Pre-Publicación 2025-27
Julio Aracena, Katerin De La Hoz, Alexis Poindron, Lilian Salinas:
An exploratory approach to the compatibility and inference of unate functions
Abstract:
Unate functions arise naturally in diverse areas of mathematics and computer science and play a central role in the modeling of gene regulatory systems with Boolean networks, where each regulator acts as an inducer or a repressor. Inferring such functions from observational data is a fundamental task that has been primarily approached from a biological perspective. We address the problem of determining whether there exists a unate function compatible with a set of observations by introducing two central concepts: the multiset of discrepancies and the coverage vector. We demonstrate that the existence of a covering vector is a necessary and sufficient condition for solving the unate compatibility problem, and we characterize the entire space of functions associated with a coverage vector, thereby formalizing the unate inference process. We propose two complementary algorithms: a coverage algorithm that efficiently constructs sparse coverage vectors, and an exploratory algorithm that analyzes collections of coverage solutions to identify patterns of influence and derive representative quasi-solutions. Experiments on synthetic datasets demonstrate scalability and feasibility, while the Drosophila ventral furrow case study indicates that, together, the algorithms constitute an exploratory approach for Boolean network inference when information is limited to observations and that they have the potential to systematically explore plausible regulatory architectures. Keywords: Unate Boolean functions, Coverage vector, Gene regulatory systems, Boolean networks, Inference.
