Related papers: Concurrency in Boolean networks
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…
Probabilistic Boolean Networks (PBNs) have been previously proposed so as to gain insights into complex dy- namical systems. However, identification of large networks and of the underlying discrete Markov Chain which describes their…
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…
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 recently introduced formalism of DB-nets has brought in a new conceptual way of modelling complex dynamic systems that equally account for the process and data dimensions, considering local data as well as persistent, transactional…
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…
In this paper we made a review of some papers about probabilistic regulatory networks (PRN), in particular we introduce our concept of homomorphisms of PRN with an example of projection of a regulatory network to a smaller one. We apply the…
In this paper we investigate a neural network model in which weights between computational nodes are modified according to a local learning rule. To determine whether local learning rules are sufficient for learning, we encode the network…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past…
A logical function can be used to characterizing a property of a state of Boolean network (BN), which is considered as an aggregation of states. To illustrate the dynamics of a set of logical functions, which characterize our concerned…
Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior…
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…
Different Boolean networks may reveal similar dynamics although their definition differs, then preventing their distinction from the observations. This raises the question about the sufficiency of a particular Boolean network for properly…
Biological networks such as gene regulatory networks possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated…
Bayesian Networks (BN) provide robust probabilistic methods of reasoning under uncertainty, but despite their formal grounds are strictly based on the notion of conditional dependence, not much attention has been paid so far to their use in…
Empirical evidence has revealed that biological regulatory systems are controlled by high-level coordination between topology and Boolean rules. In this study, we study the joint effects of degree and Boolean functions on the stability of…
A representation of the cause-effect mechanism is needed to enable artificial intelligence to represent how the world works. Bayesian Networks (BNs) have proven to be an effective and versatile tool for this task. BNs require constructing a…
Backpropagation (BP) is the standard algorithm for training the deep neural networks that power modern artificial intelligence including large language models. However, BP is energy inefficient and unlikely to be implemented by the brain.…
Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random…