Related papers: Scaling in ordered and critical random Boolean net…
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…
The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the…
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…
Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
During the last few years an area of active research in the field of complex systems is that of their information storing and processing abilities. Common opinion has it that the most interesting beaviour of these systems is found ``at the…
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…
We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even more specifically steady states of BNs. Steady states of BNs…
Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…
We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in Random Boolean…
The dynamics of Boolean networks (the N-K model) with scale-free topology are studied here. The existence of a phase transition governed by the value of the scale-free exponent of the network is shown analytically by analyzing the overlap…
We clarify the effect different sampling methods and weighting schemes have on the statistics of attractors in ensembles of random Boolean networks (RBNs). We directly measure cycle lengths of attractors and sizes of basins of attraction in…
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…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which reduces the networks to their dynamical cores. The average size of the removed part, the stable core, grows approximately linearly…
Boolean networks (BNs) are discrete-time systems where nodes are inter-connected (here we call such connection rule among nodes as network structure), and the dynamics of each gene node is determined by logical functions. In this paper, we…
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…
Characterization of the differences between biological and random networks can reveal the design principles that enable the robust realization of crucial biological functions including the establishment of different cell types. Previous…
In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…