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This book is about methodological aspects of uncertainty propagation in data processing. Uncertainty propagation is an important problem: while computer algorithms efficiently process data related to many aspects of their lives, most of these algorithms implicitly assume that the numbers they process are exact. In reality, these numbers come from measurements, and measurements are never 100% exact. Because of this, it makes no sense to translate 61 kg into pounds and get the result—as computers do—with 13 digit accuracy. In many cases—e.g., in celestial mechanics—the state of a system can be described by a few numbers: the values of the corresponding physical quantities. In such cases, for each of these quantities, we know (at least) the upper bound on the measurement error. This bound is either provided by the manufacturer of the measuring instrument—or is estimated by the user who calibrates this instrument. However, in many other cases, the description of the system is more complex than a few numbers: we need a function to describe a physical field (e.g., electromagnetic field); we need a vector in Hilbert space to describe a quantum state; we need a pseudo-Riemannian space to describe the physical space-time, etc. To describe and process uncertainty in all such cases, this book proposes a general methodology—a methodology that includes intervals as a particular case. The book is recommended to students and researchers interested in challenging aspects of uncertainty analysis and to practitioners who need to handle uncertainty in such unusual situations.
Fast After 50 is for every endurance athlete who wants to stay fast for years to come. For runners, cyclists, triathletes, swimmers, and cross-country skiers, getting older doesn’t have to mean getting slower. Drawing from the most current research on aging and sports performance, Joe Friel--America’s leading endurance sports coach--shows how athletes can race strong and stay healthy well past age 50. In his groundbreaking book Fast After 50, Friel offers a smart approach for athletes to ward off the effects of age. Friel shows athletes how to extend their racing careers for decades--and race to win. Fast After 50 presents guidelines for high-intensity workouts, focused strength training, recovery, crosstraining, and nutrition for high performance: How the body’s response to training changes with age, how to adapt your training plan, and how to avoid overtraining How to shed body fat and regain muscle density How to create a progressive plan for training, rest, recovery, and competition Workout guidelines, field tests, and intensity measurement In Fast After 50, Joe Friel shows athletes that age is just a number--and race results are the only numbers that count. With contributions from: Mark Allen, Gale Bernhardt, Amby Burfoot, Dr. Larry Creswell, John Howard, Dr. Tim Noakes, Ned Overend, Dr. John Post, Dr. Andrew Pruitt, and Lisa Rainsberger.
Presents a detailed exposition of statistical intervals and emphasizes applications in industry. The discussion differentiates at an elementary level among different kinds of statistical intervals and gives instruction with numerous examples and simple math on how to construct such intervals from sample data. This includes confidence intervals to contain a population percentile, confidence intervals on probability of meeting specified threshold value, and prediction intervals to include observation in a future sample. Also has an appendix containing computer subroutines for nonparametric statistical intervals.
Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in an easy-to-apply format Statistical intervals provide invaluable tools for quantifying sampling uncertainty. The widely hailed first edition, published in 1991, described the use and construction of the most important statistical intervals. Particular emphasis was given to intervals—such as prediction intervals, tolerance intervals and confidence intervals on distribution quantiles—frequently needed in practice, but often neglected in introductory courses. Vastly improved computer capabilities over the past 25 years have resulted in an explosion of the tools readily available to analysts. This second edition—more than double the size of the first—adds these new methods in an easy-to-apply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on: Likelihood-based statistical intervals Nonparametric bootstrap intervals Parametric bootstrap and other simulation-based intervals An introduction to Bayesian intervals Bayesian intervals for the popular binomial, Poisson and normal distributions Statistical intervals for Bayesian hierarchical models Advanced case studies, further illustrating the use of the newly described methods New technical appendices provide justification of the methods and pathways to extensions and further applications. A webpage directs readers to current readily accessible computer software and other useful information. Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition is an up-to-date working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals.
An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.
Music Theory for the Bass Player is a comprehensive and immediately applicable guide to making you a well-grounded groover, informed bandmate and all-around more creative musician. Included with this book are 89 videos that are incorporated in this ebook. This is a workbook, so have your bass and a pen ready to fill out the engaging Test Your Understanding questions! Have you always wanted to learn music theory but felt it was too overwhelming a task? Perhaps all the books seem to be geared toward pianists or classical players? Do you know lots of songs, but don't know how the chords are put together or how they work with the melody? If so, this is the book for you! • Starting with intervals as music's basic building blocks, you will explore scales and their modes, chords and the basics of harmony. • Packed with fretboard diagrams, musical examples and exercises, more than 180 pages of vital information are peppered with mind-bending quizzes, effective mnemonics, and compelling learning approaches. • Extensive and detailed photo demonstrations show why relaxed posture and optimized fingering are vital for good tone, timing and chops. • You can even work your way through the book without being able to read music (reading music is of course a vital skill, yet, the author believes it should not be tackled at the same time as the study of music theory, as they are different skills with a different practicing requirement. Reading becomes much easier once theory is mastered and learning theory on the fretboard using diagrams and patterns as illustrations, music theory is very accessible, immediately usable and fun. This is the definitive resource for the enthusiastic bassist! p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 13.0px Helvetica} p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 13.0px Helvetica; min-height: 16.0px} This book and the 89 free videos stand on their own and form a thorough source for studying music theory for the bass player. If you'd like to take it a step further, the author also offers a corresponding 20 week course; this online course works with the materials in this book and practices music theory application in grooves, fills and solos. Information is on the author's blog.
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the additional hope of stimulating experimentalists to look for more of these general phenomena of beautiful regularity, which oftentimes seem to appear near the much less understood chaotic systems. Although continuous maps of an interval to itself seem to have been first introduced to model biological systems, they can be found as models in most natural sciences as well as economics. Iterated Maps on the Interval as Dynamical Systems is a classic reference used widely by researchers and graduate students in mathematics and physics, opening up some new perspectives on the study of dynamical systems .
Why is it that certain intervals, scales, and tones sound genuine, while others sound false? Is the modern person able to experience a qualitative difference in a tone's pitch? If so, what are the implications for modern concert pitch and how instruments of fixed tuning are tuned? Renold tackles these and many other questions and provides a wealth of scientific data. Her pioneering work is the result of a lifetime of research into the Classical Greek origin of Western music and the search for modern developments. She deepens our musical understanding by using Rudolf Steiner's spiritual science as a basis, and she elucidates many of his puzzling statements about music. The results of her work include the following discoveries: - The octave has two sizes (a 'genuine' sounding octave is bigger than the "perfect octave") - There are three sizes of "perfect fifths" - An underlying "form principle" for all scales can be found - Equal temperament is not the most satisfactory method of tuning a piano - She provides a basis for some of Steiner's statements, such as, "C is always prime" and "C = 128 Hz = Sun." Intervals, Scales, Tones is a valuable resource for those who wish to understand the deeper, spiritual aspects of music.