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math.DS2026
A Bias-Corrected Weighted Logistic Model for Gene Regulatory Networks: Functional Equivalence with the Product-of-Logistics and Comparison with Weighted-Sum Formulations
Ismail Belgacem
We introduce a bias-corrected weighted-logistic (bcw) formulation for ODE models of gene regulatory networks. Each gene's regulatory function is a single sigmoid of…
math.DS2026
Beyond Linear Additive and Hill Functions: A General Logistic Reformulation of Delay-Coupled Gene Regulatory Networks with Equilibrium Analysis, Hopf Bifurcation, and Lipschitz Stability
Ismail Belgacem
Hill functions, dominant in gene regulatory network modeling, carry fundamental limitations: at non-integer cooperativity exponents, routine when fitting dose-response data, deriva…
math.DS2025
Exploring Logistic Functions as Robust Alternatives to Hill Functions in Genetic Network Modeling
Ismail Belgacem
Hill functions dominate gene regulatory network (GRN) modeling, but their fractional exponents create analytical pathologies when the Hill coefficient is non-integer -- a ubiqu…