Download or read book The Generalized Maximum Entropy Principle with Applications written by Jagat Narain Kapur and published by . This book was released on 1987 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum entropy Models in Science and Engineering written by Jagat Narain Kapur and published by John Wiley & Sons. This book was released on 1989 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Is The First Comprehensive Book About Maximum Entropy Principle And Its Applications To A Diversity Of Fields Like Statistical Mechanics, Thermo-Dynamics, Business, Economics, Insurance, Finance, Contingency Tables, Characterisation Of Probability Distributions (Univariate As Well As Multivariate, Discrete As Well As Continuous), Statistical Inference, Non-Linear Spectral Analysis Of Time Series, Pattern Recognition, Marketing And Elections, Operations Research And Reliability Theory, Image Processing, Computerised Tomography, Biology And Medicine. There Are Over 600 Specially Constructed Exercises And Extensive Historical And Bibliographical Notes At The End Of Each Chapter.The Book Should Be Of Interest To All Applied Mathematicians, Physicists, Statisticians, Economists, Engineers Of All Types, Business Scientists, Life Scientists, Medical Scientists, Radiologists And Operations Researchers Who Are Interested In Applying The Powerful Methodology Based On Maximum Entropy Principle In Their Respective Fields.
Download or read book Entropy Measures Maximum Entropy Principle and Emerging Applications written by Karmeshu and published by Springer. This book was released on 2012-10-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Entropy Optimization Principles with Applications written by Jagat Narain Kapur and published by . This book was released on 1992 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Entropy and Energy Dissipation in Water Resources written by V.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Generalized Maximum Entropy Principle for Decision Analysis written by Marlin Uluess Thomas and published by . This book was released on 1977 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalized maximum entropy principle is described for dealing with decision problems involving uncertainty but with some prior knowledge about the probability space corresponding to nature. This knowledge about the probabilistic structure is expressed through known bounds on event probabilities and moments, which is incorporated into a nonlinear programming problem. The solution provides a maximum entropy distribution which is then used in treating the decision problem as one involving risk. An example application is described that involves the selection of oil spill recovery systems for inland harbor regions. Other areas of application are identified and tables of some maximum entropy distributions resulting from a variety of moment constraints are provided.
Download or read book Measures of Information and Their Applications written by Jagat Narain Kapur and published by New Age International. This book was released on 1994 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Maximum Entropy Method written by Nailong Wu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forty years ago, in 1957, the Principle of Maximum Entropy was first intro duced by Jaynes into the field of statistical mechanics. Since that seminal publication, this principle has been adopted in many areas of science and technology beyond its initial application. It is now found in spectral analysis, image restoration and a number of branches ofmathematics and physics, and has become better known as the Maximum Entropy Method (MEM). Today MEM is a powerful means to deal with ill-posed problems, and much research work is devoted to it. My own research in the area ofMEM started in 1980, when I was a grad uate student in the Department of Electrical Engineering at the University of Sydney, Australia. This research work was the basis of my Ph.D. the sis, The Maximum Entropy Method and Its Application in Radio Astronomy, completed in 1985. As well as continuing my research in MEM after graduation, I taught a course of the same name at the Graduate School, Chinese Academy of Sciences, Beijingfrom 1987to 1990. Delivering the course was theimpetus for developing a structured approach to the understanding of MEM and writing hundreds of pages of lecture notes.
Download or read book Entropy Measures Maximum Entropy Principle and Emerging Applications written by Karmeshu and published by Springer. This book was released on 2012-11-23 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applications of the Maximum Entropy Principle to Time Dependent Processes written by Johann-Heinrich Christiaan Schonfeldt and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The maximum entropy principle, pioneered by Jaynes, provides a method for finding the least biased probability distribution for the description of a system or process, given as prior information the expectation values of a set (in general, a small number) of relevant quantities associated with the system. The maximum entropy method was originally advanced by Jaynes as the basis of an information theory inspired foundation for equilibrium statistical mechanics. It was soon realised that the method is very useful to tackle several problems in physics and other fields. In particular it constitutes a powerful tool for obtaining approximate and sometimes exact solutions to several important partial differential equations of theoretical physics. In Chapter 1 a brief review of Shannon's information measure and Jaynes' maximum entropy formalism is provided. As an illustration of the maximum entropy principle a brief explanation of how it can be used to derive the standard grand canonical formalism in statistical mechanics is given. The work leading up to this thesis has resulted in the following publications in peer-review research journals: J.-H. Sch??nfeldt and A.R. Plastino, Maximum entropy approach to the collisional Vlasov equation: Exact solutions, Physica A, 369 (2006) 408-416, J.-H. Sch??nfeldt, N. Jimenez, A.R. Plastino, A. Plastino and M. Casas, Maximum entropy principle and classical evolution equations with source terms, Physica A, 374 (2007) 573-584, J.-H. Sch??nfeldt, G.B. Roston, A.R. Plastino and A. Plastino, Maximum entropy principle, evolution equations, and physics education, Rev. Mex. Fis. E, 52 (2)(2006) 151-159. Chapter 2 is based on Sch??nfeldt and Plastino (2006). Two different ways for obtaining exact maximum entropy solutions for a reduced collisional Vlasov equation endowed with a Fokker-Planck like collision term are investigated. Chapter 3 is based on Sch??nfeldt et al. (2007). Most applications of the maximum entropy principle to time dependent scenarios involved evolution equations exhibiting the form of a continuity equations and, consequently, preserving normalization in time. In Chapter 3 the maximum entropy principle is applied to evolution equations with source terms and, consequently, not preserving normalization. We explore in detail the structure and main properties of the dynamical equations connecting the time dependent relevant mean values, the associated Lagrange multipliers, the partition function, and the entropy of the maximum entropy scheme. In particular, we compare the H-theorems verified by the maximum entropy approximate solutions with the Htheorems verified by the exact solutions. Chapter 4 is based on Sch??nfeldt et al. (2006). In chapter 4 it is discussed how the maximum entropy principle can be incorporated into the teaching of aspects of theoretical physics related to, but not restricted to, statistical mechanics. We focus our attention on the study of maximum entropy solutions to evolution equations that exhibit the form of continuity equations (eg. Liouville equation, the diffusion equation the Fokker-Planck equation, etc.).
Download or read book Maximum Entropy Information Without Probability and Complex Fractals written by Guy Jumarie and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every thought is a throw of dice. Stephane Mallarme This book is the last one of a trilogy which reports a part of our research work over nearly thirty years (we discard our non-conventional results in automatic control theory and applications on the one hand, and fuzzy sets on the other), and its main key words are Information Theory, Entropy, Maximum Entropy Principle, Linguistics, Thermodynamics, Quantum Mechanics, Fractals, Fractional Brownian Motion, Stochastic Differential Equations of Order n, Stochastic Optimal Control, Computer Vision. Our obsession has been always the same: Shannon's information theory should play a basic role in the foundations of sciences, but subject to the condition that it be suitably generalized to allow us to deal with problems which are not necessarily related to communication engineering. With this objective in mind, two questions are of utmost importance: (i) How can we introduce meaning or significance of information in Shannon's information theory? (ii) How can we define and/or measure the amount of information involved in a form or a pattern without using a probabilistic scheme? It is obligatory to find suitable answers to these problems if we want to apply Shannon's theory to science with some chance of success. For instance, its use in biology has been very disappointing, for the very reason that the meaning of information is there of basic importance, and is not involved in this approach.
Download or read book The Maximum Entropy Principle and Some of Its Engineering Applications written by Joseph Patrick Noonan and published by . This book was released on 1969 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum Entropy and Ecology written by John Harte and published by OUP Oxford. This book was released on 2011-06-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pioneering graduate textbook provides readers with the concepts and practical tools required to understand the maximum entropy principle, and apply it to an understanding of ecological patterns. Rather than building and combining mechanistic models of ecosystems, the approach is grounded in information theory and the logic of inference. Paralleling the derivation of thermodynamics from the maximum entropy principle, the state variable theory of ecology developed in this book predicts realistic forms for all metrics of ecology that describe patterns in the distribution, abundance, and energetics of species over multiple spatial scales, a wide range of habitats, and diverse taxonomic groups. The first part of the book is foundational, discussing the nature of theory, the relationship of ecology to other sciences, and the concept of the logic of inference. Subsequent sections present the fundamentals of macroecology and of maximum information entropy, starting from first principles. The core of the book integrates these fundamental principles, leading to the derivation and testing of the predictions of the maximum entropy theory of ecology (METE). A final section broadens the book's perspective by showing how METE can help clarify several major issues in conservation biology, placing it in context with other theories and highlighting avenues for future research.
Download or read book Generalized Maximum Entropy Estimation written by Tobias Sutter and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Method of Maximum Entropy written by Henryk Gzyl and published by World Scientific. This book was released on 1995 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an outgrowth of a set of lecture notes on the maximum entropy method delivered at the 1st Venezuelan School of Mathematics. This yearly event aims at acquainting graduate students and university teachers with the trends, techniques and open problems of current interest. In this book the author reviews several versions of the maximum entropy method and makes its underlying philosophy clear.
Download or read book Maximum Entropy Principle and Its Applications to Spectral Analysis and Image Reconstruction written by Ming-Tung Hsu and published by . This book was released on 1975 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum Entropy in Action written by Brian Buck and published by Oxford : Clarendon Press ; New York : Oxford University Press. This book was released on 1991 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of introductory, interdisciplinary articles and lectures covering the fundamentals of the maximum entropy approach, a powerful new technique that provides a much needed extension of the established principles of rational inference in the sciences. Maximum entropy allows the interpretation of incomplete and "noisy" data, providing a description of the underlying physical systems. It has found application in both practical and theoretical studies ranging from image enhancement to nuclear physics, and from statistical mechanics to economics. The work explores these applications with specific problems of data analysis taken from the physical sciences. It will interest all physical scientists who deal with data and its interpretation, including statisticians and statistical physicists.
