Rational design of complex phenotype via network models

The candidate solution faithfully mirrors the paper’s DSGRN-based methodology and reproduces its key definitions and results: partial-path definition of ascending hysteresis and scoring, use of essential factor graphs PGe(1)×PGe(2), enumeration of partial paths in PG(0), and the fragile-vs-robust classification via robustness = perturbed/original with a 0.5 threshold. The paper explicitly reports that most 3-node networks score near 0%, fewer than 1% exceed 50%, and exactly 14 exceed 60% in the ascending-hysteresis ranking, which the candidate states correctly . The top-14 fragile/robust split (fragile = 1–4, 13, 14; robust = 5–12) and the identification of three consistent designs among the robust set are also reported in the paper’s text and figures; the paper singles out Network 12 as the most desirable based on hysteresis score, robustness, and consistency, with DSGRN partial-path 80.91% and perturbed 64.13% exactly matching the candidate’s numbers (robustness ≈ 0.793) . Minor notes: the paper text says 14,068 networks were analyzed but the Figure 2 caption shows 14,098; the candidate adopts the text figure of 14,068, which is consistent with the stated exclusions, so this discrepancy is a paper typo rather than a model error . The candidate’s architectural remarks about Networks 13–14 reducing to a 2-node toggle-like design and being fragile are explicitly supported by the paper’s discussion .