Classical Recursion Theory

In the fifth and fourth centuries BCE, immigrants called 'metics' (metoikoi) settled in Athens without a path to citizenship. Galvanized by these political realities, classical thinkers cast a critical eye on the nativism defining democracy's membership rules and explored the city's anxieties over intermingling and passing. Yet readers continue to treat immigration and citizenship as separate phenomena of little interest to theorists writing at the time. In The Perpetual Immigrant and the Limits of Athenian Democracy, Demetra Kasimis makes visible the long-overlooked centrality of immigration to the originary practices of democracy and political theory in Athens. She dismantles the interpretive and political assumptions that have led readers to turn away from the metic and reveals the key role this figure plays in such texts as Plato's Republic. The result is a series of original readings that boldly reframes urgent questions about how democracies order their non-citizen members.

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clust

Focusing on the evolving relations between the state and market in the post-Mao reform era, Yongnian Zheng and Yanjie Huang present a theory of Chinese capitalism by identifying and analyzing three layers of the market system in the contemporary Chinese economy. These are, namely, a free market economy at the bottom, state capitalism at the top, and a middle ground in between. By examining Chinese economic practices against the dominant schools of Western political economy and classical Chinese economic thoughts, the authors set out the analytical framework of 'market in state' to conceptualize the market not as an autonomous self-regulating order but part and parcel of a state-centered order. Zheng and Huang show how state (political) principles are dominant over market (economic) principles in China's economy. As the Chinese economy continues to grow and globalize, its internal balance will likely have a large impact upon economies across the world.

Focusing on the evolving relations between the state and market in the post-Mao reform era, Yongnian Zheng and Yanjie Huang present a theory of Chinese capitalism by identifying and analyzing three layers of the market system in the contemporary Chinese economy. These are, namely, a free market economy at the bottom, state capitalism at the top, and a middle ground in between. By examining Chinese economic practices against the dominant schools of Western political economy and classical Chinese economic thoughts, the authors set out the analytical framework of 'market in state' to conceptualize the market not as an autonomous self-regulating order but part and parcel of a state-centered order. Zheng and Huang show how state (political) principles are dominant over market (economic) principles in China's economy. As the Chinese economy continues to grow and globalize, its internal balance will likely have a large impact upon economies across the world.

This book covers both classical and modern models in deep learning. The primary focus is on the theory and algorithms of deep learning. The theory and algorithms of neural networks are particularly im

Spiking neural networks (SNN) are biologically inspired computational models that represent and process information internally as trains of spikes. This monograph book presents the classical theory an

Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this transition, connecting the theory of probability, stochastic processes, functional analysis, numerical analysis, and differential geometry. It describes two classes of computational methods to leverage data for modeling dynamical systems. The first is concerned with data fitting algorithms to estimate parameters in parametric models that are postulated on the basis of physical or dynamical laws. The second is on operator estimation, which uses the data to nonparametrically approximate the operator generated by the transition function of the underlying dynamical systems. This self-contained book is suitable for graduate studies in applied mathematics, statistics, and engineering. Carefully chosen elementary examples with supplementary MATLAB® codes and append

Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples. These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions. The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level. Providing a comprehensive introduction to the description and construction of solitons, this book is ideal

This ambitious book provides a new framework for analysing global international society (GIS). In doing so, it also links the English School's approach more closely to classical sociology, constructivism, liberal institutionalism, realism and postcolonialism. It retells the expansion of international society story to explain why the differences among states are as important as their similarities in understanding the structure and dynamics of contemporary GIS. Drawing on differentiation theory, it sets out four ideal-type models for international society. These cover the 'like units' of the classical English School, as well as differentiation by geography, hierarchy/privilege, and function. These models offer a systematic way to integrate international and world society, and to understand the relationship between the deep structure of primary institutions, and the vast array of intergovernmental and international non-governmental organisations. In this pioneering book, Buzan and Schouen

This ambitious book provides a new framework for analysing global international society (GIS). In doing so, it also links the English School's approach more closely to classical sociology, constructivism, liberal institutionalism, realism and postcolonialism. It retells the expansion of international society story to explain why the differences among states are as important as their similarities in understanding the structure and dynamics of contemporary GIS. Drawing on differentiation theory, it sets out four ideal-type models for international society. These cover the 'like units' of the classical English School, as well as differentiation by geography, hierarchy/privilege, and function. These models offer a systematic way to integrate international and world society, and to understand the relationship between the deep structure of primary institutions, and the vast array of intergovernmental and international non-governmental organisations. In this pioneering book, Buzan and Schouen

Discover a modern approach to the analysis, modeling and design of high sensitivity phased arrays. Network theory, numerical methods and computational electromagnetic simulation techniques are uniquely combined to enable full system analysis and design optimization. Beamforming and array signal processing theory are integrated into the treatment from the start. Digital signal processing methods such as polyphase filtering and RFI mitigation are described, along with technologies for real-time hardware implementation. Key concepts from interferometric imaging used in radio telescopes are also considered. A basic development of theory and modeling techniques is accompanied by problem sets that guide readers in developing modeling codes that retain the simplicity of the classical array factor method while incorporating mutual coupling effects and interactions between elements. Combining current research trends with pedagogical material suitable for a first-year graduate course, this is an

This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions.

This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory. The useful background material included in the book makes it accessible to graduate students. Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area.

The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical

This book provides a new legal-sociological account of contemporary democracy. It is based on a revision of standard positions in democratic theory, reflecting the impact of global legal norms on the institutions of national states. Chris Thornhill argues that the establishment of fully democratic, fully inclusive governance systems in national societies was generally impeded by inner-societal structural factors, and that inclusive patterns of democratic citizenship only evolved on the foundation of global legal norms that were consolidated after 1945. He claims that this process can be best understood through a transposition of key insights of classical legal sociology onto the form of global society. Extensive analysis of select case studies in different regions illustrate these claims. Thornhill offers a sociological theory of global law to explain contemporary processes of democratic integration and institutional formation, and contemporary constructions of citizenship and politica

This book provides a new legal-sociological account of contemporary democracy. It is based on a revision of standard positions in democratic theory, reflecting the impact of global legal norms on the institutions of national states. Chris Thornhill argues that the establishment of fully democratic, fully inclusive governance systems in national societies was generally impeded by inner-societal structural factors, and that inclusive patterns of democratic citizenship only evolved on the foundation of global legal norms that were consolidated after 1945. He claims that this process can be best understood through a transposition of key insights of classical legal sociology onto the form of global society. Extensive analysis of select case studies in different regions illustrate these claims. Thornhill offers a sociological theory of global law to explain contemporary processes of democratic integration and institutional formation, and contemporary constructions of citizenship and politica

This introduction to the theory of Diophantine approximation pays special regard to Schmidt's subspace theorem and to its applications to Diophantine equations and related topics. The geometric viewpoint on Diophantine equations has been adopted throughout the book. It includes a number of results, some published here for the first time in book form, and some new, as well as classical material presented in an accessible way. Graduate students and experts alike will find the book's broad approach useful for their work, and will discover new techniques and open questions to guide their research. It contains concrete examples and many exercises (ranging from the relatively simple to the much more complex), making it ideal for self-study and enabling readers to quickly grasp the essential concepts.

Denying recognition or even existence to certain others, while still tolerating diversity, stabilizes a political order; or does it? Revisiting this classical question of political theory, the book tu

The first systematic analysis of the arguments made against human rights from the French Revolution to the present day. Through the writings of Edmund Burke, Jeremy Bentham, Auguste Comte, Louis de Bonald, Joseph de Maistre, Karl Marx, Carl Schmitt and Hannah Arendt, the authors explore the divergences and convergences between these 'classical' arguments against human rights and the contemporary critiques made both in Anglo-American and French political philosophy. Human Rights on Trial is unique in its marriage of history of ideas with normative theory, and its integration of British/North American and continental debates on human rights. It offers a powerful rebuttal of the dominant belief in a sharp division between human rights today and the rights of man proclaimed at the end of the eighteenth century. It also offers a strong framework for a democratic defence of human rights.

The first systematic analysis of the arguments made against human rights from the French Revolution to the present day. Through the writings of Edmund Burke, Jeremy Bentham, Auguste Comte, Louis de Bonald, Joseph de Maistre, Karl Marx, Carl Schmitt and Hannah Arendt, the authors explore the divergences and convergences between these 'classical' arguments against human rights and the contemporary critiques made both in Anglo-American and French political philosophy. Human Rights on Trial is unique in its marriage of history of ideas with normative theory, and its integration of British/North American and continental debates on human rights. It offers a powerful rebuttal of the dominant belief in a sharp division between human rights today and the rights of man proclaimed at the end of the eighteenth century. It also offers a strong framework for a democratic defence of human rights.

The notion of marginalism is central to modern economic theory. Its emergence in the 1870s underpinned the change from classical economics to modern (micro)economics, described by Schumpeter as a “rev

The notion of marginalism is central to modern economic theory. Its emergence in the 1870s underpinned the change from classical economics to modern (micro)economics, described by Schumpeter as a “rev

The aim of this collection is to illustrate the pervasive influence of humanist rhetoric on early-modern literature and philosophy. The first half of the book focuses on the classical rules of judicial rhetoric. One chapter considers the place of these rules in Shakespeare's The Merchant of Venice, while two others concentrate on the technique of rhetorical redescription, pointing to its use in Machiavelli's The Prince as well as in several of Shakespeare's plays, notably Coriolanus. The second half of the book examines the humanist background to the philosophy of Thomas Hobbes. A major new essay discusses his typically humanist preoccupation with the visual presentation of his political ideas, while other chapters explore the rhetorical sources of his theory of persons and personation, thereby offering new insights into his views about citizenship, political representation, rights and obligations and the concept of the state.

The aim of this collection is to illustrate the pervasive influence of humanist rhetoric on early-modern literature and philosophy. The first half of the book focuses on the classical rules of judicial rhetoric. One chapter considers the place of these rules in Shakespeare's The Merchant of Venice, while two others concentrate on the technique of rhetorical redescription, pointing to its use in Machiavelli's The Prince as well as in several of Shakespeare's plays, notably Coriolanus. The second half of the book examines the humanist background to the philosophy of Thomas Hobbes. A major new essay discusses his typically humanist preoccupation with the visual presentation of his political ideas, while other chapters explore the rhetorical sources of his theory of persons and personation, thereby offering new insights into his views about citizenship, political representation, rights and obligations and the concept of the state.

This book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry which captures classical concepts of differential geometry and topology by means of the rich categorical structure of a necessarily non-Boolean topos and of the systematic use of logical infinitesimal objects in it. Beginning with an introduction to those parts of topos theory and synthetic differential geometry necessary for the remainder, this clear and comprehensive text covers the general theory of synthetic differential topology and several applications of it to classical mathematics, including the calculus of variations, Mather's theorem, and Morse theory on the classification of singularities. The book represents the state of the art in synthetic differential topology and will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.

Deterrence, Choice, and Crime explores the various dimensions of modern deterrence theory, relevant research, and practical applications. Beginning with the classical roots of deterrence theory in Ces

After the demise of German Idealism, Neo-Kantianism flourished as the defining philosophical movement of Continental Europe from the 1860s until the Weimar Republic. This collection of new essays by distinguished scholars offers a fresh examination of the many and enduring contributions that Neo-Kantianism has made to a diverse range of philosophical subjects. The essays discuss classical figures and themes, including the Marburg and Southwestern Schools, Cohen, Cassirer, Rickert, and Natorp's psychology. In addition they examine lesser-known topics, including the Neo-Kantian influence on theory of law, Husserlian phenomenology, Simmel's study of Rembrandt, Cassirer's philosophy of science, Cohen's philosophy of religion in relation to Rawls and Habermas, and Rickert's theory of number. This rich exploration of a major philosophical movement will interest scholars and upper-level students of Kant, twentieth-century philosophy, continental philosophy, sociology, and psychology.

This book presents the most comprehensive and systematic description currently available of both classical and novel theories of cloud processes, providing a much-needed link between cloud theory, observation, experimental results, and cloud modeling. This volume shows why and how modern models serve as a major tool of investigation of cloud processes responsible for atmospheric phenomena, including climate change. It systematically describes classical as well as recent advancements in cloud physics, including cloud-aerosol interaction; collisions of particles in turbulent clouds; and the formation of multiphase cloud particles. As the first of its kind to serve as a practical guide for using state-of-the-art numerical cloud models, major emphasis is placed on explaining how microphysical processes are treated in modern numerical cloud resolving models. The book will be a valuable resource for advanced students, researchers and numerical model designers in cloud physics, atmospheric sc

functions and Hecke L-functions of an imaginary quadratic field，and various problems on elliptic modular forms. As to the values of Dirichlet L-functions， all previous papers and books reiterate a single old result with a single old method. After a review ofelementary Fourier analysis， the author presents completely new results with new methods. though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications， new formulas for the second factor ofthe class number of a cyclotomic field will be given. The second half of the book assumes familiarity with basic knowledge ofmodular forms. However，all definitions and facts are clearly stated， and precise references are given. The notion ofnearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke L-functions of an imaginary quadratic field. Other notable features of the book are： (1) some new results on classical E

Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modeling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modeling and understanding the atmosphere. This synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. This is an important resource for atmospheric science researchers new to multifractal theory and is also

Double-diffusive convection is a mixing process driven by the interaction of two fluid components which diffuse at different rates. Leading expert Timour Radko presents the first systematic overview of the classical theory of double-diffusive convection in a coherent narrative, bringing together the disparate literature in this developing field. The book begins by exploring idealized dynamical models and illustrating key principles by examples of oceanic phenomena. Building on the theory, it then explains the dynamics of structures resulting from double-diffusive instabilities, such as the little-understood phenomenon of thermohaline staircases. The book also surveys non-oceanographic applications, such as industrial, astrophysical and geological manifestations, and discusses the climatic and biological consequences of double-diffusive convection. Providing a balanced blend of fundamental theory and real-world examples, this is an indispensable resource for academic researchers, profes

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appe

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appe

This new and exciting book offers a fresh approach to quantitative finance and utilises novel features, including stereoscopic images which permit 3D visualisation of complex subjects without the need for additional tools. Offering an integrated approach to the subject, A First Course in Quantitative Finance introduces students to the architecture of complete financial markets before exploring the concepts and models of modern portfolio theory, derivative pricing and fixed income products in both complete and incomplete market settings. Subjects are organised throughout in a way that encourages a gradual and parallel learning process of both the economic concepts and their mathematical descriptions, framed by additional perspectives from classical utility theory, financial economics and behavioural finance. Suitable for postgraduate students studying courses in quantitative finance, financial engineering and financial econometrics as part of an economics, finance, econometric or mathem

This new and exciting book offers a fresh approach to quantitative finance and utilises novel features, including stereoscopic images which permit 3D visualisation of complex subjects without the need for additional tools. Offering an integrated approach to the subject, A First Course in Quantitative Finance introduces students to the architecture of complete financial markets before exploring the concepts and models of modern portfolio theory, derivative pricing and fixed income products in both complete and incomplete market settings. Subjects are organised throughout in a way that encourages a gradual and parallel learning process of both the economic concepts and their mathematical descriptions, framed by additional perspectives from classical utility theory, financial economics and behavioural finance. Suitable for postgraduate students studying courses in quantitative finance, financial engineering and financial econometrics as part of an economics, finance, econometric or mathem

An examination of two seemingly incongruous areas of study: classical models of argumentation and modern modes of digital communication. What can ancient rhetorical theory possibly tell us about the r

This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity. Accessible to graduate students, these notes gather results that were not previously available in textbooks or monographs and will be of wider interest to researchers in general relativity. The topics of these mini courses are: the geometry of black hole spacetimes; an introduction to quantum field theory on curved spacetimes; conformal geometry and tractor calculus; and microlocal analysis for wave propagation.

Flattery is an often overlooked political phenomenon, even though it has interested thinkers from classical Athens to eighteenth-century America. Drawing a distinction between moralistic and strategic flattery, this book offers new interpretations of a range of texts from the history of political thought. Discussing Cicero, Pliny, Castiglione, Machiavelli, Hobbes, Mandeville, Smith, and the Federalist/Anti-Federalist debates, the book engages and enriches contemporary political theory debates about rhetoric, republicanism, and democratic theory, among other topics. Flattery and the History of Political Thought shows both the historical importance and continued relevance of flattery for political theory. Additionally, the study is interdisciplinary in both subject and approach, engaging classics, literature, rhetoric, and history scholarship; it aims to bring a range of disciplines into conversation with each other as it explores a neglected - and yet important - topic.

This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peki

Focusing on the theory and applications of point processes, Point Processes for Reliability Analysis naturally combines classical results on the basic and advanced properties of point processes with r