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22
Robustness of the critical behaviour in a discrete stochastic reactiondiffusion medium
 in Proceedings of IWNC 2009
, 2010
"... Abstract. We study the steady states of a reactiondiffusion medium modelled by a stochastic 2D cellular automaton. We consider the GreenbergHastings model where noise and topological irregularities of the grid are taken into account. The decrease of the probability of excitation changes qualitati ..."
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Abstract. We study the steady states of a reactiondiffusion medium modelled by a stochastic 2D cellular automaton. We consider the GreenbergHastings model where noise and topological irregularities of the grid are taken into account. The decrease of the probability of excitation changes qualitatively the behaviour of the system from an “active” to an “extinct ” steady state. Simulations show that this change occurs near a critical threshold; it is identified as a nonequilibrium phase transition which belongs to the directed percolation universality class. We test the robustness of the phenomenon by introducing persistent defects in the topology: directed percolation behaviour is conserved. Using experimental and analytical tools, we suggest that the critical threshold varies as the inverse of the average number of neighbours per cell.
Gathering Agents on a Lattice by Coupling ReactionDiffusion
 and Chemotaxis, 2008, http://hal. inria.fr/inria00132266/en/. References in notes
"... We address the question as to which are the minimal ingredients to obtain a decentralised gathering of agents that move on a lattice. The agents and their environment are described with a stochastic model inspired from biology: the aggregation of the Dictyostelium discoideum cellular slime mold. The ..."
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We address the question as to which are the minimal ingredients to obtain a decentralised gathering of agents that move on a lattice. The agents and their environment are described with a stochastic model inspired from biology: the aggregation of the Dictyostelium discoideum cellular slime mold. The environment is an active lattice, of which cells transmit information according to a reactiondiffusion mechanism. The agents trigger excitations randomly; they move by following excitation fronts. We show that despite its simplicity this model exhibits interesting properties of selforganisation and allows to achieve the decentralised gathering. Moreover, observations show that the system has interesting robustness properties, as being able to resist to the presence of obstacles on the lattice and to resist to the addition of noise on the moves on the agents. keywords: decentralised gathering problem; pattern formation; bioinspired modelling; cellular automata; multiagent systems; selforganisation; reactiondiffusionchemotaxis; Dictyostelium discoideum; phase transitions foreword: Animations showing the experiments described in this article can be viewed at:
An FPGA Design for the Stochastic GreenbergHastings Cellular Automata
 in "International Conference on High Performance Computing & Simulation  HPCS 2010
, 2010
"... The stochastic GreenbergHastings cellular automaton is a model that mimics the propagation of reactiondiffusion waves in active media. Notably, this model undergoes a phase transition when the probability of excitation of a cell varies. We developed a specific FPGA design to study the critical beh ..."
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The stochastic GreenbergHastings cellular automaton is a model that mimics the propagation of reactiondiffusion waves in active media. Notably, this model undergoes a phase transition when the probability of excitation of a cell varies. We developed a specific FPGA design to study the critical behavior of this model. Using dedicated architectural optimizations, we obtain a significant speedup with respect to software simulation for lattice sizes of 512×512. We exploited this speedup to obtain improved estimations of the critical threshold.Our results indicate the existence of an asymptotic value of this threshold when the number of cell states increases.
Robustness of Cellular Automata in the Light of Asynchronous Information Transmission
, 2011
"... Cellular automata are classically synchronous: all cells are simultaneously updated. However, it has been proved that perturbations in the updating scheme may induce qualitative changes of behaviours. This paper presents a new type of asynchronism, the βsynchronism, where cells still update at each ..."
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Cellular automata are classically synchronous: all cells are simultaneously updated. However, it has been proved that perturbations in the updating scheme may induce qualitative changes of behaviours. This paper presents a new type of asynchronism, the βsynchronism, where cells still update at each time step but where the transmission of information between cells is disrupted randomly. We experimentally study the behaviour of βsynchronous models. We observe that, although many effects are similar to the perturbation of the update, novel phenomena occur. We particularly study phase transitions as an illustration of a qualitative variation of behaviour triggered by continuous change of the disruption probability β.
Probing robustness of cellular automata through variations of asynchronous updating
 Natural Computing (Online First
, 2012
"... Typically viewed as a deterministic model of spatial computing, cellular automata are here considered as a collective system subject to the noise inherent to natural computing. The classical updating scheme is replaced by stochastic versions which either randomly update cells or disrupt the cellto ..."
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Cited by 3 (2 self)
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Typically viewed as a deterministic model of spatial computing, cellular automata are here considered as a collective system subject to the noise inherent to natural computing. The classical updating scheme is replaced by stochastic versions which either randomly update cells or disrupt the celltocell transmission of information. We then use the novel updating schemes to probe the behaviour of Elementary Cellular Automata, and observe a wide variety of results. We study these behaviours in the scope of macroscopic statistical phenomena and microscopic analysis. Finally, we discuss the possibility to use updating schemes to probe the robustness of complex systems.
doi:10.1155/2009/639249 Research Article Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs
"... We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of the Dictyostelium discoideum cellular slime mold. The enviro ..."
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We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of the Dictyostelium discoideum cellular slime mold. The environment transmits information according to a reactiondiffusion mechanism and the agents move by following excitation fronts. Despite its simplicity this model exhibits interesting properties of selforganization and robustness to obstacles. We first describe the FPGA implementation of the environment alone, to perform large scale and rapid simulations of the complex dynamics of this reactiondiffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations. Copyright © 2009 Bernard Girau et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Author manuscript, published in "IWNC'09 (2009)" Critical phenomena in a discrete stochastic reactiondiffusion medium ∗
, 2009
"... reactiondiffusion media, stochastic cellular automata, phase trankeywords: sitions We study the steady states of a reactiondiffusion medium modelled by a stochastic 2D cellular automaton. We consider the GreenbergHastings model where noise and topological irregularities of the grid are taken int ..."
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reactiondiffusion media, stochastic cellular automata, phase trankeywords: sitions We study the steady states of a reactiondiffusion medium modelled by a stochastic 2D cellular automaton. We consider the GreenbergHastings model where noise and topological irregularities of the grid are taken into account. The decrease of the probability of excitation changes qualitatively the behaviour of the system from an “active ” to an “extinct ” steady state. Simulations show that this change occurs near a critical threshold; it is identified as a nonequilibrium phase transition which belongs to the directed percolation universality class. We test the robustness of the phenomenon by introducing persistent defects in the topology: directed percolation behaviour is conserved. Using experimental and analytical tools, we suggest that the critical threshold varies as the inverse of the average number of neighbours per cell. Foreword: See
Robustness of the Critical Behaviour in the Stochastic GreenbergHastings Cellular Automaton Model∗
, 2010
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2 3 4 5 6 RESEARCH ARTICLE Synchronous and Asynchronous Evaluation of Dynamic Neural Fields
, 2009
"... In [26], we’ve introduced a dynamic model of visual attention based on the Continuum Neural Field Theory [29] that explained attention as being an emergent property of a dynamic neural field. The fundamental property of the model is its facility to select a single stimulus out of several perfectly i ..."
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In [26], we’ve introduced a dynamic model of visual attention based on the Continuum Neural Field Theory [29] that explained attention as being an emergent property of a dynamic neural field. The fundamental property of the model is its facility to select a single stimulus out of several perfectly identical input stimuli by applying asynchronous computation. In the absence of external noise and with a zero initial state, the theoretical mathematical solution of the field equation predicts the final equilibrium state to equally represent all of the input stimuli. This finding is valid for synchronous numerical computation of the system dynamics where elements of the spatial field are computed all together at each time point. However, asynchronous computation, where elements of the spatial field are iterated in time one after the other yields different results leading the field to move towards a single stable input pattern. This behavior is in fact quite similar to the effect of noise on dynamic fields. The present work aims at studying this phenomenom in some details and characterizes the relation between noise, synchronous evaluation (the “regular ” mathematical integration) and asynchronous evaluation in the case of a simple dual particle system. More generally, we aim at explaining the behavior of a general differential equation system when it is considered as a set of particles