General Iteration graphs and Boolean automata circuits

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 deterministically, at each time step of a discretised time flow and according to a predefined order, we say that the network is updated according to block-sequential update schedule (blocks of elements are updated sequentially while, within each block, the elements are updated synchronously). Many studies, for the sake of simplicity and with some biologically motivated reasons, have concentrated on networks updated with one particular block-sequential update schedule (more often the synchronous/parallel update schedule or the sequential update schedules). The aim of this paper is to give an argument formally proven and inspired by biological considerations in favour of the fact that the choice of a particular update schedule does not matter so much in terms of the possible and likely dynamical behaviours that networks may display

On update schedules and dynamics of Boolean networks

Graduate internship repport supervised by Julio Aracena (rapport de stage de Master 1 dirigé par Julio Aracena)The dynamical properties of a Boolean network rely on several different parameters. In this document, we focus on three of them which are very closely tied to the definition itself of a Boolean network: the structure of a network, the type of local activation functions, and the update schedules. In other words, the dependencies between the elements of a network, the way each one of these elements is activated as a function of the other elements of the network and the order according to which the states of the elements of the network are updated.The central question of the work presented relates to the idea of the robustness of a Boolean network with respect to perturbations of its update schedule

Proposal for an Organic Web, The missing link between the Web and the Semantic Web, Part 1

A huge amount of information is produced in digital form. The Semantic Web stems from the realisation that dealing efficiently with this production requires getting better at interlinking digital informational resources together. Its focus is on linking data. Linking data isn't enough. We need to provide infrastructural support for linking all sorts of informational resources including resources whose understanding and fine interlinking requires domain-specific human expertise. At times when many problems scale to planetary dimensions, it is essential to scale coordination of information processing and information production, without giving up on expertise and depth of analysis, nor forcing languages and formalisms onto thinkers, decision-makers and innovators that are only suitable to some forms of intelligence. This article makes a proposal in this direction and in line with the idea of interlinking championed by the Semantic Web.Comment: Supplementary material by Guillaume Bouzige and Mathilde Noua

Block-sequential update schedules and Boolean automata circuits

International audienceOur work is set in the framework of complex dynamical systems and, more precisely, that of Boolean automata networks modeling regulation networks. We study how the choice of an update schedule impacts on the dynamics of such a network. To do this, we explain how studying the dynamics of any network updated with an arbitrary block-sequential update schedule can be reduced to the study of the dynamics of a different network updated in parallel. We give special attention to networks whose underlying structure is a circuit, that is, Boolean automata circuits. These particular and simple networks are known to serve as the "engines'' of the dynamics of arbitrary regulation networks containing them as sub-networks in that they are responsible for their variety of dynamical behaviours. We give both the number of attractors of period $p$, $\forall p\in \mathbb{N}$ and the total number of attractors in the dynamics of Boolean automata circuits updated with any block-sequential update schedule. We also detail the variety of dynamical behaviours that such networks may exhibit according to the update schedule