Applications Of Mathematics Of Uncertainty

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Applications of Mathematics of Uncertainty

Author : John N. Mordeson
Publisher : Springer Nature
ISBN 13 : 3030869962
Total Pages : 307 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Applications of Mathematics of Uncertainty by : John N. Mordeson

Download or read book Applications of Mathematics of Uncertainty written by John N. Mordeson and published by Springer Nature. This book was released on 2021-11-17 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an examination of major problems facing the world using mathematics of uncertainty. These problems include climate change, coronavirus pandemic, human tracking, biodiversity, and other grand challenges. Mathematics of uncertainty is used in a modern more general sense than traditional mathematics. Since accurate data is impossible to obtain concerning human tracking and other global problems, mathematics of uncertainty is an ideal discipline to study these problems. The authors place several scientific studies into different mathematical settings such as nonstandard analysis and soft logic. Fuzzy differentiation is used to model the spread of diseases such as the coronavirus. The book uses fuzzy graph theory to examine the problems of human tracking and illegal immigration. The book is an excellent reference source for advanced under-graduate and graduate students in mathematics and the social sciences as well as for researchers and teachers.

Mathematics of Uncertainty

Author : Hans Bandemer
Publisher : Springer Science & Business Media
ISBN 13 : 3540284575
Total Pages : 199 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Mathematics of Uncertainty by : Hans Bandemer

Download or read book Mathematics of Uncertainty written by Hans Bandemer and published by Springer Science & Business Media. This book was released on 2006 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematics of Uncertainty" provides the basic ideas and foundations of uncertainty, covering the fields of mathematics in which uncertainty, variability, imprecision and fuzziness of data are of importance. This introductory book describes the basic ideas of the mathematical fields of uncertainty from simple interpolation to wavelets, from error propagation to fuzzy sets and neural networks. The book presents the treatment of problems of interpolation and approximation, as well as observation fuzziness which can essentially influence the preciseness and reliability of statements on functional relationships. The notions of randomness and probability are examined as a model for the variability of observation and measurement results. Besides these basic ideas the book also presents methods of qualitative data analysis such as cluster analysis and classification, and of evaluation of functional relationships such as regression analysis and quantitative fuzzy data analysis.

Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems

Author : Chakraverty, S.
Publisher : IGI Global
ISBN 13 : 1466649925
Total Pages : 442 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems by : Chakraverty, S.

Download or read book Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems written by Chakraverty, S. and published by IGI Global. This book was released on 2014-01-31 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book provides the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications"--Provided by publisher.

Probability

Author : Dorian Feldman
Publisher : CRC Press
ISBN 13 : 9780824784522
Total Pages : 428 pages
Book Rating : 4.7/5 (845 download)

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Book Synopsis Probability by : Dorian Feldman

Download or read book Probability written by Dorian Feldman and published by CRC Press. This book was released on 1991-09-24 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Uncertainty Theory

Author : Baoding Liu
Publisher : Springer
ISBN 13 : 3540731652
Total Pages : 255 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Uncertainty Theory by : Baoding Liu

Download or read book Uncertainty Theory written by Baoding Liu and published by Springer. This book was released on 2007-09-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. For this new edition the entire text has been totally rewritten. The chapters on chance theory and uncertainty theory are completely new. Mathematicians, researchers, engineers, designers, and students will find this work a stimulating and useful reference.

Do Dice Play God?

Author : Ian Stewart
Publisher : Profile Books
ISBN 13 : 178283401X
Total Pages : 292 pages
Book Rating : 4.7/5 (828 download)

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Book Synopsis Do Dice Play God? by : Ian Stewart

Download or read book Do Dice Play God? written by Ian Stewart and published by Profile Books. This book was released on 2019-06-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty is everywhere. It lurks in every consideration of the future - the weather, the economy, the sex of an unborn child - even quantities we think that we know such as populations or the transit of the planets contain the possibility of error. It's no wonder that, throughout that history, we have attempted to produce rigidly defined areas of uncertainty - we prefer the surprise party to the surprise asteroid. We began our quest to make certain an uncertain world by reading omens in livers, tea leaves, and the stars. However, over the centuries, driven by curiosity, competition, and a desire be better gamblers, pioneering mathematicians and scientists began to reduce wild uncertainties to tame distributions of probability and statistical inferences. But, even as unknown unknowns became known unknowns, our pessimism made us believe that some problems were unsolvable and our intuition misled us. Worse, as we realized how omnipresent and varied uncertainty is, we encountered chaos, quantum mechanics, and the limitations of our predictive power. Bestselling author Professor Ian Stewart explores the history and mathematics of uncertainty. Touching on gambling, probability, statistics, financial and weather forecasts, censuses, medical studies, chaos, quantum physics, and climate, he makes one thing clear: a reasonable probability is the only certainty.

Mathematics of Uncertainty for Coping with World Challenges

Author : John N. Mordeson
Publisher : Springer Nature
ISBN 13 : 3030686841
Total Pages : 209 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Mathematics of Uncertainty for Coping with World Challenges by : John N. Mordeson

Download or read book Mathematics of Uncertainty for Coping with World Challenges written by John N. Mordeson and published by Springer Nature. This book was released on 2021-02-23 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book ranks countries with respect to their achievement of the Sustainable Development Goals and their vulnerability to climate change. Human livelihoods, stable economies, health, and high quality of life all depend on a stable climate and earth system, and a diversity of species and ecosystems. Climate change significantly impacts human trafficking, modern slavery, and global hunger. This book examines these global problems using techniques from mathematics of uncertainty. Since accurate data concerning human trafficking and modern slavery is impossible to obtain, mathematics of uncertainty is an ideal discipline to study these problems. The book also considers the interconnection between climate change, world hunger, human trafficking, modern slavery, and the coronavirus. Connectivity properties of fuzzy graphs are used to examine trafficking flow between regions in the world. The book is an excellent reference source for advanced undergraduate and graduate students in mathematics and the social sciences as well as for researchers and teachers.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author : Luis Tenorio
Publisher : SIAM
ISBN 13 : 1611974917
Total Pages : 275 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by : Luis Tenorio

Download or read book An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems written by Luis Tenorio and published by SIAM. This book was released on 2017-07-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems?includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.

Mathematics of Uncertainty

Author : Hans Bandemer
Publisher :
ISBN 13 :
Total Pages : 190 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Mathematics of Uncertainty by : Hans Bandemer

Download or read book Mathematics of Uncertainty written by Hans Bandemer and published by . This book was released on 2005 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fuzzy Graph Theory

Author : Sunil Mathew
Publisher : Springer
ISBN 13 : 3319714074
Total Pages : 320 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Fuzzy Graph Theory by : Sunil Mathew

Download or read book Fuzzy Graph Theory written by Sunil Mathew and published by Springer. This book was released on 2017-12-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine’s work on fuzzy interval graphs, fuzzy analogs of Marczewski’s theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger’s theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.

Uncertainty Quantification

Author : Luis Chase
Publisher : Nova Science Publishers
ISBN 13 : 9781536148626
Total Pages : 0 pages
Book Rating : 4.1/5 (486 download)

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Book Synopsis Uncertainty Quantification by : Luis Chase

Download or read book Uncertainty Quantification written by Luis Chase and published by Nova Science Publishers. This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent times, polynomial chaos expansion has emerged as a dominant technique to determine the response uncertainties of a system by propagating the uncertainties of the inputs. In this regard, the opening chapter of Uncertainty Quantification: Advances in Research and Applications, an intrusive approach called Galerkin Projection as well as non-intrusive approaches (such as pseudo-spectral projection and linear regression) are discussed.Next, the authors introduce a new methodology to determine the uncertainties of input parameters using CIRCÉ software to overcome the reliance on expert judgment. The goal is to determinate and evaluate the uncertainty bounds for physical models related to reflood model of MARS-KS code Vessel module (coupled with COBRA-TF) using both CIRCÉ and the experimental data of FEBA.Lastly, uncertainties related to rheological model parameters of skeletal muscles are modeled and analyzed, and available data are acquired and fused for hyperelastic constitutive model parameters with Neo-Hookean and Mooney-Rivlin formulations.

Sustainable Development Goals: Analysis by Mathematics of Uncertainty

Author : John N. Mordeson
Publisher : Springer Nature
ISBN 13 : 3030485234
Total Pages : 237 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Sustainable Development Goals: Analysis by Mathematics of Uncertainty by : John N. Mordeson

Download or read book Sustainable Development Goals: Analysis by Mathematics of Uncertainty written by John N. Mordeson and published by Springer Nature. This book was released on 2020-06-22 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses mathematics of uncertainty to examine how well countries are achieving the 17 Sustainable Development Goals (SDGs) set by the members of the United Nations, with a focus on climate change, human trafficking and modern slavery. Although this approach has never been used before, mathematics of uncertainty is well suited to exploring these topics due to the lack of accurate data available. The authors place several scientific studies in a mathematical setting to pave the way for future research on issues of sustainability, climate change, human trafficking and modern slavery to using a wide range of mathematical techniques. Moreover, the book ranks countries in terms of their achievement of not only the SDGs, but in particular those SDGs pertinent to climate change, human trafficking, and modern slavery, and highlights the deficiencies in the foster care system that lead to human trafficking. As such it is an excellent reference resource for advanced undergraduate and graduate students in mathematics and the social sciences, as well as for researchers and teachers.

Uncertainty Quantification

Author : Christian Soize
Publisher : Springer
ISBN 13 : 3319543393
Total Pages : 329 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Uncertainty Quantification by : Christian Soize

Download or read book Uncertainty Quantification written by Christian Soize and published by Springer. This book was released on 2017-04-24 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials. Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available. This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.

Applications of Mathematics of Uncertainty

Author : John N. Mordeson
Publisher :
ISBN 13 : 9783030869977
Total Pages : 0 pages
Book Rating : 4.8/5 (699 download)

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Book Synopsis Applications of Mathematics of Uncertainty by : John N. Mordeson

Download or read book Applications of Mathematics of Uncertainty written by John N. Mordeson and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an examination of major problems facing the world using mathematics of uncertainty. These problems include climate change, coronavirus pandemic, human tracking, biodiversity, and other grand challenges. Mathematics of uncertainty is used in a modern more general sense than traditional mathematics. Since accurate data is impossible to obtain concerning human tracking and other global problems, mathematics of uncertainty is an ideal discipline to study these problems. The authors place several scientific studies into different mathematical settings such as nonstandard analysis and soft logic. Fuzzy differentiation is used to model the spread of diseases such as the coronavirus. The book uses fuzzy graph theory to examine the problems of human tracking and illegal immigration. The book is an excellent reference source for advanced under-graduate and graduate students in mathematics and the social sciences as well as for researchers and teachers.

Uncertainty Quantification

Author : Ralph C. Smith
Publisher : SIAM
ISBN 13 : 161197321X
Total Pages : 400 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Uncertainty Quantification by : Ralph C. Smith

Download or read book Uncertainty Quantification written by Ralph C. Smith and published by SIAM. This book was released on 2013-12-02 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.

Spectral Methods for Uncertainty Quantification

Author : Olivier Le Maitre
Publisher : Springer Science & Business Media
ISBN 13 : 9048135206
Total Pages : 542 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Spectral Methods for Uncertainty Quantification by : Olivier Le Maitre

Download or read book Spectral Methods for Uncertainty Quantification written by Olivier Le Maitre and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

Decision Making Under Uncertainty

Author : Claude Greengard
Publisher : Springer Science & Business Media
ISBN 13 : 146849256X
Total Pages : 166 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Decision Making Under Uncertainty by : Claude Greengard

Download or read book Decision Making Under Uncertainty written by Claude Greengard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the ideal world, major decisions would be made based on complete and reliable information available to the decision maker. We live in a world of uncertainties, and decisions must be made from information which may be incomplete and may contain uncertainty. The key mathematical question addressed in this volume is "how to make decision in the presence of quantifiable uncertainty." The volume contains articles on model problems of decision making process in the energy and power industry when the available information is noisy and/or incomplete. The major tools used in studying these problems are mathematical modeling and optimization techniques; especially stochastic optimization. These articles are meant to provide an insight into this rapidly developing field, which lies in the intersection of applied statistics, probability, operations research, and economic theory. It is hoped that the present volume will provide entry to newcomers into the field, and stimulation for further research.