Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemeredi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

The aim of this book is to develop the combinatorics of Young tableaux and to show them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties. The first part of the book is a self-contained presentation of the basic combinatorics of Young tableaux, including the remarkable constructions of 'bumping' and 'sliding', and several interesting correspondences. In Part II these results are used to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the related Schubert polynomials. Much of this material has never appeared in book form.There are numerous exercises throughout, with hints or answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find Young Tableaux interesting and useful; students will find the intuitive presentation easy to follow.

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemeredi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Many aspects of the internal and external workings of computers can be viewed as a series of communication processes. Communication complexity is the mathematical theory of such communication processes. It is also often used as an abstract model of other aspects of computation. This book surveys this mathematical theory, concentrating on the question of how much communication is necessary for any particular process. The first part of the book is devoted to the simple two-party model introduced by Yao in 1979, which is still the most widely studied model. The second part treats newer models developed to deal with more complicated communication processes. Finally, applications of these models, including computer networks, VLSI circuits, and data structures, are treated in the third part of the book. This is an essential resource for graduate students and researchers in theoretical computer science, circuits, networks and information theory.

Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.

In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy theorem, bounds for Bass numbers, and tight closure. Throughout each chapter the authors have supplied many examples and exercises which, combined with the expository style, will make the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.

Why do Greek lorries have Metaphorés written on the side? Is it grammatically correct to say 'the best team won' after a football match? What is the difference between manly, male, masculine and macho? Bringing together Peter Trudgill's highly popular columns for the New European, this fascinating collection explores how English has been influenced, both linguistically and culturally, by its neighbouring languages in Europe. English is very much a European language and Trudgill delves in to the rich linguistic legacy that links all European languages. The bite-sized pieces are grouped together in thematically arranged sections, to allow the reader to dip in and out at will, and cover a wide range of topics, from the etymology of words, to illuminating pieces on grammar. Written in an engaging and lively style, and full of intriguing facts about language and languages in Europe, this book will appeal to both language specialists and to general readers with no prior experience.

While many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underlie the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www.cambridge.org/9780521873413.

The Cambridge Companion to Travel Writing offers a broad, specially commissioned introduction to travel writing in English between 1500 and the present. Fives essays survey the period's travel writing; six more focus on areas of particular interest--Arabia, the Amazon, Ireland, Calcutta, the Congo and California; while the final three analyse some of the theoretical and cultural dimensions to this most enigmatic and influential genre of writing. An extensive durther reading list is provided, plus a detailed chronology.

Why was it that whenever the Tudor-Stuart regime most loudly trumpeted its moderation, that regime was at its most vicious? This groundbreaking book argues that the ideal of moderation, so central to English history and identity, functioned as a tool of social, religious and political power. Thus The Rule of Moderation rewrites the history of early modern England, showing that many of its key developments - the via media of Anglicanism, political liberty, the development of empire and even religious toleration - were defined and defended as instances of coercive moderation, producing the 'middle way' through the forcible restraint of apparently dangerous excesses in Church, state and society. By showing that the quintessentially English quality of moderation was at heart an ideology of control, Ethan Shagan illuminates the subtle violence of English history and explains how, paradoxically, England came to represent reason, civility and moderation to a world it slowly conquered.

According to diverse indices of political performance, the Middle East is the world's least free region. Some believe that it is Islam that hinders liberalization. Others retort that Islam cannot be a factor because the region is no longer governed under Islamic law. This book by Timur Kuran, author of the influential Long Divergence, explores the lasting political effects of the Middle East's lengthy exposure to Islamic law. It identifies several channels through which Islamic institutions, both defunct and still active, have limited the expansion of basic freedoms under political regimes of all stripes: secular dictatorships, electoral democracies, monarchies legitimated through Islam, and theocracies. Kuran suggests that Islam's rich history carries within it the seeds of liberalization on many fronts; and that the Middle East has already established certain prerequisites for a liberal order. But there is no quick fix for the region's prevailing record of human freedoms.

This is the first book to focus on the role of education in relation to music and gender. Invoking a concept of musical patriarchy and a theory of the social construction of musical meaning, Lucy Green shows how women's musical practices and gendered musical meanings have been reproduced, hand-in-hand, through history. Dr. Green views the contemporary school music classroom as a microcosm of the wider society, and reveals the participation of music education in the continued production and reproduction of gendered musical practices and meanings.

This book presents the econometric analysis of single-equation and simultaneous-equation models in which the jointly dependent variables can be continuous, categorical, or truncated. Despite the traditional emphasis on continuous variables in econometrics, many of the economic variables encountered in practice are categorical (those for which a suitable category can be found but where no actual measurement exists) or truncated (those that can be observed only in certain ranges). Such variables are involved, for example, in models of occupational choice, choice of tenure in housing, and choice of type of schooling. Models with regulated prices and rationing, and models for program evaluation, also represent areas of application for the techniques presented by the author.

Facing global climate crisis, Karl Marx's ecological critique of capitalism more clearly demonstrates its importance than ever. This book explains why Marx's ecology had to be marginalized and even suppressed by Marxists after his death throughout the twentieth century. Marx's ecological critique of capitalism, however, revives in the Anthropocene against dominant productivism and monism. Investigating new materials published in the complete works of Marx and Engels (Marx-Engels-Gesamtausgabe), Saito offers a wholly novel idea of Marx's alternative to capitalism that should be adequately characterized as degrowth communism. This provocative interpretation of the late Marx sheds new lights on the recent debates on the relationship between society and nature and invites readers to envision a post-capitalist society without repeating the failure of the actually existing socialism of the twentieth century.
Offers a wholly new understanding of the late Marx's vision of post-capitalist society
Reconstructs the history of Marxism from an ecological perspective in order to answer why Marx's ecology has been neglected for such a long time
Offers a thorough critique of monist approach to the society-nature-relationship that is popular in political ecology

Heavy tails -extreme events or values more common than expected -emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.

The widespread availability of high-quality, high-frequency data has revolutionised the study of financial markets. By describing not only asset prices, but also market participants' actions and interactions, this wealth of information offers a new window into the inner workings of the financial ecosystem. In this original text, the authors discuss empirical facts of financial markets and introduce a wide range of models, from the micro-scale mechanics of individual order arrivals to the emergent, macro-scale issues of market stability. Throughout this journey, data is king. All discussions are firmly rooted in the empirical behaviour of real stocks, and all models are calibrated and evaluated using recent data from Nasdaq. By confronting theory with empirical facts, this book for practitioners, researchers and advanced students provides a fresh, new, and often surprising perspective on topics as diverse as optimal trading, price impact, the fragile nature of liquidity, and even the reasons why people trade at all.

Central banks in Great Britain and the United States arose early in the financial revolution. The Bank of England was created in 1694 while the first Banks of the United States appeared in 1791-1811 and 1816-36, and were followed by the Idependent Treasury, 1846-1914. These institutions, together with the Suffolk Bank and the New York Clearing House, exercised important central banking function before the creation of the Federal Reserve System in 1913. Significant monetary changes in the lives of these British and American institutions are examined within a framework that deals with the knowledge and behavior of central bankers and their interactions with economists and politicians. Central Bankers' behavior has shown considerable continuity in the influence of incentives and their interest in the stability of the financial markets. For example, the Federal Reserve's behavior during the Great Depression, the low inflation of the 1990s, and its resurgence the next decade follow from its structure and from government pressures rather than accidents of personnel.

Has China become just another capitalist country in a socialist cloak? Will the Chinese Communist Party's rule survive the next ten years of modernization and globalization? Frank Pieke investigates these conundrums in this fascinating account of how government officials are trained for placement in the Chinese Communist Party. Through in-depth interviews with staff members and aspiring trainees, he shows that while the Chinese Communist Party has undergone a radical transformation since the revolutionary years under Mao, it is still incumbent upon cadres, who are selected through a highly rigorous process, to be ideologically and politically committed to the party. It is the lessons learnt through their teachers that shape the political and economic decisions they will make in power. The book offers unique insights into the structure and the ideological culture of the Chinese government, and how it has reinvented itself over the last three decades as a neo-socialist state.

Most conceptions of human rights rely on metaphysical or theological assumptions that construe them as possible only as something imposed from outside existing communities. Most people, in other words, presume that human rights come from nature, God, or the United Nations. This book argues that reliance on such putative sources actually undermines human rights. Benjamin Gregg envisions an alternative; he sees human rights as locally developed, freely embraced, and indigenously valid. Human rights, he posits, can be created by the average, ordinary people to whom they are addressed, and that they are valid only if embraced by those to whom they would apply. To view human rights in this manner is to increase the chances and opportunities that more people across the globe will come to embrace them.