Related papers: The phase diagram of random Boolean networks with …
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…
Threshold networks are used as models for neural or gene regulatory networks. They show a rich dynamical behaviour with a transition between a frozen and a chaotic phase. We investigate the phase diagram of randomly connected threshold…
In this work we consider random Boolean networks that provide a general model for genetic regulatory networks. We extend the analysis of James Lynch who was able to proof Kauffman's conjecture that in the ordered phase of random networks,…
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…
The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean…
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 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…
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…
We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown…
We investigate Threshold Random Boolean Networks with $K = 2$ inputs per node, which are equivalent to Kauffman networks, with only part of the canalyzing functions as update functions. According to the simplest consideration these networks…
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…
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…
Chaos control in Random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. This paper…
Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior…
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…
Nested canalizing Boolean (NCF) functions play an important role in biological motivated regulative networks and in signal processing, in particular describing stack filters. It has been conjectured that NCFs have a stabilizing effect on…
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
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…