Related papers: Random maps and attractors in random Boolean netwo…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…
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…
Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the…
In the applications of Boolean networks to modeling biological systems, an important computational problem is the detection of the fixed points of these networks. This is an NP-complete problem in general. There have been various attempts…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
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…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Simplicity bias is an intriguing phenomenon prevalent in various input-output maps, characterized by a preference for simpler, more regular, or symmetric outputs. Notably, these maps typically feature high-probability outputs with simple…
Because the attractors of biological networks reflect stable behaviors (e.g., cell phenotypes), identifying control interventions that can drive a system towards its attractors (attractor control) is of particular relevance when controlling…
Despite the large quantity of information available, thorough researches in various biological databases are still needed in order to reconstruct and understand the steps that lead to known or new phenomena. By using protein-protein…
We study the target control of asynchronous Boolean networks, to identify efficacious interventions that can drive the dynamics of a given Boolean network from any initial state to the desired target attractor. Based on the application…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
The structure of ecological interactions is commonly understood through analyses of interaction networks. However, these analyses may be sensitive to sampling biases in both the interactors (the nodes of the network) and interactions (the…