Related papers: Random Boolean Networks
Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that…
Random Boolean networks (RBNs) have been a popular model of genetic regulatory networks for more than four decades. However, most RBN studies have been made with random topologies, while real regulatory networks have been found to be…
Given a Boolean network BN and a subset A of attractors of BN, we study the problem of identifying a minimal subset C of vertices of BN, such that the dynamics of BN can reach from a state s in any attractor As in A to any attractor At in A…
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…
In previous works, we introduced the notion of dominant vertices in the context of dynamical systems on networks. This is a set of nodes in the underlying network whose evolution determines the whole network's dynamics after a transient…
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…
Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the…
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…
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…
Boolean networks have been successfully used in modelling gene regulatory networks. In this paper we propose a reduction method that reduces the complexity of a Boolean network but keeps dynamical properties and topological features and…
This paper addresses the problem of finding cycles in the state transition graphs of synchronous Boolean networks. Synchronous Boolean networks are a class of deterministic finite state machines which are used for the modeling of gene…
A model of cellular metabolism due to S. Kauffman is analyzed. It consists of a network of Boolean gates randomly assembled according to a probability distribution. It is shown that the behavior of the network depends very critically on…
Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as…
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the…
The Kauffman model describes a particularly simple class of random Boolean networks. Despite the simplicity of the model, it exhibits complex behavior and has been suggested as a model for real world network problems. We introduce a novel…
Previous work in Boolean dynamical networks has suggested that the number of components that must be controlled to select an existing attractor is typically set by the number of attractors admitted by the dynamics, with no dependence on the…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a…