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Entropy, mutual information and divergence measure the randomness, dependence and dissimilarity, respectively, of random objects. In addition to their prominent role in information theory, they have found numerous applications, among others, in probability theory statistics, physics, chemistry, molecular biology, ecology, bioinformatics, neuroscience, machine learning, linguistics, and finance. Many of these applications require a universal estimate of information measures which does not assume knowledge of the statistical properties of the observed data. Over the past few decades, several nonparametric algorithms have been proposed to estimate information measures. Universal Estimation of Information Measures for Analog Sources presents a comprehensive survey of universal estimation of information measures for memoryless analog (real-valued or real vector-valued) sources with an emphasis on the estimation of mutual information and divergence and their applications. The book reviews the consistency of the universal algorithms and the corresponding sufficient conditions as well as their speed of convergence. Universal Estimation of Information Measures for Analog Sources provides a comprehensive review of an increasingly important topic in Information Theory. It will be of interest to students, practitioners and researchers working in Information Theory
This is a book presenting to a wide audience of readers, ranging from fans of science to professional researchers, some of the authors' recent discoveries in three distinct, but intimately related domains: probability theory (Bertrand's paradox), observation in physics (the measurement problem) and the modeling of experiments in psychology (quantum cognition). In all three of these domains of investigation, and the associated problems, the authors explain how to advantageously use the key notion of universal measurement, which constitutes the fil rouge of the whole text.
One of the most comprehensive texts on the market, Joint Range of Motion and Muscle Length Testing, 3rd Edition, is an easy-to-follow reference that guides you in accurately measuring range of motion and muscle length for all age groups. Written by renowned educators, Nancy Berryman Reese and William D. Bandy for both Physical Therapy and Occupational Therapy professionals, this book describes in detail the reliability and validity of each technique. A new companion web site features video clips demonstrating over 100 measurement techniques! Full-color design clearly demonstrates various techniques and landmarks. Clear technique template allows you to quickly and easily identify the information you need. Simple anatomic illustrations clearly depict the various techniques and landmarks for each joint. Coverage of range of motion and muscle length testing includes important, must-know information. Complex tool coverage prepares you to use the tape measure, goniometer, and inclinometer in the clinical setting. Over 100 videos let you independently review techniques covered in the text. Chapter on infants and children eliminates having to search through pediatric-specific books for information. Anatomical landmarks provide a fast visual reference for exactly where to place measuring devices. Chapters dedicated to length testing makes information easy to locate. UPDATED information and references includes the latest in hand and upper extremity rehabilitation.