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Author: Jagat Narain Kapur Publisher: ISBN: Category : Computers Languages : en Pages : 440
Book Description
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.
Author: Jagat Narain Kapur Publisher: ISBN: Category : Computers Languages : en Pages : 440
Book Description
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.
Author: Karmeshu Publisher: Springer ISBN: 3540362126 Category : Technology & Engineering Languages : en Pages : 300
Book Description
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.
Author: Jagat Narain Kapur Publisher: New Age International ISBN: Category : Computers Languages : en Pages : 592
Book Description
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.
Author: Shu-Cherng Fang Publisher: Springer Science & Business Media ISBN: 1461561310 Category : Business & Economics Languages : en Pages : 350
Book Description
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.
Author: V.P. Singh Publisher: Springer Science & Business Media ISBN: 9401124302 Category : Science Languages : en Pages : 583
Book Description
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.
Author: Jagat Narain Kapur
Author: Jagat Narain Kapur
Author: Parmil Kumar
Author: Karmeshu
Author: Jagat Narain Kapur
Author: Charlotte De Fraiture
Author: Charlotte Du Fraiture
Author: Shu-Cherng Fang
Author: Vasile Preda
Author: V.P. Singh
Author: Jagat Narain Kapur