Computational Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Topology write by Herbert Edelsbrunner. This book was released on 2022-01-31. Computational Topology available in PDF, EPUB and Kindle. Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The 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. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Computational Topology for Data Analysis
Computational Topology for Data Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Topology for Data Analysis write by Tamal Krishna Dey. This book was released on 2022-03-10. Computational Topology for Data Analysis available in PDF, EPUB and Kindle. Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Computational Topology for Biomedical Image and Data Analysis
Computational Topology for Biomedical Image and Data Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Topology for Biomedical Image and Data Analysis write by Rodrigo Rojas Moraleda. This book was released on 2019-07-12. Computational Topology for Biomedical Image and Data Analysis available in PDF, EPUB and Kindle. This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications. It will be of interest to medical physicists, computer scientists, and engineers, as well as undergraduate and graduate students interested in this topic. Features: Presents a practical guide to algebraic topology as well as persistence homology Contains application examples in the field of biomedicine, including the analysis of histological images and point cloud data
A Short Course in Computational Geometry and Topology
A Short Course in Computational Geometry and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Short Course in Computational Geometry and Topology write by Herbert Edelsbrunner. This book was released on 2014-04-28. A Short Course in Computational Geometry and Topology available in PDF, EPUB and Kindle. This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.
Topology for Computing
Topology for Computing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology for Computing write by Afra J. Zomorodian. This book was released on 2005-01-10. Topology for Computing available in PDF, EPUB and Kindle. The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
