Fig. 4: Example with two graphs and three time series.
From: Duality between predictability and reconstructability in complex systems
a The stochastic system consists of two possible graphs, \(g_{1}\) and \(g_{2}\), and three possible time series, \({{\bf{x}}}_{1},\, {{\bf{x}}}_{2}\), and \({{\bf{x}}}_{3}\). b, c The reconstructability \(U(G|{{{\bf{X}}}})\) (solid blue line) and the predictability \(U({{{\bf{X}}}}|G)\) (dashed orange line) are shown for \(s=1\) (b) and \(s=\frac{1}{2}\) (c). The shaded area in (c) indicates the region where \(U({{\bf{X}}}|G) \, {{{\rm{and}}}} \, U(G|{{{\bf{X}}}})\) vary in opposite directions.
