The Geometry Of Uncertainty

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The Geometry Of Uncertainty

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Author : Fabio Cuzzolin
language : en
Publisher: Springer Nature
Release Date : 2020-12-17

The Geometry Of Uncertainty written by Fabio Cuzzolin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Computers categories.

The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.

Uncertainty In Geometric Computations

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Author : Joab Winkler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Uncertainty In Geometric Computations written by Joab Winkler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book contains the proceedings of the workshop Uncertainty in Geomet ric Computations that was held in Sheffield, England, July 5-6, 2001. A total of 59 delegates from 5 countries in Europe, North America and Asia attended the workshop. The workshop provided a forum for the discussion of com putational methods for quantifying, representing and assessing the effects of uncertainty in geometric computations. It was organised around lectures by invited speakers, and presentations in poster form from participants. Computer simulations and modelling are used frequently in science and engi neering, in applications ranging from the understanding of natural and artificial phenomena, to the design, test and manufacturing stages of production. This widespread use necessarily implies that detailed knowledge of the limitations of computer simulations is required. In particular, the usefulness of a computer simulation is directly dependent on the user's knowledge of the uncertainty in the simulation. Although an understanding of the phenomena being modelled is an important requirement of a good computer simulation, the model will be plagued by deficiencies if the errors and uncertainties in it are not consid ered when the results are analysed. The applications of computer modelling are large and diverse, but the workshop focussed on the management of un certainty in three areas : Geometric modelling, computer vision, and computer graphics.

Computational Geometry With Independent And Dependent Uncertainties

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Author : Rivka Gitik
language : en
Publisher: World Scientific
Release Date : 2022-08-11

Computational Geometry With Independent And Dependent Uncertainties written by Rivka Gitik and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-11 with Computers categories.

This comprehensive compendium describes a parametric model and algorithmic theory to represent geometric entities with dependent uncertainties between them. The theory, named Linear Parametric Geometric Uncertainty Model (LPGUM), is an expressive and computationally efficient framework that allows to systematically study geometric uncertainty and its related algorithms in computer geometry.The self-contained monograph is of great scientific, technical, and economic importance as geometric uncertainty is ubiquitous in mechanical CAD/CAM, robotics, computer vision, wireless networks and many other fields. Geometric models, in contrast, are usually exact and do not account for these inaccuracies.This useful reference text benefits academics, researchers, and practitioners in computer science, robotics, mechanical engineering and related fields.

Proceedings Of The 6th International Symposium On Uncertainty Quantification And Stochastic Modelling

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Author : José Eduardo Souza De Cursi
language : en
Publisher: Springer Nature
Release Date : 2023-10-21

Proceedings Of The 6th International Symposium On Uncertainty Quantification And Stochastic Modelling written by José Eduardo Souza De Cursi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-21 with Technology & Engineering categories.

This proceedings book covers a wide range of topics related to uncertainty analysis and its application in various fields of engineering and science. It explores uncertainties in numerical simulations for soil liquefaction potential, the toughness properties of construction materials, experimental tests on cyclic liquefaction potential, and the estimation of geotechnical engineering properties for aerogenerator foundation design. Additionally, the book delves into uncertainties in concrete compressive strength, bio-inspired shape optimization using isogeometric analysis, stochastic damping in rotordynamics, and the hygro-thermal properties of raw earth building materials. It also addresses dynamic analysis with uncertainties in structural parameters, reliability-based design optimization of steel frames, and calibration methods for models with dependent parameters. The book further explores mechanical property characterization in 3D printing, stochastic analysis in computational simulations, probability distribution in branching processes, data assimilation in ocean circulation modeling, uncertainty quantification in climate prediction, and applications of uncertainty quantification in decision problems and disaster management. This comprehensive collection provides insights into the challenges and solutions related to uncertainty in various scientific and engineering contexts.

Experimental And Applied Mechanics Volume 6

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Author : Tom Proulx
language : en
Publisher: CRC Press
Release Date : 2025-08-07

Experimental And Applied Mechanics Volume 6 written by Tom Proulx and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-07 with Technology & Engineering categories.

This the sixth volume of six from the Annual Conference of the Society for Experimental Mechanics, 2010, brings together 128 chapters on Experimental and Applied Mechanics. It presents early findings from experimental and computational investigations including High Accuracy Optical Measurements of Surface Topography, Elastic Properties of Living Cells, Standards for Validating Stress Analyses by Integrating Simulation and Experimentation, Efficiency Enhancement of Dye-sensitized Solar Cell, and Blast Performance of Sandwich Composites With Functionally Graded Core.

Computational Biomechanics For Medicine

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Author : Adam Wittek
language : en
Publisher: Springer Nature
Release Date : 2024-08-29

Computational Biomechanics For Medicine written by Adam Wittek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-29 with Technology & Engineering categories.

This book presents peer-reviewed contributions from the MICCAI 2023 Computational Biomechanics for Medicine CBM XVIII Workshop held in conjunction with the 26th International MICCAI Conference. The content focuses on applications of computational biomechanics to computer-integrated medicine, which includes medical image computing, application of machine learning in image analysis and biomechanics, atlas based biomechanical simulations, novel algorithms of computational biomechanics and experimental methods for analysis of disease and injury mechanisms. The book details state-of-the-art progress in the above fields to researchers, students, and professionals.

An Introduction To The Theory Of Spatial Object Modelling For Gis

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Author : Martin Molenaar
language : en
Publisher: CRC Press
Release Date : 1998-12-15

An Introduction To The Theory Of Spatial Object Modelling For Gis written by Martin Molenaar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-15 with Technology & Engineering categories.

This text provides a background view of the object approach, related geometric aspects, the different level of data modelling and the role of geo-information theory. The rest of the book builds upon these concepts describing the applicability of broader aspects such as topology, thematic object classes and class hierarchies, object aggregation and generalization and uncertainty.

The Handbook Of Geographic Information Science

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Author : John P. Wilson
language : en
Publisher: John Wiley & Sons
Release Date : 2008-04-15

The Handbook Of Geographic Information Science written by John P. Wilson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-15 with Science categories.

This Handbook is an essential reference and a guide to the rapidly expanding field of Geographic Information Science. Designed for students and researchers who want an in-depth treatment of the subject, including background information Comprises around 40 substantial essays, each written by a recognized expert in a particular area Covers the full spectrum of research in GIS Surveys the increasing number of applications of GIS Predicts how GIS is likely to evolve in the near future

Nuclear Data For Science And Technology

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Author : K.H. Bockhoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nuclear Data For Science And Technology written by K.H. Bockhoff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Proceedings of the International Conference, Antwerp, Belgium, September 6-10, 1982

Discrete Geometry For Computer Imagery

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Author : Eric Andres
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-04-07

Discrete Geometry For Computer Imagery written by Eric Andres and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-07 with Computers categories.

This book constitutes the refereed proceedings of the 12th International Conference on Discrete Geometry for Computer Imagery, DGCI 2005, held in Poitiers, France in April 2005. The 36 revised full papers presented together with an invited paper were carefully reviewed and selected from 53 submissions. The papers are organized in topical sections on applications, discrete hierarchical geometry, discrete tomography, discrete topology, object properties, reconstruction and recognition, uncertain geometry, and visualization.