Related papers: Kauffman networks with threshold functions

To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…

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…

We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly…

We show that to correctly describe the position of the critical line in the Kauffman random boolean networks one must take into account percolation phenomena underlying the process of damage spreading. For this reason, since the issue of…

There are three main aims of this paper. 1- I explain reasons why I await life to lie significantly deeper in chaos than Kauffman approach does, however still in boundary area near `the edge of chaos and order'. The role of negative…

Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…

Chaos control in Random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. This paper…

In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…

In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural…

In a series of articles published in 1986 Derrida, and his colleagues studied two mean field treatments (the quenched and the annealed) for \textit{NK}-Kauffman Networks. Their main results lead to a phase transition curve $ K_c \, 2 \, p_c…

We consider a model for heterogeneous 'gene regulatory networks' that is a generalization of the model proposed by Chatterjee and Durrett (2011) as an "annealed approximation" of Kauffmann's (1969) random Boolean networks. In this model,…

The weights of a neural network are typically initialized at random, and one can think of the functions produced by such a network as having been generated by a prior over some function space. Studying random networks, then, is useful for a…

The complex dynamics of gene expression in living cells can be well-approximated using Boolean networks. The average sensitivity is a natural measure of stability in these systems: values below one indicate typically stable dynamics…

The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…

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…

We study the diversity of complex spatio-temporal patterns of random synchronous asymmetric neural networks (RSANNs). Specifically, we investigate the impact of noisy thresholds on network performance and find that there is a narrow and…

Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…

Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…

During the last few years an area of active research in the field of complex systems is that of their information storing and processing abilities. Common opinion has it that the most interesting beaviour of these systems is found ``at the…