People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world.

This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989. Each year the 19 Participating Institutions select, through a competitive process, several conferences proposals from the PIs, for partial funding. This conference brought together leading figures in a number of fields who were interested in finding exact answers to problems in analysis through computer methods. We thank Kenneth Meyer and Dieter Schmidt for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the dawn of the computer revolution the vast majority of scientific compu­ tation has dealt with finding approximate solutions of equations. However, during this time there has been a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, number theory and combina­ torics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools.

This book ?nds new things to do with an old idea. The proofs-as-programs paradigm constitutes a set of approaches to developing programs from proofs in constructive logic. It has been over thirty years since the paradigm was ?rst conceived. At that time, there was a belief that proofs-as-programs had the - tential for practical application to semi-automated software development. I- tial applications were mostly concerned with ?ne-grain, mathematical program synthesis. For various reasons, research interest in the area eventually tended toward more theoretic issues of constructive logic and type theory. However, in recent years, the situation has become more balanced, and there is increasingly active research in applying constructive techniques to industrial-scale, complex software engineering problems. Thismonographdetailsseveralimportantadvancesinthisdirectionofpr- tical proofs-as-programs. One of the central themes of the book is a general, abstract framework for developing new systems of program synthesis by adapting proofs-as-programs to new contexts.

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This book presents a systematic overview of cutting-edge research in the field of parametric modeling of personal income and wealth distribution, which allows one to represent how income/wealth is distributed within a given population. The estimated parameters may be used to gain insights into the causes of the evolution of income/wealth distribution over time, or to interpret the differences between distributions across countries. Moreover, once a given parametric model has been fitted to a data set, one can straightforwardly compute inequality and poverty measures. Finally, estimated parameters may be used in empirical modeling of the impact of macroeconomic conditions on the evolution of personal income/wealth distribution. In reviewing the state of the art in the field, the authors provide a thorough discussion of parametric models belonging to the “κ-generalized” family, a new and fruitful set of statistical models for the size distribution of income and wealth that they have developed over several years of collaborative and multidisciplinary research. This book will be of interest to all who share the belief that problems of income and wealth distribution merit detailed conceptual and methodological attention.

You can start by putting the DO NOT DISTURB sign. Cay, in Desert Hearts (1985). The interplay between randomness and computation is one of the most fas­ cinating scientific phenomena uncovered in the last couple of decades. This interplay is at the heart of modern cryptography and plays a fundamental role in complexity theory at large. Specifically, the interplay of randomness and computation is pivotal to several intriguing notions of probabilistic proof systems and is the focal of the computational approach to randomness. This book provides an introduction to these three, somewhat interwoven domains (i.e., cryptography, proofs and randomness). Modern Cryptography. Whereas classical cryptography was confined to the art of designing and breaking encryption schemes (or "secrecy codes"), Modern Cryptography is concerned with the rigorous analysis of any system which should withstand malicious attempts to abuse it. We emphasize two aspects of the transition from classical to modern cryptography: ( 1) the wide­ ning of scope from one specific task to an utmost wide general class of tasks; and (2) the move from an engineering-art which strives on ad-hoc tricks to a scientific discipline based on rigorous approaches and techniques.

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This book focuses on the language of educational research as well as on the language of education. It conceives both as social practices and investigates how rhetoric plays a part in the complex process of historically situated argumentation. The book aims to answer such questions as: ‘What is the nature of the arguments and the kinds of sources one relies on?’ and ‘What kind of reasoning is offered to convince practitioners?’ Taking postmodern criticism seriously, the contributors argue that the scholar or researcher cannot indulge in relativism or be satisfied with a description of particular cases. Instead, theoreticians as well as practitioners have to engage in sound thinking and dialogue. The chapters in this volume highlight relevant characteristics of the language of educational research. In addition, attention is paid to the language of particular debates which figure prominently in the wider educational context, such as the language of goals, of parenting, citizenship and capability.

The present book avoids the fantasy recipes that abound in technical analysis and focuses instead on those that are statistically correct and can be understood by newcomers as well as appreciated by professionals. The described protocols and techniques will prove invaluable in analyzing market behavior and assisting in trading decisions.

Political Analysis provides an accessible and engaging yet original introduction and distinctive contribution, to the analysis of political structures, institutions, ideas and behaviours, and above all, to the political processes through which they are constantly made and remade. Following an innovative introduction to the main approaches and concepts in political analysis, the text focuses thematically on the key issues which currently concern and divide political analysts, including the boundaries of the political; the question of structure, agency and power; the dynamics of political change; the relative significance of ideas and material factors; and the challenge posed by postmodernism which the author argues the discipline can strengthen itself by addressing without allowing it to become a recipe for paralysis.

Long awaited, this fine surgical atlas covers all aspects of neuro-otology and lateral skull base procedures in comprehensively in detail. The lavishly illustrated step-by-step guide is written by two American experts to ensure continuity between topics. The text is highly structured with step-by-step explanation of each surgical procedure and TIPS and TECHNIQUES sections as well as a PEARLS section in each chapter. More than 200 superb artwork illustrations describe each surgical procedure with nearly 600 additional intraoperative pictures with CT and MRI images to teach specific case examples. This offers a complete educational experience for the skull base surgeon in training and a thorough reference for the experienced surgeon.

This volume contains seventeen papers that were presented at the 2015 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held in Washington, D.C. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of general topics in the history and philosophy of mathematics, this meeting also honored the memories of Jacqueline (Jackie) Stedall and Ivor Grattan-Guinness; celebrated the Centennial of the Mathematical Association of America; and considered the importance of mathematical communities in a special session. These themes and many others are explored in these collected papers, which cover subjects such as

As a result of technological improvements, neuroendoscopy is now used in the treatment of many more patients, enabling the performance of previously unavailable operations with low complication rates and rapid patient recovery. This book presents the distilled experience of world experts in this evolving field. Current applications in a wide variety of settings are explained in detail and likely future developments are identified. In addition, the available neuroendoscopic instruments are reviewed and the results of international trials and collaborative studies, presented. This book will fully acquaint the reader with the breadth and depth of available neuroendoscopy techniques and their impressive therapeutic potential. It should serve as the reference book on neuroendoscopy for the next 10 years.