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Classification of Random Boolean Networks
, 2002
"... We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and difference ..."
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Cited by 68 (14 self)
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We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and differences between different types of RBNs with the aid of a public software laboratory we developed. Particularly, we find that the point attractors are independent of the updating scheme, and that RBNs are more different depending on their determinism or nondeterminism rather than depending on their synchronicity or asynchronicity. We also show a way of mapping nonsynchronous deterministic RBNs into synchronous RBNs. Our results are important for justifying the use of specific types of RBNs for modelling natural phenomena.
Studying Artificial Life Using a Simple, General Cellular Model
, 1995
"... Some of the major outstanding problems in biology are related to issues of emergence and evolution. These include: (1) how do populations of organisms traverse their adaptive landscapes? (2) what is the relation between adaptedness and fitness? (3) the formation of multicellular organisms from basi ..."
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Cited by 23 (5 self)
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Some of the major outstanding problems in biology are related to issues of emergence and evolution. These include: (1) how do populations of organisms traverse their adaptive landscapes? (2) what is the relation between adaptedness and fitness? (3) the formation of multicellular organisms from basic units or cells. In this paper we study these issues using a model which is both general and simple. The system, derived from the CA (cellular automata) model, consists of a twodimensional grid of interacting organisms which may evolve over time. We first present designed multicellular organisms which display several interesting behaviors including: reproduction, growth, mobility. We then turn our attention to evolution in various environments, including: an environment in which competition for space occurs, an IPD (Iterated Prisoner's Dilemma) environment, an environment of spatial niches, and an environment of temporal niches. One of the advantages of AL models is the opportunities they...
Asynchronism induces second order phase transitions in elementary cellular automata
 Journal of Cellular Automata
"... Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the ..."
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Cited by 22 (8 self)
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Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For some particular rules, varying the synchrony rate continuously produces a qualitative change in the behaviour of the cellular automaton. We investigate the nature of this change of behaviour using MonteCarlo simulations. We show that this phenomenon is a secondorder phase transition, which we characterise more specifically as belonging to the directed percolation or to the parity conservation universality classes studied in statistical physics.
An experimental study of robustness to asynchronism for elementary cellular automata
 COMPLEX SYSTEMS
, 2005
"... Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cellscale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance ..."
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Cited by 22 (6 self)
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Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cellscale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully represent what happens at the microscopic scale for physical, biological or social systems. One may thus wonder whether CA do keep their behavior when submitted to small perturbations of synchronicity. This work focuses on the study of onedimensional (1D) asynchronous CA with two states and nearestneighbors. We define what we mean by “the behavior of CA is robust to asynchronism ” using a statistical approach with macroscopic parameters. and we present an experimental protocol aimed at finding which are the robust 1D elementary CA. To conclude, we examine how the results exposed can be used as a guideline for the research of suitable models according to robustness criteria.
On Incentives and Updating in Agent Based Models
, 1997
"... An economy consists of agents:... This paper demonstrates how the interplay between incentives and the timing of updating can alter findings significantly in economic models with neighborhood effects. The analysis considers cellular automata models in which the timing of updating is varied from sync ..."
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Cited by 20 (1 self)
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An economy consists of agents:... This paper demonstrates how the interplay between incentives and the timing of updating can alter findings significantly in economic models with neighborhood effects. The analysis considers cellular automata models in which the timing of updating is varied from synchronous,to random asynchronous,to incentive based asynchronous. Significant and interesting differences in the dynamics and steady states are found and explained under each updating rule. Cellular automata are unfamiliar...
Asynchronous Behavior of Doublequiescent Elementary Cellular Automata
"... Abstract. In this paper we propose a probabilistic analysis of the relaxation time of elementary finite cellular automata (i.e., {0, 1} states, radius 1 and unidimensional) for which both states are quiescent (i.e., (0, 0, 0) ↦ → 0 and (1, 1, 1) ↦ → 1), under αasynchronous dynamics (i.e., each cell ..."
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Cited by 18 (1 self)
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Abstract. In this paper we propose a probabilistic analysis of the relaxation time of elementary finite cellular automata (i.e., {0, 1} states, radius 1 and unidimensional) for which both states are quiescent (i.e., (0, 0, 0) ↦ → 0 and (1, 1, 1) ↦ → 1), under αasynchronous dynamics (i.e., each cell is updated at each time step independently with probability 0 < α � 1). This work generalizes previous work in [1], in the sense that we study here a continuous range of asynchronism that goes from full asynchronism to full synchronism. We characterize formally the sensitivity to asynchronism of the relaxation times for 52 of the 64 considered automata. Our work relies on the design of probabilistic tools that enable to predict the global behaviour by counting local configuration patterns. These tools may be of independent interest since they provide a convenient framework to deal exhaustively with the tedious case analysis inherent to this kind of study. The remaining 12 automata (only 5 after symmetries) appear to exhibit interesting complex phenomena (such as polynomial/exponential/infinite phase transitions). 1
Progresses in the Analysis of Stochastic 2D Cellular Automata: a Study of Asynchronous 2D Minority
, 706
"... Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under asynchronous updates. Still, the few mathematical analyses of as ..."
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Cited by 16 (4 self)
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Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under asynchronous updates. Still, the few mathematical analyses of asynchronism focus on onedimensional probabilistic cellular automata, either on single examples or on speci c classes. As for other classic dynamical systems in physics, extending known methods from one to twodimensional systems is a long lasting challenging problem. In this paper, we address the problem of analysing an apparently simple 2D asynchronous cellular automaton: 2D Minority where each cell, when red, updates to the minority state of its neighborhood. Our experiments reveal that in spite of its simplicity, the minority rule exhibits a quite complex response to asynchronism. By focusing on the fully asynchronous regime, we are however able to describe completely the asymptotic behavior of this dynamics as long as the initial con guration satis es some natural constraints. Besides these technical results, we have strong reasons to believe that our techniques relying on de ning an energy function from the transition table of the automaton may be extended to the wider class of threshold automata. 1
Evolving Asynchronous and Scalable Nonuniform Cellular Automata
 In Proceedings of International Conference on Artificial Neural Networks and Genetic Algorithms (ICANNGA97
, 1997
"... We have previously shown that nonuniform cellular automata (CA) can be evolved to perform computational tasks, using the cellular programming algorithm. In this paper we focus on two novel issues, namely the evolution of asynchronous CAs, and the scalability of our evolved systems. We find that as ..."
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Cited by 15 (3 self)
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We have previously shown that nonuniform cellular automata (CA) can be evolved to perform computational tasks, using the cellular programming algorithm. In this paper we focus on two novel issues, namely the evolution of asynchronous CAs, and the scalability of our evolved systems. We find that asynchrony presents a more difficult case for evolution though good CAs can still be attained. We describe an empiricallyderived scaling procedure by which successful CAs of any size may be obtained from a particular evolved system. Our motivation for this study stems in part by our desire to attain realistic systems that are more amenable to implementation as `evolving ware', evolware. 1 Introduction Cellular automata (CA) are dynamical systems in which space and time are discrete. A cellular automaton consists of an array of cells, each of which can be in one of a finite number of possible states, updated synchronously in discrete time steps according to a local, identical interaction rule...
Updating schemes in random Boolean networks: Do they really matter
 In Artificial Life IX
, 2004
"... In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the complexity reduction related to different updating schemes. We also ..."
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Cited by 14 (3 self)
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In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the complexity reduction related to different updating schemes. We also report that all updating schemes yield very similar critical stability values, meaning that the “edge of chaos ” does not depend much on the updating scheme. After discussion, we conclude that synchonous RBNs are justifiable theoretical models of biological networks.
Computation by asynchronously updating cellular automata
 Journal of Statistical Physics
, 2004
"... Abstract. A known method to compute on an asynchronously updating cellular automaton is the simulation of a synchronous computing model on it. Such a scheme requires not only an increased number of cell states, but also the simulation of a global synchronization mechanism. Asynchronous systems tend ..."
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Cited by 13 (4 self)
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Abstract. A known method to compute on an asynchronously updating cellular automaton is the simulation of a synchronous computing model on it. Such a scheme requires not only an increased number of cell states, but also the simulation of a global synchronization mechanism. Asynchronous systems tend to use synchronization only on a local scale—if they use it at all. Research on cellular automata that are truly asynchronous has been limited mostly to trivial phenomena, leaving issues such as computation unexplored. This paper presents an asynchronously updating cellular automaton that conducts computation without relying on a simulated global synchronization mechanism. The 2dimensional cellular automaton employs a Mooreneighborhood and 85 totalistic transition rules describing the asynchronous interactions between the cells. Despite the probabilistic nature of asynchronous updating, the outcome of the dynamics is deterministic. This is achieved by simulating delay insensitive circuits on it, a type of asynchronous circuit that is known for its robustness to variations in the timing of signals. We implement three primitive operators on the cellular automaton from which any arbitrary delay insensitive circuit can be constructed, and show how to connect the operators such that collisions of crossing signals are avoided.