Visual elements for the interpretation of MO-ED results in the context of ¹³C MFA.

A: Chord diagram linking designs and objective (circular node elements) by inlying chords, here for the case of two objectives (right segment) and four input substrate species (left segments). An example is given with three substrates contributing to a design, roughly 25% Substrate1, 0% Substrate2, 50% Substrate3, and 25% Substrate4. The proportions in which the substrate species contribute is indicated by percentages. In addition, the (relative) frequency with which a certain proportion of a substrate species is proposed among the Pareto-optimal solutions is displayed by histograms located at the left outer bands. Information and cost values are scaled to the range of 0–100%. The graphic is created with Circos [54] (www.circos.ca). B: 2D scatter diagram representing the Pareto front with the dominated objective region being grayed-out. The slope of the Pareto front reflects the progressive increase in cost per information gain. The region of the Pareto front in the vicinity of a jump (green arrow) reveals that a higher information value requires the addition of at least one costly input substrate or measurement group which leads to a large cost increase. To the contrary, densely populated flat Pareto fronts indicate that CLE costs can be tuned well. The black bar on the right indicates the overall cost spread. C: Ternary triangles are commonly used in 13C MFA to represent mixture designs with three tracer species. The dashed lines relate the design point (yellow star) on the CD and the Pareto frontier with the mixture composition.