In this chapter, we prove quantitative estimates for the basic Ramsey questions involving hypergraphs. These involve recent developments regarding off-diagonal hypergraph Ramsey numbers. Additionally, we introduce geometric Ramsey theory and Euclidean Ramsey theory, and give classical results on canonical hypergraph Ramsey numbers.

Humans are emotional beings that reason, not reasoning beings that occasionally experience emotions. In fact, emotions are essential to good decision-making. In the world of big data and machine learning, the human potential for emotions can influence the way machine learning systems are developed and deployed and also influence the way they are perceived and used. The two manifestations of emotion that can influence decision-making are bias and noise, both of which have emotional undertones. In this chapter, I consider the impact of emotion, bias and noise and suggest a way to acknowledge and measure their impact in the realm of machine learning and big data.

This chapter explores how traders’ performance may be influenced by the rationality levels of their peers in the market. Using a Behavioural Data Science approach, the study integrates experimental methods, machine learning and large-scale digital trace analysis to examine this relationship. Specifically, we analysed data from a cryptoasset exchange over a five-week period in late 2017 and early 2018, covering over 700,000 transactions across 17 trading pairs. We complemented this behavioural trace data with an online guessing game involving 2,622 active traders, of whom 273 participated. By combining survey results and trading histories, we applied clustering algorithms to identify seven distinct trader profiles, including ‘jokers’, ‘focal point traders’ and those operating at different levels of strategic reasoning (first, second and third order), as well as ‘professional’ and ‘Nash equilibrium’ traders. The findings suggest that traders engaging in higher-order reasoning generally achieve better financial outcomes, yet even experienced professionals are not immune to behavioural biases. The chapter highlights how Behavioural Data Science methods – linking experimental insight with real-world data and computational tools – can illuminate the cognitive patterns underlying economic decision-making in digital markets.

Civil service headcount expanded, but, as it grew, relationships between civil servants and ministers deteriorated and individual civil servants became targets as perceived blockers to true Brexit. Stasis in decision-making in Theresa May’s carefully balanced Cabinet degenerated into public disagreements between ministers as collective responsibility disintegrated. Ministerial churn accelerated. Ministerial frustration at Parliament’s refusal to pass any sort of Brexit agreement under the May government boiled over, and judges found themselves in the firing line as the process of exiting was litigated. The devolved governments were reminded that conventions were just that, without legal force. Northern Ireland suffered two Executive collapses in the Brexit period, the second a direct result of Brexit tensions, which left it governed by civil servants for half the time between 2017 and 2024. Under Boris Johnson, ministers went further – prepared to embarrass the Queen over the prorogation that the Supreme Court eventually found unlawful, introducing legislation to allow them to break international law and flirting with breaking domestic law.

Medieval and medievalizing fashions have gained new visibility in alternate histories of design, which highlight novel possibilities for understanding “shared” aesthetic connections between early European, African, and Asiatic Mediterranean fashion objects. This chapter begins with a discussion of the entangled medieval histories offered by the silk textile collection of contemporary designer Walé Oyéjidé and his fashion label Ikiré Jones, and then turns to analyze the entangled histories of fashion objects depicted in medieval European literature, using Oyéjidé’s work as a guide. Looking closely at the storytelling legacies of the silk textiles in the Middle English romance Emaré and in Geoffrey Chaucer’s Troilus and Criseyde, I examine a moment when overtly exoticized fashions in crusader romances give way to more refined literary and visual citations based in an emerging perception of discerning European taste, which opens up possibilities for understanding one way that past aesthetics came not to be shared.

This chapter examines judicial supremacy, arguing that while judicial review is inherent in judicial power under a written constitution, the Supreme Court is not the final arbiter of constitutional meaning. Through an exploration of Lincoln’s response to Dred Scott (1857) in his debates with Stephen Douglas, it defends “departmentalism,” where each branch interprets the Constitution for itself in exercising its assigned functions, and rejects Douglas’s claim that the Court’s rulings are the supreme law. Lincoln maintained that court decisions bind parties to a case, but their holdings need not be treated as a “political rule,” at least not until the constitutional question is fully settled. The chapter then turns to "executive supremacy," and posits that ordinarily the President must faithfully execute laws despite any constitutional misgivings, with a narrow exceptions for laws that target exclusive executive prerogatives such as pardons or military command. This formalist approach, rooted in Founding-era practices, balances judicial review with coordinate branch authority, preventing judicial or executive supremacy and preserving the Constitution’s separation of powers.

This chapter examines Congress’s taxing and spending powers, arguing that the Constitution’s first clause in the enumeration of powers originally granted only a power to tax for national purposes, not an independent power to spend for the general welfare. Textual and historical evidence, including from the Articles of Confederation and Committee of Detail, supports this as the best reading, with spending permissible only under the Necessary and Proper Clause to further enumerated powers. The chapter critiques modern doctrine, which recognizes a broad spending power allowing Congress to influence state policies indirectly, as in South Dakota v. Dole, by attaching conditions to funds. It proposes a test distinguishing genuine spending (e.g., disaster relief) from coercive regulatory attempts (e.g., conditioning funds on state policy changes), which usurp state functions. This formalist approach, rooted in the Constitution’s federalist structure, seeks to limit Congress’s ability to undermine state autonomy through expansive spending, preserving the original balance of federal and state authority critical to the Constitution’s enduring success.

The UK government’s handling of Northern Ireland exposed serious failings in UK state negotiating capacity as well as its relative weakness not only to the EU, but also in relation to even one small EU member state, Ireland, which played a far stronger hand far better, even if it ultimately overplayed it. The UK pushback was politically costly to the Johnson government at home and with the EU, but demonstrated at last its ability to win a diplomatic victory. Though it was clear, to those who paid attention, that there were serious implications for Northern Ireland in the event of Brexit, it did not figure much in the question of continued membership or in the campaign. Those implications were much more serious once Theresa May, in her 30 June 2016 leadership speech, stated that ‘Brexit means Brexit’, and this meant ending freedom of movement. That alone determined the kind of future relationship the UK would have with the EU – outside the Single Market – with huge implications for Northern Ireland and Ireland. Yet few recognised then just how much these would come to define Brexit and post-Brexit policy.

The Song religious world exhibited remarkable variety, innovation, and vibrancy. This survey of Song divinities, religious specialists, and religious practices highlights this era’s innovations and its continuities with the medieval past. Some old deities took on greater, national prominence in the Song. New local deities also emerged. The Song government approached these deities and their cults in various ways, granting state support, banning them, and often simply turning a blind eye. Among the lettered religions, Buddhism thrived, as the Chan school won widespread elite patronage. The Daoist church benefitted from extensive state patronage in two reigns, and new therapeutic, exorcistic regimens won government support and saw extensive use in the empire. Local festivals honoring new and old deities proliferated , as did large-scale rituals for the benefit of the suffering dead in the underworld. Clergies, lay elites, and commoners borrowed and shared practices to an unprecedented degree to secure protection and blessings in this life and the next.

The sheaf of nearby cycles is defined on the closed fiber and is used to compute the cohomology of the generic fiber of a scheme over a discrete valuation ring. The dimension of the stalk of nearby cycles of a sheaf on a curve over a discrete valuation is computed by the Deligne–Kato formula. The formula involves the refined Swan conductor defined in Chapter 7. A crucial ingredient of the proof is Temkin's refinement of the stable reduction theorem asserting that after a suitable base change, normalization, and blow-up, a curve over a discrete valuation ring becomes a nodal curve.

This chapter charts the emergence of the printed newspaper, and focuses on the Low Countries where the new genre first thrived. It provides a microhistorical study of transatlantic coverage in the Dutch Republic and the Spanish Netherlands for the year 1630, when both enemies had good and bad news from the Americas to digest. Amsterdam corantos eagerly followed developments in Brazil, where forces of the Dutch West India Company captured Pernambuco, the heart of the Atlantic sugar industry, while the Antwerp newspapers, with just as much zeal, covered the impending arrival of the first Spanish treasure fleet from New Spain and Tierra Firme in more than two years. The detailed comparison of two competing newspapers operating in the same linguistic market demonstrates that the partisan press on either side of the border preferred to follow mainly good news that was waiting to happen. Yet, whereas the newspapers in the authoritarian regime of the Southern Netherlands discounted bad news altogether, the ‘free press’ in Amsterdam covered all stories arriving from across the Atlantic Ocean, thus setting a new standard of credibility that would be replicated in other European media landscapes.