19 Analysis Monitors

Real-time dynamical observers. Attach any monitor to any engine. Stream via OpenTelemetry, Prometheus, or gRPC.

Synchronisation

Order Parameter R Production
Kuramoto order parameter. R = |N−1 ∑ eiθj|. Global coherence measure, 0 (incoherent) to 1 (fully synchronised).
PLV Production
Phase-Locking Value. Pairwise phase consistency over time. Standard in neuroscience and BCI. Windowed computation for non-stationary signals.
ITPC Stable
Inter-Trial Phase Coherence. Cross-trial phase alignment for event-related paradigms. Statistical significance via Rayleigh test.
EVS Stable
Entrainment Verification System. 3-criterion test: frequency lock, phase stability, causal influence. Binary go/no-go for closed-loop control.

Complexity & Chaos

Lyapunov Exponent Production
Maximum Lyapunov exponent. Positive = chaos, zero = edge of chaos, negative = stable. Benettin algorithm with QR renormalisation.
Entropy Production Stable
Thermodynamic irreversibility rate. Non-equilibrium signature. Distinguishes active from passive synchronisation.
Chimera Detection Stable
Detects coexistent coherent/incoherent clusters. Local order parameter profiling. Kuramoto-Battogtokh chimera states.
Winding Number Stable
Topological phase wrapping count. Distinguishes locked from drifting oscillators. Integer-valued invariant.

Information & Causality

Transfer Entropy Production
Directed causal information flow between oscillators. Asymmetric: TE(X→Y) ≠ TE(Y→X). Identifies driver/responder roles in the network.
PAC Stable
Phase-Amplitude Coupling. Cross-frequency interaction: low-frequency phase modulates high-frequency amplitude. Key neural computation mechanism.
PID Stable
Partial Information Decomposition. Redundancy vs synergy in multi-oscillator interactions. Beyond pairwise mutual information.
NPE Stable
Normalised Prediction Error. Measures predictability of oscillator dynamics. Used for stochastic resonance detection and noise optimisation.

Specialised

Sleep Staging Stable
AASM-compliant sleep stage classification from R(t) trajectory. Wake/N1/N2/N3/REM mapping. Validated against polysomnography.
Psychedelic Simulation Experimental
Entropy surge model. Simulates increased neural entropy observed under psychedelics. Carhart-Harris entropic brain hypothesis.
STL Runtime Monitor Stable
Signal Temporal Logic for formal safety properties. “R must stay above 0.5 within 100 steps”. Runtime verification with quantitative semantics.
Poincaré Sections Stable
Phase space cross-sections. Visualise attractor structure, period-doubling, quasi-periodicity. Standard dynamical systems tool.
Session Start Gate Production
Startup coherence verification. Blocks actuation until R exceeds configurable threshold. Safety gate for closed-loop deployment.
HCP Connectome Experimental
Human Connectome Project coupling matrix generator. Generates realistic cortical coupling from parcellation data.