Small But Slow World: How Network Topology and Burstiness Slow Down Spreading

Communication networks show the small-world property of short paths, but the spreading dynamics in them turns out slow. We follow the time evolution of information propagation through communication networks by using the SI model with empirical data on contact sequences. We introduce null models where the sequences are randomly shuffled in different ways, enabling us to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mostly by weight-topology correlations and the bursty activity patterns of individuals

Imperfect spreading on temporal networks

We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential. We consider a process of imperfect spreading, where transmission is successful with a determined probability at each contact. We first derive an expression for the inter-success time distribution, determining the speed of the propagation, and then focus on a problem related to epidemic spreading, by estimating the epidemic threshold in a system where nodes remain infectious during a finite, random period of time. Finally, we discuss the implications of our work to design an efficient strategy to enhance spreading on temporal networks.Comment: 5 page

Evolutionary Poisson Games for Controlling Large Population Behaviors

Emerging applications in engineering such as crowd-sourcing and (mis)information propagation involve a large population of heterogeneous users or agents in a complex network who strategically make dynamic decisions. In this work, we establish an evolutionary Poisson game framework to capture the random, dynamic and heterogeneous interactions of agents in a holistic fashion, and design mechanisms to control their behaviors to achieve a system-wide objective. We use the antivirus protection challenge in cyber security to motivate the framework, where each user in the network can choose whether or not to adopt the software. We introduce the notion of evolutionary Poisson stable equilibrium for the game, and show its existence and uniqueness. Online algorithms are developed using the techniques of stochastic approximation coupled with the population dynamics, and they are shown to converge to the optimal solution of the controller problem. Numerical examples are used to illustrate and corroborate our results

On the Spread of Viruses on the Internet

We analyze the contact process on random graphs generated according to the preferential attachment scheme as a model for the spread of viruses in the Internet. We show that any virus with a positive rate of spread from a node to its neighbors has a non-vanishing chance of becoming epidemic. Quantitatively, we discover an interesting dichotomy: for it virus with effective spread rate λ, if the infection starts at a typical vertex, then it develops into an epidemic with probability λ^Θ ((log (1/ λ)/log log (1/ λ))), but on average the epidemic probability is λ^(Θ (1))