Basic Methods of Linear Functional 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

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.

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

This modern text combines fundamental principles with advanced topics and recent techniques in a rigorous and self-contained treatment of quantum field theory.Beginning with a review of basic principles, starting with quantum mechanics and special relativity, students can refresh their knowledge of elementary aspects of quantum field theory and perturbative calculations in the Standard Model. Results and tools relevant to many applications are covered, including canonical quantization, path integrals, non-Abelian gauge theories, and the renormalization group. Advanced topics are explored, with detail given on effective field theories, quantum anomalies, stable extended field configurations, lattice field theory, and field theory at a finite temperature or in the strong field regime. Two chapters are dedicated to new methods for calculating scattering amplitudes (spinor-helicity, on-shell recursion, and generalized unitarity), equipping students with practical skills for research. Acces

Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed 'scratch work' sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book w

In this book, wide-ranging sources are utilized to seek alternatives to the science-value dichotomy and to move beyond unhelpful impasses between qualitative and quantitative methods. It urges new directions of impact for psychology through intra- and interdisciplinary collaboration in order to confront unprecedented global challenges, generate questions and articulate new possibilities for a sustainable future for humanity. The analysis places the researcher as the principal instrument of any science - an affordance and an ongoing form of demand. Foregrounding 'the personal' also emphasizes continuity across arts and sciences; the interfaces of which contain the full range of resources for innovative thinking. The enduring relevance of observation, imaginative sense-making, and perspective-taking to psychology are explored. In emphasizing that 'the person' and 'the personal' reflect interconnected systems of various levels, the book calls for an appreciation and cultivation of these a

Using a wide range of professional genres such as research papers, business reports, performance commentaries, guidebooks and legal documents, this study focuses on the discourse of professional writing, employing analytic paradigms from systemic-functional linguistics, pragmatics, text analysis, sociology and anthropological linguistics. Kenneth Kong argues that while professions use different sets of practices, their use of language displays many universals. This is demonstrated through the analysis of data from a broad cross-section of professional settings such as medicine, law, business, mass media and engineering. This examination of professional discourse, and its important role in society, will be of interest to researchers in applied linguistics, to professionals who want to understand the role of language in their work, and to teachers of English for specific purposes.

《自動控制原理》介紹： This book presents a comprehensive treatment of the analysis and design of control systems. It consists of eight chapters， including the basic concepts of control systems， mathematical mod

This third edition provides a concise yet approachable introduction to seismic theory, designed as a first course for graduate students or advanced undergraduate students. It clearly explains the fundamental concepts, emphasizing intuitive understanding over lengthy derivations, and outlines the different types of seismic waves and how they can be used to resolve Earth structure and understand earthquakes. New material and updates have been added throughout, including ambient noise methods, shear-wave splitting, back-projection, migration and velocity analysis in reflection seismology, earthquake rupture directivity, and fault weakening mechanisms. A wealth of both reworked and new examples, review questions and computer-based exercises in MATLAB®/Python give students the opportunity to apply the techniques they have learned to compute results of interest and to illustrate Earth's seismic properties. More advanced sections, which are not needed to understand the other material, are fla

Verrocchio was arguably the most important sculptor between Donatello and Michelangelo but he has seldom been treated as such in art historical literature because his achievements were quickly superseded by the artists who followed him. He was the master of Leonardo da Vinci, but he is remembered as the sulky teacher that his star pupil did not need. In this book, Christina Neilson argues that Verrocchio was one of the most experimental artists in fifteenth-century Florence, itself one of the most innovative centers of artistic production in Europe. Considering the different media in which the artist worked in dialogue with one another (sculpture, painting, and drawing), she offers an analysis of Verrocchio's unusual methods of manufacture. Neilson shows that, for Verrocchio, making was a form of knowledge and that techniques of making can be read as systems of knowledge. By studying Verrocchio's technical processes, she demonstrates how an artist's theoretical commitments can be uncov

This third edition provides a concise yet approachable introduction to seismic theory, designed as a first course for graduate students or advanced undergraduate students. It clearly explains the fundamental concepts, emphasizing intuitive understanding over lengthy derivations, and outlines the different types of seismic waves and how they can be used to resolve Earth structure and understand earthquakes. New material and updates have been added throughout, including ambient noise methods, shear-wave splitting, back-projection, migration and velocity analysis in reflection seismology, earthquake rupture directivity, and fault weakening mechanisms. A wealth of both reworked and new examples, review questions and computer-based exercises in MATLAB®/Python give students the opportunity to apply the techniques they have learned to compute results of interest and to illustrate Earth's seismic properties. More advanced sections, which are not needed to understand the other material, are fla

In an incisive analysis of over two dozen clauses as well as several 'unwritten' rules and practices, The Constitutional Origins of the American Civil War shows how the Constitution aggravated the sectional conflict over slavery to the point of civil war. Going beyond the fugitive slave clause, the three-fifths clause, and the international slave trade clause, Michael F. Conlin demonstrates that many more constitutional provisions and practices played a crucial role in the bloody conflict that claimed the lives of over 750,000 Americans. He also reveals that ordinary Americans in the mid-nineteenth century had a surprisingly sophisticated knowledge of the provisions and the methods of interpretation of the Constitution. Lastly, Conlin reminds us that many of the debates that divide Americans today were present in the 1850s: minority rights vs. majority rule, original intent vs. a living Constitution, state's rights vs. federal supremacy, judicial activism vs. legislative prerogative, s

Written by the leading experts in the field, this text provides systematic coverage of the theory, physics, functional designs, and engineering applications of advanced engineered electromagnetic surfaces. All the essential topics are included, from the fundamental theorems of surface electromagnetics, to analytical models, general sheet transmission conditions (GSTC), metasurface synthesis, and quasi-periodic analysis. A plethora of examples throughout illustrate the practical applications of surface electromagnetics, including gap waveguides, modulated metasurface antennas, transmit arrays, microwave imaging, cloaking, and orbital angular momentum (OAM ) beam generation, allowing readers to develop their own surface electromagnetics-based devices and systems. Enabling a fully comprehensive understanding of surface electromagnetics, this is an invaluable text for researchers, practising engineers and students working in electromagnetics antennas, metasurfaces and optics.

Organizations and businesses strive toward excellence, and solutions to problems are based mostly on judgment and experience. However, increased competition and consumer demands require that the solutions be optimum and not just feasible. Theory leads to algorithms. Algorithms need to be translated into computer codes. Engineering problems need to be modeled. Optimum solutions are obtained using theory and computers, and then interpreted. Revised and expanded in its third edition, this textbook integrates theory, modeling, development of numerical methods, and problem solving, thus preparing students to apply optimization to real-world problems. This text covers a broad variety of optimization problems using: unconstrained, constrained, gradient, and non-gradient techniques; duality concepts; multi-objective optimization; linear, integer, geometric, and dynamic programming with applications; and finite element-based optimization. It is ideal for advanced undergraduate or graduate cours

Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed 'scratch work' sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book w

How fast is evolution, and why does it matter? The rate of evolution, and whether it is gradual or punctuated, is a hotly debated topic among biologists and paleontologists. This book compiles and compares examples of evolution from laboratory, field, and fossil record studies, analyzing them to extract their underlying rates. It concludes that while change is slow when averaged over many generations, on a generation-to-generation time scale, evolution is rapid. Chapters cover the history of evolutionary studies, from Lamarck and Darwin in the nineteenth century to the present day. An overview of the statistics of variation, dynamics of random walks, processes of natural selection and random drift, and effects of scale and time averaging are also provided, along with methods for the analysis of evolutionary time series. Containing case studies and worked examples, this book is ideal for advanced students and researchers in paleontology, biology, and anthropology.

The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier–Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.

An overview of the optical effects in solids, addressing the physics of various materials and their response to electromagnetic radiation. The discussion includes metals, semiconductors, superconductors, and insulators. The book begins by introducing the dielectric function into Maxwell's macroscopic equations and finding their plane-wave solution. The physics governing the dielectric function of various materials is then covered, both classically and using basic quantum mechanics. Advanced topics covered include interacting electrons, the anomalous skin effect, anisotropy, magneto-optics, and inhomogeneous materials. Each subject begins with a connection to the basic physics of the particular solid, after which the measurable optical quantities are derived. It allows the reader to connect measurements (reflectance, optical conductivity and dielectric function) with the underlying physics of solids. Methods of analysing experimental data are addressed, making this an ideal resource for

Developed specifically for students in the behavioral and brain sciences, this is the only textbook that provides an accessible and practical overview of the range of human neuroimaging techniques. Methods covered include functional and structural magnetic resonance imaging, positron emission tomography, electroencephalography, magnetoencephalography, multimodal imaging, and various brain stimulation methods. Experimental design, image processing, and statistical inference are also addressed, with chapters for both basic and more advanced data analyses. Key concepts are illustrated through research studies on the relationship between brain and behavior, and practice questions are included throughout to test knowledge and aid self-study. Offering just the right amount of detail for understanding how major imaging techniques can be applied to answer neuroscientific questions, and the practical skills needed for future research, this is an essential text for advanced undergraduate and gra

Developed specifically for students in the behavioral and brain sciences, this is the only textbook that provides an accessible and practical overview of the range of human neuroimaging techniques. Methods covered include functional and structural magnetic resonance imaging, positron emission tomography, electroencephalography, magnetoencephalography, multimodal imaging, and various brain stimulation methods. Experimental design, image processing, and statistical inference are also addressed, with chapters for both basic and more advanced data analyses. Key concepts are illustrated through research studies on the relationship between brain and behavior, and practice questions are included throughout to test knowledge and aid self-study. Offering just the right amount of detail for understanding how major imaging techniques can be applied to answer neuroscientific questions, and the practical skills needed for future research, this is an essential text for advanced undergraduate and gra

Geosequestration involves the deep geological storage of carbon dioxide from major industrial sources, providing a potential solution for reducing the rate of increase of atmospheric concentrations of carbon dioxide and mitigating climate change. This volume provides an overview of the major geophysical techniques and analysis methods for monitoring the movement and predictability of carbon dioxide plumes underground. Comprising chapters from eminent researchers, the book is illustrated with practical examples and case studies of active projects and government initiatives, and discusses their successes and remaining challenges. A key case study from Norway demonstrates how governments and other stake-holders could estimate storage capacity and design storage projects that meet the requirements of regulatory authorities. Presenting reasons for embracing geosequestration, technical best practice for carbon management, and outlooks for the future, this volume provides a key reference for

Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the developmen

Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject.

This comprehensive and self-contained text presents the fundamentals of optical imaging from the viewpoint of both ray and wave optics, within a single volume. Comprising three distinct parts, it opens with an introduction to electromagnetic theory, including electromagnetic diffraction problems and how they can be solved with the aid of standard numerical methods such as RCWA or FDTD. The second part is devoted to the basic theory of geometrical optics and the study of optical aberrations inherent in imaging systems, including large-scale telescopes and high-resolution projection lenses. A detailed overview of state-of-the-art optical system design provides readers with the necessary tools to successfully use commercial optical design software. The final part explores diffraction theory and concludes with vectorial wave propagation, image formation and image detection in high-aperture imaging systems. The wide-ranging perspective of this important book provides researchers and profess

Based on time-tested course material, this authoritative text examines the key topics, advanced mathematical concepts, and novel analytical tools needed to understand modern communication and radar systems. It covers computational linear algebra theory, VLSI systolic algorithms and designs, practical aspects of chaos theory, and applications in beamforming and array processing, and uses a variety of CDMA codes, as well as acoustic sensing and beamforming algorithms to illustrate key concepts. Classical topics such as spectral analysis are also covered, and each chapter includes a wealth of homework problems. This is an invaluable text for graduate students in electrical and computer engineering, and an essential reference for practitioners in communications and radar engineering.

Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.

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,

Methods and perspectives to model and measure productivity and efficiency have made a number of important advances in the last decade. Using the standard and innovative formulations of the theory and practice of efficiency and productivity measurement, Robin C. Sickles and Valentin Zelenyuk provide a comprehensive approach to productivity and efficiency analysis, covering its theoretical underpinnings and its empirical implementation, paying particular attention to the implications of neoclassical economic theory. A distinct feature of the book is that it presents a wide array of theoretical and empirical methods utilized by researchers and practitioners who study productivity issues. An accompanying website includes methods, programming codes that can be used with widely available software like MATLAB® and R, and test data for many of the productivity and efficiency estimators discussed in the book. It will be valuable to upper-level undergraduates, graduate students, and professional

Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.

What is a focus group? Why do we use them? When should we use them? When should we not? Focus Groups for the Social Science Researcher provides a step-by-step guide to undertaking focus groups, whether as a stand-alone method or alongside other qualitative or quantitative methods. It recognizes the challenges that focus groups encounter and provides tips to address them. The book highlights three unique, inter-related characteristics of focus groups. First, they are inherently social in form. Second, the data emerge organically through conversation; they are emic in nature. Finally, focus groups generate data at three levels of analysis: the individual, group, and interactive level. The book builds from these three characteristics to explain when focus groups can usefully be employed in different research designs. This is an essential text for students and researchers looking for a concise and accessible introduction to this important approach to data collection.

What is a focus group? Why do we use them? When should we use them? When should we not? Focus Groups for the Social Science Researcher provides a step-by-step guide to undertaking focus groups, whether as a stand-alone method or alongside other qualitative or quantitative methods. It recognizes the challenges that focus groups encounter and provides tips to address them. The book highlights three unique, inter-related characteristics of focus groups. First, they are inherently social in form. Second, the data emerge organically through conversation; they are emic in nature. Finally, focus groups generate data at three levels of analysis: the individual, group, and interactive level. The book builds from these three characteristics to explain when focus groups can usefully be employed in different research designs. This is an essential text for students and researchers looking for a concise and accessible introduction to this important approach to data collection.

Methods and perspectives to model and measure productivity and efficiency have made a number of important advances in the last decade. Using the standard and innovative formulations of the theory and practice of efficiency and productivity measurement, Robin C. Sickles and Valentin Zelenyuk provide a comprehensive approach to productivity and efficiency analysis, covering its theoretical underpinnings and its empirical implementation, paying particular attention to the implications of neoclassical economic theory. A distinct feature of the book is that it presents a wide array of theoretical and empirical methods utilized by researchers and practitioners who study productivity issues. An accompanying website includes methods, programming codes that can be used with widely available software like MATLAB® and R, and test data for many of the productivity and efficiency estimators discussed in the book. It will be valuable to upper-level undergraduates, graduate students, and professional

This study of Schrödinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis, microlocal analysis, functional analysis, and topology. This includes a new proof of Keel–Tao endpoint Strichartz estimates, and a new proof of Bourgain's result for radial, energy-critical NLS. It also provides a detailed presentation of scattering results for energy-critical and mass-critical equations. This book is suitable as the basis for a one-semester course, and serves as a useful introduction to nonlinear Schrödinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.

This book presents a quantitative history of constitutional law in the United States and brings together humanistic and social-scientific approaches to studying law. Using theoretical models of adjudication, Tom S. Clark presents a statistical model of law and uses the model to document the historical development of constitutional law. Using sophisticated statistical methods and historical analysis of court decisions, the author documents how social and political forces shape the path of law. Spanning the history of constitutional law since Reconstruction, this book illustrates the way in which the law evolves with American life and argues that a social-scientific approach to the history of law illuminates connections across disparate areas of the law, connected by the social context in which the Constitution has been interpreted.