Related papers: Relevant elments, Magnetization and Dynamical Prop…
This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced…
This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…
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…
The evaluation of the number of attractors in Kauffman networks by Samuelsson and Troein is generalized to critical networks with one input per node and to networks with two inputs per node and different probability distributions for update…
Random Boolean networks were introduced in 1969 by Kauffman as a model for gene regulation. By combining analytical arguments and efficient numerical simulations, we evaluate the properties of relevant components of critical random Boolean…
We investigate the influence of a deterministic but non-synchronous update on Random Boolean Networks, with a focus on critical networks. Knowing that ``relevant components'' determine the number and length of attractors, we focus on such…
Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over…
The critical Kauffman model with connectivity one is the simplest class of critical Boolean networks. Nevertheless, it exhibits intricate behavior at the boundary of order and chaos. We introduce a formalism for expressing the dynamics of…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
The Kauffman model of genetic computation highlights the importance of criticality at the border of order and chaos. The model with connectivity one is of special interest because it is exactly solvable. But our understanding of its…
We derive mostly analytically the scaling behavior of the number of nonfrozen and relevant nodes in critical Kauffman networks (with two inputs per node) in the thermodynamic limit. By defining and analyzing a stochastic process that…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advances, researchers have honed in on how the number of attractors…
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…
Neural networks are nowadays both powerful operational tools (e.g., for pattern recognition, data mining, error correction codes) and complex theoretical models on the focus of scientific investigation. As for the research branch, neural…
We apply Kauffman's automata on small-world networks to study the crossover between the short-range and the infinite-range case. We perform accurate calculations on square lattices to obtain both critical exponents and fractal dimensions.…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
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…
We study the properties of the distance between attractors in Random Boolean Networks, a prominent model of genetic regulatory networks. We define three distance measures, upon which attractor distance matrices are constructed and their…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…