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Showing 1 to 7 of 7 for “"computational topology"”.
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Computational topology on neural networks: from the data to the model
… In this work, we have studied, from a computational topology point of view, two machine learning’s pillars: the datasets considered as sets of =-dimensional points, and a specific model, artificial neural networks. we have applied topological data analysis techniques to classify …
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Patterns in dynamics
… (PH) and discuss several applications of this computational topology tool beyond its intended purpose. In particular we apply persistence to data generated by dynamical systems. The application of persistent homology to the circle map will lead us to rediscover the well-known result about the …
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Theory and algorithms for swept manifold intersections
… aided geometric design, geometric modeling, and computational topology have generated a spate of interest towards geometric objects called swept volumes. Besides their great applicability in various practical areas, the mere geometry and topology of these entities make them a perfect testbed for …
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In pursuit of linear complexity in discrete and computational geometry
Many computational problems arise naturally from geometric data. In this thesis, we consider three such problems: (i) distance optimization problems over point sets, (ii) computing contour trees over simplicial meshes, and (iii) bounding the expected complexity of weighted Voronoi diagrams. While …
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Fast algorithms for surface embedded graphs via homology
Made available in DSpace on 2014-01-16T17:54:48Z (GMT). No. of bitstreams: 3 Kyle_Fox.pdf: 3026914 bytes, checksum: c71a059d2688d88bc4678429df958563 (MD5) dissertation.zip: 35243792 bytes, checksum: 5c50fb8cf2afd614d071c635e5821a34 (MD5) license.txt: 4058 bytes, checksum: …
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Combinatorial optimization on embedded curves
… surface. Finally, we present algorithms to solve computational problems for compactly presented curves. We describe the first algorithms to compute the shortest representative of a Z2-homology class. Given a directed graph embedded on a surface of genus g with b boundary cycles, we can compute the …