7 papers · 1 filter
The effects of individual versus community-influenced isolation on SIS epidemic persistence on finite random graphs
Shirshendu Chatterjee, David Sivakoff, Matthew Wascher
The contact process, or the SIS epidemic model, is a continuous-time Markov process used to model the spread of a recurring infection on a graph. Each vertex is either healthy or i…
Disks, Surfaces, and Entanglement Percolation
Paul Duncan, Benjamin Schweinhart, David Sivakoff
We study the probability that a loop is null-homotopic -- that is, bounded by the continuous image of a disk -- in plaquette percolation on Locally, the event that…
On the Continuity of Enhancement Percolation
Paul Duncan, Benjamin Schweinhart, David Sivakoff
We study bond percolation in with an unbounded family of enhancements that enable additional bonds to act as open. A natural question is whether percolation occurs i…
Two-stage Bootstrap Percolation
Zihao Fang, Janko Gravner, David Sivakoff
We introduce and study two variants of two-stage growth dynamics in with state space . In each variant, vertices in state can be change…
Polluted Modified Bootstrap Percolation
Janko Gravner, Alexander Holroyd, Sangchul Lee +1
In the polluted modified bootstrap percolation model, sites in the square lattice are independently initially occupied with probability or closed with probability . A site b…
Phase transition in one-dimensional excitable media with variable interaction range
Ander Aguirre, Hanbaek Lyu, David Sivakoff
We investigate two discrete models of excitable media on a one-dimensional integer lattice : the -color Cyclic Cellular Automaton (CCA) and the -color Firefly C…