Greatly expanded, this new edition requires only an elementary background in discrete mathematics and offers a comprehensive introduction to the role of randomization and probabilistic techniques in modern computer science. Newly added chapters and sections cover topics including normal distributions, sample complexity, VC dimension, Rademacher complexity, power laws and related distributions, cuckoo hashing, and the Lovasz Local Lemma. Material relevant to machine learning and big data analysis enables students to learn modern techniques and applications. Among the many new exercises and examples are programming-related exercises that provide students with excellent training in solving relevant problems. This book provides an indispensable teaching tool to accompany a one- or two-semester course for advanced undergraduate students in computer science and applied mathematics.

Uncertainty is an ever-present and ineradicable aspect of politics. It affects all important issues of governance and policy, in both domestic and international contexts. Rather than treating the uncertainty of politics as a mystery, this book provides an original and direct treatment of political uncertainty as a scientifically-knowable phenomenon with well-defined principles and substantive properties. Specific applications of this theory of political uncertainty are demonstrated in diverse areas of politics, examining such questions as when and how wars break out, when and how governments collapse, and when and how political cooperation emerges. The author shows how probability and mathematical modeling can play a central role in understanding such complex and fundamental issues.

A comprehensive account of the Sino-Tibetan, a language stock comparable in size and diversification to Indo-European and comprising Chinese, Karen and over a hundred Tibetan-Burman languages. Dr Benedict presents a systematic analysis of the morphology and phonology of the main descendants of the stock, traces their family relationships and reconstructs in outline the parent language, Sino-Tibetan.

Hage and Harary present a comprehensive introduction to the use of graph theory in social and cultural anthropology. Using a wide range of empirical examples, the authors illustrate how graph theory can provide a language for expressing in a more exact fashion concepts and notions that can only be imperfectly rendered verbally. They show how graphs, digraphs and networks, together with their associated matrices and duality laws, facilitate the study of such diverse topics as mediation and power in exchange systems, reachability in social networks, efficiency in cognitive schemata, logic in kinship relations, and productivity in subsistence modes. The interaction between graphs and groups provides further means for the analysis of transformations in myths and permutations in symbolic systems. The totality of these structural models aids in the collection as well as the interpretation of field data. The presentation is clear, precise and readily accessible to the nonmathematical reader. It emphasizes the implicit presence of graph theory in much of anthropological thinking.

Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.

Introducing a unified framework for describing and understanding complex interacting systems common in physics, chemistry, biology, ecology, and the social sciences, this comprehensive overview of dynamic critical phenomena covers the description of systems at thermal equilibrium, quantum systems, and non-equilibrium systems. Powerful mathematical techniques for dealing with complex dynamic systems are carefully introduced, including field-theoretic tools and the perturbative dynamical renormalization group approach, rapidly building up a mathematical toolbox of relevant skills. Heuristic and qualitative arguments outlining the essential theory behind each type of system are introduced at the start of each chapter, alongside real-world numerical and experimental data, firmly linking new mathematical techniques to their practical applications. Each chapter is supported by carefully tailored problems for solution, and comprehensive suggestions for further reading, making this an excellent introduction to critical dynamics for graduate students and researchers across many disciplines within physical and life sciences. Mathematical techniques are introduced using instructive examples and detailed step-by-step calculations, making it easy to acquire in-depth understanding Active areas of current research, traditionally presented as distinct subfields, are presented in a way that demonstrates the underlying intimacy between these seemingly disparate phenomena

Evolutionary Phonology is a new theory of sound patterns which synthesizes results in historical linguistics, phonetics, and phonological theory. In this groundbreaking book, Juliette Blevins explores the nature of sound patterns and sound change in human language over the past 7000-8000 years. She presents a new approach to the problem of how genetically unrelated languages, from families as far apart as Native American, Australian Aboriginal, Austronesian, and Indo-European, can often show similar sound patterns, and also tackles the converse problem of why there are notable exceptions to most of the patterns that are often regarded as universal tendencies or constraints. A formal model of sound change is presented that integrates phonetic variation and patterns of misperception to account for attested sound systems, without reference to markedness or naturalness within the synchronic grammar.

Although the importance of the advent of printing for the Western world has long been recognized, it was Elizabeth Eisenstein, in her monumental, two-volume work, The Printing Revolution in Early Modern Europe, who provided the first full-scale treatment of the subject. This illustrated and abridged edition gives a stimulating survey of the communications revolution of the fifteenth century. After summarizing the initial changes introduced by the establishment of printing shops, it goes on to discuss how printing affected three major cultural movements: the Renaissance, the Reformation, and the rise of modern science. This new edition includes a new essay discussing recent controversies provoked by the first edition and reaffirms the thesis that the advent of printing entailed a communications revolution. Fully-illustrated and annotated, the book argues that the cumulative processes set in motion with the advent of printing are likely to persist despite the recent development of new communications technologies.

A Cultural History of the Atlantic World, 1250-1820 explores the idea that strong links exist in the histories of Africa, Europe and North and South America. John K. Thornton provides a comprehensive overview of the history of the Atlantic Basin before 1830 by describing political, social and cultural interactions between the continents' inhabitants. He traces the backgrounds of the populations on these three continental landmasses brought into contact by European navigation. Thornton then examines the political and social implications of the encounters, tracing the origins of a variety of Atlantic societies and showing how new ways of eating, drinking, speaking and worshipping developed in the newly created Atlantic World. This book uses close readings of original sources to produce new interpretations of its subject.

Provides an edition suitable for students of Plato and Xenophon's accounts of how Socrates, on trial for his life, defended himself and his philosophy. The Commentary explores literary, linguistic, and philosophical aspects, while the Introduction discusses Socrates, his philosophy, Socratic dialogues, and Athenian legal procedures.

Cicero saw publication as a means of perpetuating a distinctive image of himself as statesman and orator. He memorialized his spiritual and oratorical self by means of a very solid body of texts. Educationalists and schoolteachers in antiquity relied on Cicero's oratory to supervise the growth of the young into intellectual maturity. By reconstructing the main phases of textual transmission, from the first authorial dissemination of the speeches to the medieval manuscripts, and by re-examining the abundant evidence on Ciceronian scholarship from the first to the sixth century CE, Cicero and Roman Education traces the history of the exegetical tradition on Cicero's oratory and re-assesses the 'didactic' function of the speeches, whose preservation was largely determined by pedagogical factors.

We think of blue and white porcelain as the ultimate global commodity: throughout East and Southeast Asia, the Indian Ocean including the African coasts, the Americas and Europe, consumers desired Chinese porcelains. Many of these were made in the kilns in and surrounding Jingdezhen. Found in almost every part of the world, Jingdezhen's porcelains had a far-reaching impact on global consumption, which in turn shaped the local manufacturing processes. The imperial kilns of Jingdezhen produced ceramics for the court, while nearby private kilns manufactured for the global market. In this beautifully illustrated study, Anne Gerritsen asks how this kiln complex could manufacture such quality, quantity and variety. She explores how objects tell the story of the past, connecting texts with objects, objects with natural resources, and skilled hands with the shapes and designs they produced. Through the manufacture and consumption of Jingdezhen's porcelains, she argues, China participated in the early modern world.

A general account of the languages of the Soviet Union, one of the most diverse multinational and multilingual states in the world as well as one of the most important. There are some 130 languages spoken in the USSR, belonging to five main families and ranging from Russian, which is the first language of about 130,000,000 people, to Aluet, spoken only by 96 (in the 1970 census). Dr Comrie has two general aims. First, he presents the most important structural features of these languages, their genetic relationships and classification and their distinctive typological features. Secondly, he examines the social and political background to the use of functioning of the various languages in a multilingual state. The volume will be of importance and interest to linguists and to those with a broader professional interest in the Soviet Union.

Designed for researchers and graduate students in machine learning, this book introduces the theory of variational Bayesian learning, a popular machine learning method, and suggests how to make use of it in practice. Detailed derivations allow readers to follow along without prior knowledge of the specific mathematical techniques.

This book provides a general perspective on valency-changing mechanisms - passives, antipassives, causatives, applicatives - in the languages of the world. It contains a comprehensive typology of causatives by R. M. W. Dixon, and detailed descriptions of valency-changing mechanisms in ten individual languages by leading scholars, based on original fieldwork. The sample languages span five continents and every kind of structural profile. Each contributor draws out the theoretical status and implications of valency-changing derivations in their language of study, and the relevant parameters are drawn together, and typological possibilities delineated, in the editors' introduction. The volume, originally published in 2000, will interest typologists, those working in the fields of morphosyntactic variation and lexical semantics, and exponents of formal theories engaging with the range of linguistic diversity found in natural language.

The phenomenon of language contact, and how it affects the structure of languages, has been of great interest to linguists. This study looks at how grammatical forms and structures evolve when speakers of two languages come into contact, and offers an interesting insight into the mechanism that induces people to transfer grammatical structures from one language to another. Drawing on findings from languages all over the world, Language Contact and Grammatical Change shows that the transfer of linguistic material across languages is quite regular and follows universal patterns of grammaticalization - contrary to previous claims that it is a fairly irregular process - and argues that internal and external explanations of language structure and change are in no way mutually exclusive. Engaging and informative, this book will be of great interest to sociolinguists, linguistic anthropologists, and all those working on grammaticalization, language contact, and language change.