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Entropy Optimization Principles with Applications

Entropy Optimization Principles with Applications
Author: Jagat Narain Kapur
Publisher:
Total Pages: 440
Release: 1992
Genre: Computers
ISBN:
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This senior-level textbook on entropy provides a conceptual framework for the study of probabilistic systems with its elucidation of three key concepts - Shannon's information theory, Jaynes' maximum entropy principle and Kullback's minimum cross-entropy principle.

Entropy Measures, Maximum Entropy Principle and Emerging Applications

Entropy Measures, Maximum Entropy Principle and Emerging Applications
Author: Karmeshu
Publisher: Springer
Total Pages: 300
Release: 2012-10-01
Genre: Technology & Engineering
ISBN: 3540362126
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The last two decades have witnessed an enormous growth with regard to ap plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "As if assuming that inexpensive, high-speed processing would come to pass, Shan non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face". Shannon introduced the concept of entropy. The notable feature of the entropy frame work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.

Measures of Information and Their Applications

Measures of Information and Their Applications
Author: Jagat Narain Kapur
Publisher: New Age International
Total Pages: 592
Release: 1994
Genre: Computers
ISBN:
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The present book may be regarded as a successor of author's Maximum Entropy Models in Science and Engineering (Wiley), Generalized Maximum Entropy Principle (Sandford), Entropy Optimization Principles and Their Applications (Academic) and Insight into Entropy Optimizations Principles (MSTS). It contains sixty research investigations of the author on measures of entropy, directed divergence, weighted directed divergence, information, principles of maximum entropy, minimum entropy, minimum cross-entropy, minimum entropy, minimum information, minimum weighted information and maximum weighted entropy, most likely and most feasible distributions, duals of optimization problems, entropy optimization under inequality constraints, characterising moments, parameter estimation, maximum entropy approximation for a probability distribution, proving inequalities, laws of information, entropic mean, mean-entropy frontier, logistic-type growth models, birth-death processes, distributions of statistical mechanics, estimation of missing values, theorems of information theory and many others.

Entropy Optimization and Mathematical Programming

Entropy Optimization and Mathematical Programming
Author: Shu-Cherng Fang
Publisher: Springer Science & Business Media
Total Pages: 350
Release: 2012-12-06
Genre: Business & Economics
ISBN: 1461561310
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Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input-output analysis, portfolio investment, information analysis, and linear and nonlinear programming. While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader.

Entropy and Energy Dissipation in Water Resources

Entropy and Energy Dissipation in Water Resources
Author: V.P. Singh
Publisher: Springer Science & Business Media
Total Pages: 583
Release: 2012-12-06
Genre: Science
ISBN: 9401124302
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Since the landmark contributions of C. E. Shannon in 1948, and those of E. T. Jaynes about a decade later, applications of the concept of entropy and the principle of maximum entropy have proliterated in science and engineering. Recent years have witnessed a broad range of new and exciting developments in hydrology and water resources using the entropy concept. These have encompassed innovative methods for hydrologic network design, transfer of information, flow forecasting, reliability assessment for water distribution systems, parameter estimation, derivation of probability distributions, drainage-network analysis, sediment yield modeling and pollutant loading, bridge-scour analysis, construction of velocity profiles, comparative evaluation of hydrologic models, and so on. Some of these methods hold great promise for advancement of engineering practice, permitting rational alternatives to conventional approaches. On the other hand, the concepts of energy and energy dissipation are being increasingly applied to a wide spectrum of problems in environmental and water resources. Both entropy and energy dissipation have their origin in thermodynamics, and are related concepts. Yet, many of the developments using entropy seem to be based entirely on statistical interpretation and have seemingly little physical content. For example, most of the entropy-related developments and applications in water resources have been based on the information-theoretic interpretation of entropy. We believe if the power of the entropy concept is to be fully realized, then its physical basis has to be established.

Entropy Theory and its Application in Environmental and Water Engineering

Entropy Theory and its Application in Environmental and Water Engineering
Author: Vijay P. Singh
Publisher: John Wiley & Sons
Total Pages: 787
Release: 2013-01-10
Genre: Science
ISBN: 1118428609
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Entropy Theory and its Application in Environmental and Water Engineering responds to the need for a book that deals with basic concepts of entropy theory from a hydrologic and water engineering perspective and then for a book that deals with applications of these concepts to a range of water engineering problems. The range of applications of entropy is constantly expanding and new areas finding a use for the theory are continually emerging. The applications of concepts and techniques vary across different subject areas and this book aims to relate them directly to practical problems of environmental and water engineering. The book presents and explains the Principle of Maximum Entropy (POME) and the Principle of Minimum Cross Entropy (POMCE) and their applications to different types of probability distributions. Spatial and inverse spatial entropy are important for urban planning and are presented with clarity. Maximum entropy spectral analysis and minimum cross entropy spectral analysis are powerful techniques for addressing a variety of problems faced by environmental and water scientists and engineers and are described here with illustrative examples. Giving a thorough introduction to the use of entropy to measure the unpredictability in environmental and water systems this book will add an essential statistical method to the toolkit of postgraduates, researchers and academic hydrologists, water resource managers, environmental scientists and engineers. It will also offer a valuable resource for professionals in the same areas, governmental organizations, private companies as well as students in earth sciences, civil and agricultural engineering, and agricultural and rangeland sciences. This book: Provides a thorough introduction to entropy for beginners and more experienced users Uses numerous examples to illustrate the applications of the theoretical principles Allows the reader to apply entropy theory to the solution of practical problems Assumes minimal existing mathematical knowledge Discusses the theory and its various aspects in both univariate and bivariate cases Covers newly expanding areas including neural networks from an entropy perspective and future developments.

Entropy Application for Forecasting

Entropy Application for Forecasting
Author: Ana Jesus Lopez-Menendez
Publisher: MDPI
Total Pages: 200
Release: 2020-12-29
Genre: Technology & Engineering
ISBN: 3039364871
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This book shows the potential of entropy and information theory in forecasting, including both theoretical developments and empirical applications. The contents cover a great diversity of topics, such as the aggregation and combination of individual forecasts, the comparison of forecasting performance, and the debate concerning the tradeoff between complexity and accuracy. Analyses of forecasting uncertainty, robustness, and inconsistency are also included, as are proposals for new forecasting approaches. The proposed methods encompass a variety of time series techniques (e.g., ARIMA, VAR, state space models) as well as econometric methods and machine learning algorithms. The empirical contents include both simulated experiments and real-world applications focusing on GDP, M4-Competition series, confidence and industrial trend surveys, and stock exchange composite indices, among others. In summary, this collection provides an engaging insight into entropy applications for forecasting, offering an interesting overview of the current situation and suggesting possibilities for further research in this field.

Uncertainty and Information

Uncertainty and Information
Author: George J. Klir
Publisher: John Wiley & Sons
Total Pages: 499
Release: 2005-11-22
Genre: Technology & Engineering
ISBN: 0471755567
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Deal with information and uncertainty properly and efficientlyusing tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized InformationTheory contains comprehensive and up-to-date coverage of resultsthat have emerged from a research program begun by the author inthe early 1990s under the name "generalized information theory"(GIT). This ongoing research program aims to develop a formalmathematical treatment of the interrelated concepts of uncertaintyand information in all their varieties. In GIT, as in classicalinformation theory, uncertainty (predictive, retrodictive,diagnostic, prescriptive, and the like) is viewed as amanifestation of information deficiency, while information isviewed as anything capable of reducing the uncertainty. A broadconceptual framework for GIT is obtained by expanding theformalized language of classical set theory to include moreexpressive formalized languages based on fuzzy sets of varioustypes, and by expanding classical theory of additive measures toinclude more expressive non-additive measures of varioustypes. This landmark book examines each of several theories for dealingwith particular types of uncertainty at the following fourlevels: * Mathematical formalization of the conceived type ofuncertainty * Calculus for manipulating this particular type ofuncertainty * Justifiable ways of measuring the amount of uncertainty in anysituation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complexmaterial and demonstrate practical applications, generoushistorical and bibliographical notes, end-of-chapter exercises totest readers' newfound knowledge, glossaries, and an Instructor'sManual, this is an excellent graduate-level textbook, as well as anoutstanding reference for researchers and practitioners who dealwith the various problems involving uncertainty and information. AnInstructor's Manual presenting detailed solutions to all theproblems in the book is available from the Wiley editorialdepartment.