Relate OPTN ergodicity bounds to reservoir memory capacity

Determine whether the ergodicity-based memory bound for ordinal-pattern transition network (OPTN) walks relates in a simple and computable way to established reservoir-computing memory-capacity measures.

Background

The paper establishes a discrete fading-memory analogue for constrained random walks on ordinal-pattern transition networks. Under irreducibility and aperiodicity, the induced compatibility-state Markov chain forgets its initial state at a rate controlled by its subdominant eigenvalues and spectral gap. The authors explicitly identify the relationship between this mixing-based memory bound and standard reservoir-computing memory-capacity measures as unresolved.