ArticlePhysica D. Nonlinear phenomena2007
Nested Canalyzing, Unate Cascade, and Polynomial Functions.
Article in Physica D. Nonlinear phenomena, 2007. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- BioLogical: a universal analysis framework for biosystem logical dynamics.Computational and structural biotechnology journal · 2026Article
- An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks?Journal of mathematical biology · 2025Article
- Preponderance of generalized chain functions in reconstructed Boolean models of biological networks.Scientific reports · 2024Article
- Relative importance of composition structures and biologically meaningful logics in bipartite Boolean models of gene regulation.Scientific reports · 2022Article
- Article
- Attractor detection and enumeration algorithms for Boolean networks.Computational and structural biotechnology journal · 2022Review
- Molecular network control through boolean canalization.EURASIP journal on bioinformatics & systems biology · 2015Article
- Robustness, canalyzing functions and systems design.Theory in biosciences = Theorie in den Biowissenschaften · 2014Article
- Properties of Boolean networks and methods for their tests.EURASIP journal on bioinformatics & systems biology · 2013Article
- Relative stability of network states in Boolean network models of gene regulation in development.Bio SystemsArticle
Corrections and comments
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Authors and funding
3 authors.
Funding
Abstract
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory networks. In the same context, polynomial functions over finite fields have been used to develop network inference methods for gene regulatory networks. Finally, unate cascade functions have been studied in the design of logic circuits and binary decision diagrams. This paper shows that the class of nested canalyzing functions is equal to that of unate cascade functions. Furthermore, it provides a description of nested canalyzing functions as a certain type of Boolean polynomial function. Using the polynomial framework one can show that the class of nested canalyzing functions, or, equivalently, the class of unate cascade functions, forms an algebraic variety which makes their analysis amenable to the use of techniques from algebraic geometry and computational algebra. As a corollary of the functional equivalence derived here, a formula in the literature for the number of unate cascade functions provides such a formula for the number of nested canalyzing functions.
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Registered trials
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