Alex Strang is a postdoctoral instructor in computational and applied math at the University of Chicago. He received his PhD in applied math from Case Western Reserve University in 2020.
Alex studies the structures of networks that arise in a variety of disciplines including biophysics, ecology, and in competitive systems. In each field he seeks to understand the interplay between structure and dynamics. In this vein, he is particularly interested in random walks on networks associated with biophysical processes occurring at the molecular scale, and networks which representing competing agents who evolve according to a training protocol. He draws on tools from discrete topology, non-equilibrium thermodynamics, and functional form game theory to study the interplay of structure and dynamics in these systems.
He also works on Bayesian inference and sparsity promotion via hierarchical hyperpriors. His work here has focused on coordinate ascent methods for MAP estimation, sensitivity of estimators (and the effective regularize) to changes in hyperparameters, and variational methods for estimating confidence intervals.
The Network HHD: Quantifying Cyclic Competition in Trait Performance Models of Tournaments
How cyclic is competition if competitor performance is determined by their attributes, which are sampled at random?
We show that the structure of tournament graphs can be decomposed into transitive and cyclic components, where the transitive component is related to an opponent independent measure of skill, while the cyclic component captures rock-paper-scissor like interactions. The expected sizes of the components can then be computed from the number of competitors, number of pairs of competitors who compete (edges), variance in the performance on individual edges, and the correlation in performance on edges sharing an endpoint. We show that the correlation coefficient is related to how predictable your performance is when your adversary is unknown, and directly tunes the degree of cyclicity. The more correlated, the less cyclic.