David Sivakoff

Graph fission in an evolving voter model

We consider a simplified model of a social network in which individuals have one of two opinions (called 0 and 1) and their opinions and the network connections coevolve. Edges are picked at random. If the two connected individuals hold different opinions then, with probability 1 - α, one imitates the opinion of the other; otherwise (i.e., with probability α), the link between them is broken and one of them makes a new connection to an individual chosen at random (i) from those with the same opinion or (ii) from the network as a whole. The evolution of the system stops when there are no longer any discordant edges connecting individuals with different opinions. Letting ρ be the fraction of voters holding the minority opinion after the evolution stops, we are interested in how ρ depends on α and the initial fraction u of voters with opinion 1. In case (i), there is a critical value αc which does not depend on u, with ρ ≈ u for α > αc and ρ ≈ 0 for α < αc. In case (ii), the transition point αc(u) depends on the initial density u. For α > αc(u), ρ ≈ u, but for α < αc(u), we have ρ(α,u) = ρ(α,1/2). Using simulations and approximate calculations, we explain why these two nearly identical models have such dramatically different phase transitions.

Impact of coverage-dependent marginal costs on optimal HPV vaccination strategies

The effectiveness of vaccinating males against the human papillomavirus (HPV) remains a controversial subject. Many existing studies conclude that increasing female coverage is more effective than diverting resources into male vaccination. Recently, several empirical studies on HPV immunization have been published, providing evidence of the fact that marginal vaccination costs increase with coverage. In this study, we use a stochastic agent-based modeling framework to revisit the male vaccination debate in light of these new findings. Within this framework, we assess the impact of coverage-dependent marginal costs of vaccine distribution on optimal immunization strategies against HPV. Focusing on the two scenarios of ongoing and new vaccination programs, we analyze different resource allocation policies and their effects on overall disease burden. Our results suggest that if the costs associated with vaccinating males are relatively close to those associated with vaccinating females, then coverage-dependent, increasing marginal costs may favor vaccination strategies that entail immunization of both genders. In particular, this study emphasizes the necessity for further empirical research on the nature of coverage-dependent vaccination costs.

Bootstrap percolation on the Hamming torus

The Hamming torus of dimension

A Quest to Unravel the Metric Structure Behind Perturbed Networks.

d

Fast Change Point Detection on Dynamic Social Networks

is the graph with vertices

Coarsening Model on \({\mathbb{Z}^{d}}\) with Biased Zero-Energy Flips and an Exponential Large Deviation Bound for ASEP

\{1,\dots,n\}^d

Hierarchical Change Point Detection on Dynamic Networks

and an edge between any two vertices that differ in a single coordinate. Bootstrap percolation with threshold

Bootstrap percolation on products of cycles and complete graphs

\theta

Jigsaw percolation: What social networks can collaboratively solve a puzzle?

starts with a random set of open vertices, to which every vertex belongs independently with probability

Nucleation scaling in jigsaw percolation

p