Related papers: The phase diagram of random Boolean networks with …
We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but…
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…
The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations.…
Boolean Networks have been used to study numerous phenomena, including gene regulation, neural networks, social interactions, and biological evolution. Here, we propose a general method for determining the critical behavior of Boolean…
We consider a model for heterogeneous 'gene regulatory networks' that is a generalization of the model proposed by Chatterjee and Durrett (2011) as an "annealed approximation" of Kauffmann's (1969) random Boolean networks. In this model,…
Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive…
We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
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…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
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…
We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We…
Boolean networks are discrete dynamical systems in which the state (zero or one) of each node is updated at each time t to a state determined by the states at time t-1 of those nodes that have links to it. When these systems are used to…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
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…
Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of…
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…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
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…
We investigate the effect of noise on Random Boolean Networks. Noise is implemented as a probability $p$ that a node does not obey its deterministic update rule. We define two order parameters, the long-time average of the Hamming distance…