Extended Data Fig. 10: Generalization of the k model.
From: Quantifying the dynamics of failure across science, startups and security
a, The α parameter connects the potential to improve (1 − x) with the likelihood of creating new versions p through p = (1 − x)α. b, Phase diagram of the k–α model. The two-dimensional parameter space is separated into three regimes, with boundaries at kα = 1 and (k − 1)α = 1. c, The impact of δ parameter on scaling exponent γ for given k = 1, 2, 3 and α = 0.4, 0.8, 1.2. We find that δ may affect the temporal scaling parameter when it is small, but has no further effect beyond a certain point δ* = min(α, 1/(k − 1)). d, Phase diagram of the k–α–δ model for k = 3, with boundaries at α = δ, (k − 1)δ = 1, (k − 1)δ + α = 1, kα = 1 and (k−1)α = 1, respectively.
