This chapter discusses the elementary properties of Laplace operators on graphs and hypergraphs. Many interesting examples will illustrate how special eigenvalues emerge. We also introduce discrete Pólya–Cheeger constants and their dual versions and provide the initial steps relating spectral clustering, spectra of neighborhood graphs, signed Laplacians, and spectra of simplicial complexes and hypergraphs.

This chapter examines concerns that AI might replace human judges, potentially compromising the right to a fair trial and other fundamental rule of law values. Rather than dismissing these concerns, we present a balanced analysis of the opportunities and challenges posed by AI-enhanced judicial decision-making. We explore this issue through the lens of Article 6 ECHR, examining potential applications, including case management, evidence collection, and legal interpretation. We emphasise the critical need for transparency and robust safeguards to protect due process rights. Equally significant are questions surrounding perceptions of justice and the maintenance of public trust and legitimacy in judicial proceedings. Even sophisticated AI systems require continuous oversight and human interpretive expertise to ensure that litigants and the broader public perceive the technology and judicial role as efficient, fair, and reliable. The chapter concludes by developing a typology of AI in judiciary – from judicial clerks to bureaucratic judges to R. Dworkin’s idealised ‘Judge Hercules’ – examining how AI can enhance traditional judicial capabilities and improve overall judicial performance.

This concluding chapter affirms that the integration of AI into courts is no longer a question of if, but how. Courts, as constitutional institutions, face profound normative questions: how does AI affect transparency, impartiality, and public trust? While AI improves court operations in many jurisdictions, it also risks eroding judicial values and the rule of law. Global examples show diverse adoption paths, yet shared challenges, such as AI opacity, lack of judicial AI literacy, and accountability gaps, demand coordinated oversight. Ultimately, a human-centred approach to judicial AI is essential. Rather than rejecting AI or accepting it uncritically, the authors advocate a balanced path that preserves the human and interpretive role of judging.

This chapter situates the study within a broader historical, political, and scholarly context, and presents the methodology upon which it draws. First, the chapter sketches the history of Gambella as a site of encounter between the Ethiopian state and Nuer society and examines the historical and anthropological scholarships on Ethiopia’s peripheries and on the eastern frontier of Nuerland. It then discusses my own encounter with Gambella, the context and political environment in which research took place, the local religious landscape and the place of Messianic Jews in it, and the ‘data collection’ methods and research approach deployed. The final sections of the chapter explore my positionality in Gambella, as a Jewish Israeli researcher among Messianic Jews, and the sort of intersubjective encounters that informed this study.

This chapter introduces the reader to how the oil industry mobilizes political support from publics. It argues that historically, the sector has shied away from grassroots politics, or employed short-lived, financially secretive front groups. However, today this is changing. Oil firms’ contemporary outreach is apt to take the form of visible, far-reaching, and long-term campaigns that openly tout partnership between companies and citizens. This style of organizing troubles the neat binary between grassroots politics and corporate public relations. To address this, the chapter suggests we think of all political mobilization as “manufactured publics,” emphasizing the strategizing, labor, and mixture of interests inherent in all contentious political efforts. This theoretical lens allows us to explore both the affective realities of people who join pro-oil groups and the corporate interests that shape these campaigns.

Judicial systems, long considered the most tradition-bound of public institutions, are at a critical juncture. From Strasbourg to São Paulo, from Delhi to Wellington, courts around the globe confront a shared challenge: how to navigate justice in an era redefined by artificial intelligence (AI). The question is no longer whether courts will engage with AI – but how, and on whose terms. This Handbook is the first global and comparative volume that systematically examines the use of AI and digital technologies in courts. It provides an interdisciplinary and cross-jurisdictional perspective on how judicial institutions are responding to the opportunities and risks posed by AI – from e-filing systems and predictive tools to ‘robo-judging’ and AI- supported decision-making. The forty-five contributions of the Handbook are arranged across ‘Part I: AI and Courts: Context and Normative Positions’, ‘Part II: AI and Courts: Disciplinary Perspectives’, ‘Part III: AI & Tech Challenges to Judicial Values’, and ‘Part IV: AI in Courts across the Globe: Jurisdictional Perspectives’, with each part offering a distinct analytical lens on justice and judging in the age of AI. The Handbook examines not just what AI can do for courts, but also what courts must do to ensure AI enhances, rather than erodes, their fundamental role in democratic societies.

The Introduction explains why nineteenth-century Cuba is a particularly rich context for studying racialism (the assumption that social hierarchies are based on the existence of races), racial doubt (those moments when this assumption gets questioned and racial differences seem less clear), and the different groups of racialized people who mobilized doubt as they worked to reinvent themselves and their society. It also shows how the analysis of the notions at the core of each chapter – racist agnosia, farce, passing-as-open-secret, fictions of racial coherence, back talk, and the reappropriation of Blackness – illuminates present-day critiques of color blindness. Finally, it explains why the book is divided into three parts. The first part focuses on enslaved people’s testimonies and abolitionist writing that attacked illegal slavery by denouncing lies, falsification, and farce; the second one, on free people of color who wrestled with two “one-drop” rules (one which rendered a person not-white, the other which made them whiter); and the third one, on the emergence of Black Cuban writing.

This chapter surveys Pindar’s reception from the poet’s own lifetime until the Byzantine period. Four ‘moments’ of that reception are singled out from that very rich reception history. First, Plato, whose citations and evocations of Pindar were to prove crucial for the subsequent critical tradition; second, the Alexandrian grammarians who created a corpus of seventeen books of poems, and the poets (Callimachus, Theocritus, Apollonius) who reflected that new engagement with Pindar in their poems; thirdly, the critical treatises of Dionysius of Halicarnassus and the poetry of Horace, both produced at Rome in the Augustan period; and finally (and most briefly), Plutarch and the authors writing in Greek prose under the Roman Empire.

Starting from this section, we only consider undirected graphs unless stated differently in specific situations. In the definition of ${\mathrm{GL}}_{\epsilon }$, we make the choices $\alpha (\epsilon )=1$ and $\mathcal{W}(u)=⟨W\circ u,1{⟩}_{\mathcal{V}}$.1 We will specify whether $W$ is a double-well or double-obstacle potential where this is relevant. Also, we recall from Remark 2.1.9 that we choose $q=1$.

Policies have complex lives and afterlives. They interact with contingent political and social agents and are mediated by their wider contexts, from the processes that inform their conceptualisation through their enforcement.1 Prohibition in India originated in the context of late colonialism. It took shape as an idea, became part of a mass movement and crystallised into an ideal before emerging as a policy with the Madras Prohibition Act of 1937. The ensuing interactions are best understood as constituting the long-term process of prohibitioning, wherein each phase of the policy's development simultaneously overdetermined and constrained its subsequent iterations. As we have seen, this formative experience also enabled prohibition to migrate from the colonial context to the postcolonial era, its origins illuminating crucial parallels and precedents for developments that followed the achievement of independence. Through all this, prohibition bore – indeed, has borne – the imprint of the interactions that produced it, which are discernible in its manifestations as an idea, ideal and policy. As much a history of the policy as it is a history of the Indian state, Sober State has presented a history of prohibitioning that rests on three related arguments.

First, we saw that prohibition emerged as a function of the exercise of state power by the colonial and nationalist states. The colonial state engaged with alcohol policy as a means to maintain power by achieving revenue maximisation and ensuring regulatory checks and balances at a time when said power was quickly slipping out of its hands. The nationalist leadership saw the prohibition demand as a trump card that would expose the colonial state's avarice and hypocrisy, while signifying a new and superior model of governance.

Chapter 1 revisits the establishment of the League of Nations by providing an in-depth analysis of the Paris Peace Conference, with a particular focus on the negotiation of the Covenant. The chapter also explores alternative conceptualizations of order from the social sciences, law, and history. The chapter argues that the new international order constituted by the League exhibited three common characteristics. Firstly, the League was largely shaped by the dominance of the United States and Britain during the negotiations. Secondly, the core decisional logic of the League’s institutional system was political, not legal. Thirdly, the League constituted a dual international order. On the one hand, and despite its universal rhetoric, it reproduced an imperial logic by dividing countries into civilized and uncivilized ones in new ways. However, in an attempt to prevent another world war, it also sought to facilitate disarmament and collective security, primarily in Europe. In doing so, it helped stabilize the European state system by addressing several key challenges, such as the status of Danzig, the Saar and Upper Silesia, and the protection of national minorities.

Chapter 2 focuses on the early history of the League Secretariat’s Legal Section, offering a rich sociography of the first craftsmen and women responsible for the League’s legal affairs, including later famous personalities such as Åke Hammarskjöld and Georges Kaeckenbeeck. It uncovers attempts by the Dutch Director of the Legal Section, Joost van Hamel, to push for a strengthening of international law with the aim of consolidating the position and competences of the League of Nations. The Legal Section thus promoted the establishment of a Permanent Court of International Justice with compulsory jurisdiction that should be closely linked to the League, a comprehensive programme for the codification of international law, and the obligatory registration of international treaties. However, Van Hamel’s campaigns met with resistance from leadership of the League Secretariat in the shape of Secretary-General Eric Drummond, who, assisted by Under-Secretary-General Dionisio Anzilotti, focused on not antagonizing the great powers in a situation where the League Secretariat was still relatively weak.

Three-Way Tango: Politics of Liquor Production

Any account of prohibitioning in the decades leading up to the Madras Prohibition Act would necessarily be incomplete without addressing the politics of alcohol production. Colonial officials and nationalist elites were interacting as much with one another and diverse segments of society as with liquor business interests to devise policies aimed at regulating drinking. The cumulative impact of the ensuing developments had a tremendous impact on prohibitioning by influencing the momentum towards the policy's introduction in 1937.

During the period in question, liquor businesses had to contend with mounting social pressure against their trade on the one hand and political manoeuvring by both the colonial government and the Congress leadership on the other. Whilst prohibition discourse cast drinkers as victims who could eventually be redeemed of their affliction and transformed into upstanding citizens, it painted the producers, distributors and retailers of alcohol unforgivingly and with a large brush stroke as traitors of the nation. ‘A number of Indian merchants, be it said to their shame,’ charged a letter that was published in The Hindu, ‘have taken up the merchandise of liquor to ruin their countrymen.’ The most spectacular anti-alcohol protests were, unsurprisingly, directed at toddy and arrack shop contractors.

The constraints imposed on liquor business interests by, first, the colonial establishment and, subsequently, the nationalist leadership were part of an overarching political contest to dictate the terms of liquor production. If the colonial government was concerned that the emergence of liquor monopolies would result in lowered revenue yields for the state, the nationalist leadership sought the right to altogether remove liquor production from the workings of the national economy.

This chapter offers a reading of Pythian 10, Pindar’s earliest extant epinician ode. It considers the place of the myth in the poem and focuses on Pindar’s foregrounding of moments of transgression (thematic and syntactical), together with the looping or circular imagery and architecture of the ode.

In recent years, the Brazilian judiciary has announced over 100 initiatives using artificial intelligence (AI) systems, while a mounting number of juridical decisions shape how AI can be used in the country. The chapter analyses how AI impacts the Brazilian judiciary. First, we introduce the Brazilian legal systems, and explore a selection of AI initiatives to expose their benefits and shortcomings. Then we proceed to examine the policy for the usage of AI within courts in the country, focusing on the recent Resolution of the Brazilian National Council of Justice, aimed at regulating the judiciary’s production and use of AI systems. Last, we argue that the integration of AI within Brazil’s judiciary has the potential to enhance procedural efficiency and innovation. Yet, we emphasise that the guarantee of transparency, accountability, legal certainty, and digital sovereignty largely depend on the adoption and coherent implementation of a new AI Regulatory Framework and a new AI Strategy.