77 citations · 549 across the 24 of their papers we have counts for
26 papers
Randomized Urysohn-type inequalities
Thomas Hack, Peter Pivovarov
As a natural analog of Urysohn's inequality in Euclidean space, Gao, Hug, and Schneider showed in 2003 that in spherical or hyperbolic space, the total measure of totally geodesic…
Spherical centroid bodies
Florian Besau, Thomas Hack, Peter Pivovarov +1
The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in…
Prediction Error Meta Classification in Semantic Segmentation: Detection via Aggregated Dispersion Measures of Softmax Probabilities
Matthias Rottmann, Pascal Colling, Thomas-Paul Hack +4
We present a method that "meta" classifies whether seg-ments predicted by a semantic segmentation neural networkintersect with the ground truth. For this purpose, we employ measure…
Thermodynamics of Quantum Fields in Nonstationary Spacetimes
Klaus Fredenhagen, Thomas-Paul Hack, Nicola Pinamonti
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the…
Non-equilibrium steady states for the interacting Klein-Gordon field in 1+3 dimensions
Thomas-Paul Hack, Rainer Verch
Non-equilibrium steady states (NESS) describe particularly simple and stationary non-equilibrium situations. A possibility to obtain such states is to consider the asymptotic evolu…
Approaches to linear local gauge-invariant observables in inflationary cosmologies
Markus B. Fröb, Thomas-Paul Hack, Igor Khavkine
We review and relate two recent complementary constructions of linear local gauge-invariant observables for cosmological perturbations in generic spatially flat single-field inflat…