Turán’s Theorem is a cornerstone of extremal graph theory. This theorem and its generalizations are studied in this chapter, including the Erdős–Stone Theorem, Andrásfai–Erdős–Sós Theorem, the notion of stability, chromatic thresholds, and the determination of Turán numbers for color-critical graphs.

A versatile proof approach in extremal set theory is the Linear Algebra method. In order to show an upper bound on the number of sets satisfying certain conditions, we associate a vector to each set and show that the corresponding collection of vectors is linearly independent in an appropriate vector space. Then we use the elementary fact that the maximum size of a linearly independent set is at most the dimension of the space. This chapter explores this method in its myriad forms.

Agent-based modelling (ABM) in social networks offers a powerful framework for simulating individual behaviours and emergent collective patterns within dynamic and interconnected populations. This chapter explores the conceptual foundations, methodological innovations and behavioural implications of ABM in the context of social networks, with a particular focus on the modelling of communication, influence, cooperation and contagion. Drawing from the fields of behavioural science, network theory and computational social science, the chapter presents ABM as a generative tool for understanding how micro-level decision-making rules produce macro-level phenomena. It also critically evaluates the increasing use of AI-driven agents – including large language model (LLM)-powered agents and synthetic personas – in simulating realistic and context-sensitive behaviours within artificial societies. The chapter engages with ethical and methodological challenges, including representation, explainability and the problem of behavioural validity. A worked example is included, illustrating how agent-based simulations can be applied to study misinformation diffusion and norm formation in online social networks. Ultimately, the chapter argues that agent-based modelling in social networks not only advances Behavioural Data Science methodologically, but also fosters new forms of interpretive insight into the dynamics of collective behaviour in an age of digital mediation.

This chapter explores how elements of ‘sense of place’—place dependence, identity, and attachment—are essential for creating liveable, healthy communities. It discusses how community social interaction, cohesion (sense of community), and collective action enhance liveability. Addressing frequent shortcomings in defining and measuring ‘liveability’, the authors integrate recent geospatial population health research to establish connections between place, health, development, and policy. A framework linking community cognitions, attachment, and social action in response to environmental threats and disruptions is applied to brief case studies from Bulgaria and the United States illustrating varied community responses aimed at healthier, more liveable environments. Recommendations include leveraging liveability audits to evaluate local and regional impacts of disruptions, articulating threats to community identity and economic wellbeing, and embedding psychological conceptions of place into public-health and urban-planning assessments. This integrated, ecological approach aims to strengthen community responses and inform policy decisions supporting population health and wellbeing

How is people’s happiness determined by economic factors such as their income? Big data (particularly, behavioural data at scale) are essential to answering this question, but there is disagreement about the strength of evidence for causal relationships that is given by different types of analysis. This chapter reviews the different approaches to analysis that have been taken. First, it is argued that most existing literature both under-claims regarding the evidence for causality given by some types of analysis of big data, such as correlational analyses, and over-claims for other types of analyses, such as those involving panel data. Thus, even correlational data can be informative to the extent that associations are generally rare and that theoretical targets and alternatives are fully specified and given prior probabilities. Second, a new methodological problem is identified for a specific model of the income–rank relationship. According to the income rank hypothesis, people’s well-being is determined not by their income but by the ranked position that their income occupies within a social comparison group. It is shown by simulation that spurious rank effects can occur in regression analyses if there is noise in measured income, but that this problem can be reduced with the use of robust regression techniques. A new analysis of a large dataset, the Panel Study of Income Dynamics, is reported. The results show that income rank effects are not reduced by the use of robust regression techniques, suggesting that previous support for the income rank hypothesis is not due to an artefact.

After a short historical summary, the central concepts of magnetic order and hysteresis are presented. Magnetism is related to physics, materials science and industrial technology. Magnet applications are outlined, and the science is set in its social and economic context.

This chapter looks at the rise of a conservative populist movement within the Republican Party prior to 2016. A longstanding American conservative coalition simply lost control of the party it had ruled for decades. The chapter examines several key turning points in modern American political history that enabled this transformation. It begins in 1960 with an internal party fight over election narratives: Did Richard Nixon lose narrowly to John Kennedy because Nixon was too moderate or not moderate enough? It then discusses the populist 1992 presidential campaign of Pat Buchanan, who did surprisingly well against the incumbent president George H. W. Bush in the Republican primaries, and drew attention to a small but passionate caucus within the party favoring a more conservative shift and a profound hostility toward immigration. Finally, the chapter looks at the key party moments, including the Gingrich Revolution in the 1990s, the Tea Party in the late 2000s, and the events surrounding the 2012 election, that gave this faction increasing numbers and muscle.

Providing a cohesive reference for advanced undergraduates, graduate students, and even experienced researchers, this text contains both introductory and advanced material in extremal graph theory, hypergraph theory, and Ramsey theory. Along the way, this book includes many modern proof techniques in the field, such as the probabilistic method and algebraic methods. Several recent breakthroughs are presented with complete proofs, for example, recent results on the sunflower problem, and off-diagonal and geometric Ramsey theory. It is perhaps unique in containing material on both hypergraph regularity and containers.

Featuring an extensive list of exercises, this book serves as a valuable teaching resource for a variety of courses in extremal combinatorics. Each of the two parts can form the basis of separate courses, and the majority of sections are designed to match the length of a single lecture.

Wentworth Stewart was an American Evangelical Methodist pastor whose views on Americanization were greatly influenced by his religious beliefs. In his book The Making of a Nation: A Discussion of Americanism and Americanization (1920), Stewart argues that the process of ‘becoming (or being) a true American’ requires a deep emotional commitment to an ill-defined state of mind rather than a compact in which the citizen (native-born or naturalized) understands and benefits from the basic principles of a constitutional democratic republic and expects equal opportunities to enjoy the ‘fruits of liberty.’ Stewart’s conception of Americanism, as represented in his writing, relies on assumptions about the founding of the United States that entail particular and constructed ‘American values,’ along with myths about the Founders and their heirs, that simply do not hold up under close scrutiny. Stewart’s commentary constructs an idealized version of American exceptionalism as the ‘soul of the nation’ that is precious, not universally available nor easily obtainable, and that requires Americanization programs that will take a very long time for proper indoctrination in Americanism to be completed, if ever.

This chapter examines the distribution of foreign affairs powers, arguing that the Constitution’s text sufficiently allocates authority between Congress and the President without requiring unenumerated or inherent presidential powers. It rejects both formalist claims of a residual executive power and functionalist assertions of necessity-driven authority, asserting that the President’s powers, such as appointing ambassadors and treatymaking, cover essential functions like managing international relations. Historical episodes, including Washington’s Neutrality Proclamation and the Monroe Doctrine, illustrate that presidential actions rely on enumerated powers, not a broad policy-setting prerogative. The chapter argues the President does not have unilateral or exclusive authority to recognize foreign governments or to terminate treaties. Treaties are necessary for long-term international obligations and to bind state courts under Article VI, but executive agreements are constitutional if Congress has delegated the relevant authority to the President. While Congress holds most foreign affairs powers, the President’s role is robust but constrained by the Constitution’s formal structure. This formalist approach ensures a balanced separation of powers in foreign affairs.

This chapter critically examines ‘sense of place’ within a post-colonial context, addressing its theoretical complexity and the absence of Indigenous perspectives in mainstream discourse. Building on Erfani’s synthesis of over 2,000 studies, it explores four core components—place attachment, identity, satisfaction, and dependence—while highlighting their intersections with psychological sense of community. The chapter emphasises the need to integrate Indigenous worldviews, which conceive humans as inseparable from land and place, contrasting with settler-colonial paradigms rooted in ownership and separation. It advocates for Indigenous-led methodologies to measure sense of place, showcasing frameworks like the Mauri Model and Caring for Country. By bridging gaps between Western and Indigenous perspectives through participatory, Indigenous-led approaches such as ‘working two-ways’ or ‘two-eyed seeing’, the chapter aims to foster mutual understanding and sustainable practices. Ultimately, it calls for a paradigm shift toward holistic, relational conceptions of place to address environmental and cultural challenges in the Anthropocene.

Franklin K. Lane (1864–1921), born in Canada, was a lawyer and Democratic politician who served as secretary of labor in the Woodrow Wilson administration. As a strong advocate for US entry into the war in Europe, Lane used his role as interior secretary to promote programs that taught civics and English to ensure that immigrants understood the meaning of America and Americanism as he understood those terms. He believed that all Americans needed to be involved with Americanizing immigrants as well as those Americans who were not living up to their responsibilities in promoting American ideals, values, and aspirations. In a speech given in Washington, DC, on April 3, 1918, Lane invokes religious metaphors to characterize Americanization as a spiritual crusade; he states that America is a nation sanctified by ‘God,’ a ‘holy ground – because it serves the world’ – a country that is ‘tolerant,’ ‘liberal,’ ‘fair,’ and ‘kind.’ This hagiography trope of America as a ‘holy land’ that can ‘win out against all adversity’ with little more than ‘the philosophy of confidence, of optimism and faith and the righteousness of the contest we make against nature’ extends from the colonial period to the present day.

The recent surge in conversational AI has opened up new avenues for the application of Behavioural Data Science, with Generative AI, particularly LLM models such as ChatGPT, representing a promising platform for analysing human behaviour. This chapter provides an overview of the role of Generative AI models in Behavioural Data Science, highlighting their strengths and limitations. The chapter begins by introducing the principles of Generative AI models and their potential applications in Behavioural Data Science. It discusses the advantages of using Generative AI models to study human behaviour, such as their ability to analyse large volumes of unstructured data and their capacity to learn from interactions with users. The chapter then describes the different ways in which Generative AI models can be used in Behavioural Data Science, such as analysing sentiment, predicting behaviour and generating insights from user interactions. It discusses the challenges associated with using Generative AI models, such as the need for accurate training data and the potential for bias in the model. The chapter also addresses the ethical concerns associated with the use of Generative AI models, such as privacy violations and the potential for unintended consequences. It discusses ways to address these concerns, such as implementing transparency and explainability in Generative AI models. The chapter concludes by discussing the future of Generative AI models in Behavioural Data Science, highlighting the potential for interdisciplinary collaboration with other fields such as psychology and sociology. It emphasises the need for continued development and refinement of Generative AI models and their associated methods for studying human behaviour. This chapter provides an overview of the role of Generative AI models in Behavioural Data Science, highlighting their strengths and limitations. It serves as a valuable resource for researchers and practitioners in the field who are interested in utilising Generative AI models to analyse and understand human behaviour.

This chapter explores how psychology and human–AI interaction (HAI) principles shape successful AI products. Using failures like McDonald’s ill-fated AI drive-thru as cautionary tales, it shows how neglecting user needs such as control, trust, and comprehension can cause reputational and product damage. Drawing on human-centered design, cognitive psychology, and UX research, the authors argue that great AI experiences depend on anticipating how humans think, feel, and decide. They outline strategies for embedding empathy, transparency, and explainability into AI, highlighting that these lessons extend beyond engineering teams to anyone influencing AI adoption.

The success of the linear algebra method in combinatorics has led to other advanced algebraic techniques, often using polynomials in novel ways. This chapter focuses on these developments. Two highlights include the resolution of the Kakeya problem in finite fields and the combinatorial Nullstellensatz of Alon.