10 papers
A Topological Formula for Potts Lattice Gauge Theory Correlations
Paul Duncan, Benjamin Schweinhart
We exhibit a formula relating the correlation between Wilson loop variables in Potts lattice gauge theory to a topological quantity in the plaquette random cluster model. As applic…
Voronoi Percolation: Topological Stability and Giant Cycles
Benjamin Schweinhart, Morgan Shuman
We study the topological stability of Voronoi percolation in higher dimensions. We show that slightly increasing p allows a discretization that preserves increasing topological pro…
Generalized cluster algorithms for Potts lattice gauge theory
Anthony E. Pizzimenti, Paul Duncan, Benjamin Schweinhart
Monte Carlo algorithms, like the Swendsen-Wang and invaded-cluster, sample the Ising and Potts models asymptotically faster than single-spin Glauber dynamics do. Here, we generaliz…
Classification of Histopathology Slides with Persistent Homology Convolutions
Shrunal Pothagoni, Benjamin Schweinhart
Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topo…
A Cellular Representation of the Potts Lattice Higgs Model
Summer Eldridge, Malin P. Forsström, Benjamin Schweinhart
The -dimensional Potts lattice Higgs model is a random assignment of spins in to the -dimensional cells of a cell complex induced by a Hamiltonian with a Potts…
Hadwiger Models: Low-Temperature Behavior in a Natural Extension of the Ising Model
Summer Eldridge, Benjamin Schweinhart
All isometrically invariant Markov (strictly local) fields on binary assignments are induced by energy functions that can be represented as linear combinations of area, perimeter,…