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172
Abstract: Stability of the Kauffman Model
, 2001
"... Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which reduces the networks to their dynamical cores. The average size of the removed part, the stable core, grows approximately linearly with N, the number of nodes in the original networks. We show ..."
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Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which reduces the networks to their dynamical cores. The average size of the removed part, the stable core, grows approximately linearly with N, the number of nodes in the original networks. We show
Stability of the Kauffman Model
, 2001
"... : Random Boolean networks, the Kauman model, are revisited by means of a novel decimation algorithm, which reduces the networks to their dynamical cores. The average size of the removed part, the stable core, grows approximately linearly with N , the number of nodes in the original networks. We sho ..."
Abstract

Cited by 13 (0 self)
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: Random Boolean networks, the Kauman model, are revisited by means of a novel decimation algorithm, which reduces the networks to their dynamical cores. The average size of the removed part, the stable core, grows approximately linearly with N , the number of nodes in the original networks. We
The Kauffman model on SmallWorld Topology
, 2006
"... We apply Kauffman’s automata on smallworld networks to study the crossover between the shortrange and the infiniterange case. We perform accurate calculations on square lattices to obtain both critical exponents and fractal dimensions. Particularly, we find an increase of the damage propagation a ..."
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We apply Kauffman’s automata on smallworld networks to study the crossover between the shortrange and the infiniterange case. We perform accurate calculations on square lattices to obtain both critical exponents and fractal dimensions. Particularly, we find an increase of the damage propagation
Numerical and theoretical studies of noise effects in the Kauffman model
 J. Stat. Phys
, 2002
"... In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a similar kind of behavior, even when the structure of their basins ..."
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Cited by 6 (0 self)
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In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a similar kind of behavior, even when the structure of their basins
Closing probabilities in the Kauffman model: an annealed computation
, 2008
"... We define a probabilistic scheme to compute the distributions of periods, transients and weigths of attraction basins in Kauffman networks. These quantities are obtained in the framework of the annealed approximation, first introduced by Derrida and Pomeau. Numerical results are in good agreement wi ..."
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Cited by 14 (2 self)
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We define a probabilistic scheme to compute the distributions of periods, transients and weigths of attraction basins in Kauffman networks. These quantities are obtained in the framework of the annealed approximation, first introduced by Derrida and Pomeau. Numerical results are in good agreement
C.: Superpolynomial growth in the number of attractors in kauffman networks
 Physical Review Letters
, 2003
"... The Kauffman model describes a particularly simple class of random Boolean networks. Despite the simplicity of the model, it exhibits complex behavior and has been suggested as a model for real world network problems. This work is based on an earlier paper where we introduced a novel approach to ana ..."
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Cited by 33 (1 self)
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The Kauffman model describes a particularly simple class of random Boolean networks. Despite the simplicity of the model, it exhibits complex behavior and has been suggested as a model for real world network problems. This work is based on an earlier paper where we introduced a novel approach
The modular structure of Kauffman networks
, 2008
"... This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced and studied in our first paper [3], are subdivided. We show th ..."
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Cited by 24 (1 self)
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that the phase transition in Random Boolean Networks can also be described as a percolation transition. The statistical properties of the clusters of relevant elements (that we call modules) give an insight on the scaling behavior of the attractors of the critical networks that, according to Kauffman, have a
THE KAUFFMAN POLYNOMIAL AND TRIVALENT GRAPHS
"... Abstract. We construct a state model for the twovariable Kauffman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in R3. 1. ..."
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Cited by 1 (0 self)
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Abstract. We construct a state model for the twovariable Kauffman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in R3. 1.
Kauffman networks: Analysis and applications
 in Proceedings of the IEEE/ACM International Conference on ComputerAided Design
, 2005
"... Abstract — A Kauffman network is an abstract model of gene regulatory networks. Each gene is represented by a vertex. An edge from one vertex to another implies that the former gene regulates the latter. Statistical features of Kauffman networks match the characteristics of living cells. The number ..."
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Cited by 5 (2 self)
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Abstract — A Kauffman network is an abstract model of gene regulatory networks. Each gene is represented by a vertex. An edge from one vertex to another implies that the former gene regulates the latter. Statistical features of Kauffman networks match the characteristics of living cells. The number
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
Results 1  10
of
172