相关论文: From networked SIS model to the Gompertz function
Although viral spreading processes taking place in networks are often analyzed using Markovian models in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real…
In this paper we study the maximum degree of interaction which may emerge in distributed systems. It is assumed that a distributed system is represented by a graph of nodes interacting over edges. Each node has some amount of data. The…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
Disease spreading models such as the ubiquitous SIS compartmental model and its numerous variants are widely used to understand and predict the behaviour of a given epidemic or information diffusion process. A common approach to imbue more…
A social network (SN) is a social structure consisting of a group representing the interaction between them. SNs have recently been widely used and, subsequently, have become suitable and popular platforms for product promotion and…
This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the…
Edge-based network models, especially those based on bond percolation methods, can be used to model disease transmission on complex networks and accommodate social heterogeneity while keeping tractability. Here we present an application of…
We study the regularity of the score function in score-based generative models and show that it naturally adapts to the smoothness of the data distribution. Under minimal assumptions, we establish Lipschitz estimates that directly support…
We consider a stochastic SIS infection model for a population partitioned into $m$ households assuming random mixing. We solve the model in the limit $m \to \infty$ by using the self-consistent field method of statistical physics. We derive…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on the networks. We derive an analytical expression of the…
In the performance analyses of wireless networks, asymptotic quantities and properties often pro- vide useful results and insights. The asymptotic analyses become especially important when complete analytical expressions of the performance…
Understanding the behaviors of information propagation is essential for the effective exploitation of social influence in social networks. However, few existing influence models are both tractable and efficient for describing the…
It has recently been observed that the SIR distributions of a variety of cellular network models and transmission techniques look very similar in shape. As a result, they are well approximated by a simple horizontal shift (or gain) of the…
The global behaviour of the compact pairwise approximation of SIS epidemic propagation on networks is studied. It is shown that the system can be reduced to two equations enabling us to carry out a detailed study of the dynamic properties…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
The importance of modeling the spread of epidemics through a population has led to the development of mathematical models for infectious disease propagation. A number of empirical studies have collected and analyzed data on contacts between…
We study the SIR ("susceptible, infected, removed/recovered") model on directed graphs with heterogeneous transmission probabilities within the message-passing approximation. We characterize the percolation transition, predict cluster size…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…