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We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events…
We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…
A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The extinction and explosion probabilities and the mean extinction and…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Repulsive point processes arise in models where competition forces entities to be more spread apart than if placed independently. Simulation of these types of processes can be accomplished using dominated coupling from the past with a…
The analysis of the dynamics of a large class of excitable systems on locally tree-like networks leads to the conclusion that at $\lambda=1$ a continuous phase transition takes place, where $\lambda$ is the largest eigenvalue of the…
We study a "burst" event, i. e. the evolution of an initial condition having support only in a finite interval of k-space, in the continuum shell model due to Parisi. We show that the continuum equation without forcing or dissipation can be…
We investigate the crossing of an energy barrier by a self-propelled particle described by a Rayleigh friction term. We reveal the existence of a sharp transition in the external force field whereby the amplitude dramatically increases.…
The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics,…
Various classes of neurons alternate between high-frequency discharges and silent intervals. This phenomenon is called burst firing. To analyze burst activity in an insect system, grasshopper auditory receptor neurons were recorded in vivo…
We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
We introduce a model to study the delicate relation between the spreading of information and the formation of opinions in social systems. For this purpose, we propose a two-layer multiplex network model in which consensus dynamics takes…
We investigate the entanglement within a system undergoing a random, local process. We find that there is initially a phase of very fast generation and spread of entanglement. At the end of this phase the entanglement is typically maximal.…
A new automated method capable of accurately identifying bursting periods in single-point turbulent velocity field records is presented. Manual selection of the method sensitivity (tau*) and threshold (eT) are necessary for effective…
We construct the temporal network using the two-dimensional active particle systems which are described by the Vicsek model. The bursts of the interevent times for a specific pair of particles are investigated numerically. We find that for…
Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that…
Yet often neglected, dynamical interdependencies between concomitant contagion processes can alter their intrinsic equilibria and bifurcations. A particular case of interest for disease control is the emergence of explosive transitions in…
The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intensive activity followed by long times of no or reduced activity. The…
In this paper, we study a distributed parameter estimation problem with an asynchronous communication protocol over multi-agent systems. Different from traditional time-driven communication schemes, in this work, data can be transmitted…