Nonlinear Mathematics for Uncertainty and its Applications

Nonlinear Mathematics for Uncertainty and its Applications

Author: Shoumei Li

Publisher: Springer Science & Business Media

Published: 2011-07-21

Total Pages: 708

ISBN-13: 364222833X

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This volume is a collection of papers presented at the international conference on Nonlinear Mathematics for Uncertainty and Its Applications (NLMUA2011), held at Beijing University of Technology during the week of September 7--9, 2011. The conference brought together leading researchers and practitioners involved with all aspects of nonlinear mathematics for uncertainty and its applications. Over the last fifty years there have been many attempts in extending the theory of classical probability and statistical models to the generalized one which can cope with problems of inference and decision making when the model-related information is scarce, vague, ambiguous, or incomplete. Such attempts include the study of nonadditive measures and their integrals, imprecise probabilities and random sets, and their applications in information sciences, economics, finance, insurance, engineering, and social sciences. The book presents topics including nonadditive measures and nonlinear integrals, Choquet, Sugeno and other types of integrals, possibility theory, Dempster-Shafer theory, random sets, fuzzy random sets and related statistics, set-valued and fuzzy stochastic processes, imprecise probability theory and related statistical models, fuzzy mathematics, nonlinear functional analysis, information theory, mathematical finance and risk managements, decision making under various types of uncertainty, and others.


Nonlinear Expectations and Stochastic Calculus under Uncertainty

Nonlinear Expectations and Stochastic Calculus under Uncertainty

Author: Shige Peng

Publisher: Springer Nature

Published: 2019-09-09

Total Pages: 216

ISBN-13: 3662599031

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This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.


Linear and Nonlinear Inverse Problems with Practical Applications

Linear and Nonlinear Inverse Problems with Practical Applications

Author: Jennifer L. Mueller

Publisher: SIAM

Published: 2012-11-30

Total Pages: 349

ISBN-13: 1611972345

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Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.


Nonlinear Systems Analysis

Nonlinear Systems Analysis

Author: M. Vidyasagar

Publisher: SIAM

Published: 2002-01-01

Total Pages: 515

ISBN-13: 9780898719185

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When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.


Nonlinear and Complex Dynamics

Nonlinear and Complex Dynamics

Author: José António Tenreiro Machado

Publisher: Springer Science & Business Media

Published: 2011-08-28

Total Pages: 328

ISBN-13: 146140231X

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Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.


Nonlinear Programming

Nonlinear Programming

Author: Lorenz T. Biegler

Publisher: SIAM

Published: 2010-01-01

Total Pages: 411

ISBN-13: 0898719380

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This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization.


Introduction to Nonlinear Optimization

Introduction to Nonlinear Optimization

Author: Amir Beck

Publisher: SIAM

Published: 2014-10-27

Total Pages: 286

ISBN-13: 1611973651

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This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.


An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author: Luis Tenorio

Publisher: SIAM

Published: 2017-07-06

Total Pages: 275

ISBN-13: 1611974917

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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.


Proceedings of the 2011 International Conference on Informatics, Cybernetics, and Computer Engineering (ICCE2011) November 19-20, 2011, Melbourne, Australia

Proceedings of the 2011 International Conference on Informatics, Cybernetics, and Computer Engineering (ICCE2011) November 19-20, 2011, Melbourne, Australia

Author: Liangzhong Jiang

Publisher: Springer Science & Business Media

Published: 2011-11-24

Total Pages: 821

ISBN-13: 3642251943

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The volume includes a set of selected papers extended and revised from the International Conference on Informatics, Cybernetics, and Computer Engineering. A computer network, often simply referred to as a network, is a collection of computers and devices interconnected by communications channels that facilitate communications and allows sharing of resources and information among interconnected devices. Put more simply, a computer network is a collection of two or more computers linked together for the purposes of sharing information, resources, among other things. Computer networking or Data Communications (Datacom) is the engineering discipline concerned with computer networks. Computer networking is sometimes considered a sub-discipline of electrical engineering, telecommunications, computer science, information technology and/or computer engineering since it relies heavily upon the theoretical and practical application of these scientific and engineering disciplines. Networks may be classified according to a wide variety of characteristics such as medium used to transport the data, communications protocol used, scale, topology, organizational scope, etc. Electronics engineering, also referred to as electronic engineering, is an engineering discipline where non-linear and active electrical components such as electron tubes, and semiconductor devices, especially transistors, diodes and integrated circuits, are utilized to design electronic circuits, devices and systems, typically also including passive electrical components and based on printed circuit boards. The term denotes a broad engineering field that covers important subfields such as analog electronics, digital electronics, consumer electronics, embedded systems and power electronics. Electronics engineering deals with implementation of applications, principles and algorithms developed within many related fields, for example solid-state physics, radio engineering, telecommunications, control systems, signal processing, systems engineering, computer engineering, instrumentation engineering, electric power control, robotics, and many others. ICCE 2011 Volume 3 is to provide a forum for researchers, educators, engineers, and government officials involved in the general areas of Computer Engineering and Electronic Engineering to disseminate their latest research results and exchange views on the future research directions of these fields. 99 high-quality papers are included in the volume. Each paper has been peer-reviewed by at least 2 program committee members and selected by the volume editor. Special thanks to editors, staff of association and every participants of the conference. It’s you make the conference a success. We look forward to meeting you next year.


Numerical Methods for Unconstrained Optimization and Nonlinear Equations

Numerical Methods for Unconstrained Optimization and Nonlinear Equations

Author: J. E. Dennis, Jr.

Publisher: SIAM

Published: 1996-12-01

Total Pages: 394

ISBN-13: 9781611971200

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This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.