Classical Recursion Theory

The predominant view of moral virtue can be traced back to Aristotle. He believed that moral virtue must involve intellectual excellence. To have moral virtue one must have practical wisdom - the ability to deliberate well and to see what is morally relevant in a given context. Julia Driver challenges this classical theory of virtue, arguing that it fails to take into account virtues which do seem to involve ignorance or epistemic defect. Some 'virtues of ignorance' are counterexamples to accounts of virtue which hold that moral virtue must involve practical wisdom. Modesty, for example, is generally considered to be a virtue even though the modest person may be making an inaccurate assessment of his or her accomplishments. Driver argues that we should abandon the highly intellectualist view of virtue and instead adopt a consequentialist perspective which holds that virtue is simply a character trait which systematically produces good consequences.

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.

Low-speed aerodynamics is important in the design and operation of aircraft flying at low Mach number, and ground and marine vehicles. This 2001 book offers a modern treatment of the subject, both the theory of inviscid, incompressible, and irrotational aerodynamics and the computational techniques now available to solve complex problems. A unique feature of the text is that the computational approach (from a single vortex element to a three-dimensional panel formulation) is interwoven throughout. Thus, the reader can learn about classical methods of the past, while also learning how to use numerical methods to solve real-world aerodynamic problems. This second edition has a new chapter on the laminar boundary layer (emphasis on the viscous-inviscid coupling), the latest versions of computational techniques, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for thr

This book contains a collection of Michael D. Bordo's essays, written singly and with colleagues, on the classical gold standard and related regimes based directly or indirectly on gold convertibility. The gold standard (and its variants) was the basis for both international and domestic monetary arrangements from the third quarter of the nineteenth century until 1971 when President Nixon closed the US gold window, effectively ending the Bretton Woods International Monetary System. Although the gold standard and its variants are now history, it still has great appeal for policymakers and scholars. Several desirable features of the gold standard have resources for the ongoing issue of international monetary reform. They include its record as a stable nominal anchor; its automaticity; and its role as a credible commitment mechanism. The essays in this collection are organized around several themes: gold and the international monetary system; the commodity theory of money; the gold standa

This 1998 book provides a sophisticated alternative to existing accounts of the role of the intellectual in modern democracy. Arguing that society suffers from a systemic deliberation deficit, Jeffrey Goldfarb explores the potential of the intellectual as democratic agent, at once civilizing political contestation and subverting complacent consensus. The sentimental Leftist view of the intellectual as guardian of democracy and the demonising Rightist view of the intellectual as obstructor of progress, are both shown to be flawed. Instead, intellectuals are portrayed as special kinds of 'strangers' who pay careful attention to their critical faculties, equipping them uniquely to address the most pressing issues of today. Professor Goldfarb deploys classical and contemporary social theory to analyse a diverse set of intellectuals in action, from Socrates in fifth-century Athens to Malcolm X and Toni Morrison in twentieth-century America, and, drawing on personal acquaintance, the politic

This 1998 book provides a sophisticated alternative to existing accounts of the role of the intellectual in modern democracy. Arguing that society suffers from a systemic deliberation deficit, Jeffrey Goldfarb explores the potential of the intellectual as democratic agent, at once civilizing political contestation and subverting complacent consensus. The sentimental Leftist view of the intellectual as guardian of democracy and the demonising Rightist view of the intellectual as obstructor of progress, are both shown to be flawed. Instead, intellectuals are portrayed as special kinds of 'strangers' who pay careful attention to their critical faculties, equipping them uniquely to address the most pressing issues of today. Professor Goldfarb deploys classical and contemporary social theory to analyse a diverse set of intellectuals in action, from Socrates in fifth-century Athens to Malcolm X and Toni Morrison in twentieth-century America, and, drawing on personal acquaintance, the politic

This book, first published in 1998, treats turbulence from the point of view of dynamical systems. The exposition centres around a number of important simplified models for turbulent behaviour in systems ranging from fluid motion (classical turbulence) to chemical reactions and interfaces in disordered systems.The modern theory of fractals and multifractals now plays a major role in turbulence research, and turbulent states are being studied as important dynamical states of matter occurring also in systems outside the realm of hydrodynamics, i.e. chemical reactions or front propagation. The presentation relies heavily on simplified models of turbulent behaviour, notably shell models, coupled map lattices, amplitude equations and interface models, and the focus is primarily on fundamental concepts such as the differences between large and small systems, the nature of correlations and the origin of fractals and of scaling behaviour. This book will be of interest to graduate students and

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory t

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory t

This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Volume 2 gives an account of the principal methods used in developing a theory of algebraic varieties in spaces of n dimensions. Applications of these methods are also given to some of the more important varieties which occur in projective geometry. The ground field is without characteristic. Since geometry over any field without characteristic conforms to the general pattern of geometry over the field of complex numbers, a sound algebraic basis for classical geometry is provided. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed.

This book is about one of the most baffling of all paradoxes – the famous Liar paradox. Suppose we say: 'We are lying now'. Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers and offers his own solutions and in the process assesses other attempts to solve the paradox. Unlike such attempts, Simmons' 'singularity' solution does not abandon classical semantics and does not appeal to the kind of hierarchical view found in Barwise's and Etchemendy's The Liar. Moreover, Simmons' solution resolves the vexing problem of semantic universality – the problem of whether there are semantic concepts beyond the expressive reach of a natural language such as English.

This book examines the love elegies of the Roman poets Tibullus, Propertius and Ovid from the point of view of the way the meanings attributed to the poems arise out of the interests and preoccupations of the cultural situation in which they are read. Each study is centred around a reading of a poem or poems together with a discussion of a variety of sophisticated theoretical approaches. All Latin texts and terms are translated or closely paraphrased. Although the book concentrates on the work of the Roman elegists, the challenging insights it offers into the processes involved in the reading and appropriation of the texts of the past are relevant to scholars and students of classical literature in general, and its discussion of such key issues as history, textuality, representation, discourse, gender, ideology and metaphor will be of concern to those interested in literary theory and cultural studies.

This book focuses on the relationship between the process of production of commodities and the process of social reproduction of the labouring population, and seeks to restore that problematic relationship to the central place it had in the analysis of Smith, Ricardo, and Marx. The argument is directly opposed to that of the wages-fund theorists, who rejected the classical view of labour as a very special type of commodity whose price was determined exogenously by material, historical and institutional factors. By substituting a strict supply-and-demand mechanism they and their followers effectively removed the whole question of social reproduction from economic theory. This rendered marginal or analytically invisible certain fundamental aspects of the system. In this investigation the author draws on the history of economic thought, social history, and applied economics, using the surplus definition of profit. The resulting perspective, centred on the relation between production and

The practice of growing two or more crops together is widespread throughout the tropics and is becoming increasingly practised in temperate agriculture. The benefits of nutrient exchange, reduced weed competition and pathogen control can generate substantial improvements in growth and yield. In this book John Vandermeer, a leading worker on the subject, shows how classical ecological principles, especially those relating to competition and population ecology, can be applied to intercropping. Despite the large amount of research activity directed towards the subject over the last 20 years, the practice of intercropping has, until now, received very little serious academic attention. The Ecology of Intercropping is unique in approaching the question of intercropping from a theoretical point of view. In addition the details of the approach will take as their starting point well-accepted ecological theory. Using this basis the author shows how the approach can be used to design and evaluat

The use of geometric methods in classical mechanics has proven to be a fruitful exercise, with the results being of wide application to physics and engineering. Here Professor Marsden concentrates on these geometric aspects, and especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, in

In this book, Professor Nicholson outlines social scientific approaches to international relations and then describes the problems of rational decision-making in conflict situations. He shows how rationality is in many strategic situations hard to define and often leads to paradoxes such as the prisoners' dilemma. In the following part the author explores rational beliefs about the international system. He examines theories of arms races, alliances and the international problems of ecology. Here he is critical of the classical school of international relations for a lack of rigour in dealing with the problems of evidence and belief. Finally, Michael Nicholson discusses the philosophy of science, policy and ethics. This book is both an exposition and a defence of a social scientific approach to international relations. With its emphasis on social scientific approaches, theory building and testing - and above all its clarity and accessibility - it provides students with a key to understa

The study of spatial processes and their applications is an important topic in statistics and finds wide application particularly in computer vision and image processing. This book is devoted to statistical inference in spatial statistics and is intended for specialists needing an introduction to the subject and to its applications. One of the themes of the book is the demonstration of how these techniques give new insights into classical procedures (including new examples in likelihood theory) and newer statistical paradigms such as Monte-Carlo inference and pseudo-likelihood. Professor Ripley also stresses the importance of edge effects and of lack of a unique asymptotic setting in spatial problems. Throughout, the author discusses the foundational issues posed and the difficulties, both computational and philosophical, which arise. The final chapters consider image restoration and segmentation methods and the averaging and summarising of images. Thus, the book will find wide appeal

This book covers the basic, mainly classical, physics of the properties of solids and liquids. The main emphasis is on macroscopic characteristics of materials, although their is some discussion of the atomic or molecular phenomena that underlie the macroscopic effects. Topics that are discussed in detail include the elastic properties of solids, with applications to acoustic waves and the deformation and stability of rods and struts; static and dynamic properties of liquids, with applications to interfacial phenomena and fluid flow characteristics; and diffusion in solids and liquids, with applications to Brownian motion, heat conduction and creep. The coverage combines treatments of the more traditional aspects of these topics with details of developments, such as novel materials, catastrophe theory and soliton propagation. This textbook will be suitable for second- and third-year undergraduates in universities and polytechnics taking courses in the properties of condensed matters in

Two essays on utilitarianism, written from opposite points of view, by J. J. C. Smart and Bernard Williams. In the first part of the book Professor Smart advocates a modern and sophisticated version of classical utilitarianism; he tries to formulate a consistent and persuasive elaboration of the doctrine that the rightness and wrongness of actions is determined solely by their consequences, and in particular their consequences for the sum total of human happiness. In Part II Bernard Williams offers a sustained and vigorous critique of utilitarian assumptions, arguments and ideals. He finds inadequate the theory of action implied by utilitarianism, and he argues that utilitarianism fails to engage at a serious level with the real problems of moral and political philosophy, and fails to make sense of notions such as integrity, or even human happiness itself. This book should be of interest to welfare economists, political scientists and decision-theorists.

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.

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

While neo-classical analysis works well for studying impersonal exchange in markets, it fails to explain why people conduct themselves the way they do in their personal relationships with family, neighbors, and friends. In Humanomics, Nobel Prize-winning economist Vernon L. Smith and his long-time co-author Bart J. Wilson bring their study of economics full circle by returning to the founder of modern economics, Adam Smith. Sometime in the last 250 years, economists lost sight of the full range of human feeling, thinking, and knowing in everyday life. Smith and Wilson show how Adam Smith's model of sociality can re-humanize twenty-first century economics by undergirding it with sentiments, fellow feeling, and a sense of propriety - the stuff of which human relationships are built. Integrating insights from The Theory of Moral Sentiments and the Wealth of Nations into contemporary empirical analysis, this book shapes economic betterment as a science of human beings.

While neo-classical analysis works well for studying impersonal exchange in markets, it fails to explain why people conduct themselves the way they do in their personal relationships with family, neighbors, and friends. In Humanomics, Nobel Prize-winning economist Vernon L. Smith and his long-time co-author Bart J. Wilson bring their study of economics full circle by returning to the founder of modern economics, Adam Smith. Sometime in the last 250 years, economists lost sight of the full range of human feeling, thinking, and knowing in everyday life. Smith and Wilson show how Adam Smith's model of sociality can re-humanize twenty-first century economics by undergirding it with sentiments, fellow feeling, and a sense of propriety - the stuff of which human relationships are built. Integrating insights from The Theory of Moral Sentiments and the Wealth of Nations into contemporary empirical analysis, this book shapes economic betterment as a science of human beings.

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.

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

This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems

The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers.

The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough present

The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough present

The querelle des anciens et des modernes - the question whether writers should imitate the classics or use literary forms which seemed more suited to their own era - had been debated in Europe since the earliest days of the Renaissance. In seventeenth-century France, the modernist faction, led by Perrault, argued that a literary work owed its essential character to the prevailing social and cultural conditions; the more advanced the culture, the better its literature was likely to be. This reflected badly on classical writers since antiquity in this sense was manifestly inferior to contemporary France. It reflected particularly badly on Homer, since the great Homeric epics were seen as products of a primitive age. This book analyses the development of the querelle following the adoption of this theory, and also touches on a number of important incidental issues. Throughout, Dr Simonsuuri relates the development of ideas about Homer to developments in the fields of aesthetics, social th

Traces the central role played by aristocratic patronage in the transformation of the city of Rome at the end of antiquity. It moves away from privileging the administrative and institutional developments related to the rise of papal authority as the paramount theme in the city's post-classical history. Instead the focus shifts to the networks of reciprocity between patrons and their dependents. Using material culture and social theory to challenge traditional readings of the textual sources, the volume undermines the teleological picture of ecclesiastical sources such as the Liber Pontificalis, and presents the lay, clerical, and ascetic populations of the city of Rome at the end of antiquity as interacting in a fluid environment of alliance-building and status negotiation. By focusing on the city whose aristocracy is the best documented of any ancient population, the volume makes an important contribution to understanding the role played by elites across the end of antiquity.

Edward Comentale exposes the links between art, literature and early twentieth-century capitalism. Comentale shows how apparently progressive avant-garde movements in their celebration of individualism, competition and labor worked hand in hand with a market defined by a monstrous increase in production and consumption. Most importantly, he unearths an alternative modernist practice based on a special kind of production that both critiques and challenges economic production at large. He goes on to argue that the British avant-garde, which has often been criticized for its emphasis on classical stasis and restraint, sought to halt this market activity and to think of less destructive ways of communal belonging. Comentale provides an interdisciplinary study examining art and sculpture as well as writing by Virginia Woolf, T. S. Eliot and H. D. among others, in the light of psychoanalytic, economic and political theory. This book will be of interest to scholars of literary and cultural mo

This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate non-trivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a non-specialist audience. Even in the later chapters, where the factorisation principles are applied to geometrical processes, the prerequisites are only standard courses on probability and analysis. The main ideas presented here have application to such areas as stereology and tomography, geometrical statistics, pattern and texture analysis. This book will b

Traces the central role played by aristocratic patronage in the transformation of the city of Rome at the end of antiquity. It moves away from privileging the administrative and institutional developments related to the rise of papal authority as the paramount theme in the city's post-classical history. Instead the focus shifts to the networks of reciprocity between patrons and their dependents. Using material culture and social theory to challenge traditional readings of the textual sources, the volume undermines the teleological picture of ecclesiastical sources such as the Liber Pontificalis, and presents the lay, clerical, and ascetic populations of the city of Rome at the end of antiquity as interacting in a fluid environment of alliance-building and status negotiation. By focusing on the city whose aristocracy is the best documented of any ancient population, the volume makes an important contribution to understanding the role played by elites across the end of antiquity.

This 2007 book provides a systematic and self-contained account of the fast-developing theory of complex social networks. Social networks are central to the understanding of most socio-economic phenomena in the modern world. The classical approach to studying them relies on a methodology that abstracts from their size and complexity. In contrast, the approach taken in this book keeps complexity at the core, whilst integrating it with the incentive considerations that are preeminent in traditional economic analysis. The treatment starts with a detailed discussion of the basic models that act as 'benchmarks' for the complex-network literature: random networks, small worlds, and scale-free networks, before studying three different forces that underlie almost all network phenomena in social contexts: diffusion, search, and play. Finally, these forces are combined into a unified framework that is brought to bear on the issue of network formation and the coevolution of agents' behaviour and

Synthetic Differential Geometry is a method of reasoning in differential geometry and differential calculus, based on the assumption of sufficiently many nilpotent elements on the number line, in particular numbers d such that d2=0. The use of nilpotent elements allows one to replace the limit processes of calculus by purely algebraic calculations and notions. For the first half of the book, first published in 2006, familiarity with differential calculus and abstract algebra is presupposed during the development of results in calculus and differential geometry on a purely axiomatic/synthetic basis. In the second half basic notions of category theory are presumed in the construction of suitable Cartesian closed categories and the interpretation of logical formulae within them. This is a second edition of Kock's classical text from 1981. Many notes have been included, with comments on developments in the field from the intermediate years, and almost 100 new bibliographic entries have bee

Spanning a variety of disciplines, this 1995 enquiry focuses on one particular Pauline characteristic: the apostle's habit of making matters of faith the object of logical appraisal. A tracing of the elliptical patterns of argument in Romans 1-8 illustrates this habit and, at the same time, displays how Paul's vigorous persistence in it seems often not to be matched by the solidity, or at any rate the lucidity, of his logic. By viewing Paul against the background of semiology, more especially the semiological theory of Umberto Eco, new light is shed on the genesis of Paul's reasoning. The discussion which ensues is marked by an interesting and productive combination of modern linguistics and classical logic. Moreover, the singular potential of today's techniques of 'fuzzy' logical analysis for measuring the intellectual muscle of Paul's argumentation is brought out dramatically by the uniqueness of his semiological situation. His rationality takes on a new face.

Abstract economic theory may be timeless and potentially universal in its application, but macroeconomics has to be seen in its historical context. The nature of the policy regime, the behaviour of the economy and the beliefs of professional economists all interact, and influence each other. This short historical account of monetary regimes since 1900 shows how the role of policy has changed, and how this has related to experience of inflation and the real economy, as well as to changes in political philosophies. The narrative concentrates on developments in America, Europe and Japan from the era of the classical gold standard, via the era of policy intervention and reduced faith in the market to the present 'neo-liberal' regimes. The 'grand narrative' of the century is a journey 'to Utopia and back'. It is argued that no school of macroeconomics is right for all time; different theoretical models may be appropriate, for different periods and regimes.