Related papers: Dynamical Instability in Boolean Networks as a Per…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or…
Boolean networks have been widely used to explore aspects of gene regulation, traditionally with a single network. A modified form of the model to explore the effects of increasing the number of gene states has also recently been…
Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions (from molecules in gene regulatory…
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…
Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline…
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…
Probabilistic Boolean Networks have been proposed for estimating the behaviour of dynamical systems as they combine rule-based modelling with uncertainty principles. Inferring PBNs directly from gene data is challenging however, especially…
Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without any closer correspondence to each other. With the example system of the fission yeast cell cycle control…
The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the…
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…
Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…
Many discrete models of biological networks rely exclusively on Boolean variables and many tools and theorems are available for analysis of strictly Boolean models. However, multilevel variables are often required to account for threshold…
We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be controlled to drive its dynamics from an initial steady state (or attractor) to a target steady state. Due to the phenomenon…
Boolean Networks and their dynamics are of great interest as abstract modeling schemes in various disciplines, ranging from biology to computer science. Whereas parallel update schemes have been studied extensively in past years, the level…
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…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of \textit{S. cerevisiae} and \textit{S. pombe}.…