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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 49 (8 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 11 (2 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.
Asynchronous random Boolean network model based on elementary cellular automata
 REV. E
"... 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 3 (0 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.
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" is ou ..."
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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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Cited by 2 (0 self)
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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.
Finding Agents in a TwoDimensional Boolean STaM
 In: Artificial Intelligence and Cognitive Science, Proceeding of the 13 th Irish Conference, AICS 2000
"... Abstract. A simple discrete mathematical model of a space, time and matter manifold, called a STaM, is described which is intended as a framework within which to study agents and multiagent systems. In this paper we concentrate on twodimensional Boolean STaMs, and report implemented algorithms for ..."
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Cited by 1 (1 self)
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Abstract. A simple discrete mathematical model of a space, time and matter manifold, called a STaM, is described which is intended as a framework within which to study agents and multiagent systems. In this paper we concentrate on twodimensional Boolean STaMs, and report implemented algorithms for detecting agents within them. A specific example STaM is given, some experimental results presented, and conclusions drawn. 1
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
ABSTRACT Simulating Large Random Boolean Networks
"... 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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Cited by 1 (0 self)
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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. KEY WORDS random boolean network; time series analysis; high memory; simulation. 1
Macroscopicorde From Reversible and Stochastic Lattice Growth Models
, 1999
"... This thesis advances the understanding of how autonomous microscopic physical processes give rise to macroscopic structure. A unifying theme is the use of physically motivated microscopic models of discrete systems which incorporate the constraints of locality, uniformity, and exact conservation law ..."
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This thesis advances the understanding of how autonomous microscopic physical processes give rise to macroscopic structure. A unifying theme is the use of physically motivated microscopic models of discrete systems which incorporate the constraints of locality, uniformity, and exact conservation laws. The features studied include: stochastic nonequilibrium fluctuations; use of pseudorandomness in dynamical simulations; the thermodynamics of pattern formation; recurrence times of finite discrete systems; and computation in physical models. I focus primarily on pattern formation: transitions from a disordered to an ordered macroscopic state. Using an irreversible stochastic model of pattern formation in an open system driven by an external source of noise, I study thin film growth. I focus on the regimes of growth and the average properties of the resulting rough surfaces. I also show that this model couples sensitively to the imperfections of various pseudorandom number generators...
Development of a Framework for Managing the Technology Adoption Life Cycle Using Chaos and Complexity Theories
"... Unlike more stable industries, hightech firms must constantly be in a strategy development phase. These companies are in desperate need of assistance in strategy formulation. Chaos and Complexity theories can provide a powerful approach to support the development of business strategies to deal with ..."
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Unlike more stable industries, hightech firms must constantly be in a strategy development phase. These companies are in desperate need of assistance in strategy formulation. Chaos and Complexity theories can provide a powerful approach to support the development of business strategies to deal with these fastmoving environments. This paper analyzes the different schemes provided by Chaos and Complexity theories and their possible applications to study cycles of products, processes, and organizational innovations in the hightech industries. This analysis includes the definitions and previous work accomplished in similar areas. In addition, a case study is selected (the disk drive industry) and preliminary work using attractors, phase diagrams and neural networks is discussed.