Classical Recursion Theory

This enthusiastic introduction to the fundamentals of information theory builds from classical Shannon theory through to modern applications in statistical learning. Includes over 210 student exercises, emphasising practical applications in statistics, machine learning and modern communication theory. Accompanied by online instructor solutions.

When we talk about a jazz "standard" we usually mean one of the many songs that jazz musicians repeatedly play as part of their core repertoire. But unlike musical works in the tradition of so-called classical music, standards--whether plucked from the "Great American Songbook" or from recordings by other jazz musicians--are always being transformed in performance. They are rearranged and improvised upon, given new chords and altered melodies. These transformations might be small and seemingly unimportant, or they might be radical revisions. Which raises the question: across all of these various performances, what gives a standard its identity? In Hearing Double author Brian Kane answers that question by offering a new theory of musical works that can account for the unique challenges presented by standards. Building from the bottom up--from the actual practices of jazz musicians toward their philosophical implications--he gives a comprehensive theory of how a standard can undergo radi

This book embarks on a thorough review of Eastern and Western philosophies of propriety over the past 2,500 years, followed by an investigation of the ideas of propriety found in five key schools of economics: classical, neoclassical, institutional, behavioral, and cultural economics. The author then outlines the core principles and recommended practices for the study and implementation of propriety economics in the future. With its unique mixture of theory, literature reviews, methods, and case studies, this book will be useful not only to economic scholars, but also historians, policy makers, and any reader with an interest in making the economy work better for the benefit of all humankind.

Adopting an innovative and theoretical approach, Greek Tragedy and the Digital is an original study of the encounter between Greek tragedy and digital media in contemporary performance. It challenges Greek tragedy conventions through the contemporary arsenal of sound masks, avatars, live code poetry, new media art and digital cognitive experimentations. These technological innovations in performances of Greek tragedy shed new light on contemporary transformations and adaptations of classical myths, while raising emerging questions about how augmented reality works within interactive and immersive environments. Drawing on cutting-edge productions and theoretical debates on performance and the digital, this collection considers issues including performativity, liveness, immersion, intermediality, aesthetics, technological fragmentation, conventions of the chorus, theatre as hypermedia and reception theory in relation to Greek tragedy. Case studies include Kzryztof Warlikowski, Jan F

New edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process.In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features:Thoroughly updated material throughoutNew chapters on boosting, ad

This self-contained introduction to machine learning, designed from the start with engineers in mind, will equip students with everything they need to start applying machine learning principles and algorithms to real-world engineering problems. With a consistent emphasis on the connections between estimation, detection, information theory, and optimization, it includes: an accessible overview of the relationships between machine learning and signal processing, providing a solid foundation for further study; clear explanations of the differences between state-of-the-art techniques and more classical methods, equipping students with all the understanding they need to make informed technique choices; demonstration of the links between information-theoretical concepts and their practical engineering relevance; reproducible examples using Matlab, enabling hands-on student experimentation. Assuming only a basic understanding of probability and linear algebra, and accompanied by lecture slide

This textbook offers a detailed and uniquely self-contained presentation of quantum and gauge field theories. Writing from a modern perspective, the author begins with a discussion of advanced dynamics and special relativity before guiding students steadily through the fundamental principles of relativistic quantum mechanics and classical field theory. This foundation is then used to develop the full theoretical framework of quantum and gauge field theories. The introductory, opening half of the book allows it to be used for a variety of courses, from advanced undergraduate to graduate level, and students lacking a formal background in more elementary topics will benefit greatly from this approach. Williams provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigour. Worked examples are included throughout the text and end-of-chapter problems help students to reinforce key concepts. A fully worked solutions manual is available online for instruc

This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of π, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in te

Religious freedom is one of the most debated and controversial human rights in contemporary public discourse. At once a universally held human right and a flash point in the political sphere, religious freedom has resisted scholarly efforts to define its parameters. Taliaferro explores a different way of examining the tensions between the aims of religion and the needs of political communities, arguing that religious freedom is a uniquely difficult human right to uphold because it rests on two competing conceptions, human and divine. Drawing on classical natural law, Taliaferro expounds a new, practical theory of religious freedom for the modern world. By examining conceptions of law such as Sophocles' Antigone, Maimonides' Guide of the Perplexed, Ibn Rushd's Middle Commentary on Aristotle's Rhetoric, and Tertullian's writings, The Possibility of Religious Freedom explains how expanding our notion of law to incorporate such theories can mediate conflicts of human and divine law and pro

An attempt to feel and investigate the quality of time, with references to Jonathan Crary, Paul B. Preciado, Charles Baudelaire, and Walter Benjamin. “This book could have been called The Contemporary Condition of Sleeping and Reading in the Heart of (and in Spite of) the Logosphere and Various Media Streams, but frankly, I Can’t Sleep sounds better, plus it’s true.”―Lionel Ruffel The diaristic form of I Can't Sleep is an attempt to feel and investigate the quality of time, making reference to Jonathan Crary, Bernard Stiegler, Yves Citton, Paul B. Preciado, Charles Baudelaire, and above all Walter Benjamin. Written in a style that borrows not from classical forms of theory or prose, but operates in between fiction and nonfiction to investigate the very concept of the contemporary, I Can't Sleep uses a quite old but often renewed method―in this sense a very contemporary one―consisting of starting from one’s own personal situation.

Hope for us has a positive connotation. Yet it was criticized in classical antiquity as a distraction from the present moment, as the occasion for irrational and self-destructive thinking, and as a presumption against the gods. To what extent do arguments against hope today remain useful? If hope sounds to us like a good thing, that reaction stems from a progressive political tradition grounded in the French Revolution, aspects of Romantic literature and the influence of the Abrahamic faiths. Ranging both wide and deep, Adam Potkay examines the cases for and against hope found in literature from antiquity to the present. Drawing imaginatively on several fields and creatively juxtaposing poetry, drama, and novels alongside philosophy, theology and political theory, the author brings continually fresh insights to a subject of perennial interest. This is a bold and illuminating new treatment of a long-running literary debate as complex as it is compelling.

Covering both theory and experiment, this text describes the behaviour of homogeneous and density-stratified fluids over and around topography. Its presentation is suitable for advanced undergraduate and graduate students in fluid mechanics, as well as for practising scientists, engineers, and researchers. Using laboratory experiments and illustrations to further understanding, the author explores topics ranging from the classical hydraulics of single-layer flow to more complex situations involving stratified flows over two- and three-dimensional topography, including complex terrain. A particular focus is placed on applications to the atmosphere and ocean, including discussions of downslope windstorms, and of oceanic flow over continental shelves and slopes. This new edition has been restructured to make it more digestible, and updated to cover significant developments in areas such as exchange flows, gravity currents, waves in stratified fluids, stability, and applications to the atm

Covering both theory and experiment, this text describes the behaviour of homogeneous and density-stratified fluids over and around topography. Its presentation is suitable for advanced undergraduate and graduate students in fluid mechanics, as well as for practising scientists, engineers, and researchers. Using laboratory experiments and illustrations to further understanding, the author explores topics ranging from the classical hydraulics of single-layer flow to more complex situations involving stratified flows over two- and three-dimensional topography, including complex terrain. A particular focus is placed on applications to the atmosphere and ocean, including discussions of downslope windstorms, and of oceanic flow over continental shelves and slopes. This new edition has been restructured to make it more digestible, and updated to cover significant developments in areas such as exchange flows, gravity currents, waves in stratified fluids, stability, and applications to the atm

Spiral Bound explores the potential for yoga as a healing modality by examining the body's anatomical structure as it has evolved embryonically. With a light touch approach, Karen weaves together threads of development to see how our morphological constraints arise in the earliest moments of life and how this rotation lays the spiral groundwork for rotational kinematics that encompass all tissue. This book sets out to link theory with practice, all at a conversational level richly illustrated with full-color photographs and drawings that bring the biomotion to life for practitioners and teachers of yoga. This book for anyone seeking to simplify the parts-list pedagogy of classical anatomy with contemporary research in fascia literature for an integrated approach especially suitable to postural yoga.

Surprisingly little is known about what ancient Confucian thinkers struggled with in their own social and political contexts and how these struggles contributed to the establishment and further development of classical Confucian political theory. Leading scholar of comparative political theory, Sungmoon Kim offers a systematic philosophical account of the political theories of Mencius and Xunzi, investigating both their agreements and disagreements as the champions of the Confucian Way against the backdrop of the prevailing realpolitik of the late Warring States period. Together, they contributed to the formation of Confucian virtue politics, in which concerns about political order and stability and concerns about moral character and moral enhancement are deeply intertwined. By presenting their political philosophies in terms of constitutionalism, Kim shows how they each developed the ability to authorize the ruler's legitimate use of power in domestic and interstate politics in ways c

How can the classical Karnatik music of South India illuminate performers' and researchers' understanding of the art music of seventeenth-century Italy, and specifically Monteverdi's operas? Both art forms attach great value to the skill of vocal ornamentation, and by exploring the singer's practice moving between them, this Element reveals how intercultural approaches can enable the reconsideration of the history of Western music from a global perspective. Using methods from historical and comparative musicology, theory and practice-based research, Charulatha Mani analyses vocal ornamentation and technique and arrives at an innovative approach to studying musics from the past. Musical practice, the author argues, is an enactment of hybridity and the artistic product of plurality. Specifically, in early modern Europe the fluid movement of musicians from the East paved the way to a plurality of musical cultures. This finding holds deep implications for diversity in and decolonisation of

本書是一部傑作，書中的第一部分重點講述了勢能理論及其相關的拉普拉斯方程和熱方程；第二部分深入分析了和第一部分相關的隨機過程理論部分。這部科學巨著，調理清楚、深刻明晰地研究了問題涉及的這兩個方面，進而取代了零散地，語言上不一致的大量散落在各個圖書館的大量的書籍和科技文獻，但並不是一個百科全書。書中並不是將所有的知識點簡單相加，而是用自己獨特的方式從基礎開始進行系統講述，所以學習這本書並不需要太多的基

In this book, Omar Farahat presents a new way of understanding the work of classical Islamic theologians and legal theorists who maintained that divine revelation is necessary for the knowledge of the norms and values of human actions. Through a reconstruction of classical Ashʿarī-Muʿtazilī debates on the nature and implications of divine speech, Farahat argues that the Ashʿarī attachment to revelation was not a purely traditionalist position. Rather, it was a rational philosophical commitment emerging from debates in epistemology and theology. He further argues that the particularity of this model makes its distinctive features helpful for contemporary scholars who defend a form of divine command theory. Farahat's volume thus constitutes a new reading of the issue of reason and revelation in Islam and breaks new ground in Islamic theology, law and ethics.

This book focuses on current theoretical and empirical research into countability in the nominal domain, and to a lesser extent in the verbal domain. The presented state-of-the-art studies are situated within compositional semantics combined with the theory of mereology, and draw on a wealth of data, some of which have hitherto been unknown, from a number of typologically distinct languages. Some contributions propose enrichments of classical extensional mereology with topological and temporal notions as well as with type theory and probabilistic models. The book also presents analyses that rely on cutting-edge empirical research (experimental, corpus-based) into meaning in language. It is suitable as a point of departure for original research or material for seminars in semantics, philosophy of language, psycholinguistics and other fields of cognitive science. It is of interest not only to a semanticist, but also to anybody who wishes to gain insights into the contemporary research in

Play is crucial to the learning and development of children in the early years. The third edition of Play in the Early Years is a comprehensive introduction to the theory and practice of play for children from birth to 8 years old. Drawing on classical and contemporary theories, this text examines social, cultural and institutional approaches to play, and explores a range of strategies for successfully integrating play into early years settings and primary classrooms. This edition features a new chapter on conceptual playworlds, which demonstrates what conceptual playworlds look like to infants and toddlers, pre-schoolers, and children transitioning into school. The text features classroom vignettes and photographs designed to help students connect theory to practice, and reflection questions and research activities encourage in-depth reflection and extend learning. Highly regarded by early childhood researchers and practitioners alike, Play in the Early Years remains an essential reso

From Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, Bäcklund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed comp

In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, includi

Of the Presocratic thinkers traditionally credited with the foundation of Greek philosophy, Xenophanes, Parmenides and Empedocles are exceptional for writing in verse. This is the first book-length, literary-critical study of their work. It locates the surviving fragments in their performative and wider cultural contexts, applying intertextual and intratextual analyses in order to reconstruct the significance and impact they conveyed for ancient audiences and readers. Building on insights from literary theory and the philosophy of literature, the book sheds new light on these authors' philosophical projects and enriches our appreciation of their works as literary artefacts. It also expands our knowledge of the genres in which they wrote, of the literary culture of the Western Greek world, and of the development of Greek poetics from the Archaic to the Classical periods, exposing the influence of these thinkers on more famous Sophistic and Platonic ideas about literature.

The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient. Tools such as random matrix theory and the study of large sample covariance matrices can efficiently process these big data sets and help make sense of modern, deep learning algorithms. Presenting an introductory calculus course for random matrices, the book focusses on modern concepts in matrix theory, generalising the standard concept of probabilistic independence to non-commuting random variables. Concretely worked out examples and applications to financial engineering and portfolio construction make this unique book an essential tool for physicists, engineers, data analysts, and economists.

This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends these

Summarizes the proceedings and keynote presentations from a conference held in Brussels, Belgium. This work focuses on results in classical Hopf algebras as well as the classification theory of finite

Intersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference.

Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau f

Since Aristotle, the concept of the magnanimous or great-souled man was employed by philosophers of antiquity to describe individuals who attained the highest degree of virtue. Greatness of soul (magnitudo animi or magnanimitas) was part of the language of Classical and Hellenistic virtue theory central to the education of Ambrose and Augustine. Yet as bishops they were conscious of fundamental differences between Christian and pagan visions of virtue. Greatness of soul could not be appropriated whole cloth. Instead, the great-souled man had to be baptized to conform with Christian understandings of righteousness, compassion, and humility. In this book, J. Warren Smith traces the development of the ideal of the great-souled man from Plato and Aristotle to latter adaptions by Cicero, Seneca, and Plutarch. He then examines how Ambrose's and Augustine's theological commitments influenced their different critiques, appropriations, and modifications of the language of magnanimity.

The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.

This clear and pedagogical text delivers a concise overview of classical and quantum statistical physics. Essential Statistical Physics shows students how to relate the macroscopic properties of physical systems to their microscopic degrees of freedom, preparing them for graduate courses in areas such as biophysics, condensed matter physics, atomic physics and statistical mechanics. Topics covered include the microcanonical, canonical, and grand canonical ensembles, Liouville's Theorem, Kinetic Theory, non-interacting Fermi and Bose systems and phase transitions, and the Ising model. Detailed steps are given in mathematical derivations, allowing students to quickly develop a deep understanding of statistical techniques. End-of-chapter problems reinforce key concepts and introduce more advanced applications, and appendices provide a detailed review of thermodynamics and related mathematical results. This succinct book offers a fresh and intuitive approach to one of the most challenging

An appeal for the importance of theory, utopia, and close consideration of our contemporary dark times What does any particular theory allow us to do? What is the value of doing so? And who benefits? In Invoking Hope, Phillip E. Wegner argues for the undiminished importance of the practices of theory, utopia, and a deep and critical reading of our current situation of what Bertolt Brecht refers to as finsteren Zeiten, or dark times. Invoking Hope was written in response to three events that occurred in 2016: the five hundredth anniversary of the publication of Thomas More's Utopia; the one hundredth anniversary of the founding text in theory, Ferdinand de Saussure's Course in General Linguistics; and the rise of the right-wing populism that culminated in the election of Donald Trump.Wegner offers original readings of major interventions in theory alongside dazzling utopian imaginaries developed from classical Greece to our global present-from Theodor Adorno, Ernst Bloch, Alain Badiou,

What can a study of antiquity contribute to the interdisciplinary paradigm of the environmental humanities? And how does this recent paradigm influence the way we perceive human-'nature' interactions in pre-modernity? By asking these and a number of related questions, this Element aims to show why the ancient tradition still matters in the Anthropocene. Offering new perspectives to think about what directions the ecological turn could take in classical studies, it revisits old material, including ancient Greek religion and mythology, with central concepts of contemporary environmental theory. It also critically engages with forms of classical reception in current debates, arguing that ancient ecological knowledge is a powerful resource for creating alternative world views.

Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.

The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel–Hopf, Poincaré–Birkhoff–Witt, and Cartier–Milnor–Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and ca

Wigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.