Related papers: Asymptotics of a time bounded cylinder model

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…

In this paper are presented first results of a theoretical study on the role of non-monotone interactions in Boolean automata networks. We propose to analyse the contribution of non-monotony to the diversity and complexity in their…

In previous works, we introduced the notion of dominant vertices in the context of dynamical systems on networks. This is a set of nodes in the underlying network whose evolution determines the whole network's dynamics after a transient…

This work studies two types of computer networking models. The primary focus is to understand the different dynamical phenomena observed in practice due to the presence of severe nonlinearities, delays and widely varying operating…

Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…

It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network…

Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…

Biological processes, including cell differentiation, organism development, and disease progression, can be interpreted as attractors (fixed points or limit cycles) of an underlying networked dynamical system. In this paper, we study the…

The vast majority of strategies aimed at controlling contagion processes on networks considers the connectivity pattern of the system as either quenched or annealed. However, in the real world many networks are highly dynamical and evolve…

Typical properties of computing circuits composed of noisy logical gates are studied using the statistical physics methodology. A growth model that gives rise to typical random Boolean functions is mapped onto a layered Ising spin system,…

We prove a central limit theorem for network formation models with strategic interactions and homophilous agents. Since data often consists of observations on a single large network, we consider an asymptotic framework in which the network…

Many biological regulatory systems process signals out of steady state and respond with a physiological delay. A simple model of regulation which respects these features shows how the ability of a delayed output to transmit information is…

In practice, wireless networks are deployed over finite domains, the level of mobility is different at different locations, and user mobility is correlated over time. All these features have an impact on the temporal properties of…

Boolean network models of molecular regulatory networks have been used successfully in computational systems biology. The Boolean functions that appear in published models tend to have special properties, in particular the property of being…

We study a random resistors network model on a euclidean geometry $\bt{Z}^d$. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per…

We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…

We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…

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 wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…

Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget…