Written by some of the founders of complexity theory and complexity theories of cities (CTC), this Handbook expertly guides the reader through over forty years of intertwined developments: the emergence of general theories of complex self-organized systems and the consequent emergence of CTC.

A novel, integrative approach to cities as complex adaptive systems, applicable to issues ranging from innovation to economic prosperity to settlement patterns. Human beings around the world increasingly live in urban environments. In Introduction to Urban Science, Luis Bettencourt takes a novel, integrative approach to understanding cities as complex adaptive systems, claiming that they require us to frame the field of urban science in a way that goes beyond existing theory in such traditional disciplines as sociology, geography, and economics. He explores the processes facilitated by and, in many cases, unleashed for the first time by urban life through the lenses of social heterogeneity, complex networks, scaling, circular causality, and information. Though the idea that cities are complex adaptive systems has become mainstream, until now those who study cities have lacked a comprehensive theoretical framework for understanding cities and urbanization, for generating useful and falsifiable predictions, and for constructing a solid body of empirical evidence so that the discipline of urban science can continue to develop. Bettencourt applies his framework to such issues as innovation and development across scales, human reasoning and strategic decision-making, patterns of settlement and mobility and their influence on socioeconomic life and resource use, inequality and inequity, biodiversity, and the challenges of sustainable development in both high- and low-income nations. It is crucial, says Bettencourt, to realize that cities are not "zero-sum games" and that knowledge, human cooperation, and collective action can build a better future.

This Handbook shows the enormous impetus given to the scientific debate by linking planning as a science of purposeful interventions and complexity as a science of spontaneous change and non-linear development. Emphasising the importance of merging planning and complexity, this comprehensive Handbook also clarifies key concepts and theories, presents examples on planning and complexity and proposes new ideas and methods which emerge from synthesising the discipline of spatial planning with complexity sciences.

The renaissance in urban theory draws directly from a fresh focus on the neglected realities of cities beyond the west and embraces the global south as the epicentre of urbanism. This Handbook engages the complex ways in which cities of the global south and the global north are rapidly shifting, the imperative for multiple genealogies of knowledge production, as well as a diversity of empirical entry points to understand contemporary urban dynamics. The Handbook works towards a geographical realignment in urban studies, bringing into conversation a wide array of cities across the global south – the ‘ordinary’, ‘mega’, ‘global’ and ‘peripheral’. With interdisciplinary contributions from a range of leading international experts, it profiles an emergent and geographically diverse body of work. The contributions draw on conflicting and divergent debates to open up discussion on the meaning of the city in, or of, the global south; arguments that are fluid and increasingly contested geographically and conceptually. It reflects on critical urbanism, the macro- and micro-scale forces that shape cities, including ideological, demographic and technological shifts, and constantly changing global and regional economic dynamics. Working with southern reference points, the chapters present themes in urban politics, identity and environment in ways that (re)frame our thinking about cities. The Handbook engages the twenty-first-century city through a ‘southern urban’ lens to stimulate scholarly, professional and activist engagements with the city.

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

This ground-breaking Handbook presents a state-of-the-art exploration of entropy, complexity and spatial dynamics from fundamental theoretical, empirical and methodological perspectives. It considers how foundational theories can contribute to new advances, including novel modeling and empirical insights at different sectoral, spatial and temporal scales.

Michael Batty offers a comprehensive view of urban dynamics in the context of complexity theory, presenting models that demonstrate how complexity theory can embrace a myriad of processes and elements that combine into organic wholes.

This book provides an introduction to the role of diversity in complex adaptive systems. A complex system--such as an economy or a tropical ecosystem--consists of interacting adaptive entities that produce dynamic patterns and structures. Diversity plays a different role in a complex system than it does in an equilibrium system, where it often merely produces variation around the mean for performance measures. In complex adaptive systems, diversity makes fundamental contributions to system performance. Scott Page gives a concise primer on how diversity happens, how it is maintained, and how it affects complex systems. He explains how diversity underpins system level robustness, allowing for multiple responses to external shocks and internal adaptations; how it provides the seeds for large events by creating outliers that fuel tipping points; and how it drives novelty and innovation. Page looks at the different kinds of diversity--variations within and across types, and distinct community compositions and interaction structures--and covers the evolution of diversity within complex systems and the factors that determine the amount of maintained diversity within a system. Provides a concise and accessible introduction Shows how diversity underpins robustness and fuels tipping points Covers all types of diversity The essential primer on diversity in complex adaptive systems

"This book exposes research accounts which seek to convey an appreciation for local differences, for the empowerment of people and for the human-centred design of urban technology"--Provided by publisher.

The SAGE Handbook of the 21st Century City focuses on the dynamics and disruptions of the contemporary city in relation to capricious processes of global urbanisation, mutation and resistance. An international range of scholars engage with emerging urban conditions and inequalities in experimental ways, speaking to new ideas of what constitutes the urban, highlighting empirical explorations and expanding on contributions to policy and design. The handbook is organised around nine key themes, through which familiar analytic categories of race, gender and class, as well as binaries such as the urban/rural, are readdressed. These thematic sections together capture the volatile processes and intricacies of urbanisation that reveal the turbulent nature of our early twenty-first century: Hierarchy: Elites and Evictions Productivity: Over-investment and Abandonment Authority: Governance and Mobilisations Volatility: Disruption and Adaptation Conflict: Vulnerability and Insurgency Provisionality: Infrastructure and Incrementalism Mobility: Re-bordering and De-bordering Civility: Contestation and Encounter Design: Speculation and Imagination This is a provocative, inter-disciplinary handbook for all academics and researchers interested in contemporary urban studies.