Institute rhOne alpin des systemes complexes

Sainte-Foy-lès-Lyon, France

Institute rhOne alpin des systemes complexes

Sainte-Foy-lès-Lyon, France
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Demongeot J.,French National Center for Scientific Research | Demongeot J.,Institute Rhone alpin des Systemes Complexes | Noual M.,University of Lyon | Noual M.,Institute Rhone alpin des Systemes Complexes | And 2 more authors.
24th IEEE International Conference on Advanced Information Networking and Applications Workshops, WAINA 2010 | Year: 2010

In line with fields of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is, Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on the number of attractors of Boolean automata circuits. We prove how to obtain formally the exact value of the total number of attractors of a circuit of arbitrary size n as well as, for every positive integer p, the number of its attractors of period p depending on whether the circuit has an even or an odd number of inhibitions. As a consequence, we obtain that both numbers depend only on the parity of the number of inhibitions and not on their distribution along the circuit. © 2010 IEEE.


Demongeot J.,Joseph Fourier University | Demongeot J.,Institute rhOne alpin des systemes complexes | Elena A.,Joseph Fourier University | Noual M.,University of Lyon | And 4 more authors.
Journal of Theoretical Biology | Year: 2011

This paper proposes a study of biological regulation networks based on a multi-level strategy. Given a network, the first structural level of this strategy consists in analysing the architecture of the network interactions in order to describe it. The second dynamical level consists in relating the patterns found in the architecture to the possible dynamical behaviours of the network. It is known that circuits are the patterns that play the most important part in the dynamics of a network in the sense that they are responsible for the diversity of its asymptotic behaviours. Here, we pursue further this idea and argue that beyond the influence of underlying circuits, intersections of circuits also impact significantly on the dynamics of a network and thus need to be payed special attention to. For some genetic regulation networks involved in the control of the immune system ("immunetworks"), we show that the small number of attractors can be explained by the presence, in the underlying structures of these networks, of intersecting circuits that "inter-lock". © 2011 Elsevier Ltd.


Melliti T.,University of Évry Val d'Essonne | Regnault D.,University of Évry Val d'Essonne | Richard A.,University of Nice Sophia Antipolis | Sene S.,University of Évry Val d'Essonne | Sene S.,Institute Rhone alpin des Systemes Complexes
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2013

Since the 1980's, automata networks have been at the centre of numerous studies, from both theoretical (around the computational abilities) and applied (around the modelling power of real phenomena) standpoints. In this paper, basing ourselves on the seminal works of Robert and Thomas, we focus on a specific family of Boolean automata networks, those without negative cycles. For these networks, subjected to both asynchronous and elementary updating modes, we give new answers to well known problems (some of them having already been solved) about their convergence towards stable configurations. For the already solved ones, the proofs given are much simpler and neater than the existing ones. For the others, in any case, the proofs presented are constructive. © 2013 Springer-Verlag.


Martin F.M.P.,Aix - Marseille University | Martin F.M.P.,University of Lyon | Martin F.M.P.,Institute Rhone Alpin des Systemes Complexes
Psychological Methods | Year: 2013

I introduce the Bayesian assessment of scaling (BAS), a simple but powerful Bayesian hypothesis contrast methodology that can be used to test hypotheses on the scaling regime exhibited by a sequence of behavioral data. Rather than comparing parametric models, as typically done in previous approaches, the BAS offers a direct, nonparametric way to test whether a time series exhibits fractal scaling. The BAS provides a simpler and faster test than do previous methods, and the code for making the required computations is provided. The method also enables testing of finely specified hypotheses on the scaling indices, something that was not possible with the previously available methods. I then present 4 simulation studies showing that the BAS methodology outperforms the other methods used in the psychological literature. I conclude with a discussion of methodological issues on fractal analyses in experimental psychology. © 2013 American Psychological Association.


Demongeot J.,Joseph Fourier University | Elena A.,Joseph Fourier University | Noual M.,Ecole Normale Superieure de Lyon | Noual M.,Institute Rhone alpin des Systemes Complexes | And 2 more authors.
Proceedings - 25th IEEE International Conference on Advanced Information Networking and Applications Workshops, WAINA 2011 | Year: 2011

The multi-scale strategy in studying biological regulatory networks analysis is based on two level of analysis. The first level is structural and consists in examining the architecture of the interaction graph underlying the network and the second level is functional and analyse the regulatory properties of the network. We apply this dual approach to the "immunetworks" involved in the control of the immune system. As a result, we show that the small number of attractors of these networks is due to the presence of intersecting circuits in their interaction graphs. We obtain an upper bound of the number of attractors of the whole network by multiplying the number of attractors of each of its strongly connected components. We detect first the strongly connected components in the architecture of the interaction digraph of the network. Secondly, we study the dynamical function of the attractors by looking further inside these components, notably when they form circuits (intersecting or not). © 2011 IEEE.


Melliti T.,University of Évry Val d'Essonne | Noual M.,Aix - Marseille University | Regnault D.,University of Évry Val d'Essonne | Sene S.,Aix - Marseille University | And 2 more authors.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2015

Because interaction networks occupy more and more space in our current life (social networks) and in our understanding of living systems(biological regulation networks), it seems necessary to develop the knowledge regarding them. By using Boolean automata networks as models of interaction networks, we present new results about the influence of cycles on their dynamics. Cycles in the architecture of boolean networks are known to be the primary engine of dynamical complexity. As a first particular case, we focus on cycle intersections and provide a characterisation of the dynamics of asynchronous Boolean automata networks composed of two cycles that intersect at one automaton. To do so, we introduce an efficient formalism inspired by algorithms to define long sequences of updates, which allows a more efficient description of their dynamics. © Springer International Publishing Switzerland 2015


Comet J.-P.,University of Nice Sophia Antipolis | Noual M.,University of Nice Sophia Antipolis | Richard A.,University of Nice Sophia Antipolis | Aracena J.,University of Concepción | And 7 more authors.
Bulletin of Mathematical Biology | Year: 2013

It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it "generates" several stable states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of "generates." Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results. © 2013 Society for Mathematical Biology.


Noual M.,University of Lyon | Noual M.,Institute Rhone alpin des Systemes Complexes | Regnault D.,University of Évry Val d'Essonne | Sene S.,University of Évry Val d'Essonne | Sene S.,Institute Rhone alpin des Systemes Complexes
Theoretical Computer Science | Year: 2013

This paper aims at presenting motivations and first results of a prospective theoretical study on the role of non-monotone interactions in the modelling process of biological regulation networks. Focusing on discrete models of these networks, namely, Boolean automata networks, we propose to analyse the contribution of non-monotony to the diversity and complexity in their dynamical behaviours. More precisely, in this paper, we start by detailing some motivations, both mathematical and biological, for our interest in non-monotony, and we discuss how it may account for phenomena that cannot be produced by monotony only. Then, to build some understanding in this direction, we show some preliminary results on the dynamical behaviours of some specific non-monotone Boolean automata networks called xor circulant networks. © 2012 Elsevier B.V. All rights reserved.


Noual M.,University of Lyon | Noual M.,Institute Rhone alpin des Systemes Complexes
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2012

This paper presents a combinatorial study to characterise the dynamics of intersecting Boolean automata circuits and more specifically that of double Boolean automata circuits. Explicit formulae are given to count the number of periodic configurations and attractors of these networks and a conjecture proposes a comparison between the number of attractors of isolated circuits and that of double circuits. The aim of this study is to give intuition on the way circuits interact and how a circuits intersection modifies the "degrees of freedom" of the overall network. © 2012 Springer-Verlag.


Delaplace F.,University of Évry Val d'Essonne | Klaudel H.,University of Évry Val d'Essonne | Melliti T.,University of Évry Val d'Essonne | Sene S.,University of Évry Val d'Essonne | Sene S.,Institute Rhone alpin des Systemes Complexes
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2012

This paper investigates questions related to modularity in biological interaction networks. We develop a discrete theoretical framework based on the analysis of the asymptotic dynamics of biological interaction networks. More precisely, we exhibit formal conditions under which agents of interaction networks can be grouped into modules, forming a modular organisation. Our main result is that the conventional decomposition into strongly connected components fulfills the formal conditions of being a modular organisation. We also propose a modular and incremental algorithm for an efficient equilibria computation. Furthermore, we point out that our framework enables a finer analysis providing a decomposition in elementary modules, possibly smaller than strongly connected components. © 2012 Springer-Verlag.

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