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(a) (b) (c) (d) (e) Figure 1: The initial point set of the Venus torso (a) was disturbed with a 3% normal and tangential noise to produce the initial noisy point set (b). Figures (c) and (d) show the point set after 20 respectively 50 iterations of the anisotropic fairing algorithm which detects and emphasizes high principal curvature values. Figure (e)(More)
3 Introduction In the first part of this thesis we discuss a new notion of curvature for cell complexes, introduced by Forman [26], and some variations of it. This notion is purely combinatorial and uses local data to define a combinatorial curvature, enabling us to deduce global topological properties. Before we outline Part I, we point out important(More)
We present an efficient algorithm for computing a function that minimizes the number of critical points among all functions within a prescribed distance δ from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with persistence(More)
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lower bound on the chromatic number χ(G) of a graph G. We introduce the shore subdivision of simplicial complexes and use it to show an upper bound to this topological lower bound and to construct a strong 2-deformation retraction from the box complex (in the(More)
Annexin A1 is a glucocorticoid-regulated, anti-inflammatory protein, which plays an important role as an endogenous regulator of the inflammatory response. Many of these anti-inflammatory properties are retained in the N-terminal annexin A1 peptide Ac1-25, which is released from the full-length protein by a neutrophil elastase. To elucidate whether the(More)
Background in history of music. The German Baroque music composer Georg Philipp Telemann was one of the most influential composers of his time with a large repertoire of musical styles. The reflection of musical influences of Telemann on other composers and the detection of musical influences in Telemann's oeuvre are interesting research questions.(More)
Realisations of associahedra can be obtained from the classical permutahedron by removing some of its facets and the set of facets is determined by the diagonals of certain labeled convex planar n-gons as shown by Hohlweg and Lange (2007). Ardila, Benedetti, and Doker (2010) expressed polytopes of this type as Minkowski sums and differences of scaled faces(More)