相关论文: A Finite Memory Interacting P\'{o}lya Contagion Ne…

In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…

In this paper, we analyze the infection spreading dynamics of malware in a population of cyber nodes (i.e., computers or devices). Unlike most prior studies where nodes are reactive to infections, in our setting some nodes are active…

We consider a version of the classical P\'olya urn scheme which incorporates innovations. The space $S$ of colors is an arbitrary measurable set. After each sampling of a ball in the urn, one returns $C$ balls of the same color and…

When an infection spreads in a community, an individual's probability of becoming infected depends on both her susceptibility and exposure to the contagion through contact with others. While one often has knowledge regarding an individual's…

Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent…

We consider SIS contagion processes over networks where, a classical assumption is that individuals' decisions to adopt a contagion are based on their immediate neighbors. However, recent literature shows that some attributes are more…

Typically, contagion strength is modeled by a transmission rate $\lambda$, whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their…

We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into…

We consider a system of $N$ particles interacting through their empirical distribution on a finite state space in continuous time. In the formal limit as $N\to\infty$, the system takes the form of a nonlinear (McKean--Vlasov) Markov chain.…

We propose a method of detecting a phase transition in a generalized P\'olya urn in an information cascade experiment. The method is based on the asymptotic behavior of the correlation $C(t)$ between the first subject's choice and the…

We present a model of contagion that unifies and generalizes existing models of the spread of social influences and micro-organismal infections. Our model incorporates individual memory of exposure to a contagious entity (e.g., a rumor or…

We discuss a model of motion of substance through the nodes of a channel of a network. The channel can be modeled by a chain of urns where each urn can exchange substance with the neighboring urns. In addition the urns can exchange…

The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the…

We propose a Markov model for the spread of Hepatitis C virus (HCV) among drug users who use injections. We then proceed to an asymptotic analysis (large initial population) and show that the Markov process is close to the solution of a non…

Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that…

We study the stochastic system of interacting neurons introduced in De Masi et al. (2015) and in Fournier and L\"ocherbach (2016) in a diffusive scaling. The system consists of $N$ neurons, each spiking randomly with rate depending on its…

Markov chain Monte Carlo (MCMC) methods are frequently used to approximately simulate high-dimensional, multimodal probability distributions. In adaptive MCMC methods, the transition kernel is changed "on the fly" in the hope to speed up…

Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short…

This paper studies efficient algorithms for dynamic curing policies and the corresponding network design problems to guarantee the fast extinction of epidemic spread in a susceptible-infected-susceptible (SIS) model. We consider a Markov…

Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…