Table 1.

A table describing all of the measures described here, and how they can be intuitively interpreted. The measures are broadly categorized into several groups, including which embedding they are applied to (EPC versus OPN), and the general mathematical fields they are derived from (EPC, information theory).

measure	category	formalism	interpretation
maximum persistence	EPC/TDA	the length of the longest lived cycle in the Rips filtration	the degree of ‘higher-order’ structure present in the EPC
total number of cycles	EPC/TDA	the total number of cycles that appears over the Rips filtration	how constrained are the interactions between all channels?
maximum number of cycles	EPC/TDA	the maximum number of cycles present at a given moment in the Rips filtration	how constrained are the interactions between all channels?
number of nodes	OPN	the number of unique nodes in the OPN	the size of the repetoir of available states
number of edges	OPN	the number of unique edges in the OPN	the flexibility with which the system transitions through micro-states
determinism	OPN/info. theory	the average entropy of the out-going edges for each node	how predictable is the future given the present?
degeneracy	OPN/info. theory	how much information is lost when states run together	how recoverable is the past given the present?
modularity	OPN	how well the nodes in the OPN can be clustered	the tendancy for the system to get ‘stuck’ in smaller subsets of the state space
permutation entropy	time series/info. theory	the entropy of the permutation-embedded series	how ‘flat’ the overall state-space is
Lyapunov exponent	time series	the ‘chaoticity’ of the time series	how predictable is the time series; how sensitive to perturbation