Basic Methods of Linear Functional Analysis

The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded- and vanishing-mean oscillations, and asymptotic methods for large structured determinants, among others. This friendly introduction to Toeplitz theory covers the classical spectral theory of Toeplitz forms and Wiener–Hopf integral operators and their manifestations throughout modern functional analysis. Numerous solved exercises illustrate the results of the main text and introduce subsidiary topics, including recent developments. Each chapter ends with a survey of the present state of the theory, making this a valuable work for the beginning graduate student and established researcher alike. With biographies of the principal creators of the theory and historical context also woven into the text, this book is a complete source on Toeplitz theory.

The fundamental algorithms in data mining and machine learning form the basis of data science, utilizing automated methods to analyze patterns and models for all kinds of data in applications ranging from scientific discovery to business analytics. This textbook for senior undergraduate and graduate courses provides a comprehensive, in-depth overview of data mining, machine learning and statistics, offering solid guidance for students, researchers, and practitioners. The book lays the foundations of data analysis, pattern mining, clustering, classification and regression, with a focus on the algorithms and the underlying algebraic, geometric, and probabilistic concepts. New to this second edition is an entire part devoted to regression methods, including neural networks and deep learning.

This enduringly popular undergraduate textbook has been thoroughly reworked and updated, and now comprises twelve chapters covering the same breadth of topics as earlier editions, but in a substantially modernized fashion to facilitate classroom teaching. Covering both theoretical and applied aspects of geophysics, clear explanations of the physical principles are blended with step-by-step derivations of the key equations and over 400 explanatory figures to explain the internal structure and properties of the planet, including its petroleum and mineral resources. New topics include the latest data acquisition technologies, such as satellite geophysics, planetary landers, ocean bottom seismometers, and fibre optic methods, as well as recent research developments in ambient noise interferometry, seismic hazard analysis, rheology, and numerical modelling - all illustrated with examples from the scientific literature. Student-friendly features include separate text boxes with auxiliary exp

Forensic linguistics is at the cutting edge of the undercover policing of child sexual abuse on the open internet and dark web, and language and identity is a fundamental part of this. The authors have drawn on their extensive experience in training undercover officers to develop innovative methods in identifying the creation and performance of online personas, crucial in detecting identity disguise online. This groundbreaking book demonstrates these methods through case studies, whilst also exploring the link between language and identity. By bringing together previously opposed positions in forensic authorship analysis, the book develops a novel theory of linguistic identity, which will resonate not just in forensic authorship research but in sociolinguistics more widely. This unique forensic linguistic project has real-life impact in assisting the police in their investigation of online abusers, and has impact for students and researchers of linguistics, through its contribution to

This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix no

On its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis–Alvis duality map and Mackey's theorem and the results that can be deduced from it, before moving on to a discussion of Deligne–Lusztig induction and Lusztig's Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.

On its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis–Alvis duality map and Mackey's theorem and the results that can be deduced from it, before moving on to a discussion of Deligne–Lusztig induction and Lusztig's Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.

This enduringly popular undergraduate textbook has been thoroughly reworked and updated, and now comprises twelve chapters covering the same breadth of topics as earlier editions, but in a substantially modernized fashion to facilitate classroom teaching. Covering both theoretical and applied aspects of geophysics, clear explanations of the physical principles are blended with step-by-step derivations of the key equations and over 400 explanatory figures to explain the internal structure and properties of the planet, including its petroleum and mineral resources. New topics include the latest data acquisition technologies, such as satellite geophysics, planetary landers, ocean bottom seismometers, and fibre optic methods, as well as recent research developments in ambient noise interferometry, seismic hazard analysis, rheology, and numerical modelling - all illustrated with examples from the scientific literature. Student-friendly features include separate text boxes with auxiliary exp

This book challenges the conventional wisdom that policy performance is the most important determinant of regime support. It does so by focusing on two countries where performance and support do not match. Chile is the economic envy of every country in Latin America, yet support has been surprisingly anemic. By contrast, Venezuela managed to maintain extremely high levels of support during the reign of Hugo Chávez despite severe failures of governance. Resolution of these paradoxes requires turning away from policy decisions and focusing instead on how those decisions are made. Taking inspiration from democratic theory and social psychology, this book argues that extensive opportunities for direct participation in the political process engenders in citizens strong feelings of efficacy - a sense of control over the course of politics. Rhodes-Purdy uses a mixed-methods approach to test this theory, including qualitative case studies, analysis of survey data, and experimental methods.

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every cha

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every cha

Preferential Services Liberalization offers the first, comprehensive analysis of the conditions that the World Trade Organization sets for preferential trade agreements (PTAs) in the area of services. Johanna Jacobsson provides an in-depth analysis of the relevant GATS rules, puts forward a practical method to analyze services PTAs, and applies the method to services agreements concluded by the EU. The result is a detailed examination of the legal criteria for services PTAs and methods to study them, combined with a better understanding of the level of liberalization reached by the EU and its member states. This book does go beyond the EU in analyzing the implications that multi-level governance has for international services liberalization. It proposes a new approach to study services commitments of any federal state and argues that lower levels of government should receive more attention in international negotiations over services trade.

This book highlights some of the latest currents in Whitman scholarship and demonstrates how Whitman's work can speak to and transform discussions in literary studies during a time of great intellectual ferment. It is organized into three sections, addressing aesthetics and politics, new reading methods, and histories of the critical imagination. This volume contains innovative work on Whitman in a range of fields. With the explosion of the digitization of books and periodicals in the past few years, the entire sense of Whitman's career is changing, and these essays are informed by the latest revelations among primary sources. The New Walt Whitman Studies shows how the latest concerns of literary analysis, from surface reading to ecocriticism to the digital humanities, emerged from an engagement with Whitman's work.

Written by a pioneer in the field, this text provides a complete introduction to X-ray microscopy, providing all of the technical background required to use, understand and even develop X-ray microscopes. Starting from the basics of X-ray physics and focusing optics, it goes on to cover imaging theory, tomography, chemical and elemental analysis, lensless imaging, computational methods, instrumentation, radiation damage, and cryomicroscopy, and includes a survey of recent scientific applications. Designed as a 'one-stop' text, it provides a unified notation, and shows how computational methods in different areas are linked with one another. Including numerous derivations, and illustrated with dozens of examples throughout, this is an essential text for academics and practitioners across engineering, the physical sciences and the life sciences who use X-ray microscopy to analyze their specimens, as well as those taking courses in X-ray microscopy.

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecula

Fully revised to match the more traditional sequence of course materials, this full-color second edition presents the basic principles and methods of thermodynamics using a clear and engaging style and a wealth of end-of-chapter problems. It includes five new chapters on topics such as mixtures, psychometry, chemical equilibrium, and combustion, and discussion of the Second Law of Thermodynamics has been expanded and divided into two chapters, allowing instructors to introduce the topic using either the cycle analysis in Chapter 6 or the definition of entropy in Chapter 7. Online ancillaries including new LMS testbanks, a password-protected solutions manual, prepared PowerPoint lecture slides, instructional videos, and figures in electronic format are available at www.cambridge.org/thermo

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecula

The fourth edition of Statistical Concepts for the Behavioral Sciences emphasizes contemporary research problems to better illustrate the relevance of statistical analysis in scientific research. All statistical methods are introduced in the context of a realistic problem, many of which are from contemporary published research. These studies are fully referenced so students can easily access the original research. The uses of statistics are then developed and presented in a conceptually logical progression for increased comprehension by using the accompanying workbook and the problem sets. Several forms of practice problems are available to students and presented in a manner that assists students in mastering component pieces before integrating them together to tackle more complicated, real-world problems.

This unique book examines the role non-doctrinal research methods play in international legal research: what do they add to the traditional doctrinal analysis of law and what do they neglect? Focusing

Doubt over the trustworthiness of published empirical results is not unwarranted and is often a result of statistical mis-specification: invalid probabilistic assumptions imposed on data. Now in its second edition, this bestselling textbook offers a comprehensive course in empirical research methods, teaching the probabilistic and statistical foundations that enable the specification and validation of statistical models, providing the basis for an informed implementation of statistical procedure to secure the trustworthiness of evidence. Each chapter has been thoroughly updated, accounting for developments in the field and the author's own research. The comprehensive scope of the textbook has been expanded by the addition of a new chapter on the Linear Regression and related statistical models. This new edition is now more accessible to students of disciplines beyond economics and includes more pedagogical features, with an increased number of examples as well as review questions and e

This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overv

This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overv

The second edition of Nuclear Safety provides the most up to date methods and data needed to evaluate the safety of nuclear facilities and related processes using risk-informed safety analysis, and pr

2D Semiconductor Materials and Devices reviews the basic science and state-of-art technology of 2D semiconductor materials and devices. Chapters discuss the basic structure and properties of 2D semiconductor materials, including both elemental (silicene, phosphorene) and compound semiconductors (transition metal dichalcogenide), the current growth and characterization methods of these 2D materials, state-of-the-art devices, and current and potential applications.

Nietzsche, a trained philologist, frequently urges his readers to interpret him carefully. In this book, Mark Alfano combines detailed close reading with digital methods (corpus analysis and semantic network visualization) to reframe our understanding of this major figure. He argues that virtue is a neglected concept in Nietzsche's writings, and sets out a fresh interpretation of Nietzschean virtues as well-calibrated drives. As different people embody different constellations of drives, so virtues differ from person to person. For Nietzsche himself, Alfano argues, five virtues are essential: curiosity, courage, a sense of humor, and pathos of distance (that is, contemptuousness) toward one's self and toward one's society. This innovative and original book will be invaluable for historians of philosophy, contemporary researchers in moral psychology and virtue theory, and philosophers interested in the fast-growing methodologies of the digital humanities.

Over the past decades, public trust in medical professionals has steadily declined. This decline of trust and its replacement by ever tighter regulations is increasingly frustrating physicians. However, most discussions of trust are either abstract philosophical discussions or social science investigations not easily accessible to clinicians. The authors, one a surgeon-turned-philosopher, the other an analytical philosopher working in medical ethics, joined their expertise to write a book which straddles the gap between the practical and theoretical. Using an approach grounded in the methods of conceptual analysis found in analytical philosophy which also draws from approaches to medical diagnosis, the authors have conceived an internally coherent and comprehensive definition of trust to help elucidate the concept and explain its decline in the medical context. This book should appeal to all interested in the ongoing debate about the decline of trust - be it as medical professionals, m

Unique in its clarity, examples, and range, Physical Mathematics explains simply and succinctly the mathematics that graduate students and professional physicists need to succeed in their courses and research. The book illustrates the mathematics with numerous physical examples drawn from contemporary research. This second edition has new chapters on vector calculus, special relativity and artificial intelligence and many new sections and examples. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations, Bessel functions, and spherical harmonics, the book explains topics such as the singular value decomposition, Lie algebras and group theory, tensors and general relativity, the central limit theorem and Kolmogorov's theorems, Monte Carlo methods of experimental and theoretical physics, Feynman's path integrals, and the standard model of cosmology.

In this Element and its accompanying second Element, A Practical Introduction to Regression Discontinuity Designs: Extensions, Matias Cattaneo, Nicolás Idrobo, and Rocıìo Titiunik provide an accessible and practical guide for the analysis and interpretation of regression discontinuity (RD) designs that encourages the use of a common set of practices and facilitates the accumulation of RD-based empirical evidence. In this Element, the authors discuss the foundations of the canonical Sharp RD design, which has the following features: (i) the score is continuously distributed and has only one dimension, (ii) there is only one cutoff, and (iii) compliance with the treatment assignment is perfect. In the second Element, the authors discuss practical and conceptual extensions to this basic RD setup.

This volume of new essays presents groundbreaking interpretations of some of the most central themes of Wittgenstein's philosophy. A distinguished group of contributors demonstrates how Wittgenstein's thought can fruitfully be applied to contemporary debates in epistemology, metaphilosophy and philosophy of language. The volume combines historical and systematic approaches to Wittgensteinian methods and perspectives, with essays providing detailed analysis that will be accessible to students as well as specialists. The result is a rich and illuminating picture of a key figure in twentieth-century philosophy and his continuing importance to philosophical study.

Doubt over the trustworthiness of published empirical results is not unwarranted and is often a result of statistical mis-specification: invalid probabilistic assumptions imposed on data. Now in its second edition, this bestselling textbook offers a comprehensive course in empirical research methods, teaching the probabilistic and statistical foundations that enable the specification and validation of statistical models, providing the basis for an informed implementation of statistical procedure to secure the trustworthiness of evidence. Each chapter has been thoroughly updated, accounting for developments in the field and the author's own research. The comprehensive scope of the textbook has been expanded by the addition of a new chapter on the Linear Regression and related statistical models. This new edition is now more accessible to students of disciplines beyond economics and includes more pedagogical features, with an increased number of examples as well as review questions and e

This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exerc

This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exerc

Over 100 years ago Harald Bohr identified a deep problem about the convergence of Dirichlet series, and introduced an ingenious idea relating Dirichlet series and holomorphic functions in high dimensions. Elaborating on this work, almost twnety years later Bohnenblust and Hille solved the problem posed by Bohr. In recent years there has been a substantial revival of interest in the research area opened up by these early contributions. This involves the intertwining of the classical work with modern functional analysis, harmonic analysis, infinite dimensional holomorphy and probability theory as well as analytic number theory. New challenging research problems have crystallized and been solved in recent decades. The goal of this book is to describe in detail some of the key elements of this new research area to a wide audience. The approach is based on three pillars: Dirichlet series, infinite dimensional holomorphy and harmonic 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

A comprehensive analysis of Donald Trump's legal history reveals his temperament, methods, character, and morality. Unlike all previous presidents who held distinguished positions in government or th

International courts and tribunals now operate globally and in several world regions, playing significant roles in international law and global governance. However, these courts vary significantly in terms of their practices, procedures, and the outcomes they produce. Why do some international courts perform better than others? Which factors affect the outcome of these courts and tribunals? The Performance of International Courts and Tribunals is an interdisciplinary study featuring approaches, methods and authorship from law and political science, which proposes the concept of performance to describe the processes and outcomes of international courts. It develops a framework for evaluating and explaining performance by offering a broad comparative analysis of international courts, covering several world regions and the areas of trade, investment, the environment, human rights and criminal law, and offers interdisciplinary accounts to explain how and why international court performance

Symbolic data analysis is a relatively new field that provides a range of methods for analyzing complex datasets. Standard statistical methods do not have the power or flexibility to make sense of ver

Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to