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.

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.

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

Entropy theory has wide applications to a range of problems in the fields of environmental and water engineering, including river hydraulic geometry, fluvial hydraulics, water monitoring network design, river flow forecasting, floods and droughts, river network analysis, infiltration, soil moisture, sediment transport, surface water and groundwater quality modeling, ecosystems modeling, water distribution networks, environmental and water resources management, and parameter estimation. Such applications have used several different entropy formulations, such as Shannon, Tsallis, Rényi, Burg, Kolmogorov, Kapur, configurational, and relative entropies, which can be derived in time, space, or frequency domains. More recently, entropy-based concepts have been coupled with other theories, including copula and wavelets, to study various issues associated with environmental and water resources systems. Recent studies indicate the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering, including establishing and explaining physical connections between theory and reality. The objective of this Special Issue is to provide a platform for compiling important recent and current research on the applications of entropy theory in environmental and water engineering. The contributions to this Special Issue have addressed many aspects associated with entropy theory applications and have shown the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering.

This book presents the result of an innovative challenge, to create a systematic literature overview driven by machine-generated content. Questions and related keywords were prepared for the machine to query, discover, collate and structure by Artificial Intelligence (AI) clustering. The AI-based approach seemed especially suitable to provide an innovative perspective as the topics are indeed both complex, interdisciplinary and multidisciplinary, for example, climate, planetary and evolution sciences. Springer Nature has published much on these topics in its journals over the years, so the challenge was for the machine to identify the most relevant content and present it in a structured way that the reader would find useful. The automatically generated literature summaries in this book are intended as a springboard to further discoverability. They are particularly useful to readers with limited time, looking to learn more about the subject quickly and especially if they are new to the topics. Springer Nature seeks to support anyone who needs a fast and effective start in their content discovery journey, from the undergraduate student exploring interdisciplinary content, to Master- or PhD-thesis developing research questions, to the practitioner seeking support materials, this book can serve as an inspiration, to name a few examples. It is important to us as a publisher to make the advances in technology easily accessible to our authors and find new ways of AI-based author services that allow human-machine interaction to generate readable, usable, collated, research content.

This book explores non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems, drawing on relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It offers a self-contained theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.

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.

It is our great pleasure to welcome you to the 11th International Conference on Neural Information Processing (ICONIP 2004) to be held in Calcutta. ICONIP 2004 is organized jointly by the Indian Statistical Institute (ISI) and Jadavpur University (JU). We are con?dent that ICONIP 2004, like the previous conf- ences in this series,will providea forum for fruitful interactionandthe exchange of ideas between the participants coming from all parts of the globe. ICONIP 2004 covers all major facets of computational intelligence, but, of course, with a primary emphasis on neural networks. We are sure that this meeting will be enjoyable academically and otherwise. We are thankful to the track chairs and the reviewers for extending their support in various forms to make a sound technical program. Except for a few cases, where we could get only two review reports, each submitted paper was reviewed by at least three referees, and in some cases the revised versions were againcheckedbythereferees. Wehad470submissionsanditwasnotaneasytask for us to select papers for a four-day conference. Because of the limited duration of the conference, based on the review reports we selected only about 40% of the contributed papers. Consequently, it is possible that some good papers are left out. We again express our sincere thanks to all referees for accomplishing a great job. In addition to 186 contributed papers, the proceedings includes two plenary presentations, four invited talks and 18 papers in four special sessions. The proceedings is organized into 26 coherent topical groups.

Features a broad introduction to recent research on Turing’s formula and presents modern applications in statistics, probability, information theory, and other areas of modern data science Turing's formula is, perhaps, the only known method for estimating the underlying distributional characteristics beyond the range of observed data without making any parametric or semiparametric assumptions. This book presents a clear introduction to Turing’s formula and its connections to statistics. Topics with relevance to a variety of different fields of study are included such as information theory; statistics; probability; computer science inclusive of artificial intelligence and machine learning; big data; biology; ecology; and genetics. The author provides examinations of many core statistical issues within modern data science from Turing's perspective. A systematic approach to long-standing problems such as entropy and mutual information estimation, diversity index estimation, domains of attraction on general alphabets, and tail probability estimation is presented in light of the most up-to-date understanding of Turing's formula. Featuring numerous exercises and examples throughout, the author provides a summary of the known properties of Turing's formula and explains how and when it works well; discusses the approach derived from Turing's formula in order to estimate a variety of quantities, all of which mainly come from information theory, but are also important for machine learning and for ecological applications; and uses Turing's formula to estimate certain heavy-tailed distributions. In summary, this book: • Features a unified and broad presentation of Turing’s formula, including its connections to statistics, probability, information theory, and other areas of modern data science • Provides a presentation on the statistical estimation of information theoretic quantities • Demonstrates the estimation problems of several statistical functions from Turing's perspective such as Simpson's indices, Shannon's entropy, general diversity indices, mutual information, and Kullback–Leibler divergence • Includes numerous exercises and examples throughout with a fundamental perspective on the key results of Turing’s formula Statistical Implications of Turing's Formula is an ideal reference for researchers and practitioners who need a review of the many critical statistical issues of modern data science. This book is also an appropriate learning resource for biologists, ecologists, and geneticists who are involved with the concept of diversity and its estimation and can be used as a textbook for graduate courses in mathematics, probability, statistics, computer science, artificial intelligence, machine learning, big data, and information theory. Zhiyi Zhang, PhD, is Professor of Mathematics and Statistics at The University of North Carolina at Charlotte. He is an active consultant in both industry and government on a wide range of statistical issues, and his current research interests include Turing's formula and its statistical implications; probability and statistics on countable alphabets; nonparametric estimation of entropy and mutual information; tail probability and biodiversity indices; and applications involving extracting statistical information from low-frequency data space. He earned his PhD in Statistics from Rutgers University.

This volume covers the fields of measurement and information acqulSltlon. It contains a collection of papers representing the current research trends in these areas. What are those trends? The first one is the enormous growth in the amount of information and the amazing technologies, which make this information available anywhere and anytime. The second one is a substantial development of methods of the information presentation including, to name just a few, multimedia, virtual environment, computer animation. The third one is the all-time boosting demand for improving the quality of decisions made on the base of this information in various applications ranging from engineering to business. Nowadays information acquisition should not only provide more information but also provide it in such a way as to assure effective and efficient processing of this information. And here comes a relatively new methodology of soft computing. Application of soft computing in measurement and information acquisition is considered in this volume.