4 papers
Ollivier's Ricci Curvature on Complex-weighted Graphs
Yu Tian, Eleanor Wiesler, Melanie Weber
Understanding the geometry of complex networks is critical for effective modeling and analysis across domains. While discrete notions of Ricci curvature have emerged as powerful to…
A Probabilistic Framework for Improving Dense Object Detection in Underwater Image Data via Annealing-Based Data Augmentation
Eleanor Wiesler, Trace Baxley
Object detection models typically perform well on images captured in controlled environments with stable lighting, water clarity, and viewpoint, but their performance degrades subs…
Graph Neural Network-Informed Predictive Flows for Faster Ford-Fulkerson and PAC-Learnability
Eleanor Wiesler, Trace Baxley
We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm…
Ollivier-Ricci Curvature of Riemannian Manifolds and Directed Graphs with Applications to Graph Neural Networks
Eleanor P Wiesler
This thesis is an exposition of Ollivier-Ricci Curvature of metric spaces as introduced by Yann Ollivier, which is based upon the 1-Wasserstein Distance and optimal transport theor…