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A superconductor is a remarkable emergent state of matter in which electrons pair up and develop long range phase coherence resulting in zero resistance and perfect diamagnetism. How can a superconductor decohere? A thin superconducting film can be driven insulating in a remarkable number of ways: decreasing thickness, increasing disorder, changing the gate voltage, or applying a magnetic field. Such superconductor-insulator transitions (SIT) are quantum phase transitions of strongly correlated electrons occurring at very low temperatures. This chapter gives an overview of the field, with particular emphasis on recent developments. This chapter describes how the theoretical understanding of SITs has evolved over the years, and how the increasing quality of experimental data is beginning to reveal the importance of amplitude and phase fluctuations. Most importantly new paradigms have been developed to describe these phenomena. This chapter contains numerous references to the contributions by various authors in subsequent chapters

This chapter presents a theoretical treatment of two types of superconductor-insulator transitions — the disorder-tuned transition and the parallel-magnetic-field-tuned transition. This is performed within the framework of the attractive Hubbard model, which is a ‘minimal’ lattice model that nevertheless captures much of the essential physics. The effects of hopping, attraction, disorder, and parallel magnetic field are taken into account one by one in proressively more refined approximations, from pairing-of-exact-eigenstates to Bogoliubov-de Gennes to determinant quantum Monte Carlo. By examining the successes and failures of each approach, the chapter elucidates the role of amplitude and phase fluctuations. This pedagogical approach provides considerable details of the calculation of thermodynamic, transport, and spectral properties, such that a suitably inclined reader should be able to reproduce many of the results.

This chapter fleshes out an inductive framework for understanding stasis and critical transitions. The framework has been developed with a lens on Brazil, but to illustrate its wider applicability, this chapter applies the framework very generally to understand the critical transitions in Argentina from the early twentieth century to 2014. The key elements in the framework are beliefs and leadership, which interact synergistically and vary across countries. Because beliefs and leadership cannot be measured rigorously and classified, the use of the framework necessarily involves subjectivity and interpretation. With more case studies applying this framework, more general lessons on the dynamics among beliefs, power, leadership, institutions, policies, and outcomes that form stasis or development can be constructed.

Social change results from mental mechanisms in individuals and from social mechanisms for the interactions of thinking individuals. The mental mechanisms operate with images, concepts, rules, analogies, and emotions, all of which derive from neural mechanisms based on an important kind of neural process called semantic pointers. The interactions of individuals contribute to changes in their mental representations through cognitive and emotional communication that transfers, prompts, and instigates semantic pointers. Changes in the mental states and behaviors of individuals and groups result from changes in representations and interactions. Explanation of social changes requires identification of emergent properties of groups that are not simply the sum of change of changes in individuals. Social change resulting from cognitive and social mechanisms often results from critical transitions, not just gradual accumulations. Emotional gestalt shifts are important critical transitions that occur when individuals and groups reconfigure their arrays of attitudes and values.

This chapter takes a detour into the critical transition made by Patrick Lung Kong (1934–2014) and Cecile Tang Shu-shuen (b. 1941). Different in background and artistic orientation, both Lung and Tang stirred up controversies and debates over their filmic interventions into politics and society. Didactic and prescriptive at times, Lung’s films display a greater confidence in the city’s modern institutions and the liberal values they represent, which inevitably alienated him from the anti-capitalist and anti-colonial politics of the left-wing. Critical of both the Communist regime in Mainland China and the capitalist society of Hong Kong, Tang has been regarded as a pioneer in women’s cinema. Her small corpus and short-lived directorial career (see below) notwithstanding, her work exhibits an avant-garde quality in foregrounding female subjectivity and gender identity. The careers of Lung and Tang revealed the complex entanglement between film and politics, or more generally the conditions of political representation, even when law and order together with the capitalist lifestyle had remained intact under colonial rule well after the Cultural Revolution and the 1967 riots.

This chapter offers some conjectures about the future of Brazil, especially in light of recent declarations that the Brazilian miracle has vanished once again. It attempts to reconcile Brazil's current political and economic situation with the more optimistic forecast this volume has set out so far, by using the institutional possibility frontiers (IPF) to interpret this paradox. The IPF illustrates this by showing the trade-offs existing in any country between disorder and dictatorship (authoritarianism) and reveals that a state that has more powers to control disorder also has more for dictatorial abuse. The chapter also returns to the analytical framework already expounded in the previous chapter, and finally predicts Brazil's likelihood for another critical transition to a society more akin to the current developed countries in the world.

Dynamical systems are complex systems that fluctuate over time. Sudden transitions occur after reaching a tipping point that can have detrimental consequences, such as the sudden collapse of a coral reef. A slow rate of recovery from smaller challenges can serve as a warning for critical transitions. The increasing importance of complex systems for understanding science requires excellent instruction. NetLogo modules offer one approach for learning about emergent interactions. A review of instruction distinguished between the teaching of complex systems in biology, chemistry, computer science, earth science, ecology, physics, and engineering. Most instruction has focused on the domains of biology and ecology although there is a need to extend coverage to other topics. There is also need for more research on effective teaching because instruction on complex systems is still in its infancy.

This chapter lays out a brief conceptual dynamic to interpret the past fifty years in Brazil. Its framework rests on tying together the key concepts of windows of opportunity, beliefs, dominant network, leadership, institutions, and outcomes. The chapter argues that it is the dynamics of the concepts that led to institutional change in Brazil and in turn a new trajectory. It then discusses the important dominant networks in power, along with their beliefs, in four periods: 1964–1984 (the military years); 1985–1993 (the early years back to democracy); 1993–2002 (Fernando Henrique Cardoso's presidency); and 2002–2014 (the Luiz Inácio Lula da Silva and Dilma Rousseff years).

This chapter examines Cardoso's presidency, arguing that his leadership was not solely top-down; rather, the Cardoso team coordinated other organizations and citizens to buy into the Plano Real. It argues that, first, Brazil entered into a virtuous path toward a critical transition, which was not inevitable. Second, to quell inflation entailed up-front costs and coordination problems that required leadership, which the Brazilians resolved by maintaining that social inclusion would still be given priority as long as it was fiscally sound. Third, new economic and political actors developed a stake in the reform process and formed a constituency that did not exist before: firms redeployed their assets in new profitable ways (as opposed to rent seeking) and politicians increasingly voted for public goods.