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Computational Topology for Data Analysis
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Delaunay Mesh Generation
Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why thes
Computational Topology
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.
Topological Data Analysis with Applications
This timely text introduces topological data analysis from scratch, with detailed case studies.
Algorithms for Data and Computation Privacy
This book introduces the state-of-the-art algorithms for data and computation privacy. It mainly focuses on searchable symmetric encryption algorithms and privacy preserving multi-party computation algorithms. This book also introduces algorithms for breaking privacy, and gives intuition on how to design algorithm to counter privacy attacks. Some well-designed differential privacy algorithms are also included in this book. Driven by lower cost, higher reliability, better performance, and faster deployment, data and computing services are increasingly outsourced to clouds. In this computing paradigm, one often has to store privacy sensitive data at parties, that cannot fully trust and perform...
Predicting Structured Data
State-of-the-art algorithms and theory in a novel domain of machine learning, prediction when the output has structure.
Topological Data Analysis for Scientific Visualization
Combining theoretical and practical aspects of topology, this book provides a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a painstaking but intuitive manner, with numerous high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in detail, and their application is carefully demonstrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis for lecturers, students and researchers.
Curve and Surface Reconstruction
Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book, first published in 2007, shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi- and Delaunay-based techniques, implicit surface-based methods and Morse theory-based methods are covered. Scientists and engineers working in drug design, medical imaging, CAD, GIS, and many other areas will benefit from this first book on the subject.
Computational Topology for Biomedical Image and Data Analysis
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
Topological Data Analysis for Genomics and Evolution
Biology has entered the age of Big Data. A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology as well as mathematicians interested in applied topology.
