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The concept of a nested canalizing Boolean function has been studied over the course of the last decade in the context of understanding the regulatory logic of molecular interaction networks, such as gene regulatory networks. Such functions…

Boolean network models of molecular regulatory networks have been used successfully in computational systems biology. The Boolean functions that appear in published models tend to have special properties, in particular the property of being…

Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The…

Identifying features of molecular regulatory networks is an important problem in systems biology. It has been shown that the combinatorial logic of such networks can be captured in many cases by special functions called nested canalyzing in…

We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and…

Inferring dynamic biochemical networks is one of the main challenges in systems biology. Given experimental data, the objective is to identify the rules of interaction among the different entities of the network. However, the number of…

The canalizing properties of biological functions have been mainly studied in the context of Boolean modelling of gene regulatory networks. An important mathematical consequence of canalization is a low average sensitivity, which ensures in…

This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…

Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behavior which is sensitive to any small perturbations.In order to reduce the chaotic behavior and to attain…

Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behaviour which is sensitive to any small perturbations. In order to reduce the chaotic behaviour and to…

We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any activity ratio and we determine the functional form of this boundary which has a nontrivial fractal structure. We further observe that the…

Canalization is a key organizing principle in complex systems, particularly in gene regulatory networks. It describes how certain input variables exert dominant control over a function's output, thereby imposing hierarchical structure and…

Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…

This paper provides a collection of mathematical and computational tools for the study of robustness in nonlinear gene regulatory networks, represented by time- and state-discrete dynamical systems taking on multiple states. The focus is on…

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of…

We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…

Canalization of genetic regulatory networks has been argued to be favored by evolutionary processes due to the stability that it can confer to phenotype expression. We explore whether a significant amount of canalization and partial…

Many researchers have studied symmetry properties of various Boolean functions. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used to model certain biological phenomena. We identify some interesting…

Nested canalization (NC) is a property of Boolean functions which has been recently extended to multivalued functions. We study the effect of the Van Ham mapping (from multivalued to Boolean functions) on this property. We introduce the…

We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any given activity ratio and we characterize the sensitivity boundary which has a nontrivial fractal structure. We further observe, on an extensive…