Methods

Structural vector autoregressive (VAR) models are important tools for empirical work in macroeconomics, finance, and related fields. This book not only reviews the many alternative structural VAR approaches discussed in the literature, but also highlights their pros and cons in practice. It provides guidance to empirical researchers as to the most appropriate modeling choices, methods of estimating, and evaluating structural VAR models. The book traces the evolution of the structural VAR methodology and contrasts it with other common methodologies, including dynamic stochastic general equilibrium (DSGE) models. It is intended as a bridge between the often quite technical econometric literature on structural VAR modeling and the needs of empirical researchers. The focus is not on providing the most rigorous theoretical arguments, but on enhancing the reader's understanding of the methods in question and their assumptions. Empirical examples are provided for illustration.

Structural vector autoregressive (VAR) models are important tools for empirical work in macroeconomics, finance, and related fields. This book not only reviews the many alternative structural VAR approaches discussed in the literature, but also highlights their pros and cons in practice. It provides guidance to empirical researchers as to the most appropriate modeling choices, methods of estimating, and evaluating structural VAR models. The book traces the evolution of the structural VAR methodology and contrasts it with other common methodologies, including dynamic stochastic general equilibrium (DSGE) models. It is intended as a bridge between the often quite technical econometric literature on structural VAR modeling and the needs of empirical researchers. The focus is not on providing the most rigorous theoretical arguments, but on enhancing the reader's understanding of the methods in question and their assumptions. Empirical examples are provided for illustration.

The measurement methods used in financial accounting affect our perception of the value and performance of businesses by determining the amount of reported profit or loss and the resources of the business. Thus, measurement affects shareholders and other stakeholders in the business. It has even been suggested that the world financial crisis of 2007–2010 was partly due to the mis-measurement of financial instruments. In this book, Geoffrey Whittington provides a unique survey of the theory and practice of measurement in financial accounts. It seeks to define and illustrate alternative methods, using simple numerical examples, and to analyse their theoretical properties. Also, it summarises extensive empirical evidence and the historical development of ideas and practice. It is essential reading for advanced undergraduate and postgraduate students studying financial accounting, as well as practitioners and policy-makers concerned with accounting standards.

The measurement methods used in financial accounting affect our perception of the value and performance of businesses by determining the amount of reported profit or loss and the resources of the business. Thus, measurement affects shareholders and other stakeholders in the business. It has even been suggested that the world financial crisis of 2007–2010 was partly due to the mis-measurement of financial instruments. In this book, Geoffrey Whittington provides a unique survey of the theory and practice of measurement in financial accounts. It seeks to define and illustrate alternative methods, using simple numerical examples, and to analyse their theoretical properties. Also, it summarises extensive empirical evidence and the historical development of ideas and practice. It is essential reading for advanced undergraduate and postgraduate students studying financial accounting, as well as practitioners and policy-makers concerned with accounting standards.

Bone is the tissue most frequently recovered archaeologically and is the material most commonly studied by biological anthropologists, who are interested in how skeletons change shape during growth and across evolutionary time. This volume brings together a range of contemporary studies of bone growth and development to highlight how cross-disciplinary research and new methods can enhance our anthropological understanding of skeletal variation. The novel use of imaging techniques from developmental biology, advanced sequencing methods from genetics, and perspectives from evolutionary developmental biology improve our ability to understand the bases of modern human and primate variation. Animal models can also be used to provide a broad biological perspective to the systematic study of humans. This volume is a testament to the drive of anthropologists to understand biological and evolutionary processes that underlie changes in bone morphology and illustrates the continued value of incor

Written by an internationally recognized teacher and researcher, this book provides a thorough, modern treatment of the aerodynamic principles of helicopters and other rotating-wing vertical lift aircraft such as tilt rotors and autogiros. The text begins with a unique technical history of helicopter flight, and then covers basic methods of rotor aerodynamic analysis, and related issues associated with the performance of the helicopter and its aerodynamic design. It goes on to cover more advanced topics in helicopter aerodynamics, including airfoil flows, unsteady aerodynamics, dynamic stall, and rotor wakes, and rotor-airframe aerodynamic interactions, with final chapters on autogiros and advanced methods of helicopter aerodynamic analysis. Extensively illustrated throughout, each chapter includes a set of homework problems. Advanced undergraduate and graduate students, practising engineers, and researchers will welcome this thoroughly revised and updated text on rotating-wing aerodyn

Multilayer networks, in particular multilayer social networks, where users belong to and interact on different networks at the same time, are an active research area in social network analysis, computer science, and physics. These networks have traditionally been studied within these separate research communities, leading to the development of several independent models and methods to deal with the same set of problems. This book unifies and consolidates existing practical and theoretical knowledge on multilayer networks including data collection and analysis, modeling, and mining of multilayer social network systems, the evolution of interconnected social networks, and dynamic processes such as information spreading. A single real dataset is used to illustrate the concepts presented throughout the book, demonstrating both the practical utility and the potential shortcomings of the various methods. Researchers from all areas of network analysis will learn new aspects and future directi

Multilayer networks, in particular multilayer social networks, where users belong to and interact on different networks at the same time, are an active research area in social network analysis, computer science, and physics. These networks have traditionally been studied within these separate research communities, leading to the development of several independent models and methods to deal with the same set of problems. This book unifies and consolidates existing practical and theoretical knowledge on multilayer networks including data collection and analysis, modeling, and mining of multilayer social network systems, the evolution of interconnected social networks, and dynamic processes such as information spreading. A single real dataset is used to illustrate the concepts presented throughout the book, demonstrating both the practical utility and the potential shortcomings of the various methods. Researchers from all areas of network analysis will learn new aspects and future directi

Many problems in biology require an understanding of the relationships among variables in a multivariate causal context. Exploring such cause-effect relationships through a series of statistical methods, this book explains how to test causal hypotheses when randomised experiments cannot be performed. This completely revised and updated edition features detailed explanations for carrying out statistical methods using the popular and freely available R statistical language. Sections on d-sep tests, latent constructs that are common in biology, missing values, phylogenetic constraints, and multilevel models are also an important feature of this new edition. Written for biologists and using a minimum of statistical jargon, the concept of testing multivariate causal hypotheses using structural equations and path analysis is demystified. Assuming only a basic understanding of statistical analysis, this new edition is a valuable resource for both students and practising biologists.

How are two or more languages learned and contained in the same mind or the same community? This handbook presents an up-to-date view of the concept of multi-competence, exploring the research questions it has generated and the methods that have been used to investigate it. The book brings together psychologists, sociolinguists, Second Language Acquisition (SLA) researchers, and language teachers from across the world to look at how multi-competence relates to their own areas of study. This comprehensive, state-of-the-art exploration of multi-competence research and ideas offers a powerful critique of the values and methods of classical SLA research, and an exciting preview of the future implications of multi-competence for research and thinking about language. It is an essential reference for all those concerned with language learning, language use and language teaching.

In the summer of 2014 leading experts in the theory of water waves gathered at the Newton Institute for Mathematical Sciences in Cambridge for four weeks of research interaction. A cross-section of those experts was invited to give introductory-level talks on active topics. This book is a compilation of those talks and illustrates the diversity, intensity, and progress of current research in this area. The key themes that emerge are numerical methods for analysis, stability and simulation of water waves, transform methods, rigorous analysis of model equations, three-dimensionality of water waves, variational principles, shallow water hydrodynamics, the role of deterministic and random bottom topography, and modulation equations. This book is an ideal introduction for PhD students and researchers looking for a research project. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics.

This book represents the first comprehensive examination of templatic constructions - namely, linguistic structures involving unexpected linear stipulation - in both morphology and syntax from a typological perspective. It provides a state-of-the-art overview of the previous literature, develops a new typology for categorizing templatic constructions across grammatical domains, and examines their cross-linguistic variation by employing cutting-edge computational methods. It will be of interest to descriptive linguists seeking to gain a better sense of the diversity of the world's templatic constructions, theoretical linguists developing restrictive models of possible templates, and typologists interested in the attested range of patterns of linear stipulation and the application of new kinds of multivariate methods to cross-linguistic data. The new typological framework is illustrated in detail via a number of case studies involving languages of Africa, Europe, Asia, and the Americas,

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

Uniting classical and modern photonics approaches by presenting optical analyses as solutions of Maxwell's equations, this unique book enables students and practising engineers to fully understand the similarities and differences between the different methods. The book begins with a thorough discussion of plane wave analysis, which provides a clear understanding of optics without considering boundary condition or device configuration. It then goes on to cover diffraction analysis of many applications, including a rigorous analysis of TEM waves using Maxwell's equations with boundaries. Laser cavity modes and Gaussian beams are presented, modal analysis is covered, and approximation methods are discussed (including the perturbation technique, coupled mode analysis, and super mode analysis). With theory linked to practical examples throughout, it provides a clear understanding of the interplay between plane wave, diffraction and modal analysis, and how the different techniques can be app

This comprehensive review of the emotive and often controversial topic of abortion provides clinicians with a multidisciplinary focus on abortion services, discussing clinical topics in their sociological, legal and ethical context. It is particularly timely as novel methods of service delivery make this vital resource more accessible, allowing abortion to be performed in community settings. Topics include medical and surgical methods of abortion, ultrasound scanning, pain control, complications, and abortion in women with medical conditions, as well as ethics, stigma, and human rights. Written by leading authorities in their subject areas, Abortion Care is essential reading for medical and nursing specialists and forms a useful resource in the delivery of graduate courses in the fields of obstetrics and gynaecology and sexual and reproductive healthcare. It is also of interest to professionals involved in planning, delivering and managing women's health services, including counsellors

The second edition of Computational Fluid Dynamics represents a significant improvement from the first edition. However, the original idea of including all computational fluid dynamics methods (FDM, FEM, FVM); all mesh generation schemes; and physical applications to turbulence, combustion, acoustics, radiative heat transfer, multiphase flow, electromagnetic flow, and general relativity is still maintained. The second edition includes a new section on preconditioning for EBE-GMRES and a complete revision of the section on flowfield-dependent variation methods, which demonstrates more detailed computational processes and includes additional example problems. For those instructors desiring a textbook that contains homework assignments, a variety of problems for FDM, FEM and FVM are included in an appendix. To facilitate students and practitioners intending to develop a large-scale computer code, an example of FORTRAN code capable of solving compressible, incompressible, viscous, inviscid

This revised and updated edition focuses on constrained ordination (RDA, CCA), variation partitioning and the use of permutation tests of statistical hypotheses about multivariate data. Both classification and modern regression methods (GLM, GAM, loess) are reviewed and species functional traits and spatial structures analysed. Nine case studies of varying difficulty help to illustrate the suggested analytical methods, using the latest version of Canoco 5. All studies utilise descriptive and manipulative approaches, and are supported by data sets and project files available from the book website: http://regent.prf.jcu.cz/maed2/. Written primarily for community ecologists needing to analyse data resulting from field observations and experiments, this book is a valuable resource to students and researchers dealing with both simple and complex ecological problems, such as the variation of biotic communities with environmental conditions or their response to experimental manipulation.

Intelligent technical systems, which combine mechanical, electrical and software engineering with methods from control engineering and advanced mathematics, go far beyond the state of the art in mechatronics and open up fascinating perspectives. Among these systems are so-called self-optimizing systems, which are able to adapt their behavior autonomously and flexibly to changing operating conditions. The Collaborative Research Center 614 "Self-optimizing concepts and structures in mechanical engineering" pursued the long-term aim to enable others to develop dependable self-optimizing systems. Assuring their dependability poses new challenges. However, self-optimization also offers the possibility to adapt the system's behavior to improve dependability during operation. The aim of this book is to provide methods and techniques to master the challenges and to exploit the possibilities given by self-optimization. The reader will be able to develop self-optimizing systems that fulfill and

Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity sci

Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for resear

The principles of signal processing are fundamental to the operation of many everyday devices. This book introduces the basic theory of digital signal processing, with emphasis on real-world applications. Sampling, quantization, the Fourier transform, filters, Bayesian methods and numerical considerations are covered, then developed to illustrate how they are used in audio, image, and video processing and compression, and in communications. The book concludes with methods for the efficient implementation of algorithms in hardware and software. Intuitive arguments rather than mathematical ones are used wherever possible, and links between various signal processing techniques are stressed. The advantages and disadvantages of different approaches are presented in the context of real-world examples, enabling the reader to choose the best solution to a given problem. With over 200 illustrations and over 130 exercises (including solutions), this book will appeal to practitioners working in s

Aimed at graduates and researchers, and requiring only a basic knowledge of multi-variable calculus, this introduction to computer-based partial differential equation (PDE) modeling provides readers with the practical methods necessary to develop and use PDE mathematical models in biomedical engineering. Taking an applied approach, rather than using abstract mathematics, the reader is instructed through six biomedical example applications, each example characterized by step-by-step discussions of established numerical methods and implemented in reliable computer routines. Adopting this technique, the reader will understand how PDE models are formulated, implemented and tested. Supported by a set of rigorously tested general purpose PDE routines online, and with enhanced understanding through animations, this book will be ideal for anyone faced with interpreting large experimental data sets that need to be analyzed with PDE models in biomedical engineering.

Symposium BB, 'Solution Synthesis of Inorganic Films and Nanostructured Materials', was held during the 2012 MRS Spring Meeting in San Francisco, California, on April 9–13, 2012. It focused on solution synthesis approaches for the growth of a wide-range of advanced functional inorganic thin film and nanostructured materials. Recent results were presented on the growth of: (i) highly crystalline, nanopatterned and composite functional oxide films, (ii) nanoparticles and nanocrystals, and (iii) self-assembled nanostructures by various chemical solution methods. A strong increased interest in low-cost and high throughput synthesis of functional and multifunctional inorganic materials indicates the worldwide importance of such synthetic methods. The symposium promoted information exchange between worldwide researchers from universities and national labs and engineers from industry. The papers in this proceedings volume provide a glimpse of the recent developments in the chemical solution g

The small sample properties of estimators and tests are frequently too complex to be useful or are unknown. Much econometric theory is therefore developed for very large or asymptotic samples where it is assumed that the behaviour of estimators and tests will adequately represent their properties in small samples. Refined asymptotic methods adopt an intermediate position by providing improved approximations to small sample behaviour using asymptotic expansions. Dedicated to the memory of Michael Magdalinos, whose work is a major contribution to this area, this book contains chapters directly concerned with refined asymptotic methods. In addition, there are chapters focusing on new asymptotic results; the exploration through simulation of the small sample behaviour of estimators and tests in panel data models; and improvements in methodology. With contributions from leading econometricians, this collection will be essential reading for researchers and graduate students concerned with th

Many research problems in cryospheric science, such as global warming-induced permafrost degradation, require information about the subsurface, which can be imaged using geophysical methods. This book is a practical guide to the application of geophysical techniques in mountainous and polar terrain, where the harsh environment and nature of the subsurface pose particular challenges. It starts with an introduction to the main geophysical methods and then demonstrates their application in periglacial environments through various case studies - written by a team of international experts. The final part of the book presents a series of reference tables with typical values of geophysical parameters for periglacial environments. This handbook is a valuable resource for glaciologists, geomorphologists and geologists requiring an introduction to geophysical techniques, as well as for geophysicists lacking experience of planning and conducting field surveys in cold regions.

State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also p

State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also p

This book is intended to provide the reader with a firm conceptual and empirical understanding of basic information-theoretic econometric models and methods. Because most data are observational, practitioners work with indirect noisy observations and ill-posed econometric models in the form of stochastic inverse problems. Consequently, traditional econometric methods in many cases are not applicable for answering many of the quantitative questions that analysts wish to ask. After initial chapters deal with parametric and semiparametric linear probability models, the focus turns to solving nonparametric stochastic inverse problems. In succeeding chapters, a family of power divergence measure-likelihood functions are introduced for a range of traditional and nontraditional econometric-model problems. Finally, within either an empirical maximum likelihood or loss context, Ron C. Mittelhammer and George G. Judge suggest a basis for choosing a member of the divergence family.

This book is intended to provide the reader with a firm conceptual and empirical understanding of basic information-theoretic econometric models and methods. Because most data are observational, practitioners work with indirect noisy observations and ill-posed econometric models in the form of stochastic inverse problems. Consequently, traditional econometric methods in many cases are not applicable for answering many of the quantitative questions that analysts wish to ask. After initial chapters deal with parametric and semiparametric linear probability models, the focus turns to solving nonparametric stochastic inverse problems. In succeeding chapters, a family of power divergence measure-likelihood functions are introduced for a range of traditional and nontraditional econometric-model problems. Finally, within either an empirical maximum likelihood or loss context, Ron C. Mittelhammer and George G. Judge suggest a basis for choosing a member of the divergence family.

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.

The imaging methods used to evaluate patients with suspected vertebral injuries have undergone radical changes in the past decade, the most significant being the ascendancy of computed tomography (CT) to become the primary investigative modality. Issues such as high radiation dose associated with CT studies and health care reform and cost containment also have a significant impact on clinical decision-making. This new edition of the classic landmark text for vertebral trauma imaging provides an in-depth discussion on the indications and methods of imaging the spine based on currently available clinical evidence. Every chapter has been extensively revised and the illustrations represent state-of-the-art imaging. A completely new chapter on pediatric injuries has been added. Imaging of Vertebral Trauma, third edition, is an invaluable and essential tool in the assessment of any patient with suspected vertebral or spinal cord injury.

Graph theory and the fields of natural language processing and information retrieval are well-studied disciplines. Traditionally, these areas have been perceived as distinct, with different algorithms, different applications and different potential end-users. However, recent research has shown that these disciplines are intimately connected, with a large variety of natural language processing and information retrieval applications finding efficient solutions within graph-theoretical frameworks. This book extensively covers the use of graph-based algorithms for natural language processing and information retrieval. It brings together topics as diverse as lexical semantics, text summarization, text mining, ontology construction, text classification and information retrieval, which are connected by the common underlying theme of the use of graph-theoretical methods for text and information processing tasks. Readers will come away with a firm understanding of the major methods and applicat

In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.

In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.

Games provide mathematical models for interaction. Numerous tasks in computer science can be formulated in game-theoretic terms. This fresh and intuitive way of thinking through complex issues reveals underlying algorithmic questions and clarifies the relationships between different domains. This collection of lectures, by specialists in the field, provides an excellent introduction to various aspects of game theory relevant for applications in computer science that concern program design, synthesis, verification, testing and design of multi-agent or distributed systems. Originally devised for a Spring School organised by the GAMES Networking Programme in 2009, these lectures have since been revised and expanded, and range from tutorials concerning fundamental notions and methods to more advanced presentations of current research topics. This volume is a valuable guide to current research on game-based methods in computer science for undergraduate and graduate students. It will also in

Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses wi

The second edition of Computational Fluid Dynamics represents a significant improvement from the first edition. However, the original idea of including all computational fluid dynamics methods (FDM, FEM, FVM); all mesh generation schemes; and physical applications to turbulence, combustion, acoustics, radiative heat transfer, multiphase flow, electromagnetic flow, and general relativity is still maintained. The second edition includes a new section on preconditioning for EBE-GMRES and a complete revision of the section on flowfield-dependent variation methods, which demonstrates more detailed computational processes and includes additional example problems. For those instructors desiring a textbook that contains homework assignments, a variety of problems for FDM, FEM and FVM are included in an appendix. To facilitate students and practitioners intending to develop a large-scale computer code, an example of FORTRAN code capable of solving compressible, incompressible, viscous, inviscid

Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book, first published in 2007, shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi- and Delaunay-based techniques, implicit surface-based methods and Morse theory-based methods are covered. Scientists and engineers working in drug design, medical imaging, CAD, GIS, and many other areas will benefit from this first book on the subject.

Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to sele