Characterizations of Information Measures

Characterizations of Information Measures
Author: Bruce Ebanks
Publisher: World Scientific
Total Pages: 300
Release: 1998
Genre: Mathematics
ISBN: 9789810230067

"This book is highly recommended for all those whose interests lie in the fields that deal with any kind of information measures. It will also find readers in the field of functional analysis..".Mathematical Reviews

Characterization Of Information Measures

Characterization Of Information Measures
Author: Bruce Ebanks
Publisher: World Scientific
Total Pages: 293
Release: 1998-04-04
Genre: Mathematics
ISBN: 9814497878

How should information be measured? That is the motivating question for this book. The concept of information has become so pervasive that people regularly refer to the present era as the Information Age. Information takes many forms: oral, written, visual, electronic, mechanical, electromagnetic, etc. Many recent inventions deal with the storage, transmission, and retrieval of information. From a mathematical point of view, the most basic problem for the field of information theory is how to measure information. In this book we consider the question: What are the most desirable properties for a measure of information to possess? These properties are then used to determine explicitly the most “natural” (i.e. the most useful and appropriate) forms for measures of information.This important and timely book presents a theory which is now essentially complete. The first book of its kind since 1975, it will bring the reader up to the current state of knowledge in this field.

On Measures of Information and Their Characterizations

On Measures of Information and Their Characterizations
Author: Acze?l
Publisher: Academic Press
Total Pages: 248
Release: 1975-12-17
Genre: Computers
ISBN: 0080956246

This book deals with measures of information (the most important ones being called entropies), their properties, and, reciprocally, with questions concerning which of these properties determine known measures of information, and which are the most general formulas satisfying reasonable requirements on practical measures of information. Thisis the first book investigating this subject in depth.

Handbook of Measure Theory

Handbook of Measure Theory
Author: E. Pap
Publisher: Elsevier
Total Pages: 1633
Release: 2002-10-31
Genre: Mathematics
ISBN: 0080533094

The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.

Handbook of Functional Equations

Handbook of Functional Equations
Author: Themistocles M. Rassias
Publisher: Springer
Total Pages: 394
Release: 2014-11-21
Genre: Mathematics
ISBN: 1493912860

This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications. The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with several applications of interdisciplinary nature. The chapters of this handbook focus mainly on both old and recent developments on the equation of homomorphism for square symmetric groupoids, the linear and polynomial functional equations in a single variable, the Drygas functional equation on amenable semigroups, monomial functional equation, the Cauchy–Jensen type mappings, differential equations and differential operators, operational equations and inclusions, generalized module left higher derivations, selections of set-valued mappings, D’Alembert’s functional equation, characterizations of information measures, functional equations in restricted domains, as well as generalized functional stability and fixed point theory.

Reliability Modelling with Information Measures

Reliability Modelling with Information Measures
Author: N. Unnikrishnan Nair
Publisher: CRC Press
Total Pages: 299
Release: 2022-11-17
Genre: Business & Economics
ISBN: 100079282X

The book deals with the application of various measures of information like the entropy, divergence, inaccuracy, etc. in modelling lifetimes of devices or equipment in reliability analysis. This is an emerging area of study and research during the last two decades and is of potential interest in many fields. In this work the classical measures of uncertainty are sufficiently modified to meet the needs of lifetime data analysis. The book provides an exhaustive collection of materials in a single volume to make it a comprehensive source of reference. The first treatise on the subject. It brings together the work that have appeared in journals on different disciplines. It will serve as a text for graduate students and practioners of special studies in information theory, as well as statistics and as a reference book for researchers. The book contains illustrative examples, tables and figures for clarifying the concepts and methodologies, the book is self-contained. It helps students to access information relevant to careers in industry, engineering, applied statistics, etc.

Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing

Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing
Author: Jean-Francois Giovannelli
Publisher: John Wiley & Sons
Total Pages: 323
Release: 2015-02-02
Genre: Technology & Engineering
ISBN: 1118827074

The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has since recognized that these matters are more interesting and they have become the subject of much greater enthusiasm. From the application field’s point of view, a significant part of the book is devoted to conventional subjects in the field of inversion: biological and medical imaging, astronomy, non-destructive evaluation, processing of video sequences, target tracking, sensor networks and digital communications. The variety of chapters is also clear, when we examine the acquisition modalities at stake: conventional modalities, such as tomography and NMR, visible or infrared optical imaging, or more recent modalities such as atomic force imaging and polarized light imaging.

Non-Additive Measures

Non-Additive Measures
Author: Vicenc Torra
Publisher: Springer
Total Pages: 207
Release: 2013-10-23
Genre: Technology & Engineering
ISBN: 3319031554

This book provides a comprehensive and timely report in the area of non-additive measures and integrals. It is based on a panel session on fuzzy measures, fuzzy integrals and aggregation operators held during the 9th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2012) in Girona, Spain, November 21-23, 2012. The book complements the MDAI 2012 proceedings book, published in Lecture Notes in Computer Science (LNCS) in 2012. The individual chapters, written by key researchers in the field, cover fundamental concepts and important definitions (e.g. the Sugeno integral, definition of entropy for non-additive measures) as well some important applications (e.g. to economics and game theory) of non-additive measures and integrals. The book addresses students, researchers and practitioners working at the forefront of their field.

Optical Document Security: Measurement, Characterization and Visualization

Optical Document Security: Measurement, Characterization and Visualization
Author: Mikael Lindstrand
Publisher: Linköping University Electronic Press
Total Pages: 101
Release: 2019-04-12
Genre:
ISBN: 9176852067

Documents of high value, such as passports, tickets and banknotes, facilitate means for authentication. Authentication processes aim at mitigating counterfeit “passable products”. The arsenal of “security features” in the business is abundant but an effective and reliable counterfeit mitigating system need an architectural approach rather than either relying on one feature only, or vaguely motivated aggregated security features. Optically variable device (OVD) is a concept in the industry, including costefficient and unique authentication functionality. OVD based features may serve as the main counterfeit mitigating functionality, as in banknotes. For higher value documents, such as passports, security architectural design may include multimodal (combined) features in which OVD is one characterizing and necessary aspect. Thereby a successful counterfeit need not only to simulate (“hack”) electronic based security features, such as radio frequency based identifier combined with public key infrastructure based cryptography (PKI) but also simulate OVD functionality. Combined feature authentication, based e.g. on PKI and OVD that relies on principally different physics and hence technology competences is of especial interest. Well-architectured and implemented, such multimodal counterfeit mitigating systems are effective to the degree that producing passable products requiring more resources than potentially illegitimately gained by the counterfeiter. Irrespective of level of ambition and efforts spent on counterfeit mitigation, OVD remains critically important as a security concept. One feature of OVD is the possibility to include a human inspector in the authentication procedure. Including such “man-in-the-loop” reduces the risk of successful and unnoticed simulations of algorithms, such as PKI. One challenge of OVD is a lack of standards or even measurements characterizing the significant aspects influencing a human based inspection. This thesis introduces a system able to measure, characterize and visualize the significant aspects influencing a human based inspection of OVD features. The contribution includes the development of a multidimensional and high-dynamic range (HDR) color measurement system of spatial and angular resolution. The capturing of HDR images is particularly demanding for certain high contrast OVD features and require innovative algorithms to achieve the necessary high contrast sensitivity function of the imaging sensor. Representing the significant aspects influencing a human based inspection of OVD requires a considerable amount of data. The development of an appropriate information protocol is therefore of importance, to facilitate further analysis, data processing and visualization. The information protocol transforming the measurement data into characterizing information is a second significant achievement of the presented work in this thesis. To prove the applicability measurements, visualizations and statistically based analyses have been developed for a selection of previously unsolved problems, as defined by senior scientists and representatives of central banks. Characterization and measurements of the degree to which OVD deteriorate with circulation is one such problem. One particular benefit of the implemented suggested solution is the characterization and measurement aim at aspects influencing human based (“first line”) inspection. The principally difference in the problems treated indicates the generality of the system, which is a third significant project achievement. The system developed achieves the accuracy and precision including a resolution, dynamic range and contrast sensitivity function required for a technology independent standard protocol of “optical document security” OVDs. These abilities facilitate the definition and verification of program of requirements for the development of new security documents. Adding also the capability of interlinking first, second and third line inspection based characterizations may prove a particular valuable combination, which is a fourth significant project achievement. The information content (Entropy) of characterized OVDs and OVD production limitations in combination opens for OVD based novel applications of “physically unclonable functions” (PUF). This is of significance as it would generalize the established OVDs to facilitate multimodal verification, including PUF verification. The OVDs would thereby transform into a combined PUF first line inspection facilitating security feature.

Information Theory

Information Theory
Author: Imre Csiszár
Publisher: Cambridge University Press
Total Pages: 522
Release: 2011-06-30
Genre: Technology & Engineering
ISBN: 113949998X

Csiszár and Körner's book is widely regarded as a classic in the field of information theory, providing deep insights and expert treatment of the key theoretical issues. It includes in-depth coverage of the mathematics of reliable information transmission, both in two-terminal and multi-terminal network scenarios. Updated and considerably expanded, this new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics. The presentations of all core subjects are self contained, even the advanced topics, which helps readers to understand the important connections between seemingly different problems. Finally, 320 end-of-chapter problems, together with helpful hints for solving them, allow readers to develop a full command of the mathematical techniques. It is an ideal resource for graduate students and researchers in electrical and electronic engineering, computer science and applied mathematics.