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Author : P. Zeephongsekul
Publisher :
ISBN 13 : 9780864441256
Total Pages : 10 pages
Book Rating : 4.4/5 (412 download)
Download or read book Maximum Entropy Principle and the Lagrange Interpolation Polynomials written by P. Zeephongsekul and published by . This book was released on 1987 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henryk Gzyl
Publisher : World Scientific
ISBN 13 : 9810218125
Total Pages : 161 pages
Book Rating : 4.8/5 (12 download)
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.
Author : Jagat Narain Kapur
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (91 download)
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.
Author : Nailong Wu
Publisher : Springer Science & Business Media
ISBN 13 : 3642606296
Total Pages : 336 pages
Book Rating : 4.6/5 (426 download)
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.
Author : Jagat Narain Kapur
Publisher : John Wiley & Sons
ISBN 13 : 9788122402162
Total Pages : 660 pages
Book Rating : 4.4/5 (21 download)
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.
Author :
Publisher : Academic Press
ISBN 13 : 0128028688
Total Pages : 399 pages
Book Rating : 4.1/5 (28 download)
Download or read book Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part A written by and published by Academic Press. This book was released on 2015-08-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a series of articles concerning current important topics in quantum chemistry. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology Features detailed reviews written by leading international researchers
Author : Jagat Narain Kapur
Publisher :
ISBN 13 : 9780920574256
Total Pages : 213 pages
Book Rating : 4.5/5 (742 download)
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:
Author : Johann-Heinrich Christiaan Schonfeldt
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (956 download)
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.).
Author : Karmeshu
Publisher : Springer
ISBN 13 : 9783642535055
Total Pages : 297 pages
Book Rating : 4.5/5 (35 download)
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.
Author : Saeed V. Vaseghi
Publisher : John Wiley & Sons
ISBN 13 : 0470740167
Total Pages : 544 pages
Book Rating : 4.4/5 (77 download)
Download or read book Advanced Digital Signal Processing and Noise Reduction written by Saeed V. Vaseghi and published by John Wiley & Sons. This book was released on 2008-12-23 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Digital signal processing plays a central role in the development of modern communication and information processing systems. The theory and application of signal processing is concerned with the identification, modelling and utilisation of patterns and structures in a signal process. The observation signals are often distorted, incomplete and noisy and therefore noise reduction, the removal of channel distortion, and replacement of lost samples are important parts of a signal processing system. The fourth edition of Advanced Digital Signal Processing and Noise Reduction updates and extends the chapters in the previous edition and includes two new chapters on MIMO systems, Correlation and Eigen analysis and independent component analysis. The wide range of topics covered in this book include Wiener filters, echo cancellation, channel equalisation, spectral estimation, detection and removal of impulsive and transient noise, interpolation of missing data segments, speech enhancement and noise/interference in mobile communication environments. This book provides a coherent and structured presentation of the theory and applications of statistical signal processing and noise reduction methods. Two new chapters on MIMO systems, correlation and Eigen analysis and independent component analysis Comprehensive coverage of advanced digital signal processing and noise reduction methods for communication and information processing systems Examples and applications in signal and information extraction from noisy data Comprehensive but accessible coverage of signal processing theory including probability models, Bayesian inference, hidden Markov models, adaptive filters and Linear prediction models Advanced Digital Signal Processing and Noise Reduction is an invaluable text for postgraduates, senior undergraduates and researchers in the fields of digital signal processing, telecommunications and statistical data analysis. It will also be of interest to professional engineers in telecommunications and audio and signal processing industries and network planners and implementers in mobile and wireless communication communities.
Author : James H. Justice
Publisher : Cambridge University Press
ISBN 13 : 9780521096034
Total Pages : 0 pages
Book Rating : 4.0/5 (96 download)
Download or read book Maximum Entropy and Bayesian Methods in Applied Statistics written by James H. Justice and published by Cambridge University Press. This book was released on 2009-01-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers by leading researchers in their respective fields contains contributions showing the use of the maximum entropy method in many of the fields in which it finds application. In the physical, mathematical and biological sciences it is often necessary to make inferences based on insufficient data. The problem of choosing one among the many possible conclusions or models which are compatible with the data may be resolved in a variety of ways. A particularly appealing method is to choose the solution which maximizes entropy in the sense that the conclusion or model honours the observed data but implies no further assumptions not warranted by the data. The maximum entropy principle has been growing in importance and acceptance in many fields, perhaps most notably statistical physics, astronomy, geophysics, signal processing, image analysis and physical chemistry. The papers included in this volume touch on most of the current areas of research activity and application, and will be of interest to research workers in all fields in which the maximum entropy method may be applied.
Author : Jason Smith
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (13 download)
Download or read book Maximum Entropy and Information Theory Approaches to Economics written by Jason Smith and published by . This book was released on 2018 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the natural sciences, complex non-linear systems composed of large numbers of smaller subunits provide an opportunity to apply the tools of statistical mechanics and information theory. The principle of maximum entropy can usually provide shortcuts in the treatment of these complex systems. However, there is an impasse to straightforward application to social and economic systems: the lack of well-defined constraints for Lagrange multipliers. This is typically treated in economics by introducing marginal utility as a Lagrange multiplier.Jumping off from Gary Becker's 1962 paper "Irrational Behavior and Economic Theory" -- a maximum entropy argument in disguise -- we introduce Peter Fielitz and Guenter Borchardt's concept of "information equilibrium" presented in arXiv:0905.0610v4 [physics.gen-ph] as a means of applying maximum entropy methods even in cases where well-defined constraints such as energy conservation required to define Lagrange multipliers and partition functions are not obvious (i.e. economics). From these initial steps we are able to motivate a well-defined constraint in terms of growth rates and develop a formalism for ensembles of markets described by information equilibrium conditions. We apply information equilibrium to a description of the US unemployment rate, connect it to search and matching theory, and empirical regularities such as Okun's Law. This represents a step toward Lee Smolin's call for a "statistical economics" analogous to statistical mechanics in arXiv:0902.4274 [q-fin.GN].
Author : Gelu Popescu
Publisher : American Mathematical Soc.
ISBN 13 : 9781470404727
Total Pages : 83 pages
Book Rating : 4.4/5 (47 download)
Download or read book Entropy and Multivariable Interpolation written by Gelu Popescu and published by American Mathematical Soc.. This book was released on 2006 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define a new notion of entropy for operators on Fock spaces and positive multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (e.g., multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive multi-Toeplitz kernels on free semigroups (resp. multi-analytic operators) and consequences concerning the extreme points of the unit ball of the noncommutative analytic Toeplitz algebra 'F ninfty'. We obtain several geometric characterizations of the central intertwining lifting, a maximal principle, and a permanence principle for the noncommutative commutant lifting theorem. Under certain natural conditions, we find explicit forms for the maximal entropy solution of this multivariable commutant lifting theorem. All these results are used to solve maximal entropy interpolation problems in several variables. We obtain explicit forms for the maximal entropy solution (as well as its entropy) of the Sarason, Caratheodory-Schur, and Nevanlinna-Pick type interpolation problems for the noncommutative (resp. commutative) analytic Toeplitz algebra 'F ninfty' (resp. In particular, we provide explicit forms for the maximal entropy solutions of several interpolation problems on the unit ball of '\mathbb{C n'.
Author : T.J. Sullivan
Publisher : Springer
ISBN 13 : 3319233955
Total Pages : 351 pages
Book Rating : 4.3/5 (192 download)
Download or read book Introduction to Uncertainty Quantification written by T.J. Sullivan and published by Springer. This book was released on 2015-12-14 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.
Author :
Publisher :
ISBN 13 :
Total Pages : 1244 pages
Book Rating : 4.3/5 (91 download)
Download or read book Index of Mathematical Papers written by and published by . This book was released on 1985 with total page 1244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Israel' Cudikovič Gohberg
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (65 download)
Download or read book A Maximum Entropy Principle in the General Framework of the Band Method written by Israel' Cudikovič Gohberg and published by . This book was released on 1989 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jenny Farmer
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (885 download)
Download or read book Maximum Entropy Probability Distribution written by Jenny Farmer and published by . This book was released on 2014 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a set of randomly sampled experimental data, a numeric algorithm has been developed to determine a probability distribution function that represents the data. The algorithm is based on the maximum entropy method in information theory, which states that the solution that maximizes entropy while satisfying known constraints is presumed to be the correct solution. The probability distribution function is expressed as an exponential of a series expansion over Chebyshev polynomials where the expansion coefficients are formally Lagrange multipliers and must be determined. The method for finding these Lagrange multipliers is through an iterative trial-and-error approach. After each guess for the coefficients, the trial solution is evaluated according to how well it represents the data. This assessment is performed by using the cumulative distribution function to transform the data to uniformly distributed random data, and then comparing the transformed data to known results for a uniform distribution using binning and ordered statistics. The algorithm is presented in the form of a highly adaptive and flexible tool that does not assume prior knowledge about the data, but provides many documented settings to allow for maximum efficiency in the event the user has more information about the data or has specific requirements. To demonstrate the power and flexibility of this approach, it has been tested and compared against known distributions, many of which have specific properties known to cause standard methods to fail. Each of these examples demonstrates a convergence to the true function as the sample size increases.
