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Computational Topology - an Introduction
TLDR
This book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles.
Algorithms in Combinatorial Geometry
  • H. Edelsbrunner
  • Mathematics
    EATCS Monographs in Theoretical Computer Science
  • 1987
TLDR
This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.
Stability of Persistence Diagrams
The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram
Topological Persistence and Simplification
TLDR
Fast algorithms for computing persistence and experimental evidence for their speed and utility are given for topological simplification within the framework of a filtration, which is the history of a growing complex.
Three-dimensional alpha shapes
TLDR
This article introduces the formal notion of the family of α-shapes of a finite point set in R, a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter α ε R controlling the desired level of detail.
Persistent Homology — a Survey
Persistent homology is an algebraic tool for measuring topological features of shapes and functions. It casts the multi-scale organization we frequently observe in nature into a mathematical
On the shape of a set of points in the plane
TLDR
A generalization of the convex hull of a finite set of points in the plane leads to a family of straight-line graphs, "alpha -shapes," which seem to capture the intuitive notions of "fine shape" and "crude shape" of point sets.
Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design
TLDR
Analysis of the FK506 binding protein, and of compounds developed in SAR by NMR, indicates that CAST pocket computation may provide a priori identification of target proteins for linked‐fragment design.
Efficient algorithms for agglomerative hierarchical clustering methods
TLDR
A centroid SAHN clustering algorithm that requires 0(n2) time, in the worst case, for fixedk and for a family of dissimilarity measures including the Manhattan, Euclidean, Chebychev and all other Minkowski metrics is described.
Geometry and Topology for Mesh Generation
  • H. Edelsbrunner
  • Physics, Computer Science
    Cambridge monographs on applied and computational…
  • 28 May 2001
1. Delaunay triangulations 2. Triangle meshes 3. Combinatorial topology 4. Surface simplification 5. Delaunay tetrahedrizations 6. Tetrahedron meshes 7. Open problems.
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