{"paper":{"title":"A Bias-Corrected Weighted Logistic Model for Gene Regulatory Networks: Functional Equivalence with the Product-of-Logistics and Comparison with Weighted-Sum Formulations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ismail Belgacem","submitted_at":"2026-06-03T10:39:18Z","abstract_excerpt":"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 $\\sigma(\\lambda S_i+\\lambda b_i)$ of the signed weighted regulator sum $S_i$, with a combinatorial bias $b_i=-\\lambda^{-1}\\log(2^{m_i}-1)$ depending only on the in-degree $m_i$ and the steepness $\\lambda$. We prove this is the unique single-sigmoid correction recovering the critical-point value $1/2^{m_i}$ of the product-of-logistics model and sharing its canonical equilibrium $x_i^*=\\kappa_i/(\\gamma_i 2^{m_i})$ under self-consistency"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04709","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04709/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}