Algorithm 1:

How to interpret the TDMI for a population of time series

if there are enough points to estimate $\overline{I}$ (usually ∼100 pairs of points per representative individual are required)

then,

estimate δI and HΘ

ifδI > BIRPthen

the population is heterogeneous

if${\mathfrak{H}}_S~0$then

supports (or ranges) are diverse or disjoint

elseif${\mathfrak{H}}_S~1$, then

supports (or ranges) are uniform

endif

elseifδI ≤ BIRP, then

the population is homogeneous

endif

ifHΘ ∼ 0, then

the population is well represented

elseifHΘ ∼ 1, then

the portions of the population are overrepresented

endif

else if not enough pairs to estimate $\overline{I}$, then

estimate $\hat{I}$, ${\mathfrak{H}}_S$, and HΘ

if${\mathfrak{H}}_S~0$, then

supports (or ranges) are diverse or disjoint

if there are enough pairs of points per patient to estimate a PDF for each patient at the specific δt,then

$V_{\hat{S}}(p)$ (i.e., V(p) relative to the abstract supports)

if$V_{\hat{S}}(p)~1$, then

the population used to estimate $\hat{I}$ has graph-based heterogeneity

elseif$V_{\hat{S}}(p)~0$, then

the population used to estimate $\hat{I}$ is graphically homogeneous

endif

elseif it is not possible to accurately estimate a PDF for each patient at the specific δt,then

it is not possible to determine the contribution of the graph-based heterogeneity to the overall heterogeneity

endif

elseif${\mathfrak{H}}_S~1$, then

supports (or ranges) are uniform

if$V_{\overline{\mathfrak{S}}}(p)~1$, then

the population used to estimate $\hat{I}$ has graph-based heterogeneity

elseif$V_{\overline{\mathfrak{S}}}(p)~0$, then

the population used to estimate $\hat{I}$ is homogeneous

endif

ifHΘ ∼ 0, then

the population is well represented

elseifHΘ ∼ 1, then

the portions of the population are overrepresented

endif

{NOTE: there are 10 possible sharp interpretations for both δI and $\hat{I}$-only cases.}

{All TDMI interpretations should include: I-like quantities (e.g., $\hat{I}$, δI, etc), population diversity qualification (support- and graph-based contributions to diversity; if they are unknown, this should be specified), and the make-up of the population used to estimate the I-based quantities (e.g., HΘ.}.

{NOTE: even under the best circumstances, it may be difficult to determine what proportion of the heterogeneity is due to support-based versus graph-based diversity.}