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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.
On the Limits of BottomUp Computer Simulation: Towards a Nonlinear Modeling Culture
, 2003
"... In the complexity and simulation communities there is growing support for the use of bottomup computerbased simulation in the analysis of complex systems. The presumption is that because these models are more complex than their linear predecessors they must be more suited to the modeling of system ..."
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Cited by 16 (3 self)
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In the complexity and simulation communities there is growing support for the use of bottomup computerbased simulation in the analysis of complex systems. The presumption is that because these models are more complex than their linear predecessors they must be more suited to the modeling of systems that appear, superficially at least, to be (compositionally and dynamically) complex. Indeed the apparent ability of such models to allow the emergence of collective phenomena from quite simple underlying rules is very compelling. But does this `evidence' alone `prove' that nonlinear bottomup models are superior to simpler linear models when considering complex systems behavior? Philosophical explorations concerning the efficacy of models, whether they be formal scientific models or our personal worldviews, has been a popular pastime for many philosophers, particularly philosophers of science. This paper offers yet another critique of modeling that uses the results and observations of nonlinear mathematics and bottomup simulation themselves to develop a modeling paradigm that is significantly broader than the traditional modelfocused paradigm. In this broader view of modeling we are encouraged to concern ourselves more with the modeling process rather than the (computer) model itself and embrace a nonlinear modeling culture. This emerging view of modeling also counteracts the growing preoccupation with nonlinear models over linear models.
N.: Complexity and information: Measuring emergence, selforganization, and homeostasis at multiple scales
 Complexity
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Asynchronous random Boolean network model based on elementary cellular automata
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"... This paper considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number k of parent nodes, which is fixed for all nodes. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. We make use of a Boolean ..."
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Cited by 6 (1 self)
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This paper considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number k of parent nodes, which is fixed for all nodes. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. We make use of a Boolean rule that is a generalization of rule 126 of elementary cellular automata. We provide formulae for the probability of finding a node in state 1 at a time t for the class of Asynchronous Random Boolean Networks (ARBN) in which only one node is updated at every time step, and for the class of Generalized ARBNs (GARBN) in which a random number of nodes can be updated at each time point. We use simulation methods to generate consecutive states of the network for both the real system and the models under the various schemes. The results match well. We study the dynamics of the models through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show, both theoretically and by example, that the ARBNs generate an ordered behavior regardless of the updating scheme used, whereas the GARBNs have behaviors that range from order to chaos depending on the type of random variable used to determine the number of nodes to be updated and the parameter combinations.
Computing networks: A general framework to contrast neural and swarm cognitions
 Paladyn, Journal of Behavioral Robotics
, 2010
"... This paper presents the Computing Networks (CNs) framework. CNs are used to generalize neural and swarm architectures. Artificial neural networks, ant colony optimization, particle swarm optimization, and realistic biological models are used as examples of instantiations of CNs. The description of t ..."
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Cited by 5 (5 self)
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This paper presents the Computing Networks (CNs) framework. CNs are used to generalize neural and swarm architectures. Artificial neural networks, ant colony optimization, particle swarm optimization, and realistic biological models are used as examples of instantiations of CNs. The description of these architectures as CNs allows their comparison. Their differences and similarities allow the identification of properties that enable neural and swarm architectures to perform complex computations and exhibit complex cognitive abilities. In this context, the most relevant characteristics of CNs are the existence multiple dynamical and functional scales. The relationship between multiple dynamical and functional scales with adaptation, cognition (of brains
Understanding robustness in random Boolean networks
 Artificial Life XI: Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems
, 2008
"... Long used as a framework for abstract modelling of genetic regulatory networks, the Random Boolean Network model possesses interesting robustnessrelated behaviour. We introduce coherency, a new measure of robustness based on a system’s state space, and defined as the probability of switching betw ..."
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Cited by 3 (0 self)
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Long used as a framework for abstract modelling of genetic regulatory networks, the Random Boolean Network model possesses interesting robustnessrelated behaviour. We introduce coherency, a new measure of robustness based on a system’s state space, and defined as the probability of switching between attraction basins due to perturbation. We show that this measure has both upper and randomcase bounds, and that these bounds are based on the size of individual attractor basins within the system. A mechanism for calculating these bounds is introduced, and the bounds are then used to define structural coherency, a measure of robustness attributable to system structure. Using these measures, we show that the decrease in coherency that occurs in the Random Boolean Network as its connectivity increases is related to a loss of structure in the system’s state space.
On the Dynamics of P Systems
 PREPROCEEDINGS OF FIFTH WORKSHOP IN MEMBRANE COMPUTING, WMC5
, 2004
"... P systems are considered in the dynamical perspective of biological and biochemical systems. In this sense, the focus of computational processes is in their behavioral patterns rather than in their final states encoding answers to initial inputs. The framework of "state transition dynamics&q ..."
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Cited by 2 (0 self)
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P systems are considered in the dynamical perspective of biological and biochemical systems. In this sense, the focus of computational processes is in their behavioral patterns rather than in their final states encoding answers to initial inputs. The framework of "state transition dynamics" is outlined where general dynamical concepts are formulated in completely discrete terms. A metabolic algorithm is defined which computes the evolution of P systems when initial states and reaction parameters are given. This algorithm is applied to the analysis of important oscillatory phenomena of biological interest.
Simulating Large Random Boolean Networks
, 2007
"... The Kauffman NK, or random boolean network, model is an important tool for exploring the properties of large scale complex systems. There are computational challenges in simulating large networks with high connectivities. We describe some highperformance data structures and algorithms for implemen ..."
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The Kauffman NK, or random boolean network, model is an important tool for exploring the properties of large scale complex systems. There are computational challenges in simulating large networks with high connectivities. We describe some highperformance data structures and algorithms for implementing largescale simulations of the random boolean network model using various storage types provided by the D programming language. We discuss the memory complexity of an optimised simulation code and present some measured properties of large networks.
Structural Circuits and Attractors in Kauffman Networks
"... There has been some ambiguity about the growth of attractors in Kauffman networks with network size. Some recent work has linked this to the role and growth of circuits or loops of boolean variables. Using numerical methods we have investigated the growth of structural circuits in Kauffman networks ..."
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Cited by 2 (0 self)
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There has been some ambiguity about the growth of attractors in Kauffman networks with network size. Some recent work has linked this to the role and growth of circuits or loops of boolean variables. Using numerical methods we have investigated the growth of structural circuits in Kauffman networks and suggest that the exponential growth in the number of structural circuits places a lower bound on the complexity of the growth of boolean dependency loops and hence of the number of attractors. We use a fast and exact circuit enumeration method that does not rely on sampling trajectories. We also explore the role of structural selfedges, or selfinputs in the NKmodel, and how they affect the number of structural circuits and hence of attractors.
Agents and MAS in STaMs
 In: Foundations and Applications of MultiAgent Systems: UKMAS 19962000 (ed
"... Abstract. We propose an abstract mathematical model of space and time within which to study agents, multiagent systems and their environments. The model is unusual in three ways: an attempt is made to reduce the structure and behaviour of agents and their environment to the properties of the “matte ..."
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Cited by 1 (1 self)
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Abstract. We propose an abstract mathematical model of space and time within which to study agents, multiagent systems and their environments. The model is unusual in three ways: an attempt is made to reduce the structure and behaviour of agents and their environment to the properties of the “matter ” of which they are composed, a “block time ” perspective is taken rather than a “past/present/future ” perspective, and the emphasis is placed on discovering agents within the model, rather than on designing agents into it. The model is developed in a little semiformal detail, some relevant experimental computational results are reported, and questions prompted by the model are discussed. 1