2501.07349
Predicting System Dynamics of Universal Growth Patterns in Complex Systems
Leila Hedayatifar, Alfredo J. Morales, Dominic E. Saadi, Rachel A. Rigg, Olha Buchel, Amir Akhavan, Egemen Sert, Aabir Abubaker Kar, Mehrzad Sasanpour, Irving R. Epstein, Yaneer Bar-Yam
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper specifies a joint specification p(t0,m′,A′)=p(A′|m′,t0)p(m′|t0)p(t0) with (i) uniform start times t0∈[0.32,1], (ii) a piecewise-constant p(m′|t0) with weights 0.57, 0.03, 0.40 and lower cutoff m′a(t0)=0.5+e^{1.5 t0^4}, and (iii) a Normal p(A′|m′,t0) whose mean/SD depend on m′ below 6.5 and are (1, ln(1.5)) above 6.5; it also states y(t)=A/(1+e^{−m(t−t0)}) and that the slope equals the gradient at the inflection time. These ingredients are all documented in the paper, but no explicit normalization or marginal derivations are carried out. The candidate solution correctly verifies normalization, derives the A′ marginal as a mixture, and provides E[A′], Var(A′) via the tower laws, and it confirms y′(t0)=Am/4, consistent with the paper’s description of the slope parameter. Hence both are consistent and correct, with the model supplying the missing derivations.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The probabilistic construction p(t0,m′,A′)=p(A′|m′,t0)p(m′|t0)p(t0) with uniform t0, piecewise p(m′|t0) and Normal p(A′|m′,t0) is well-posed and empirically justified; the sigmoid link y(t)=A/(1+e\^{−m(t−t0)}) with slope as the gradient at the inflection time is standard. The only gaps are expository: explicitly stating that the omitted m′ bands carry zero mass in the model, and offering a brief normalization note or appendix with the unconditional A′ mixture and basic moments would improve clarity without changing substance.