This paper studies a meta-simplex concept and geometric embedding framework for multi-
population replicator dynamics. Central results are two embedding theorems which …

The assignment flow recently introduced in the J. Math. Imaging and Vision 58/2 (2017)
constitutes a high-dimensional dynamical system that evolves on a statistical product …

Deep learning has achieved great success in academic benchmarks but fails to work
effectively in the real world due to the potential dataset bias. The current learning methods …

This paper introduces assignment flows for density matrices as state spaces for
representation and analysis of data associated with vertices of an underlying weighted …

This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling
metric data on graphs. The G-PDE is derived as a nonlocal reparametrization of the …

This paper introduces a novel approach to uncertainty quantification of image labelings
determined by assignment flows. Local uncertainties caused by ambiguous data and noise …

Structured prediction is the task of jointly predicting realizations of multiple coupled random
variables. This statistical problem is central to many advanced applications of deep learning …

In this thesis, we focus on the image labeling problem which is the task of performing unique
pixel-wise label decisions to simplify the image while reducing its redundant information. We …

Glaucoma is an irreversible but preventable disease, and one of the main causes of
blindness worldwide. The ONH represents the intraocular section of the optic nerve, which is …