Related papers: The Modular Structure of Kauffman Networks
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
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…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
We continue our consideration of a class of models describing the reversible dynamics of $N$ Boolean variables, each with $K$ inputs. We investigate in detail the behavior of the Hamming distance as well as of the distribution of orbit…
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.…
We analyze the synchronization transition for a pair of coupled identical Kauffman networks in the chaotic phase. The annealed model for Kauffman networks shows that synchronization appears through a transcritical bifurcation, and provides…
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,…
Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected…
We discuss duality properties of critical Boltzmann planar maps such that the degree of a typical face is in the domain of attraction of a stable distribution with parameter $\alpha\in(1,2]$. We consider the critical Bernoulli bond…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…
Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore,…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
In most systems, its division into interacting constituent elements gives rise to a natural network structure. Analyzing the dynamics of these elements and the topology of these natural graphs gave rise to the fields of (nonlinear) dynamics…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…