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| entropy principle and its applications: Entropy Measures, Maximum Entropy Principle and Emerging Applications Karmeshu, 2012-10-01 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. |
| entropy principle and its applications: Entropy and Energy Dissipation in Water Resources V.P. Singh, M. Fiorentino, 2012-12-06 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 principle and its applications: Entropy Optimization Principles with Applications Jagat Narain Kapur, Hiremaglur K. Kesavan, 1992 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 principle and its applications: Entropy Theory and its Application in Environmental and Water Engineering Vijay P. Singh, 2013-02-18 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 principle and its applications: Entropy Theory and its Application in Environmental and Water Engineering Vijay P. Singh, 2013-01-10 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 principle and its applications: Principles and Applications of Thermodynamics Mr. Rohit Manglik, 2024-03-09 EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels. |
| entropy principle and its applications: An Introduction to Kolmogorov Complexity and Its Applications Ming Li, Paul Vitányi, 2019-06-11 This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features. This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gács-Kučera theorem, the Day-Gács theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovász local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution. Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface. As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science. |
| entropy principle and its applications: Entropy Theory in Hydrologic Science and Engineering Vijay P. Singh, 2014-09-22 A THOROUGH INTRODUCTION TO ENTROPY THEORY AND ITS APPLICATIONS IN HYDROLOGIC SCIENCE AND ENGINEERING This comprehensive volume addresses basic concepts of entropy theory from a hydrologic engineering perspective. The application of these concepts to a wide range of hydrologic engineering problems is discussed in detail. The book is divided into sections--preliminaries, rainfall and evapotranspiration, subsurface flow, surface flow, and environmental considerations. Helpful equations, solutions, tables, and diagrams are included throughout this practical resource. Entropy Theory in Hydrologic Science and Engineering covers: Introduction to entropy theory Maximum entropy production principle Performance measures Morphological analysis Evaluation and design of sampling and measurement networks Precipitation variability Rainfall frequency distributions Evaluation of precipitation forecasting schemes Assessment of potential water resources availability Evaporation Infiltration Soil moisture Groundwater flow Rainfall-runoff modeling Streamflow simulation Hydrologic frequency analysis Streamflow forecasting River flow regime classification Sediment yield Eco-index |
| entropy principle and its applications: Nonlinear Functional Analysis and its Applications E. Zeidler, 2013-12-11 As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? ( y) What typical applications are there? Vll Preface viii Special emphasis is placed on motivation. |
| entropy principle and its applications: Conceptual Density Functional Theory and Its Application in the Chemical Domain Nazmul Islam, Savas Kaya, 2018-06-13 In this book, new developments based on conceptual density functional theory (CDFT) and its applications in chemistry are discussed. It also includes discussion of some applications in corrosion and conductivity and synthesis studies based on CDFT. The electronic structure principles—such as the electronegativity equalization principle, the hardness equalization principle, the electrophilicity equalization principle, and the nucleophilicity equalization principle, along studies based on these electronic structure principles—are broadly explained. In recent years some novel methodologies have been developed in the field of CDFT. These methodologies have been used to explore mutual relationships between the descriptors of CDFT, namely electronegativity, hardness, etc. The mutual relationship between the electronegativity and the hardness depend on the electronic configuration of the neutral atomic species. The volume attempts to cover almost all such methodology. Conceptual Density Function Theory and Its Application in the Chemical Domain will be an appropriate guide for research students as well as the supervisors in PhD programs. It will also be valuable resource for inorganic chemists, physical chemists, and quantum chemists. The reviews, research articles, short communications, etc., covered by this book will be appreciated by theoreticians as well as experimentalists. |
| entropy principle and its applications: Entropy Theory in Hydraulic Engineering Vijay P. Singh, 2014 Vijay Singh explains the basic concepts of entropy theory from a hydraulic perspective and demonstrates the theory's application in solving practical engineering problems. |
| entropy principle and its applications: Entropy-Based Parameter Estimation in Hydrology V.P. Singh, 2013-04-17 Since the pioneering work of Shannon in the late 1940's on the development of the theory of entropy and the landmark contributions of Jaynes a decade later leading to the development of the principle of maximum entropy (POME), the concept of entropy has been increasingly applied in a wide spectrum of areas, including chemistry, electronics and communications engineering, data acquisition and storage and retreival, data monitoring network design, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, image processing, management sciences, operations research, pattern recognition and identification, photogrammetry, psychology, physics and quantum mechanics, reliability analysis, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, and so on. New areas finding application of entropy have since continued to unfold. The entropy concept is indeed versatile and its applicability widespread. In the area of hydrology and water resources, a range of applications of entropy have been reported during the past three decades or so. This book focuses on parameter estimation using entropy for a number of distributions frequently used in hydrology. In the entropy-based parameter estimation the distribution parameters are expressed in terms of the given information, called constraints. Thus, the method lends itself to a physical interpretation of the parameters. Because the information to be specified usually constitutes sufficient statistics for the distribution under consideration, the entropy method provides a quantitative way to express the information contained in the distribution. |
| entropy principle and its applications: Computational Science and Its Applications - ICCSA 2003 Vipin Kumar, 2003-05-08 The three-volume set, LNCS 2667, LNCS 2668, and LNCS 2669, constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2003, held in Montreal, Canada, in May 2003. The three volumes present more than 300 papers and span the whole range of computational science from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The proceedings give a unique account of recent results in computational science. |
| entropy principle and its applications: Fundamentals of Engineering Thermodynamics R. Yadav , 2023-05-10 Thermodynamics deals with energy interactions between material bodies. It is the science of 3E’s, namely, Energy, Entropy and Equilibrium. The applications of its laws and principles are found in all fields of energy technology, notably, in steam, gas and nuclear power plants, internal combustion engines, gas turbines, jet propulsion, refrigeration, air conditioning, compressors, gas dynamics, and direct energy conversion. Starting with the basic concept, the book discusses the important topics such as basic concepts, heat and work energy, ideal and real gases, zeroth, first and second laws of thermodynamics, entropy and third law, available energy and exergy, gas power cycles, vapour power cycles, general thermodynamic relations, refrigeration cycles, psychrometry, non-reactive mixtures, reactive mixture, chemical equilibrium, direct energy conversion, compressible flows, and heat transfer. The book is an essential text for BE/ B.Tech for Mechanical Engineering students, UPSC and GATE examinations. |
| entropy principle and its applications: Discover Entropy And The Second Law Of Thermodynamics: A Playful Way Of Discovering A Law Of Nature Arieh Ben-naim, 2010-08-03 This is a sequel to the author's book entitled “Entropy Demystified” (Published by World Scientific, 2007). The aim is essentially the same as that of the previous book by the author: to present Entropy and the Second Law as simple, meaningful and comprehensible concepts. In addition, this book presents a series of “experiments” which are designed to help the reader discover entropy and the Second Law. While doing the experiments, the reader will encounter three most fundamental probability distributions featuring in Physics: the Uniform, the Boltzmann and the Maxwell-Boltzmann distributions. In addition, the concepts of entropy and the Second Law will emerge naturally from these experiments without a tinge of mystery. These concepts are explained with the help of a few familiar ideas of probability and information theory.The main “value” of the book is to introduce entropy and the Second Law in simple language which renders it accessible to any reader who can read and is curious about the basic laws of nature. The book is addressed to anyone interested in science and in understanding natural phenomenon. It will afford the reader the opportunity to discover one of the most fundamental laws of physics — a law that has resisted complete understanding for over a century. The book is also designed to be enjoyable.There is no other book of its kind (except “Entropy Demystified” by the same author) that offers the reader a unique opportunity to discover one of the most profound laws — sometimes viewed as a mysterious — while comfortably playing with familiar games. There are no pre-requisites expected from the readers; all that the reader is expected to do is to follow the experiments or imagine doing the experiments and reach the inevitable conclusions. |
| entropy principle and its applications: Noise Theory and Application to Physics Philippe Réfrégier, 2012-12-06 I had great pleasure in reading Philippe Refregier's book on the theory of noise and its applications in physics. The main aim of the book is to present the basic ideas used to characterize these unwanted random signals that obscure information content. To this end, the author devotes a sigificant part of his book to a detailed study of the probabilistic foundations of fluctuation theory. Following a concise and accurate account of the basics of probability the ory, the author includes a detailed study of stochastic processes, emphasizing the idea of the correlation function, which plays a key role in many areas of physics. Physicists often assume that the noise perturbing a signal is Gaussian. This hypothesis is justified if one can consider that the noise results from the superposition of a great many independent random perturbations. It is this fact that brings the author to discuss the theory underlying the addition of random variables, accompanied by a wide range of illustrative examples. Since noise affects information, the author is naturally led to consider Shannon's information theory, which in turn brings him to the altogether fundamental idea of entropy. This chapter is completed with a study of com plexity according to Kolmogorov. This idea is not commonly discussed in physics and the reader will certainly appreciate the clear presentation within these pages. |
| entropy principle and its applications: Non-equilibrium Thermodynamics and the Production of Entropy Axel Kleidon, Ralph D. Lorenz, 2004-11-18 The present volume studies the application of concepts from non-equilibrium thermodynamics to a variety of research topics. Emphasis is on the Maximum Entropy Production (MEP) principle and applications to Geosphere-Biosphere couplings. Written by leading researchers from a wide range of backgrounds, the book presents a first coherent account of an emerging field at the interface of thermodynamics, geophysics and life sciences. |
| entropy principle and its applications: Maximum Entropy and Ecology John Harte, 2011-06-23 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. |
| entropy principle and its applications: Optimization and Artificial Intelligence in Civil and Structural Engineering B.H. Topping, 2013-03-14 This volume and its companion volume includes the edited versions of the principal lectures and selected papers presented at the NATO Advanced Study Institute on Optimization and Decision Support Systems in Civil Engineering. The Institute was held in the Department of Civil Engineering at Heriot-Watt University, Edinburgh from June 25th to July 6th 1989 and was attended by eighty participants from Universities and Research Institutes around the world. A number of practising civil and structural engineers also attended. The lectures and papers have been divided into two volumes to reflect the dual themes of the Institute namely Optimization and Decision Support Systems in Civil Engineering. Planning for this ASI commenced in late 1986 when Andrew Templeman and I discussed developments in the use of the systems approach in civil engineering. A little later it became clear that much of this approach could be realised through the use of knowledge-based systems and artificial intelligence techniques. Both Don Grierson and John Gero indicated at an early stage how important it would be to include knowledge-based systems within the scope of the Institute. The title of the Institute could have been: 'Civil Engineering Systems' as this would have reflected the range of systems applications to civil engineering problems considered by the Institute. These volumes therefore reflect the full range of these problems including: structural analysis and design; water resources engineering; geotechnical engineering; transportation and environmental engineering. |
| entropy principle and its applications: Advances in Mathematics and Applications Carlile Lavor, Francisco A. M. Gomes, 2018-09-07 This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics. |
| entropy principle and its applications: From Strange Simplicity to Complex Familiarity Manfred Eigen, 2013-05-23 This book presents a vivid argument for the almost lost idea of a unity of all natural sciences. It starts with the strange physics of matter, including particle physics, atomic physics and quantum mechanics, cosmology, relativity and their consequences (Chapter I), and it continues by describing the properties of material systems that are best understood by statistical and phase-space concepts (Chapter II). These lead to entropy and to the classical picture of quantitative information, initially devoid of value and meaning (Chapter III). Finally, information space and dynamics within it are introduced as a basis for semantics (Chapter IV), leading to an exploration of life and thought as new problems in physics (Chapter V). Dynamic equations - again of a strange (but very general) nature - bring about the complex familiarity of the world we live in. Surprising new results in the life sciences open our eyes to the richness of physical thought, and they show us what can and what cannot be explained by a Darwinian approach. The abstract physical approach is applicable to the origins of life, of meaningful information and even of our universe. |
| entropy principle and its applications: The Structure of Physical Chemistry Sir Cyril Norman Hinshelwood, C. N. Hinshelwood, 2005-10-13 This is not a traditional textbook. It aims to reveal in one single continuous logical development what each successive kind of physical hypothesis tells us about the nature of things. |
| entropy principle and its applications: Measurement Technology and its Application Prasad Yarlagadda, Yun Hae Kim, 2012-12-13 Selected, peer reviewed papers from the 2012 International Conference on Measurement, Instrumentation and Automation (ICMIA 2012), September 15-16, 2012, Guangzhou, China |
| entropy principle and its applications: Advances and Applications of DSmT for Information Fusion (Collected Works. Volume 5) Florentin Smarandache, Jean Dezert, Albena Tchamova, 2023-12-27 This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 (available at fs.unm.edu/DSmT-book4.pdf or www.onera.fr/sites/default/files/297/2015-DSmT-Book4.pdf) in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. We want to thank all the contributors of this fifth volume for their research works and their interests in the development of DSmT, and the belief functions. We are grateful as well to other colleagues for encouraging us to edit this fifth volume, and for sharing with us several ideas and for their questions and comments on DSmT through the years. We thank the International Society of Information Fusion (www.isif.org) for diffusing main research works related to information fusion (including DSmT) in the international fusion conferences series over the years. Florentin Smarandache is grateful to The University of New Mexico, U.S.A., that many times partially sponsored him to attend international conferences, workshops and seminars on Information Fusion. Jean Dezert is grateful to the Department of Information Processing and Systems (DTIS) of the French Aerospace Lab (Office National d’E´tudes et de Recherches Ae´rospatiales), Palaiseau, France, for encouraging him to carry on this research and for its financial support. Albena Tchamova is first of all grateful to Dr. Jean Dezert for the opportunity to be involved during more than 20 years to follow and share his smart and beautiful visions and ideas in the development of the powerful Dezert-Smarandache Theory for data fusion. She is also grateful to the Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, for sponsoring her to attend international conferences on Information Fusion. |
| entropy principle and its applications: Uncertainty Quantification with R Eduardo Souza de Cursi, 2024-05-06 This book is a rigorous but practical presentation of the Bayesian techniques of uncertainty quantification, with applications in R. This volume includes mathematical arguments at the level necessary to make the presentation rigorous and the assumptions clearly established, while maintaining a focus on practical applications of Bayesian uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R allows the reader to solve more complex problems involving a more significant number of variables. Users will be able to use examples laid out in the text to solve medium-sized problems. The list of topics covered in this volume includes basic Bayesian probabilities, entropy, Bayesian estimation and decision, sequential Bayesian estimation, and numerical methods. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of Bayesian uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning. |
| entropy principle and its applications: Natural Language Processing Yue Zhang, Zhiyang Teng, 2021-01-07 This undergraduate textbook introduces essential machine learning concepts in NLP in a unified and gentle mathematical framework. |
| entropy principle and its applications: Applied Mathematical Analysis and Computations I Divine Wanduku, Shijun Zheng, Haomin Zhou, Zhan Chen, Andrew Sills, Ephraim Agyingi, 2024-11-09 This volume convenes selected, peer-reviewed research and survey articles that address the modern state-of-the-art in varied areas of applied mathematical analysis. They primarily include presentations as well as invited contributions for the 1st Southern Georgia Mathematics Conference (SGMC) that was virtually held on April 2—3, 2021 at the Georgia Southern University, Statesboro, USA. Papers in this volume incorporate both advanced theory and methods from mathematical analysis, and cover myriad topics like imaging and inverse problems, evolutionary PDEs, symbolic computation, dynamics and data analysis, data science, computational mathematics, and more. This first volume focuses on mathematical analysis theory and applications. These studies and findings contained herein will be of interest to researchers and graduate students working in the fields of mathematical analysis, modeling, data analysis and computation, with applications in many interdisciplinary applied sciences, as in statistics, physics, biology, and medical imaging. They are particularly relevant to those at the forefront of applied mathematical and statistical analysis, as well as data science and other computational science disciplines. In its first edition, the Southern Georgia Mathematics Conference brought together 74 speakers from 70 different institutions, from the USA, Canada, Austria, and Botswana. Attendees included faculty, researchers, experts, graduate and undergraduate students from all over the world. |
| entropy principle and its applications: Information Dynamics Harald Atmanspacher, Herbert Scheingraber, 2013-11-11 Proceedings of a NATO ASI held in Irsee/Kaufbeuren, Germany, June 15--26, 1990 |
| entropy principle and its applications: Nonextensive Statistical Mechanics and Its Applications Sumiyoshi Abe, Yuko Okamoto, 2008-01-11 Nonextensive statistical mechanics is now a rapidly growing field and a new stream in the research of the foundations of statistical mechanics. This generalization of the well-known Boltzmann--Gibbs theory enables the study of systems with long-range interactions, long-term memories or multi-fractal structures. This book consists of a set of self-contained lectures and includes additional contributions where some of the latest developments -- ranging from astro- to biophysics -- are covered. Addressing primarily graduate students and lecturers, this book will also be a useful reference for all researchers working in the field. |
| entropy principle and its applications: Jñānabha , 2000 |
| entropy principle and its applications: Principles of Continuum Mechanics Zdeněk Martinec, 2019-05-31 This book addresses the basic concepts of continuum mechanics, that is, the classical field theory of deformable bodies. The theory is systematically developed, from the kinematics to the balance equations, the material theory, and the entropy principles. In turn, the linear-elastic solids, the ideal liquid and the Newtonian liquid are presented in detail as concrete applications. The book concludes by covering the theory of small motions in a medium with a finite prestress. In general, the emphasis is on presenting the content in a clear and straightforward way that requires only an elementary grasp of calculus, linear algebra, and Newtonian mechanics. The book is intended for students of physics, mechanics, engineering and the geosciences, as well as applied mathematics, with a year or more of college calculus behind them. |
| entropy principle and its applications: Extended Thermodynamics Ingo Müller, Tommaso Ruggeri, 2013-03-08 Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and gases of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation. |
| entropy principle and its applications: Statistical Mechanics And The Physics Of Many-particle Model Systems Alexander Leonidovich Kuzemsky, 2017-02-24 The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models.This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography.The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques. |
| entropy principle and its applications: A General Theory of Entropy Kofi Kissi Dompere, 2019-08-02 This book presents an epistemic framework for dealing with information-knowledge and certainty-uncertainty problems within the space of quality-quantity dualities. It bridges between theoretical concepts of entropy and entropy measurements, proposing the concept and measurement of fuzzy-stochastic entropy that is applicable to all areas of knowing under human cognitive limitations over the epistemological space. The book builds on two previous monographs by the same author concerning theories of info-statics and info-dynamics, to deal with identification and transformation problems respectively. The theoretical framework is developed by using the toolboxes such as those of the principle of opposites, systems of actual-potential polarities and negative-positive dualities, under different cost-benefit time-structures. The category theory and the fuzzy paradigm of thought, under methodological constructionism-reductionism duality, are used in the fuzzy-stochastic and cost-benefit spaces to point to directions of global application in knowing, knowledge and decision-choice actions. Thus, the book is concerned with a general theory of entropy, showing how the fuzzy paradigm of thought is developed to deal with the problems of qualitative-quantitative uncertainties over the fuzzy-stochastic space, which will be applicable to conditions of soft-hard data, fact, evidence and knowledge over the spaces of problem-solution dualities, decision-choice actions in sciences, non-sciences, engineering and planning sciences to abstract acceptable information-knowledge elements. |
| entropy principle and its applications: Maximum-Entropy and Bayesian Methods in Science and Engineering G. Erickson, C.R. Smith, 1988-08-31 This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics, held at Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 How Does the Brain Do Plausible Reasoning? (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle. |
| entropy principle and its applications: Information and Software Technologies Robertas Damaševičius, Giedrė Vasiljevienė, 2018-08-28 This book constitutes the refereed proceedings of the 24th International Conference on Information and Software Technologies, ICIST 2018, held in Vilnius, Lithuania, in October 2018. The 48 papers presented were carefully reviewed and selected from 124 submissions. The papers are organized in topical sections on information systems; business intelligence for information and software systems; software engineering; and information technology applications. |
| entropy principle and its applications: Thermodynamics and Its Applications Michael Modell, Robert C. Reid, 1983 |
| entropy principle and its applications: Science and Information Theory Leon Brillouin, 2013-07-17 Geared toward upper-level undergraduates and graduate students, this classic resource by a giant of 20th-century mathematics applies principles of information theory to Maxwell's demon, thermodynamics, and measurement problems. 1962 edition. |
| entropy principle and its applications: Mathematical Modeling J. N. Kapur, 2023-02-15 This book can be used in courses on mathematical modeling at the senior undergraduate or graduate level, or used as a reference for in-service scientists and engineers. The book provides an overview of mathematical modeling through a panoramic view of applications of mathematics in science and technology. In each chapter, mathematical models are chosen from the physical, biological, social, economic, management, and engineering sciences. The models deal with different concepts, but have a common mathematical structure and bring out the unifying influence of mathematical modeling in different disciplines. Features: Provides a balance between theory and applications Features models from the physical, biological, social, economic, management, and engineering sciences |
| entropy principle and its applications: Synergetic Agents Hermann Haken, Paul Levi, 2012-07-18 This book addresses both multi robot systems and miniaturization to the nanoscale from a unifying point of view, but without leaving aside typical particularities of either. The unifying aspect is based on the concept of information minimization whose precise formulation is the Haken-Levi-principle. The authors introduce basic concepts of multi-component self-organizing systems such as order parameters (well known from equilibrium and non-equilibrium phase transitions) and the slaving principle (which establishes a link to dynamical systems). Among explicit examples is the docking manoeuvre of two robots in two and three dimensions. The second part of the book deals with the rather recently arising field of molecular robotics. It is particularly here where nature has become a highly influential teacher for the construction of robots. In living biological cells astounding phenomena occur: there are molecules (proteins) that literally walk on polymer strands and transport loads that are heavier than their carriers, or molecules that, by joint action, contract muscles. The book provides the reader with an insight into these phenomena, especially by a detailed theoretical treatment of the molecular mechanism of muscle contraction. At the molecular level, for an appropriate approach the use of quantum theory is indispensable. The authors introduce and use it in a form that avoids all the clumsy calculations of wave-functions. They present a model which is based on an elementary version of quantum field theory and allows taking into account the impact of the surrounding on the quantum mechanical activity of a single molecule. By presenting explicit and pedagogical examples, the reader gets acquainted with the appropriate modelling of the walking behaviour of single molecular robots and their collective behaviour. The further development of multi-robot systems and particularly of molecular robots will require the cooperation of a variety of disciplines. Therefore the book appeals to a wide audience including researchers, instructors, and advanced graduate students. |
Entropy | An Open Access Journal from MDPI
Entropy is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI.
Entropy - MDPI
The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas. It was originally introduced by Clausius in 1865 along abstract lines …
Entropy: From Thermodynamics to Information Processing - MDPI
Oct 14, 2021 · Entropy is most commonly defined as “disorder”, although it is not a good analogy since “order” is a subjective human concept, and “disorder” cannot always be obtained from …
Toward Improved Understanding of the Physical Meaning of …
Jul 22, 2016 · The overall direction of entropy increase indicates the direction of naturally occurring heat transfer processes in an isolated system that consists of internally interacting …
A Brief Review of Generalized Entropies - MDPI
Another very popular generalized entropy was introduced by Tsallis as a generalization of the Boltzmann–Gibbs entropy (Section 3.1) to describe the properties of physical systems with …
Entropy | Aims & Scope - MDPI
Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage …
Entropy: The Markov Ordering Approach - MDPI
The entropy maximum principle was applied to many physical and chemical problems. At the same time J.W. Gibbs mentioned that entropy maximizers under a given energy are energy …
Thermodynamics, Statistical Mechanics and Entropy - MDPI
Nevertheless, the canonical entropy is appropriate for calculating the thermodynamic entropy. Consider three macroscopic systems labeled A , B , and C . Let systems A and B be …
Applications of Entropy in Data Analysis and Machine Learning: A …
Dec 23, 2024 · Given the plethora of entropies in the literature, we have selected a representative group, including the classical ones. The applications summarized in this review nicely illustrate …
Entropy and Uncertainty - MDPI
We give a survey of the basic statistical ideas underlying the definition of entropy in information theory and their connections with the entropy in the theory of dynamical systems and in …
Entropy | An Open Access Journal from MDPI
Entropy is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI.
Entropy - MDPI
The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas. It was originally introduced by Clausius in 1865 along abstract lines focusing …
Entropy: From Thermodynamics to Information Processing - MDPI
Oct 14, 2021 · Entropy is most commonly defined as “disorder”, although it is not a good analogy since “order” is a subjective human concept, and “disorder” cannot always be obtained from …
Toward Improved Understanding of the Physical Meaning of …
Jul 22, 2016 · The overall direction of entropy increase indicates the direction of naturally occurring heat transfer processes in an isolated system that consists of internally interacting (non-isolated) …
A Brief Review of Generalized Entropies - MDPI
Another very popular generalized entropy was introduced by Tsallis as a generalization of the Boltzmann–Gibbs entropy (Section 3.1) to describe the properties of physical systems with long …
Entropy | Aims & Scope - MDPI
Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage …
Entropy: The Markov Ordering Approach - MDPI
The entropy maximum principle was applied to many physical and chemical problems. At the same time J.W. Gibbs mentioned that entropy maximizers under a given energy are energy minimizers …
Thermodynamics, Statistical Mechanics and Entropy - MDPI
Nevertheless, the canonical entropy is appropriate for calculating the thermodynamic entropy. Consider three macroscopic systems labeled A , B , and C . Let systems A and B be constructed …
Applications of Entropy in Data Analysis and Machine Learning: A
Dec 23, 2024 · Given the plethora of entropies in the literature, we have selected a representative group, including the classical ones. The applications summarized in this review nicely illustrate …
Entropy and Uncertainty - MDPI
We give a survey of the basic statistical ideas underlying the definition of entropy in information theory and their connections with the entropy in the theory of dynamical systems and in …
