Related papers: Asymptotics of a time bounded cylinder model
A random boolean cellular automaton is a network of boolean gates where the inputs, the boolean function, and the initial state of each gate are chosen randomly. In this article, each gate has two inputs. Let $a$ (respectively $c$) be the…
We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
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…
We develop a probabilistic framework for global modeling of the traffic over a computer network. This model integrates existing single-link (-flow) traffic models with the routing over the network to capture the global traffic behavior. It…
Monotone systems, also known as order-preserving or cooperative systems, are prevalent in models of engineering applications such as transportation and biological networks. In this paper, we investigate the problem of finding a control…
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…
Deterministic and stochastic Boolean network models are build for the dynamics of negative feedback loops of the p53 pathways. It is shown that the main function of the negative feedback in the p53 pathways is to keep p53 at a low steady…
Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method.…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
The paper is concerned with the interplay between network structure and traffic dynamics in a communications network, from the viewpoint of end-to-end performance of packet transfer. We use a model of network generation that allows the…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
A class of dynamic threshold models is proposed, for describing the upset of collective actions in social networks. The agents of the network have to decide whether to undertake a certain action or not. They make their decision by comparing…
The paper investigates the throughput behavior of single-commodity dynamical flow networks governed by monotone distributed routing policies. The networks are modeled as systems of ODEs based on mass conversation laws on directed graphs…
We discuss the ability of a network with non linear relays and chaotic dynamics to transmit signals, on the basis of a linear response theory developed by Ruelle \cite{Ruelle} for dissipative systems. We show in particular how the dynamics…
As generalizations of random graphs, random simplicial complexes have been receiving growing attention in the literature. In this paper, we naturally extend the Random Connection Model (RCM), a random graph that has been extensively studied…
Entanglement, a fundamental feature of quantum mechanics, has long been recognized as a valuable resource in enabling secure communications and surpassing classical limits. However, previous research has primarily concentrated on static…
The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between…