This was published following my bachelor thesis, in which I programmed a system for nonmonotonic belief change operations.
Another publication about my bachelor thesis.
A paper about the work of my colleague Alex. I helped a little. It is about finite elements calculations with a Laplace operator that does not act on ordinary functions but on sections of nontrivial real line bundles.
Another paper about Alex's topic. This time it is about complex line bundles.
A paper about the subject of my master and doctor thesis.
Ein Paper über das Thema meiner Master- und Doktorarbeit.
Can one hear what has been painted on a drum?
It is about a similarity measure for images: Imagine the image painted on a drum membrane using a paint that modifies the density and tension of the membrane,
and thus also the sound of the drum. Two images are then compared by comparing the frequency spectra of the drums.
This paper presents two extensions of the previous: First, the procedure is generalized to work with color images. Second, a distance measure is described that compares not only the frequencies but also the structure of the pairwise overlap of the energy density of the drum's eigenvibrations. This is meaningful because the energy of an eigenvibration tends to be localized in a region of the image bounded by color contrasts. In the edge-weighted graph of pairwise overlap degrees, the regions of the image then form characteristic clusters within which there is high pairwise overlap.
Errata: Some formulas contain a variable S that is defined nowhere. It should say C instead.