Here is an accessible, algorithmically oriented guide to some of the most interesting techniques of complexity theory. The book shows that simple algorithms are at the heart of complexity theory. The book is organized by technique rather than by topic. Each chapter focuses on one technique: what it is, and what results and applications it yields.
Chaos and complexity are the new buzz words in both science and contemporary society. The ideas they represent have enormous implications for the way we understand and engage with the world. Complexity Theory and the Social Sciences introduces students to the central ideas which surround the chaos/complexity theories. It discusses key concepts before using them as a way of investigating the nature of social research. By applying them to such familiar topics as urban studies, education and health, David Byrne allows readers new to the subject to appreciate the contribution which complexity theory can make to social research and to illuminating the crucial social issues of our day.
An insightful view on how to use the power of complexity theory to manage projects more successfully Current management practices require adherence to rigid, global responses unsuitable for addressing the changing needs of most projects. Complexity Theory and Project Management shifts this paradigm to create opportunities for expanding the decision-making process in ways that promote flexibility—and increase effectiveness. It informs readers on the managerial challenges of juggling project requirements, and offers them a clear roadmap on how to revise perspectives and reassess priorities to excel despite having an unpredictable workflow. One of the first books covering the subject of complexity theory for project management, this useful guide: Explains the relationship of complexity theory to virtual project management Supplies techniques, tips, and suggestions for building effective and successful teams in the virtual environment Presents current information about best practices and relevant proactive tools Makes a strong case for including complexity theory in PMI®'s PMBOK® Guide Complexity Theory and Project Management gives a firsthand view on the future of complexity theory as a driving force in the management field, and allows project managers to get a head start in applying its principles immediately to produce more favorable outcomes. (PMI and PMBOK are registered marks of the Project Management Institute, Inc.)
A complete treatment of fundamentals and recent advances in complexity theory Complexity theory studies the inherent difficulties of solving algorithmic problems by digital computers. This comprehensive work discusses the major topics in complexity theory, including fundamental topics as well as recent breakthroughs not previously available in book form. Theory of Computational Complexity offers a thorough presentation of the fundamentals of complexity theory, including NP-completeness theory, the polynomial-time hierarchy, relativization, and the application to cryptography. It also examines the theory of nonuniform computational complexity, including the computational models of decision trees and Boolean circuits, and the notion of polynomial-time isomorphism. The theory of probabilistic complexity, which studies complexity issues related to randomized computation as well as interactive proof systems and probabilistically checkable proofs, is also covered. Extraordinary in both its breadth and depth, this volume: * Provides complete proofs of recent breakthroughs in complexity theory * Presents results in well-defined form with complete proofs and numerous exercises * Includes scores of graphs and figures to clarify difficult material An invaluable resource for researchers as well as an important guide for graduate and advanced undergraduate students, Theory of Computational Complexity is destined to become the standard reference in the field.
Complexity theory illuminates the many interactions between natural and social systems, providing a better understanding of the general principles that can help solve some of today's most pressing environmental issues. Complexity theory was developed from key ideas in economics, physics, biology, and the social sciences and contributes to important new concepts for approaching issues of environmental sustainability such as resilience, scaling, and networks. Complexity Theory for a Sustainable Future is a hands-on treatment of this exciting new body of work and its applications, bridging the gap between theoretical and applied perspectives in the management of complex adaptive systems. Focusing primarily on natural resource management and community-based conservation, the book features contributions by leading scholars in the field, many of whom are among the leaders of the Resilience Alliance. Theoreticians will find a valuable synthesis of new ideas on resilience, sustainability, asymmetries, information processing, scaling, and networks. Managers and policymakers will benefit from the application of these ideas to practical approaches and empirical studies linked to social-ecological systems. Chapters present new twists on such existing approaches as scenario planning, scaling analyses, and adaptive management, and the book concludes with recommendations on how to manage natural resources, how to involve stakeholders in the dynamics of a system, and how to explain the difficult topic of scale. A vital reference for an emerging discipline, this volume provides a clearer understanding of the conditions required for systems self-organization, since the capacity of any system to self-organize is crucial for its sustainability over time.
The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.
Contents 11. 2. 2. Four Main Areas of Dispute 247 11. 2. 3. Summary . . . 248 11. 3. Making Sense of the Issues . . 248 11. 3. 1. Introduction . . . . 248 11. 3. 2. The Scientific Approach 248 11. 3. 3. Science and Matters of Society . 249 11. 3. 4. Summary . 251 11. 4. Tying It All Together . . . . 251 11. 4. 1. Introduction . . . . 251 11. 4. 2. A Unifying Framework 251 11. 4. 3. Critical Systems Thinking 253 11. 4. 4. Summary 254 11. 5. Conclusion 254 Questions . . . 255 REFERENCES . . . . . . . . . . . . . . . . . . . 257 INDEX . . . . . . . . . . . . . . . . . . . . . . 267 Chapter One SYSTEMS Origin and Evolution, Terms and Concepts 1. 1. INTRODUCTION We start this book with Theme A (see Figure P. I in the Preface), which aims to develop an essential and fundamental understanding of systems science. So, what is systems science? When asked to explain what systems science is all about, many systems scientists are confronted with a rather daunting task. The discipline tends to be presented and understood in a fragmented way and very few people hold an overview understanding of the subject matter, while also having sufficient in-depth competence in many and broad-ranging subject areas where the ideas are used. Indeed, it was precisely this difficulty that identified the need for a comprehensive well-documented account such as is presented here in Dealing with Complexity.
Interest in complexity theory, a relation of chaos theory, has become well established in the business community in recent years. Complexity theory argues that systems are complex interactions of many parts which cannot be predicted by accepted linear equations. In this book, Keith Morrison introduces complexity theory to the world of education, drawing out its implications for school leadership. He suggests that schools are complex, nonlinear and unpredictable systems, and that this impacts significantly within them. As schools race to keep up with change and innovation, he suggests that it is possible to find order without control and to lead without coercion. Key areas: * schools and self-organisation * leadership for self-organisation * supporting emergence through the learning organisation * schools and their environments * communication * fitness landscapes This book will be of interest to headteachers and middle managers, and those on higher level courses in educational leadership and management.
