Related papers: Generating Boolean Functions on Totalistic Automat…
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…
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…
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 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…
Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…
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…
Boolean networks are discrete dynamical systems in which the state (zero or one) of each node is updated at each time t to a state determined by the states at time t-1 of those nodes that have links to it. When these systems are used to…
When we focus on finite dynamical systems from both the computability/complexity and the modelling standpoints, automata networks seem to be a particularly appropriate mathematical model on which theory shall be developed. In this paper,…
This article is set in the field of regulation networks modeled by discrete dynamical systems. It focuses on Boolean automata networks. In such networks, there are many ways to update the states of every element. When this is done…
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…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is…
We simulate an actin filament as an automaton network. Every atom takes two or three states and updates its state, in discrete time, depending on a ratio of its neighbours in some selected state. All atoms/automata simultaneously update…
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…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
An automata network is a finite graph where each node holds a state from some finite alphabet and is equipped with an update function that changes its state according to the configuration of neighboring states. More concisely, it is given…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
A random boolean cellular automaton is a network of boolean gates where the inputs, the boolean function, and the initial state of each gate are chosen randomly. In this article, each gate has two inputs. Let $a$ (respectively $c$) be the…
Boolean networks are discrete dynamical systems where each automaton has its own Boolean function for computing its state according to the configuration of the network. The updating mode then determines how the configuration of the network…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…