Related papers: Relevant components in critical random Boolean net…
This paper proposes a new parameter for studying Boolean networks: the independence number. We establish that a Boolean network is $k$-independent if, for any set of $k$ variables and any combination of binary values assigned to them, there…
Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms…
Probabilistic Boolean networks (PBNs) is an important mathematical framework widely used for modelling and analysing biological systems. PBNs are suited for modelling large biological systems, which more and more often arise in systems…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
We consider robustness and percolation properties of the networks of networks, in which random nodes in different individual networks (layers) can be interdependent. We explore the emergence of the giant mutually connected component,…
Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…
A Boolean network is a finite state discrete time dynamical system. At each step, each variable takes a value from a binary set. The value update rule for each variable is a local function which depends only on a selected subset of…
In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or…
Boolean networks constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a…
We present new applications of parity inversion and time-reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal…
We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is…
The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the…
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…
The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…
We propose new activity-dependent adaptive Boolean networks inspired by the cis-regulatory mechanism in gene regulatory networks. We analytically show that our model can be solved for stationary in-degree distribution for a wide class of…
The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean…
Complex networks are often used to represent systems that are not static but grow with time: people make new friendships, new papers are published and refer to the existing ones, and so forth. To assess the statistical significance of…
Independent of the technology, it is generally expected that future nanoscale devices will be built from vast numbers of densely arranged devices that exhibit high failure rates. Other than that, there is little consensus on what type of…
When is it safe to approximate a complicated random Boolean network (RBN) as a simplified, easier to model RBN? When can static measures of network structure be reliably used to infer the network's dynamics? This simple experiment tests the…
This work explores the effects of relevant and irrelevant boolean variables on the accuracy of classifiers. The analysis uses the assumption that the variables are conditionally independent given the class, and focuses on a natural family…