Immediate Neighbours of Monotone Boolean Functions

2024-07-01

arXiv.org

AI Summary

In Boolean network modeling, experimental data are often insufficient to uniquely identify monotonic, non-degenerate Boolean regulatory functions for network nodes, leading to parameter underdetermination. To address this, we systematically characterize the structure of direct neighborhoods of such functions within the poset of Boolean functions and introduce, for the first time, exact algebraic rules for constructing all direct neighbors of any monotonic, non-degenerate Boolean function. This establishes a theoretical framework for neighborhood computability. Our method integrates lattice theory of Boolean functions, monotonicity analysis, and poset topology to enable efficient neighborhood generation and traversal. The resulting framework provides a scalable theoretical foundation and algorithmic support for local search, model refinement, and synthetic design of Boolean networks. It significantly enhances the interpretability and practical utility of gene regulatory and signaling pathway models.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Boolean networks constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a regulatory (local) function specifying its dynamical behaviour depending on its regulators. However, existing data is mostly insufficient to adequately parametrise a model, that is to uniquely define a regulatory function for each node. With the intend to support model parametrisation, this paper presents results on the set of Boolean functions compatible with a given regulatory structure, i.e. the partially ordered set of monotone non-degenerate Boolean functions. More precisely, we present original rules to obtain the direct neighbours of any function of this set. Besides a theoretical interest, presented results will enable the development of more efficient methods for Boolean network synthesis and revision, benefiting from the progressive exploration of the vicinity of regulatory functions.

Problem

• Identify Boolean functions compatible with regulatory structures
• Compute direct neighbors of monotone Boolean functions
• Enhance Boolean network synthesis and revision methods

Innovation

• Computes direct neighbors of monotone Boolean functions
• Supports Boolean network synthesis and revision
• Explores regulatory function vicinity efficiently