Table 1.

Definition of the tuple Ω, Ψ, S, A, M, p, q, P or self-evidencing.

A sample spaceΩ from which random fluctuations ω ∈ Ω are drawn

External states${\mathit{f}}_{\mathit{\Psi }}:\mathit{\Psi }\times \mathit{A}\times \mathit{\Omega }\stackrel{{\mathit{f}}_{\mathit{\Psi }}}{\to }\mathit{\Psi }\in {\mathbb{R}}^{\mathit{\Psi }}$– states of the world (e.g. extracellular milieu) that depend on themselves and active states

Sensory states${\mathit{f}}_{\mathit{S}}:\mathit{\Psi }\times \mathit{A}\times \mathit{\Omega }\stackrel{{\mathit{f}}_{\mathit{S}}}{\to }\mathit{S}\in {\mathbb{R}}^{\mathit{S}}$– states of sensors (e.g. receptor activity) but depend upon external and active states

Active states${\mathit{f}}_{\mathit{A}}:\mathit{S}\times \mathit{M}\times \mathit{\Omega }\stackrel{{\mathit{f}}_{\mathit{A}}}{\to }\mathit{A}\in {\mathbb{R}}^{\mathit{A}}$ – states of action on the world (e.g. exocytosis of signalling molecules) that depend upon sensory and internal states

Internal states${\mathit{f}}_{\mathit{M}}:\mathit{S}\times \mathit{M}\times \mathit{\Omega }\stackrel{{\mathit{f}}_{\mathrm{M}}}{\to }\mathrm{M}\in {\mathbb{R}}^{\mathrm{M}}$ – the internal states of a system (e.g. genetic transcription) that depend on themselves and sensory states

Generative modelp(ψ, S, A, μ|m) – a probability density function over external, sensory, active and internal states for a system denoted by m

Variational densityq(ψ|μ) – a probability density function over external states parameterised by internal states