Related papers: Quantifying the complexity of random Boolean netwo…
In the load balancing problem, each node in a network is assigned a load, and the goal is to equally distribute the loads among the nodes, by preforming local load exchanges. While load balancing was extensively studied in static networks,…
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…
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…
The complex dynamics of gene expression in living cells can be well-approximated using Boolean networks. The average sensitivity is a natural measure of stability in these systems: values below one indicate typically stable dynamics…
This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological…
Since their introduction, Boolean networks have been traditionally studied in view of their rich dynamical behavior under different update protocols and for their qualitative analogy with cell regulatory networks. More recently, tools…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
Boolean networks are a general model of interacting entities, with applications to biological phenomena such as gene regulation. Attractors play a central role, and the schedule of entities update is a priori unknown. This article presents…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end Tononi et al.…
Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…
Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we…
A number of complexity measures for Boolean functions have previously been introduced. These include (1) sensitivity, (2) block sensitivity, (3) witness complexity, (4) subcube partition complexity and (5) algorithmic complexity. Each of…
The analysis of network data has gained considerable interest in recent years. This also includes the analysis of large, high-dimensional networks with hundreds and thousands of nodes. While exponential random graph models serve as…
We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…
Modularity is a quantity which has been introduced in the context of complex networks in order to quantify how close a network is to an ideal modular network in which the nodes form small interconnected communities that are joined together…
Chaos control in Random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. This paper…
We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of…
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…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…