相关论文: Mean-field models of dynamics on networks via mome…

This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…

In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the…

In a previous paper Sharkey et al. [13] proved the exactness of closures at the level of triples for Markovian SIR (susceptible-infected-removed) dynamics on tree-like networks. This resulted in a deterministic representation of the…

The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different…

We investigate the dynamics of an epidemiological susceptible-infected-susceptible (SIS) model on an adaptive network. This model combines epidemic spreading (dynamics on the network) with rewiring of network connections (topological…

Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…

Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To…

In previous work, we developed the scaled SIS process, which models the dynamics of SIS epidemics over networks. With the scaled SIS process, we can consider networks that are finite-sized and of arbitrary topology (i.e., we are not…

Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks. These networks are highly dynamic and they are growing incessantly. Inspired by the concept…

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…

The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general…

Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…

We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a…

In this paper, we study the dynamics of epidemic processes taking place in adaptive networks of arbitrary topology. We focus our study on the adaptive susceptible-infected-susceptible (ASIS) model, where healthy individuals are allowed to…

Self-adaptive dynamics occurs in many physical systems such as socio-economics, neuroscience, or biophysics. We formalize a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the…

Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…

We analyze a class of stochastic processes, referred to as asynchronous and semi-anonymous dynamics (ASD), over directed labeled random networks. These processes are a natural tool to describe general best-response and noisy best-response…

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…

We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much…

Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…