Methods of Nonlinear Analysis

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

Astronomy needs statistical methods to interpret data, but statistics is a many-faceted subject that is difficult for non-specialists to access. This handbook helps astronomers analyze the complex data and models of modern astronomy. This second edition has been revised to feature many more examples using Monte Carlo simulations, and now also includes Bayesian inference, Bayes factors and Markov chain Monte Carlo integration. Chapters cover basic probability, correlation analysis, hypothesis testing, Bayesian modelling, time series analysis, luminosity functions and clustering. Exercises at the end of each chapter guide readers through the techniques and tests necessary for most observational investigations. The data tables, solutions to problems, and other resources are available online at www.cambridge.org/9780521732499. Bringing together the most relevant statistical and probabilistic techniques for use in observational astronomy, this handbook is a practical manual for advanced und

Motor development is an integral part of the developmental process. Understanding the organization of the sensory-motor system and its adaptations in response to environmental factors is a vital part of understanding individual development as a whole. This volume describes and discusses human motor development using longitudinal study methods, and from an interdisciplinary perspective. Researchers from a variety of different backgrounds and disciplines provide a broad-ranging analysis of human motor development, from both the practical and theoretical standpoint, in a book which will be of great interest to paediatricians, psychologists, developmental biologists, developmental psychiatrists and neurologists as well as to research scientists in these fields.

This book attempts an interpretation of Revolutionary American culture. It argues that the cultural identity of the United States, like its political identity, emerged from a quarrel with the Old World. Europeans believed that the Revolution had 'turned the world upside down'. American intellectuals tried to construct a republic which refuted European criticism. They failed, but in failing they created an attitude to the terrain which became a central theme in American culture. The book employs the methods of perceptual geography and close textual analysis to examine images of the terrain and to propose close links between imaginative literature and a wide range of non-literary writing.

This concise, easy-to-read pocket guide offers medical trainees, researchers, and clinicians at every level the perfect resource on Evidence Based Medicine (EBM). Based on the author's many years of experience teaching EBM to medical students and medical residents at Columbia University, this handy title addresses not only all the basic concepts and issues in EBM, but also takes an example-based approach and is replete with numerous illustrations. This brief book provides readers with all the tools needed to tell the good from the bad in healthcare research. It discusses every type of study design, from the assessment of diagnostic tests to clinical trials and meta-analysis. The work also introduces readers to novel methods, such as the Bayesian analysis of clinical trials. In addition, to help readers better retain the information, the guide includes thought-provoking review questions and answers in an appendix. In all, Pocket Evidence-Based Medicine: A Survival Guide for Clinicians a

Do you need to understand feedback? Perhaps you're a little rusty on theory basics? Dig in to this self-contained guide for an accessible and concise explanation of the fundamentals. Distills the relevant essence of linear system theory, calculus, differential equations, linear algebra, basic physics, numerical methods, and complex analysis, and links them back to an explanation of feedback theory. Provides a tight synthesis of analytical and conceptual understanding. Maintains a focus on common use cases. Whether you are a struggling undergraduate, a doctoral student preparing for your qualifying exams, or an industry practitioner, this easy-to-understand book invites you to relax, enjoy the material, and follow your curiosity.

Do you need to understand feedback? Perhaps you're a little rusty on theory basics? Dig in to this self-contained guide for an accessible and concise explanation of the fundamentals. Distills the relevant essence of linear system theory, calculus, differential equations, linear algebra, basic physics, numerical methods, and complex analysis, and links them back to an explanation of feedback theory. Provides a tight synthesis of analytical and conceptual understanding. Maintains a focus on common use cases. Whether you are a struggling undergraduate, a doctoral student preparing for your qualifying exams, or an industry practitioner, this easy-to-understand book invites you to relax, enjoy the material, and follow your curiosity.

Tracing almost 200 years of history, Explaining Tort and Crime explains the development of tort law and criminal law in England compared with other legal systems. Referencing legal systems from around the globe, it uses innovative comparative and historical methods to identify patterns of legal development, to investigate the English law of fault doctrine across tort and crime, and to chart and explain three procedural interfaces: criminal powers to compensate, timing rules to control parallel actions, and convictions as evidence in later civil cases. Matthew Dyson draws on decades of research to offer an analysis of the field, examining patterns of legal development, visible as motifs in the law of many legal systems.

Directed primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences. It contains all the usual topics covered in a first-year course such as vectors, matrices, differential equations, basic mathematical functions and their analysis, and power series. There is a strong emphasis on qualitative understanding (such as curve sketching) and practical methods of solution. The latter take due account of the impact of computers on the subject. The principles of mathematical expression are illustrated by copious examples taken from a wide range of topics in physics and chemistry. Each of the short chapters concludes with a summary and a large number of problems.

Based on a course taught by the author, this book combines the theoretical underpinnings of statistics with the practical analysis of Earth sciences data using MATLAB. The book is organized to introduce the underlying concepts, and then extends these to the data, covering methods that are most applicable to Earth sciences. Topics include classical parametric estimation and hypothesis testing, and more advanced least squares-based, nonparametric, and resampling estimators. Multivariate data analysis, not often encountered in introductory texts, is presented later in the book, and compositional data is treated at the end. Datasets and bespoke MATLAB scripts used in the book are available online, as well as additional datasets and suggested questions for use by instructors. Aimed at entering graduate students and practicing researchers in the Earth and ocean sciences, this book is ideal for those who want to learn how to analyse data using MATLAB in a statistically-rigorous manner.

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

●Practical applications include examples, over 500 homework problems, and computer problems.●Describes techniques to convert analog signals, the analysis of linear time-invariant discrete-time systems and signals in the time domain, and bilateral and unilateral z-transform methods.●Analyzes signals and systems in the frequency domain, the Fourier series and transform in continuous- and discrete-time signals, and the sampling and reconstruction of continuous-time signals.●Examines realizations of IIR and FIR systems and techniques to design digital filters.●Looks at sampling-rate conversion and applications to multirate digital signal processing.●Discusses linear prediction, optimum linear filters and single-channel adaptive filers based on the LMS and RLS algorithms.

After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.

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.

Quantum transport is a diverse field, sometimes combining seemingly contradicting concepts - quantum and classical, conduction and insulating - within a single nanodevice. Quantum transport is an essential and challenging part of nanoscience, and understanding its concepts and methods is vital to the successful fabrication of devices at the nanoscale. This textbook is a comprehensive introduction to the rapidly developing field of quantum transport. The authors present the comprehensive theoretical background, and explore the groundbreaking experiments that laid the foundations of the field. Ideal for graduate students, each section contains control questions and exercises to check readers' understanding of the topics covered. Its broad scope and in-depth analysis of selected topics will appeal to researchers and professionals working in nanoscience.

These two volumes provide a comprehensive guide and source book on the marine use of composite materials. The first volume, Fundamental Aspects, provides a rigourous development of theory. Areas covered include materials science, environmental aspects, production technology, structural analysis, finite-element methods, materials failure mechanisms and the role of standard test procedures. An appendix gives tables of the mechanical properties of common polymeric composites and laminates in marine use. The second volume, Practical Considerations, examines how the theory can be used in the design and construction of marine structures, including boats, submersibles, offshore structures and other deep-ocean installations. These volumes will provide an up-to-date comprehensive introduction and reference to this important and fast-growing area.

How do developing states decide who gets access to public goods like electricity, water, and education? Power and the Vote breaks new ground by showing that the provision of seemingly universal public goods is intricately shaped by electoral priorities. In doing so, this book introduces new methods using high-resolution satellite imagery to study the distribution of electricity across and within the developing world. Combining cross-national evidence with detailed sub-national analysis and village-level data from India, Power and the Vote affirms the power of electoral incentives in shaping the distribution of public goods and challenges the view that democracy is a luxury of the rich with little relevance to the world's poor.

How do developing states decide who gets access to public goods like electricity, water, and education? Power and the Vote breaks new ground by showing that the provision of seemingly universal public goods is intricately shaped by electoral priorities. In doing so, this book introduces new methods using high-resolution satellite imagery to study the distribution of electricity across and within the developing world. Combining cross-national evidence with detailed sub-national analysis and village-level data from India, Power and the Vote affirms the power of electoral incentives in shaping the distribution of public goods and challenges the view that democracy is a luxury of the rich with little relevance to the world's poor.

Divination was an important and distinctive aspect of religion in both ancient China and ancient Greece, and this book will provide the first systematic account and analysis of the two side by side. Who practised divination in these cultures and who consulted it? What kind of questions did they ask, and what methods were used to answer those questions? As well as these practical aspects, Lisa Raphals also examines divination as a subject of rhetorical and political narratives, and its role in the development of systematic philosophical and scientific inquiry. She explores too the important similarities, differences and synergies between Greek and Chinese divinatory systems, providing important comparative evidence to reassess Greek oracular divination.

With signal combining and detection methods now representing a key application of signal processing in communication systems, this book provides a range of key techniques for receiver design when multiple received signals are available. Various optimal and suboptimal signal combining and detection techniques are explained in the context of multiple-input multiple-output (MIMO) systems, including successive interference cancellation (SIC) based detection and lattice reduction (LR) aided detection. The techniques are then analyzed using performance analysis tools. The fundamentals of statistical signal processing are also covered, with two chapters dedicated to important background material. With a carefully balanced blend of theoretical elements and applications, this book is ideal for both graduate students and practising engineers in wireless communications.

This book demonstrates that the state-contingent approach provides the best way to think about all problems in the economics of uncertainty, including problems of consumer choice, the theory of the firm, and principal agent relationships. The authors demonstrate that dual methods apply under uncertainty and that the dual representations can be developed for stochastic technologies. Moreover, proper exploitation of the properties of alternative primal and dual representations of preferences allows analysts to generalize and extend the results of the existing literature on preferences under uncertainty, thus making expected-utility theory largely superfluous for many decisions. These insights open the way for developments in the basic theory of production under uncertainty, the theory of hedging behavior, the analysis of agency problems and the theory of production insurance.

This book demonstrates that the state-contingent approach provides the best way to think about all problems in the economics of uncertainty, including problems of consumer choice, the theory of the firm, and principal agent relationships. The authors demonstrate that dual methods apply under uncertainty and that the dual representations can be developed for stochastic technologies. Moreover, proper exploitation of the properties of alternative primal and dual representations of preferences allows analysts to generalize and extend the results of the existing literature on preferences under uncertainty, thus making expected-utility theory largely superfluous for many decisions. These insights open the way for developments in the basic theory of production under uncertainty, the theory of hedging behavior, the analysis of agency problems and the theory of production insurance.

In this wide-ranging survey of ancient Greek narrative from archaic epic to classical prose, Alex Purves shows how stories unfold in space as well as in time. She traces a shift in authorial perspective, from a godlike overview to the more focused outlook of human beings caught up in a developing plot, inspired by advances in cartography, travel, and geometry. Her analysis of the temporal and spatial dimensions of ancient narrative leads to new interpretations of important texts by Homer, Herodotus, and Xenophon, among others, showing previously unnoticed connections between epic and prose. Drawing on the methods of classical philology, narrative theory, and cultural geography, Purves recovers a poetics of spatial representation that lies at the core of the Greeks' conception of their plots.

In this wide-ranging survey of ancient Greek narrative from archaic epic to classical prose, Alex Purves shows how stories unfold in space as well as in time. She traces a shift in authorial perspective, from a godlike overview to the more focused outlook of human beings caught up in a developing plot, inspired by advances in cartography, travel, and geometry. Her analysis of the temporal and spatial dimensions of ancient narrative leads to new interpretations of important texts by Homer, Herodotus, and Xenophon, among others, showing previously unnoticed connections between epic and prose. Drawing on the methods of classical philology, narrative theory, and cultural geography, Purves recovers a poetics of spatial representation that lies at the core of the Greeks' conception of their plots.

To what extent do courts in Latin America protect individual rights and limit governments? This volume answers these fundamental questions by bringing together today's leading scholars of judicial politics. Drawing on examples from Argentina, Brazil, Chile, Mexico, Colombia, Costa Rica and Bolivia, the authors demonstrate that there is widespread variation in the performance of Latin America's constitutional courts. In accounting for this variation, the contributors push forward ongoing debates about what motivates judges; whether institutions, partisan politics and public support shape inter-branch relations; and the importance of judicial attitudes and legal culture. The authors deploy a range of methods, including qualitative case studies, paired country comparisons, statistical analysis and game theory.

To what extent do courts in Latin America protect individual rights and limit governments? This volume answers these fundamental questions by bringing together today's leading scholars of judicial politics. Drawing on examples from Argentina, Brazil, Chile, Mexico, Colombia, Costa Rica and Bolivia, the authors demonstrate that there is widespread variation in the performance of Latin America's constitutional courts. In accounting for this variation, the contributors push forward ongoing debates about what motivates judges; whether institutions, partisan politics and public support shape inter-branch relations; and the importance of judicial attitudes and legal culture. The authors deploy a range of methods, including qualitative case studies, paired country comparisons, statistical analysis and game theory.

The first English translation of Li Bozhong's pioneering study An Early Modern Economy in China uses sophisticated analysis to reconstruct the GDP of the Yangzi Delta. In this innovative economic history, Li provides a basis for understanding the Delta's economy, an area of unprecedented growth in modern times. Using quantitative research Li carefully reconstructs the economies of the region, combining three methods for estimating GDP: output, income, and expenditure. The result reveals the structure and level of income and production in this highly commercialized and urbanized part of China, establishing a benchmark for future reconstructions of regional economies through GDP. This is a landmark text in the field of economic history which has had a great impact on understanding Chinese economic history in global perspective.

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.

This book provides an account of developments and applications of social accounts. It concentrates particularly on the methods of social accounting that Richard Stone, Nobel Laureate in Economics, developed and applied during his long and distinguished career. The contributors to the volume examine applications of social accounts in economics and demography, addressing issues of new formulations and specifications at the national and regional levels. Economic structure and issues of structural change are investigated within the context of social accounts matrices, and Linear Expenditure Systems are used to model population change and household consumption. The importance of social accounts matrices (SAM) in generating Computable General Equilibrium (CGE) models and the enormous potential that both SAM and CGE models have for policy analysis are stressed.

This book provides an account of developments and applications of social accounts. It concentrates particularly on the methods of social accounting that Richard Stone, Nobel Laureate in Economics, developed and applied during his long and distinguished career. The contributors to the volume examine applications of social accounts in economics and demography, addressing issues of new formulations and specifications at the national and regional levels. Economic structure and issues of structural change are investigated within the context of social accounts matrices, and Linear Expenditure Systems are used to model population change and household consumption. The importance of social accounts matrices (SAM) in generating Computable General Equilibrium (CGE) models and the enormous potential that both SAM and CGE models have for policy analysis are stressed.

This book uniquely presents accurate and up-to-date information related to crops in small and fragmented agricultural lands with mixed cropping patterns. The book involves research using remote sensing (RS), Global Positioning Systems (GPS) and Geographic Information Systems (GIS) to develop crop inventories in three growing seasons in three villages across India to inform decision makers and planners on best practices for agricultural management. The data analysis of crop details using various geospatial technologies fills in gaps in statistical agriculture research, and provides reliable, replicable and efficient methods for generating agricultural statistics. The book will be of interest to statisticians, planners and decision makers in crop management and production.

First published in 1990, Archaeological Prospecting and Remote Sensing surveys some of the highly ingenious non-destructive methods for detecting and mapping remains of ancient cultures that have vanished from the modern surface. Techniques include low-level air photography, magnetic, thermal, electric, and electromagnetic geophysical prospecting. A mathematical analysis of the phenomena and measurements is given together with the techniques for interpretation of results using computerized image processing. Archaeological prospecting used with image processing has emerged as a universal tool. The aim is to build a visual geographic system available for use by conservationists, historians and scientists alike. The team of authors comprises an archaeologist, two geophysicists and an applied mathematician who have collaborated to produce a book of immense value in this innovative field of study.

This is the first book devoted to the Queen's Men, one of the major acting companies of the age of Shakespeare. In describing the troupe's position in the general political situation and the London theatre scene of the 1580s, the authors break new ground by showing how Elizabethan theatre history can be refocused by concentrating on the company which produced the plays rather than on the authors who wrote them. The book combines a thorough examination of documentary evidence with textual and critical analysis, to provide a full account of the characteristics which gave the company its identity: its acting style, staging methods, touring patterns and repertoire. The conclusions will interest Elizabethan historians as well as students and scholars of early modern theatre.

This is the first book devoted to the Queen's Men, one of the major acting companies of the age of Shakespeare. In describing the troupe's position in the general political situation and the London theatre scene of the 1580s, the authors break new ground by showing how Elizabethan theatre history can be refocused by concentrating on the company which produced the plays rather than on the authors who wrote them. The book combines a thorough examination of documentary evidence with textual and critical analysis, to provide a full account of the characteristics which gave the company its identity: its acting style, staging methods, touring patterns and repertoire. The conclusions will interest Elizabethan historians as well as students and scholars of early modern theatre.

Written in an easy-to-follow approach, the text will help the readers to understand the techniques and applications of image fusion for remotely sensed multi-spectral images. It covers important multi-resolution fusion concepts along with the state-of-the-art methods including super resolution and multi stage guided filters. It includes in depth analysis on degradation estimation, Gabor Prior and Markov Random Field (MRF) Prior. Concepts such as guided filter and difference of Gaussian are discussed comprehensively. Novel techniques in multi-resolution fusion by making use of regularization are explained in detail. It also includes different quality assessment measures used in testing the quality of fusion. Real-life applications and plenty of multi-resolution images are provided in the text for enhanced learning.

A systematic, unified treatment of orthogonal transform methods for signal processing, data analysis and communications, this book guides the reader from mathematical theory to problem solving in practice. It examines each transform method in depth, emphasizing the common mathematical principles and essential properties of each method in terms of signal decorrelation and energy compaction. The different forms of Fourier transform, as well as the Laplace, Z-, Walsh–Hadamard, Slant, Haar, Karhunen–Loève and wavelet transforms, are all covered, with discussion of how each transform method can be applied to real-world experimental problems. Numerous practical examples and end-of-chapter problems, supported by online Matlab and C code and an instructor-only solutions manual, make this an ideal resource for students and practitioners alike.

Coercive diplomacy - the use of threats and assurances to alter another state's behavior - is indispensable to international relations. Most scholarship has focused on whether and when states are able to use coercive methods to achieve their desired results. However, employing game-theoretic tools, statistical modeling, and detailed case study analysis, Power Plays builds and tests a theory that explains how states develop strategies of coercive diplomacy, how their targets shield themselves from these efforts, and the implications for interstate relations. Focusing on the World Trade Organization, Power Plays argues that coercive diplomacy often precludes cooperation due to fears of exploitation, but that international institutions can solve these problems by convincing states to eschew certain tools for coercive purposes.

Coercive diplomacy - the use of threats and assurances to alter another state's behavior - is indispensable to international relations. Most scholarship has focused on whether and when states are able to use coercive methods to achieve their desired results. However, employing game-theoretic tools, statistical modeling, and detailed case study analysis, Power Plays builds and tests a theory that explains how states develop strategies of coercive diplomacy, how their targets shield themselves from these efforts, and the implications for interstate relations. Focusing on the World Trade Organization, Power Plays argues that coercive diplomacy often precludes cooperation due to fears of exploitation, but that international institutions can solve these problems by convincing states to eschew certain tools for coercive purposes.

This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.