The Functional Resonance Analysis Method

The sheer number of variables of complex dynamic systems do not allow their workings or failures to be understood by linear thinking or standard analytical methods. Hollnagel (U. of Southern Denmark)

Resilience engineering has consistently argued that safety is more than the absence of failures. Since the first book was published in 2006, several book chapters and papers have demonstrated the adva

With strong numerical and computational focus, this book serves as an essential resource on the methods for functional neuroimaging analysis, diffusion weighted image analysis, and longitudinal VBM an

Functional Magnetic Resonance Imaging (fMRI) has become a standard tool for mapping the working brain's activation patterns, both in health and in disease. It is an interdisciplinary field and crosses the borders of neuroscience, psychology, psychiatry, radiology, mathematics, physics and engineering. Developments in techniques, procedures and our understanding of this field are expanding rapidly. In this second edition of Introduction to Functional Magnetic Resonance Imaging, Richard Buxton – a leading authority on fMRI – provides an invaluable guide to how fMRI works, from introducing the basic ideas and principles to the underlying physics and physiology. He covers the relationship between fMRI and other imaging techniques and includes a guide to the statistical analysis of fMRI data. This book will be useful both to the experienced radiographer, and the clinician or researcher with no previous knowledge of the technology.

Functional magnetic resonance imaging (fMRI) has become the most popular method for imaging brain function. Handbook of Functional MRI Data Analysis provides a comprehensive and practical introduction to the methods used for fMRI data analysis. Using minimal jargon, this book explains the concepts behind processing fMRI data, focusing on the techniques that are most commonly used in the field. This book provides background about the methods employed by common data analysis packages including FSL, SPM and AFNI. Some of the newest cutting-edge techniques, including pattern classification analysis, connectivity modeling and resting state network analysis, are also discussed. Readers of this book, whether newcomers to the field or experienced researchers, will obtain a deep and effective knowledge of how to employ fMRI analysis to ask scientific questions and become more sophisticated users of fMRI analysis software.

Functional data is data in the form of curves that is becoming a popular method for interpreting scientific data. Statistical Analysis of Functional Data provides an authoritative account of function

Functional magnetic resonance imaging (fMRI) measures quick, tiny metabolic changes that take place in the brain, providing the most sensitive method currently available for identifying, investigating

Functional magnetic resonance imaging (fMRI) measures quick, tiny metabolic changes that take place in the brain, providing the most sensitive method currently available for identifying, investigating

The Bellman function, a powerful tool originating in control theory, can be used successfully in a large class of difficult harmonic analysis problems and has produced some notable results over the last thirty years. This book by two leading experts is the first devoted to the Bellman function method and its applications to various topics in probability and harmonic analysis. Beginning with basic concepts, the theory is introduced step-by-step starting with many examples of gradually increasing sophistication, culminating with Calderón–Zygmund operators and end-point estimates. All necessary techniques are explained in generality, making this book accessible to readers without specialized training in non-linear PDEs or stochastic optimal control. Graduate students and researchers in harmonic analysis, PDEs, functional analysis, and probability will find this to be an incisive reference, and can use it as the basis of a graduate course.

In recent years, numerous scientific investigations have studied the anatomical, biomechanical and functional role of structures involved in the human knee joint. The Finite Element Method (FEM) has b

A guide to all aspects of experimental design and data analysis for fMRI experiments, completely revised and updated for the second edition. Functional magnetic resonance imaging (fMRI), which allows

Using data drawn primarily from the American Southwest, Stephen Plog shows that there are basic problems with the methods archaeologists traditionally use to classify and analyse prehistoric pottery. Archaeologists have studied the painted designs and other stylistic (that is, non-functional) characteristics on different types of prehistoric artifacts in order to infer information about prehistoric social organization and cultural change. Such studies usually argue that the degree of similarity between the designs found on ceramic vessels at different prehistoric sites were occupied or from the amount of interaction between the people who occupied them. In Stylistic Variation in Prehistoric Ceramics, the author proposes that many factors, rather than just two, cause design or stylistic variation on artifacts. He demonstrates flaws in the logic and method of previous studies and suggests that the ways in which designs have been classified and understood are often inappropriate. Employin

Using data drawn primarily from the American Southwest, Stephen Plog shows that there are basic problems with the methods archaeologists traditionally use to classify and analyse prehistoric pottery. Archaeologists have studied the painted designs and other stylistic (that is, non-functional) characteristics on different types of prehistoric artifacts in order to infer information about prehistoric social organization and cultural change. Such studies usually argue that the degree of similarity between the designs found on ceramic vessels at different prehistoric sites were occupied or from the amount of interaction between the people who occupied them. In Stylistic Variation in Prehistoric Ceramics, the author proposes that many factors, rather than just two, cause design or stylistic variation on artifacts. He demonstrates flaws in the logic and method of previous studies and suggests that the ways in which designs have been classified and understood are often inappropriate. Employin

This book presents the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems. The authors extend the theory to include vector exponential series. The first part of the book presents the modern theory of exponentials, using an operator theory approach. The second part of the book extends and upgrades the method of moments - one of the most powerful tools in the flourishing theory of the control of distributed parameter systems. The book then goes on to discuss the controllability of systems described by parabolic and hyperbolic PDEs for internal, boundary, initial, and pointwise control. Typical applications to optimal control problems are also considered. Researchers in control theory, operator theory, functional analysis and partial differential equations will find much to interest them in this treatise.

This book presents the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems. The authors extend the theory to include vector exponential series. The first part of the book presents the modern theory of exponentials, using an operator theory approach. The second part of the book extends and upgrades the method of moments - one of the most powerful tools in the flourishing theory of the control of distributed parameter systems. The book then goes on to discuss the controllability of systems described by parabolic and hyperbolic PDEs for internal, boundary, initial, and pointwise control. Typical applications to optimal control problems are also considered. Researchers in control theory, operator theory, functional analysis and partial differential equations will find much to interest them in this treatise.

This 5th edition of this popular graduate textbook, presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. It includes numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The R package 'astsa' has had major updates and the text will reflect those updates. In general, the graphics have been improved. New topics include random number generation, modeling and fitting predator-prey interactions, more emphasis on structural models, testing for linearity, discussion of EM algorithm is more extensive, Bayesian analysis of state space models and MCMC is more extensive (including new scripts in astsa), particle methods are introduced, stochastic volatility coverage is expanded, changepoint detection is introduced (new topic).The

Functional magnetic resonance imaging (fMRI), which allows researchers to observeneural activity in the human brain noninvasively, has revolutionized the scientific study of themind. An fMRI experimen

This comprehensive introduction to the calculus of variations and its main principles also presents their real-life applications in various contexts: mathematical physics, differential geometry, and optimization in economics. Based on the authors' original work, it provides an overview of the field, with examples and exercises suitable for graduate students entering research. The method of presentation will appeal to readers with diverse backgrounds in functional analysis, differential geometry and partial differential equations. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. Since much of the material has a strong geometric flavor, the authors have supplemented the text with figures to illustrate the abstract concepts. Its extensive reference list and index also make this a valuable resource for researchers working in a variety of fields who are interested in partial differential equations and functional

From the reviews: "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a hig

A careful and accessible exposition of a functional analytic approach to initial boundary value problems for semilinear parabolic differential equations, with a focus on the relationship between analytic semigroups and initial boundary value problems. This semigroup approach is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of pseudo-differential operators, one of the most influential works in the modern history of analysis. Complete with ample illustrations and additional references, this new edition offers both streamlined analysis and better coverage of important examples and applications. A powerful method for the study of elliptic boundary value problems, capable of further extensive development, is provided for advanced undergraduates or beginning graduate students, as well as mathematicians with an interest in functional analysis and partial differential equations.

A systematic program design method can help developers ensure the correctness and performance of programs while minimizing the development cost. This book describes a method that starts with a clear specification of a computation and derives an efficient implementation by step-wise program analysis and transformations. The method applies to problems specified in imperative, database, functional, logic and object-oriented programming languages with different data, control and module abstractions. Designed for courses or self-study, this book includes numerous exercises and examples that require minimal computer science background, making it accessible to novices. Experienced practitioners and researchers will appreciate the detailed examples in a wide range of application areas including hardware design, image processing, access control, query optimization and program analysis. The last section of the book points out directions for future studies.

A systematic program design method can help developers ensure the correctness and performance of programs while minimizing the development cost. This book describes a method that starts with a clear specification of a computation and derives an efficient implementation by step-wise program analysis and transformations. The method applies to problems specified in imperative, database, functional, logic and object-oriented programming languages with different data, control and module abstractions. Designed for courses or self-study, this book includes numerous exercises and examples that require minimal computer science background, making it accessible to novices. Experienced practitioners and researchers will appreciate the detailed examples in a wide range of application areas including hardware design, image processing, access control, query optimization and program analysis. The last section of the book points out directions for future studies.

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, st

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, st

The global biodiversity crisis is one of humanity's most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question 'what is diversity?' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.

The global biodiversity crisis is one of humanity's most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question 'what is diversity?' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.

Cluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I use? How should I handle outliers? Classification assigns new observations to groups given previously classified observations, and also has open questions about parameter tuning, robustness and uncertainty assessment. This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions. It builds the basic ideas in an accessible but rigorous way, with extensive data examples and R code; describes modern approaches to high-dimensional data and networks; and explains such recent advances as Bayesian regularization, non-Gaussian model-based clustering, cluster merging, variable selection, semi-supervised and robust classification, clustering of functional data, text and images, and co-cl

In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its relevance in several important respects. Many branches of classical analysing have their origins in the rigourous discussion of problems in applies mathematics and theoretical physics, and the classical treatment of the theory of partial differential equations still provides the best method of treating many physical problems. A knowledge of the classical theory is essential for pure mathematics who intend to undertake research in this field, whatever approach they ultimately adopt. The numerical analyst needs a knowledge of classical theory in order to decide whether a problem has a uni

The purpose of this book is to introduce Fourier descriptors as a method for measuring the shape of whole or parts of organisms. Fourier descriptors refer to the utilization of Fourier analysis, primarily the Fourier series as a curve-fitting technique, that can numerically describe the outline (shape) of irregular structures such as are commonly found in living organisms. The quantitative characterization of irregular forms is often a first step towards elucidation of the underlying biological processes, whether they be genetic, evolutionary, or functional. The first five chapters discuss the theory behind the use of Fourier descriptors and the remaining chapters show case studies of how they can be used in various fields of biology such as anatomy, cell biology, medicine and dentistry. This book is solely devoted to this subject and will be of interest to all those interested in biological morphometrics.

The purpose of this book is to introduce Fourier descriptors as a method for measuring the shape of whole or parts of organisms. Fourier descriptors refer to the utilization of Fourier analysis, primarily the Fourier series as a curve-fitting technique, that can numerically describe the outline (shape) of irregular structures such as are commonly found in living organisms. The quantitative characterization of irregular forms is often a first step towards elucidation of the underlying biological processes, whether they be genetic, evolutionary, or functional. The first five chapters discuss the theory behind the use of Fourier descriptors and the remaining chapters show case studies of how they can be used in various fields of biology such as anatomy, cell biology, medicine and dentistry. This book is solely devoted to this subject and will be of interest to all those interested in biological morphometrics.

Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science, and many applied fields (economics and finance, pattern recognition and image processing, data fusion, etc.). This is a comprehensive, rigorous and self-contained exposition of aggregation functions. Classes of aggregation functions covered include triangular norms and conorms, copulas, means and averages, and those based on nonadditive integrals. The properties of each method, as well as their interpretation and analysis, are studied in depth, together with construction methods and practical identification methods. Special attention is given to the nature of scales on which values to be aggregated are defined (ordinal, interval, ratio

When this book was first published in 1953, certain methods for the estimation of the functional groups in organic compounds were widely known and used, but many other simple methods remained unnoticed and used, though they give better results. A review of the literature to the end of 1951 is made here, and all the important ways of analysis are described with full details. Abstracts and references to other methods are given and many special estimations are described in outline. The following compounds and groupings are included: olefines, alcohols, enols, phenols, mercaptans, aldehides and ketones, acetyl, benzoyl, methoxyl, ethoxyl, propoxyl, butoxyl, methylimino, ethylimino, methyl and ethyl groups attached to sulphur, the methyl group attached to carbon, amines and amino compounds, nitro, nitroso, cyano, and isocyanates and isothiocyanates. Several alternative experiments are described for each, so that it should always be possible to select a method suitable for a particular group