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Author: Anatolij T. Fomenko
Publisher: Springer Science & Business Media
ISBN: 4431669566
Category : Mathematics
Languages : en
Pages : 398
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Book Description
The flood of information through various computer networks such as the In ternet characterizes the world situation in which we live. Information worlds, often called virtual spaces and cyberspaces, have been formed on computer networks. The complexity of information worlds has been increasing almost exponentially through the exponential growth of computer networks. Such nonlinearity in growth and in scope characterizes information worlds. In other words, the characterization of nonlinearity is the key to understanding, utiliz ing and living with the flood of information. The characterization approach is by characteristic points such as peaks, pits, and passes, according to the Morse theory. Another approach is by singularity signs such as folds and cusps. Atoms and molecules are the other fundamental characterization ap proach. Topology and geometry, including differential topology, serve as the framework for the characterization. Topological Modeling for Visualization is a textbook for those interested in this characterization, to understand what it is and how to do it. Understanding is the key to utilizing information worlds and to living with the changes in the real world. Writing this textbook required careful preparation by the authors. There are complex mathematical concepts that require designing a writing style that facilitates understanding and appeals to the reader. To evolve a style, we set as a main goal of this book the establishment of a link between the theoretical aspects of modern geometry and topology, on the one hand, and experimental computer geometry, on the other.
Author: Anatolij T. Fomenko
Publisher: Springer Science & Business Media
ISBN: 4431669566
Category : Mathematics
Languages : en
Pages : 398
Get Book Here
Book Description
The flood of information through various computer networks such as the In ternet characterizes the world situation in which we live. Information worlds, often called virtual spaces and cyberspaces, have been formed on computer networks. The complexity of information worlds has been increasing almost exponentially through the exponential growth of computer networks. Such nonlinearity in growth and in scope characterizes information worlds. In other words, the characterization of nonlinearity is the key to understanding, utiliz ing and living with the flood of information. The characterization approach is by characteristic points such as peaks, pits, and passes, according to the Morse theory. Another approach is by singularity signs such as folds and cusps. Atoms and molecules are the other fundamental characterization ap proach. Topology and geometry, including differential topology, serve as the framework for the characterization. Topological Modeling for Visualization is a textbook for those interested in this characterization, to understand what it is and how to do it. Understanding is the key to utilizing information worlds and to living with the changes in the real world. Writing this textbook required careful preparation by the authors. There are complex mathematical concepts that require designing a writing style that facilitates understanding and appeals to the reader. To evolve a style, we set as a main goal of this book the establishment of a link between the theoretical aspects of modern geometry and topology, on the one hand, and experimental computer geometry, on the other.
Author: Valerio Pascucci
Publisher: Springer Science & Business Media
ISBN: 3642150144
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. . The editors have brought together the most prominent and best recognized researchers in the field of topology-based data analysis and visualization for a joint discussion and scientific exchange of the latest results in the field. This book contains the best 20 peer-reviewed papers resulting from the discussions and presentations at the third workshop on "Topological Methods in Data Analysis and Visualization", held 2009 in Snowbird, Utah, US. The 2009 "TopoInVis" workshop follows the two successful workshops in 2005 (Slovakia) and 2007 (Germany).
Author: Peer-Timo Bremer
Publisher: Springer Science & Business
ISBN: 3319040995
Category : Mathematics
Languages : en
Pages : 276
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Book Description
This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The volume also features material on core research challenges such as the representation of large and complex datasets and integrating numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made on finding experimental solutions to open problems in the sector. They provide an inclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for future progress. With papers by some of the world’s leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine.
Author: Ingrid Hotz
Publisher: Springer Nature
ISBN: 3030835006
Category : Mathematics
Languages : en
Pages : 372
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Book Description
This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.
Author: Tamal Krishna Dey
Publisher: Cambridge University Press
ISBN: 1009103199
Category : Mathematics
Languages : en
Pages : 456
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Book Description
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.
Author: Torsten Möller
Publisher: Springer Science & Business Media
ISBN: 3540499261
Category : Computers
Languages : en
Pages : 348
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Book Description
The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.
Author: Janis Osis
Publisher: Elsevier
ISBN: 0128093536
Category : Computers
Languages : en
Pages : 277
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Book Description
Topological UML Modeling: An Improved Approach for Domain Modeling and Software Development presents a specification for Topological UML® that combines the formalism of the Topological Functioning Model (TFM) mathematical topology with a specified software analysis and design method. The analysis of problem domain and design of desired solutions within software development processes has a major impact on the achieved result – developed software. While there are many tools and different techniques to create detailed specifications of the solution, the proper analysis of problem domain functioning is ignored or covered insufficiently. The design of object-oriented software has been led for many years by the Unified Modeling Language (UML®), an approved industry standard modeling notation for visualizing, specifying, constructing, and documenting the artifacts of a software-intensive system, and this comprehensive book shines new light on the many advances in the field. - Presents an approach to formally define, analyze, and verify functionality of existing processes and desired processes to track incomplete or incorrect functional requirements - Describes the path from functional and nonfunctional requirements specification to software design with step-by-step creation and transformation of diagrams and models with very early capturing of security requirements for software systems. - Defines all modeling constructs as extensions to UML®, thus creating a new UML® profile which can be implemented in existing UML® modeling tools and toolsets
Author: Helwig Hauser
Publisher: Springer Science & Business Media
ISBN:
Category : Computers
Languages : en
Pages : 246
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Book Description
This book presents 13 peer-reviewed papers as written results from the 2005 workshop "Topology-Based Methods in Visualization" that was initiated to enable additional stimulation in this field. It contains a survey of the state-of-the-art, as well original work by leading experts that has not been published before, spanning both theory and applications. It captures key concepts and novel ideas and serves as an overview of current trends in its subject.
Author: Tosiyasu L. Kunii
Publisher: Springer Science & Business Media
ISBN: 4431679413
Category : Computers
Languages : en
Pages : 346
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Book Description
The worlds synthesized in the cyberspaces of networked computers are the theme of Cyberworlds. Cyberspaces have come into prominence with the de velopment of the Internet and are expected to expand drastically with the emergence of national and international information systems. The purpose is to discover the architecture and design of cy of the book Cyberworlds berworlds by synthesizing worlds in cyberspaces. The underlying philosophy is crucial to the success of the architecture, and an initial effort is made to delineate it at the beginning of the book. The book's topics are selected to clarify the issues of the philosophy, architecture, and design of cyberworlds through a wide variety of case studies. The approach presented in the book is thus characterized as synthetic rather than analytic. There already are numbers of books with observations and analyses of cyberworlds. They warn of the danger of widespread crimes and accidents in the cyberworlds, for instance. Without a philosophy and methodologies of how to architecturally design and synthesize the cyber worlds, the worlds in cyberspaces tend to be arbitrarily extended, disordered, and, in extreme cases, criminal. This book is intended to benefit readers by providing them with a possible direction to take in deciding how to synthesize worlds in cyberspaces. Cre ating new worlds in new spaces with almost unlimited dimension and scale is an immense challenge. In principle, anyone at any moment can participate in the creation. The book serves as a creator's reference and also as a design guidebook.
Author: Charles D. Hansen
Publisher: Elsevier
ISBN: 0080481647
Category : Technology & Engineering
Languages : en
Pages : 1061
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Book Description
The Visualization Handbook provides an overview of the field of visualization by presenting the basic concepts, providing a snapshot of current visualization software systems, and examining research topics that are advancing the field. This text is intended for a broad audience, including not only the visualization expert seeking advanced methods to solve a particular problem, but also the novice looking for general background information on visualization topics. The largest collection of state-of-the-art visualization research yet gathered in a single volume, this book includes articles by a "who's who of international scientific visualization researchers covering every aspect of the discipline, including:·Virtual environments for visualization·Basic visualization algorithms·Large-scale data visualization·Scalar data isosurface methods·Visualization software and frameworks·Scalar data volume rendering·Perceptual issues in visualization·Various application topics, including information visualization.* Edited by two of the best known people in the world on the subject; chapter authors are authoritative experts in their own fields;* Covers a wide range of topics, in 47 chapters, representing the state-of-the-art of scientific visualization.
