Related papers: Large Deviations of Mean-Field Jump-Markov Process…

In this paper, we are concerned with stochastic susceptible-exposed-infected-removed epidemics on complete graphs with vertex-dependent transition rates. Large and moderate deviations of empirical density fields of our models are given.…

This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…

Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…

We consider an SIR-type (Susceptible $\to$ Infected $\to$ Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model…

The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security. In this paper, statistical techniques for link prediction based on the…

Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…

Complex systems of many interacting components exhibit patterns of recurrence and emergent behaviors in their time evolution that can be understood from a new perspective of physics of information dynamics, modeled after one such system,…

Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…

How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…

We study large communication networks of the mean-field type. The input flows to the nodes of the network are supposed to be stationary and with low rate. We show that such a network is ergodic, i.e. it goes to the stationary state, which…

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set…

We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite…

We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be non-linear and path…

We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a…

We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differential equations in discrete time. The neurons interact…

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic…

We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive…

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…

In this paper we introduce a new notion of convergence of sparse graphs which we call Large Deviations or LD-convergence and which is based on the theory of large deviations. The notion is introduced by "decorating" the nodes of the graph…

We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and…