4,704 research outputs found
AHC interview with Ulrich Bauer
No full textOctober 12, 2012Digital recordingDr. Ulrich Bauer was born 1933 as Ulrich Bauernfreund in Vienna, Austria. His father was a physician, and his mother was a pianist. In January 1939, Ulrich and his mother left Vienna for the Netherlands. His father was interned in Buchenwald but was released upon the intervention of a relative in the Netherlands. The family immigrated to New York in October 1939. Ulrich Bauer later went to Basel, Switzerland to study medicine.Austrian Heritage Collectio
Johann Bayer. - Johann Engel. - Georg Tannstetter. - Cyprian Leovitius. - Ulrich Schiegg. - Wilhelm Bauer
No full textJohann Bayer. - Johann Engel. - Georg Tannstetter. - Cyprian Leovitius. - Ulrich Schiegg. - Wilhelm Bauer. - In: Gelehrtes Schwaben / [Red.: Gerhard Stumpf]. - Augsburg : Hofmann-Dr., 1990. - S. 84-92, 96-9
Johann Bayer. - Johann Engel. - Georg Tannstetter. - Cyprian Leovitius. - Ulrich Schiegg. - Wilhelm Bauer
No full textJohann Bayer. - Johann Engel. - Georg Tannstetter. - Cyprian Leovitius. - Ulrich Schiegg. - Wilhelm Bauer. - In: Gelehrtes Schwaben / [Red.: Gerhard Stumpf]. - Augsburg : Hofmann-Dr., 1990. - S. 84-92, 96-9
Generating parametric models of tubes from laser scans
No full textWe present an automatic method for computing an accurate parametric model of a piecewise defined pipe surface, consisting of cylinder and torus segments, from an unorganized point set. Our main contributions are reconstruction of the spine curve of a pipe surface from surface samples, and approximation of the spine curve by G(1) continuous circular arcs and line segments. Our algorithm accurately outputs the parametric data required for bending machines to create the reconstructed tube. (C) 2009 Elsevier Ltd. All rights reserved
On the Metric Distortion of Embedding Persistence Diagrams into Separable Hilbert Spaces
No full textPersistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their diagram distances, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of persistence diagrams into Reproducing Kernel Hilbert Spaces, in which all computations can be performed easily. Since persistence diagrams enjoy theoretical stability guarantees for the diagram distances, the metric properties of the feature map, i.e., the relationship between the Hilbert distance and the diagram distances, are of central interest for understanding if the persistence diagram guarantees carry over to the embedding. In this article, we study the possibility of embedding persistence diagrams into separable Hilbert spaces with bi-Lipschitz maps. In particular, we show that for several stable embeddings into infinite-dimensional Hilbert spaces defined in the literature, any lower bound must depend on the cardinalities of the persistence diagrams, and that when the Hilbert space is finite dimensional, finding a bi-Lipschitz embedding is impossible, even when restricting the persistence diagrams to have bounded cardinalities
Efficient Computation of Image Persistence
No full textWe present an algorithm for computing the barcode of the image of a morphism in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. The algorithm makes use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. The clearing optimization works particularly well in the context of relative cohomology, and using previous duality results we can translate the barcodes of images in relative cohomology to those in absolute homology. This forms the basis for an implementation of image persistence computations for inclusions of filtrations of Vietoris-Rips complexes in the framework of the software Ripser
Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris-Rips Filtrations
No full textMotivated by computational aspects of persistent homology for Vietoris-Rips
filtrations, we generalize a result of Eliyahu Rips on the contractibility of
Vietoris-Rips complexes of geodesic spaces for a suitable parameter depending
on the hyperbolicity of the space. We consider the notion of geodesic defect to
extend this result to general metric spaces in a way that is also compatible
with the filtration. We further show that for finite tree metrics the
Vietoris-Rips complexes collapse to their corresponding subforests. We relate
our result to modern computational methods by showing that these collapses are
induced by the apparent pairs gradient, which is used as an algorithmic
optimization in Ripser, explaining its particularly strong performance on
tree-like metric data.Comment: 18 pages. Extended version of SoCG 2022 pape
Wrapping Cycles in Delaunay Complexes: Bridging Persistent Homology and Discrete Morse Theory
No full textWe study the connection between discrete Morse theory and persistent homology in the context of shape reconstruction methods. Specifically, we consider the construction of Wrap complexes, introduced by Edelsbrunner as a subcomplex of the Delaunay complex, and the construction of lexicographic optimal homologous cycles, also considered by Cohen-Steiner, Lieutier, and Vuillamy in a similar setting. We show that for any cycle in a Delaunay complex for a given radius parameter, the lexicographically optimal homologous cycle is supported on the Wrap complex for the same parameter, thereby establishing a close connection between the two methods. We obtain this result by establishing a fundamental connection between reduction of cycles in the computation of persistent homology and gradient flows in the algebraic generalization of discrete Morse theory.22 pages. Full version of SoCG 2024 pape
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