Related papers: Influence and Dynamic Behavior in Random Boolean N…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
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…
Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Societies are quintessential open systems, shaped by internal dynamics as well as external influences. The question is how these external influences alter the collective behavior and network dynamics. To answer this, we investigate…
For years, we have been building models of gene regulatory networks, where recent advances in molecular biology shed some light on new structural and dynamical properties of such highly complex systems. In this work, we propose a novel…
We examined the effects of inhomogeneity on the dynamics and structural properties using Boolean networks. Two different power-law rank outdegree distributions were embedded to determine the role of hubs. The degree of randomness and…
We investigate the effect of noise on Random Boolean Networks. Noise is implemented as a probability $p$ that a node does not obey its deterministic update rule. We define two order parameters, the long-time average of the Hamming distance…
This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
Boolean networks, first developed in the late 1960s as a tool for studying complex disordered dynamical systems, consist of nodes governed by Boolean functions whose evolution is entirely deterministic in that the state of the network at a…
Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive…
We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…
Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by…
A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…