Related papers: Analysis of random Boolean networks using the aver…

The critical boundaries separating ordered from chaotic behavior in randomly wired S-state networks are calculated. These networks are a natural generalization of random Boolean nets and are proposed as on extended approach to genetic…

The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between…

This paper proposes and investigates a Boolean gossip model as a simplified but non-trivial probabilistic Boolean network. With positive node interactions, in view of standard theories from Markov chains, we prove that the node states…

Boolean networks are used to model biological networks such as gene regulatory networks. Often Boolean networks show very chaotic behavior which is sensitive to any small perturbations.In order to reduce the chaotic behavior and to attain…

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be…

Boolean networks have been successfully used in modelling gene regulatory networks. In this paper we propose a reduction method that reduces the complexity of a Boolean network but keeps dynamical properties and topological features and…

We derive mostly analytically the scaling behavior of the number of nonfrozen and relevant nodes in critical Kauffman networks (with two inputs per node) in the thermodynamic limit. By defining and analyzing a stochastic process that…

In this paper we consider a network of boolean agents that compete for a limited resource. The agents play the so called Generalized Minority Game where the capacity level is allowed to vary externally. We study the properties of such a…

The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study…

We study quantum neural networks made by parametric one-qubit gates and fixed two-qubit gates in the limit of infinite width, where the generated function is the expectation value of the sum of single-qubit observables over all the qubits.…

As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states…

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…

Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…

We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of…

We develop a general method to explore how the function performed by a biological network can constrain both its structural and dynamical network properties. This approach is orthogonal to prior studies which examine the functional…

Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…

Here we propose a generic mechanism - networked buffering - for generating robust traits in complex systems that requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role…

We show that the success of cooperation in an evolutionary prisoner's dilemma on a complex network can be predicted by a simple, quantitative network analysis using mean field parameters. The criterion is shown to be accurate on a wide…

Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean…

The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…