15 citations · 27 across the 7 of their papers we have counts for
9 papers
Forward Reachable Sets: Analytically derived properties of connected components for dynamic networks
Benjamin Armbruster, Li Wang, Martina Morris
Formal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a funct…
Optimal timing of cross-sectional network samples in longitudinal network studies
Ekkehard Beck, Benjamin Armbruster
When choosing the timing of cross-sectional network snapshots in longitudinal social network studies, the effect on the precision of parameter estimates generally plays a minor rol…
A Short Proof of Strassen's Theorem Using Convex Analysis
Benjamin Armbruster
We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generali…
A simple and general proof for the convergence of Markov processes to their mean-field limits
Benjamin Armbruster
Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed tha…
Elementary proof of convergence to the mean-field model for the SIR process
Ekkehard Beck, Benjamin Armbruster
The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equ…
Bounds for the expected value of one-step processes
Benjamin Armbruster, Ádám Besenyei, Péter L. Simon
Mean-field models are often used to approximate Markov processes with large state-spaces. One-step processes, also known as birth-death processes, are an important class of such pr…