std), and external/recording noise (amp_noise, sensor_noise).

2. Calculating Connectivity Measures (IB_analysis.py)

   a. Calculate Standard Connectivity Measures: PLV, PLI, wPLI, CCorr, COH, iCOH, envCorr, and powCorr

   b. Calculate Mutual Information: Histogram, Box Kernel, Gaussian, KSG, and Symbolic Estimators

   c. Calculate Integrated Information Decomposition Measures: Time-Delayed Mutual Information, Transfer Entropy, Pure Information Transfer, Redundancy, and Synergy

3. Statistical Analysis (statistical_analysis.R)