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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. Source


Melliti T.,University of Evry Val dEssonne | Noual M.,Aix - Marseille University | Regnault D.,University of Evry Val dEssonne | 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 Source


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. Source


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. Source


Delaplace F.,University of Evry Val dEssonne | Klaudel H.,University of Evry Val dEssonne | Melliti T.,University of Evry Val dEssonne | Sene S.,University of Evry Val dEssonne | 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. Source

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