Related papers: The phase diagram of random Boolean networks with …
We prove that the fully asynchronous dynamics of a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ without negative loop can be simulated, in a very specific way, by a monotone Boolean network with $2n$ components. We then use this result to…
We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of…
We discuss, in this paper, the dynamical properties of extremely diluted, non-monotonic neural networks. Assuming parallel updating and the Hebb prescription for the synaptic connections, a flow equation for the macroscopic overlap is…
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped…
Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give…
We consider a model recently proposed by Chatterjee and Durrett [CD2011] as an "annealed approximation" of boolean networks, which are a class of cellular automata on a random graph, as defined by S. Kauffman [K69]. The starting point is a…
We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical…
Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of \textit{S. cerevisiae} and \textit{S. pombe}.…
We calculate the network fluid regime and phase diagrams of binary mixtures of patchy colloids, using Wertheim's first order perturbation theory and a generalization of Flory-Stockmayer's theory of polymerization. The colloids are modelled…
Gene regulatory networks exhibit remarkable stability, maintaining functional phenotypes despite genetic and environmental perturbations. Discrete dynamical models, such as Boolean networks, provide systems biologists with a tractable…
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
Standard Random Boolean Networks display an order-disorder phase transition. We add to the standard Random Boolean Networks a disconnection rule which couples the control and order parameters. By this way, the system is driven to 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, first developed in the late 1960s as a tool for studying complex disordered dynamical systems, consist of nodes governed by Boolean functions whose evolution is entirely deterministic in that the state of the network at a…
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…
Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline…
The analysis of the dynamics of a large class of excitable systems on locally tree-like networks leads to the conclusion that at $\lambda=1$ a continuous phase transition takes place, where $\lambda$ is the largest eigenvalue of the…
We consider a model for gene regulatory networks that is a modification of Kauffmann's (1969) random Boolean networks. There are three parameters: $n =$ the number of nodes, $r =$ the number of inputs to each node, and $p =$ the expected…
Many biological systems, such as metabolic pathways, exhibit bistability behavior: these biological systems exhibit two distinct stable states with switching between the two stable states controlled by certain conditions. Since…
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…