Related papers: Hitting times of threshold exceedances and their d…
In complex networks there are overlapping substructures or "circles" that consist of nodes belonging to multiple cohesive subgroups. Yet the role of these overlapping nodes in influence spreading processes remains underexplored. In the…
Threshold cascade models have been used to describe spread of behavior in social networks and cascades of default in financial networks. In some cases, these networks may have multiple kinds of interactions, such as distinct types of social…
Epidemiological contact network models have emerged as an important tool in understanding and predicting the spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
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…
Exact analytical solutions of the time-dependent Schr\"odinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value…
In this paper, we focus on the hitting times of a stochastic epidemic model presented by \cite{Gray}. Under the help of the auxiliary stopping times, we investigate the asymptotic limits of the hitting times by the variations of calculus…
Spreading processes on graphs arise in a host of application domains, from the study of online social networks to viral marketing to epidemiology. Various discrete-time probabilistic models for spreading processes have been proposed. These…
We investigate the impact of misinformation about the contact structure on the ability to predict disease outbreaks. We base our study on 31 empirical temporal networks and tune the frequencies in errors in the node identities or timestamps…
In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time…
The spreading of virus infection is here simulated over artificial human networks. The real-space urban life of people is modeled as a modified scale-free network with constraints. A scale-free network has been adopted in several studies…
It is a fundamental question in disease modelling how the initial seeding of an epidemic, spreading over a network, determines its final outcome. Research in this topic has primarily concentrated on finding the seed configuration which…
Over the past few years, insights from computer science, statistical physics, and information theory have revealed phase transitions in a wide array of high-dimensional statistical problems at two distinct thresholds: One is the…
In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…
It is well known that, under broad assumptions, the time-scaled point process of exceedances of a high level by a stationary sequence converges to a compound Poisson process as the level grows. The purpose of this note is to demonstrate…
First-passage times are often the most relevant aspect of a complex Markovian network, because they signify when information processing has resulted in a definite decision. Previous studies have shown that for kinetic proofreading networks…
Network redundancy is one of the spatial network structural properties critical to robustness against cascading failures in power networks. The waiting-time distributions for network partitions in cascading failures explain how the spatial…