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We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in…
Stochastic reaction networks with mass-action kinetics provide a useful framework for understanding processes -- biochemical and otherwise -- in homogeneous environments. However, cellular reactions are often compartmentalized, either at…
Reaction networks are commonly used to model the evolution of populations of species subject to transformations following an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete…
A certain degree of inhibition is a common trait of dynamical networks in nature, ranging from neuronal and biochemical networks, to social and technological networks. We study here the role of inhibition in a representative dynamical…
Activated Random Walks, on $\mathbb{Z}^d$ for any $d\geqslant 1$, is an interacting particle system, where particles can be in either of two states: active or frozen. Each active particle performs a continuous-time simple random walk during…
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…
Living systems operate out of equilibrium, continuously consuming energy to sustain organised, functional states. Their emergent behaviour usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
We investigate, via Brownian dynamics simulations, the reaction dynamics of a simple, non-linear chemical network (the Willamowski-Rossler network) under spatial confinement and crowding conditions. Our results show that the presence of…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
Network structure strongly constrains the range of dynamic behaviors available to a complex system. These system dynamics can be classified based on their response to perturbations over time into two distinct regimes, ordered or chaotic,…
We study a stochastic two-species chemical reaction system with two mechanisms. One mechanism consists of chemical interactions which govern the overall drift of species amounts in the system; the other mechanism consists of resampling,…
We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-II intermittency and random dynamics. We analytically deduce the law for the distribution of the laminar…
We study a family of binary state, socially-inspired contagion models which incorporate imitation limited by an aversion to complete conformity. We uncover rich behavior in our models whether operating with either probabilistic or…
In this report trial-to-trial variations in the synchronized responses of neural networks are offered as evidence for excitation-inhibition ratio being a dynamic variable over time scales of minutes. Synchronized network responses to…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
Recent advances have shown that introducing dependency interactions between two superconducting networks can trigger abrupt, hysteretic normal-superconductor phase transitions. In this study, we demonstrate that such behavior can also arise…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
We consider a natural class of reaction networks which consist of reactions where either two species can inactivate each other (i.e., sequestration), or some species can be transformed into another (i.e., transmutation), in a way that gives…