Functional Analysis 2008

Functional Verification Coverage Measurement and Analysis addresses a means of quantitatively assessing functional verification progress. Without this process, design and verification engineers, and their management, are left guessing whether or not they have completed verifying the device they are designing. Using the techniques described in this book, they will learn how to build a toolset which allows them to know how close they are to functional closure.

This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments.

One of the most intriguing questions facing modern science is the inner workings of the human brain. Functional magnetic resonance imaging (fMRI) is a powerful tool used to study the human brain in action. The data produced from mapping the active processes within the brain present many challenges to statisticians, computer scientists, engineers and other data analysts, due to their complex structure and the ever-increasing sophistication of the scientific questions being posed by researchers. This book represents the first in-depth discussion of statistical methodology, which it couples with an introduction to the scientific background needed to understand the data.

One of the most intriguing questions facing modern science is the inner workings of the human brain. Functional magnetic resonance imaging (fMRI) is a powerful tool used to study the human brain in action. The data produced from mapping the active processes within the brain present many challenges to statisticians, computer scientists, engineers and other data analysts, due to their complex structure and the ever-increasing sophistication of the scientific questions being posed by researchers. This book represents the first in-depth discussion of statistical methodology, which it couples with an introduction to the scientific background needed to understand the data.

One of the most intriguing questions facing modern science is the inner workings of the human brain. Functional magnetic resonance imaging (fMRI) is a powerful tool used to study the human brain in action. The data produced from mapping the active processes within the brain present many challenges to statisticians, computer scientists, engineers and other data analysts, due to their complex structure and the ever-increasing sophistication of the scientific questions being posed by researchers. This book represents the first in-depth discussion of statistical methodology, which it couples with an introduction to the scientific background needed to understand the data.

Many nonlinear problems in physics, engineering, biology, and social sciences can be reduced to finding critical points of functionals. While minimax and Morse theories provide answers to many situations and problems on the existence of multiple critical points of a functional, they often cannot provide much-needed additional properties of these critical points. Sign-changing critical point theory has emerged as a new area of rich research on critical points of a differentiable functional with important applications to nonlinear elliptic PDEs.

In the quest for accurate and efficient analysis of the diverse area encompassed by functional foods and nutraceuticals, analysts encounter unique challenges.