Related papers: Bounds on the Average Sensitivity of Nested Canali…
In this paper, we obtain complete characterization for nested canalyzing functions (NCFs) by obtaining its unique algebraic normal form (polynomial form). We introduce a new concept, LAYER NUMBER for NCF. Based on this, we obtain explicit…
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…
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…
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…
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…
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…
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…
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…
Based on a recent characterization of nested canalyzing function (NCF), we obtain the formula of the sensitivity of any NCF. Hence we find that any sensitivity of NCF is between $\frac{n+1}{2}$ and $n$. Both lower and upper bounds are…
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…
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…
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…
The complex dynamics of gene expression in living cells can be well-approximated using Boolean networks. The average sensitivity is a natural measure of stability in these systems: values below one indicate typically stable dynamics…
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…
Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on…
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…
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…
Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…
Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity. For both Boolean values $b\in\{0,1\}$, we…
Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity. For both Boolean values $b\in\{0,1\}$, we…