Related papers: Dynamics of Boolean networks - an exact solution
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the…
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…
The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean…
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…
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 constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a…
Since their introduction, Boolean networks have been traditionally studied in view of their rich dynamical behavior under different update protocols and for their qualitative analogy with cell regulatory networks. More recently, tools…
A first step is taken towards understanding often observed non-robustness phenomena of deep neural net (DNN) classifiers. This is done from the perspective of Boolean functions by asking if certain sequences of Boolean functions represented…
Boolean network models of molecular regulatory networks have been used successfully in computational systems biology. The Boolean functions that appear in published models tend to have special properties, in particular the property of being…
We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We…
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…
We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network…
We study classes of dynamical systems that can be obtained by constructing recursive networks with monotone Boolean functions. Stack filters in nonlinear signal processing are special cases of such systems. We show an analytical connection…
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…
Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component…
Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their…
Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive…