Quantum Measurement Theory and its Applications


Book Description

Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition.




Entropy Measures, Maximum Entropy Principle and Emerging Applications


Book Description

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.




Measures of Information and Their Applications


Book Description

The present book may be regarded as a successor of author's Maximum Entropy Models in Science and Engineering (Wiley), Generalized Maximum Entropy Principle (Sandford), Entropy Optimization Principles and Their Applications (Academic) and Insight into Entropy Optimizations Principles (MSTS). It contains sixty research investigations of the author on measures of entropy, directed divergence, weighted directed divergence, information, principles of maximum entropy, minimum entropy, minimum cross-entropy, minimum entropy, minimum information, minimum weighted information and maximum weighted entropy, most likely and most feasible distributions, duals of optimization problems, entropy optimization under inequality constraints, characterising moments, parameter estimation, maximum entropy approximation for a probability distribution, proving inequalities, laws of information, entropic mean, mean-entropy frontier, logistic-type growth models, birth-death processes, distributions of statistical mechanics, estimation of missing values, theorems of information theory and many others.




Applications of Measure Theory to Statistics


Book Description

This book aims to put strong reasonable mathematical senses in notions of objectivity and subjectivity for consistent estimations in a Polish group by using the concept of Haar null sets in the corresponding group. This new approach – naturally dividing the class of all consistent estimates of an unknown parameter in a Polish group into disjoint classes of subjective and objective estimates – helps the reader to clarify some conjectures arising in the criticism of null hypothesis significance testing. The book also acquaints readers with the theory of infinite-dimensional Monte Carlo integration recently developed for estimation of the value of infinite-dimensional Riemann integrals over infinite-dimensional rectangles. The book is addressed both to graduate students and to researchers active in the fields of analysis, measure theory, and mathematical statistics.




Measures of Information and Their Applications to Various Disciplines


Book Description

The present book provides the applications of uncertain measures to the field of queueing theory for measuring variations in steady and non-steady birth-death process. Moreover, we have given the applications of probabilistic measures by studying the maximum entropy principle. Another field of interest is the theory of coding which deals with probability distributions only but we have extended the idea to fuzzy distributions by proving new fuzzy coding theorems corresponding to the well-known measures of weighted fuzzy entropy. The book also deals with the applications of measures of entropy for the study of contingency tables and thus provides applications to the field of statistics. I sincerely hope that the present volume of the book will be useful to all those interested in information measures and their applications in a variety of disciplines. Moreover, it will be a source of inspiration and encouragement to research scholars and teachers to discourse the subject for the discovery of new insights.




Random Measures, Theory and Applications


Book Description

Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.




Measurement Theory and Applications for the Social Sciences


Book Description

Which types of validity evidence should be considered when determining whether a scale is appropriate for a given measurement situation? What about reliability evidence? Using clear explanations illustrated by examples from across the social and behavioral sciences, this engaging text prepares students to make effective decisions about the selection, administration, scoring, interpretation, and development of measurement instruments. Coverage includes the essential measurement topics of scale development, item writing and analysis, and reliability and validity, as well as more advanced topics such as exploratory and confirmatory factor analysis, item response theory, diagnostic classification models, test bias and fairness, standard setting, and equating. End-of-chapter exercises (with answers) emphasize both computations and conceptual understanding to encourage readers to think critically about the material. ÿ







Cosine Measures of Linguistic Neutrosophic Numbers and Their Application in Multiple Attribute Group Decision-Making


Book Description

The linguistic neutrosophic numbers (LNNs) can express the truth, indeterminacy, and falsity degrees independently by three linguistic variables. Hence, they are an effective tool for describing indeterminate linguistic information under linguistic decision-making environments. Similarity measures are usual tools in decision-making problems.




Conditional Measures and Applications


Book Description

In response to unanswered difficulties in the generalized case of conditional expectation and to treat the topic in a well-deservedly thorough manner, M.M. Rao gave us the highly successful first edition of Conditional Measures and Applications. Until this groundbreaking work, conditional probability was relegated to scattered journal articles and