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• 1. Introduction
• Part I. Mathematics: 2. Spaces and filtrations
• 3. Group theory
• 4. Homology
• 5. Morse theory
• 6. New results
• Part II. Algorithms: 7. The persistence algorithms
• 8. Topological simplification
• 9. The Morse-Smale algorithm
• 10. The linking number algorithm
• Part III. Applications: 11. Software
• 12. Experiments
• 13. Applications.
• (source: Nielsen Book Data)

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.
(source: Nielsen Book Data)

• Part 1 Basic theory: E-graphs - special cell-decomposition of 2-manifolds
• crystallizations - the Ferri-Gagliardi moves
• diagrams of E-graphs and Ferri's switching lemma. Part 2 Generating surgery moves: quadricolours, hinges, commuters
• relations among the generating moves
• connections with Lickorish's construction. Part 3 Invariants: the fundamental and the homology groups
• the vertex group ... is there something new here?
• linking invariants. Part 4 Classes of 3-gems: the "planar" class and lens spaces
• gists - special symmetries on 3-manifolds. Part 5 Theory for a catalogue of 3-gems: shortcuts for inserting the 4th colour
• the TS-moves and the U-move. Appendices: all 3-gems up to 28 vertices. (Part Contents).
• (source: Nielsen Book Data)

This text provides a guide to dealing with 3-manifolds by computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included. In order to help the classification, various invariants are presented, including the new quantum invariants.
(source: Nielsen Book Data)

• 1. Introduction
• Part I. Mathematics: 2. Spaces and filtrations
• 3. Group theory
• 4. Homology
• 5. Morse theory
• 6. New results
• Part II. Algorithms: 7. The persistence algorithms
• 8. Topological simplification
• 9. The Morse-Smale algorithm
• 10. The linking number algorithm
• Part III. Applications: 11. Software
• 12. Experiments
• 13. Applications.
• (source: Nielsen Book Data)

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.
(source: Nielsen Book Data)

• H. Bruin, An Overview of Unimodal Inverse Limit Spaces.- B. Barany, M. Rams, K. Simon, Dimension Theory of Some Non Markovian Rapellers Part I: A General Introduction.- B. Barany, M. Rams, K. Simon, Dimension Theory of Some Non Markovian Repellers: Part II: Dynamically Defined Function Graphs.- K. Lesniak, Iterated Function Systems - A Topological Approach Attractors.- H. Kato, Zero Dimensional Covers of Dynamical Systems.- H. Kato, Chaotic Continua in Chaotic Dynamical Systems.- R. L. Devaney, S. M. Marotta, Mandelpinski Necklaces in the Parameter Planes of Rational Maps.- Kit C Chan, Some Examples of Hypercyclic Operators and Universal Sequences of Operators.- Kit C Chan, Some Basic Properties of Hypercyclic Operators.- Kit C Chan, The Testing Ground of Weighted Shift Operators for Hypercyclicity.- D. Drozdov, M. Samuel, A. Tetenov, On -deformations of Polygonal Dendrites.- A. Tetenov, K. Kamalutdinov, V. Aseev, General Position Theorems and its Applications.- A. Raj P, V. Kumar P B, The nth iterate of a map with dense orbit.- Aswathy R K, S. Mathew, Finite Products of Irregular Iterated Function Systems and Their Separation Properties.- A. Akbar, Mubeena T, Periodic Points of N-dimensional Toral Automorphisms.- S. Jose, V. Kumar P B, Julia Sets in Topological Spaces.- K U Sreeja, V. Kumar P B, Ramkumar P B, Julia, Sets of Some Graphs Using Independence Polynomials.- P. Frosini, An Introduction to the Notion of Natural Pseudo Distance in Topological Data Analysis.- A. Cerri, P. Frosini, A Brief Introduction to Multidimensional Persistent Betti Numbers.- N. Quercioli, Some New Methods to Build Group Equivariant Non Expansive Operators in TDA.- Y. Dabaghian, Topological Stability of the Hippocampal Spatial Map and Synaptic Transience.- A. Jacob, Ramkumar P B, Intuitionistic Fuzzy Graph Morphological Topology.- A. G. Pillai, Ramkumar P B, Some Properties of the Bitopological Space Associated with the 3-Uniform Semigraph of Cycle graph.- D. Chandran R, Ramkumar P B, Hypergraph Topology.
• (source: Nielsen Book Data)

This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9-11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.
(source: Nielsen Book Data)

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.
(source: Nielsen Book Data)

• The Persistent Homology of Dual Digital Image Constructions (V. Robins).- Morse-based Fibering of the Persistence Rank Invariant (C. Landi).- Local Versus Global Distances for Zigzag and Multi Parameter Persistence Modules (E. Gasparovic).- Tile-transitive tilings of the Euclidean and hyperbolic planes by ribbons (V. Robins).- Graph Pseudometrics from a Topological Point of View (J. Tan).- Nerve theorems for fixed points of neural networks (C. Curto).- Combinatorial Conditions for Directed Collapsing (T. Fasy).- Lions and contamination, triangular grids, and Cheeger constants (L. Gibson).- A Topological Approach for Motion Track Discrimination (S. Tymochko).- Persistent topology of protein space (W. Hamilton).- Mappering Mecklenburg County: Exploring Census data for potential communities of interest (M. Thatcher).- Stitch Fix for Mapper and Topological Gains (B. Wang).
• (source: Nielsen Book Data)

This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field. Some of the featured topics include topological data analysis of power law structure in neural data; a nerve theorem for directional graph covers; topological or homotopical invariants for directed graphs encoding connections among a network of neurons; and the issue of approximation of objects by digital grids, including precise relations between the persistent homology of dual cubical complexes.
(source: Nielsen Book Data)

• Table of Contents Navigating and Modeling in Blender The Fundamentals of Topology Deforming Topology Improving Topology Using UV Maps Topology on a Humanoid Head Topology on a Humanoid Body Topology on a Hard Surface Optimizing Geometry for a Reduced Triangle Count.
• (source: Nielsen Book Data)

A comprehensive introduction to 3D modeling, from the fundamental ideas of topology to in-depth examples that will help you take your projects to the next level Key Features Overcome complex topology problems while working through projects Learn to topologize quad-based and non-quad-based meshes with step-by-step examples Optimize your models by reducing the triangle count to improve performance Book DescriptionThis book is an introduction to modeling and an in-depth look at topology in Blender, written by a Blender topology specialist with years of experience with the software. As you progress through its chapters, you'll conquer the basics of quad-based topology using triangles and Ngons, and learn best practices and things to avoid while modeling and retopologizing. The pages are full of illustrations and examples with in-depth explanations that showcase each step in an easy-to-follow format. Squeaky Clean Topology in Blender starts by introducing you to the user interface and navigation. It then goes through an overview of the modeling techniques and hotkeys that will be necessary to understand the examples. With the modeling basics out of the way, the next stop on our journey is topology. Working through projects like a character and a sci-fi blaster, the book will illustrate and work through complex topology problems, and present solutions to those problems. These examples focus on deforming character models, non-deforming hard surface models, and optimizing these models by reducing the triangle count. By the end of this book, you will be able to identify the general flow of a shape's topology, identify and solve issues in your topology, and come out with a model ready for UV unwrapping, materials, and rigging. What you will learn Identify the general flow of a model's topology, and what might cause issues Understand the topology of a character, and the joints that they make up Handle non-quad based topology Lay out your meshes for UV seams Explore and use hotkeys to get things done faster Optimize models for a reduced triangle count Who this book is forThis book is for character modelers, sculptors, poly modelers, and hard surface modelers. Whether you're looking for an introduction to modeling, optimizing high poly or sculpted models, or just a deeper dive into the subject of topology, this book will walk you through the topology workflow from beginning to end.
(source: Nielsen Book Data)

• Preface.- The Rank Invariant Stability via Interleavings (Claudia Landi).- Persistent Homology Over Directed Acyclic Graphs (Erin Wolf Chambers and David Letscher).- A Complete Characterization of the 1-Dimensional Intrinsic Cech Persistence Diagrams for Metric Graphs (Ellen Gasparovic, Maria Gommel, et al).- Comparing Directed and Weighted Road Maps (Alyson Bittner, Brittany Terese Fasy, et al).- Sweeping Costs of Planar Domains (Brooks Adams, Henry Adams, and Colin Roberts).- Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology (Paul Bendich, Ellen Gasparovic, et al).- Density of local maxima of the distance function to a set of points in the plane (Nina Amenta, Erin Chambers, et al).- Mind the Gap: A Study in Global Development through Persistent Homology (Andrew Banman and Lori Ziegelmeier).- Cluster Identification via Persistent Homology and other Clustering Techniques, with Application to Liver Transplant Data (Berhanu A. Wubie, Axel Andres, et al).- Pseudo-multidimensional persistence and its applications (Catalina Betancourt, Mathieu Chalifour, et al).
• (source: Nielsen Book Data)

Based on the first Workshop for Women in Computational Topology that took place in 2016, this volume assembles new research and applications in computational topology. Featured articles range over the breadth of the discipline, including topics such as surface reconstruction, topological data analysis, persistent homology, algorithms, and surface-embedded graphs. Applications in graphics, medical imaging, and GIS are discussed throughout the book. Four of the papers in this volume are the product of working groups that were established and developed during the workshop. Additional papers were also solicited from the broader Women in Computational Topology network. The volume is accessible to a broad range of researchers, both within the field of computational topology and in related disciplines such as statistics, computational biology, and machine learning.
(source: Nielsen Book Data)