In this chapter, we introduce the theory of Lovász extensions as a powerful tool for studying eigenvalue problems and, in particular, Cheeger-type inequalities.

An important topic which has seen a considerable amount of attention in recent years concerns the continuum limits of the graph-based models discussed in this book1.

The increasing reliance on algorithmic and AI systems by judges is reshaping the judiciary and its way of working in numerous ways. One aspect that has remain under- examined is how the judicial duty to state reasons may be affected. This refers to the obligation of judges to provide reasons whenever they rule in a case. In fact, the duty constitutes an essential component of the rule of law and the right to a fair trial, and fulfils important normative goals, such as legitimacy, transparency, and accountability of the judicial decision-making process. The chapter therefore first provides a concise conceptualisation of the duty, including its underlying normative goals. It then examines how and to what extent the judicial duty to state reasons can be impacted whenever judges rely on AI systems, focusing on the impact of such systems on the underlying normative goals of the duty. The chapter concludes with some reflections on how the duty can be safeguarded in the age of automation.

Prohibitioning and the Constitution of India

Prohibition was reviewed and re-conceptualised following the achievement of independence, when the foundations of the modern Indian state were formally established. In the long run, the prohibition ideal filtered through new administrative and legal frameworks that nevertheless bore the imprint of both colonialism and the struggle against it. As the independent Indian republic was premised upon the founding principles of secular democracy and federalism, prohibition had to reckon with both debates relating to personal liberties and issues of state autonomy.

Following independence, the national democratic state – having won the mandate of representing national society – sought to intervene in that domain in order to transform it. The processes that had accompanied the birth of the Indian nation had brought forth institutions, structures and practices that enabled policies like prohibition to be operationalised through the workings of the state. However, the problem remained that a national society still had to be fashioned anew from the fluid, overlapping identities that made up the fabric of Indian social life. Amidst such a ‘recalcitrant social’, which, Prathama Banerjee argues, continued to function as ‘a network of multiple nodes of caste, community and regional sovereignties’, postcolonial governmentality appeared from the very outset ‘a compromised project’.

In this, however, postcolonial governmentality did not constitute as radical a rupture from the colonial past as Banerjee's discussion would suggest. The careful balancing act that the nationalist government attempted to strike between ‘mobilising the social and mobilising the political’ had already set the tone for things to come before independence was achieved; prohibition's colonial-era origins are a case in point.

This chapter ties together the arguments of the book and sketches out their broader implications. It addresses, in particular, three issues. The first is what Messianic claims regarding divine indexicality and authority may tell us about political culture and local perceptions of secular government authority in the South Sudan-Ethiopia borderlands. The second is whether the Messianic preoccupation with truth and self-awareness is a distinctively ‘modern’ disposition or an attitude that is historically and culturally informed and therefore also speaks to local notions of spiritual mediation. Finally, the chapter returns to Christian Zionism and Africa’s Messianic frontier and sketches out some of the ways in which the case of Gambella’s Messianic Jews may be indicative of processes and trends evident among African born-again Christians more broadly.

The Permanent Court of International Justice (1919–1946) may be seen as an unprecedented institutional experiment. Its impact and output have been substantial, and consequently its legacy might equally be called fundamental. This chapter seeks to demonstrate the veracity of the foregoing statements, situating the Court in its contemporary context while building on similar scholarly ventures that were undertaken previously. In contrast to earlier inquiries, the study reflects rather more broadly on the institution’s positioning, especially on how it interacted with the principal organs of the League of Nations. It begins by placing a focus on the Court’s inception, from an idea to fully settled status. Thereafter, the chapter analyses the environment within which the Court functioned, and the interplay with its League interlocutors. Next, a review is undertaken of a series of leading pronouncements, both judgments and advisory opinions, concentrating on those verdicts that have obtained a genuinely enduring value. Drawing from these analyses, an assessment is made of the Court’s overall contribution to the multilateral order against the background of interwar-era politics followed in turn by a brief series of concluding observations.

What was the place of international law in the League of Nations? Drawing up the balance from the many perspectives on this question offered in the Handbook, the Conclusion first and foremost acknowledges the complex reality observed in many chapters of an oftentimes messy interplay between politics and law, a reality that defies any generalizing account of either ‘failure’ or ‘progress’ achieved through the League. Instead, it points at three overarching developments that can be discerned: (1) the continuing impact of ‘peace through law’ ideals throughout the League years in spite of their suppression during the Paris Peace Conference; (2) the imperial, civilizational but also geographical differences the League of Nations and its international law helped sustain but also contested from the perspective of (legal) equality; and (3) the transformation of international law into a prerequisite of global governance which prevailed also after the League of Nations collapsed.

This chapter looks at a series of English poets who have identified Pindar as a poet of freedom – both metrical and political – before turning to some modern Greek poets who have been influenced by this aspect of the English Pindaric tradition. Among the poets discussed are Abraham Cowley, Thomas Gray, A. E. Stallings, Andreas Kalvos, and Angelos Sikelianos.

Chapter 3 offers an overview of the role of international law in the International Labour Organization (ILO) during the first quarter-century of its existence. The chapter focuses on three kinds of international ordering conducted in, by, and through the ILO: the ordering of class relations through the systematic construction of international labour law; the ordering of inter-polity relations, arising from the extension of the ILO’s activities to non-metropolitan states and territories; and the ordering of international institutional relations. The chapter shows how international law was deeply implicated in each of these forms of international ordering and, in turn, transformed through them in a variety of ways. It examines the expanding range of legal activities conducted in and through the ILO; considers its role in reproducing civilizational hierarchies as its focus widened beyond Europe; and details its contributions to the development of international organizations law. The outcomes of the ILO’s normative work were often ambivalent, simultaneously advancing workers’ rights while reinscribing racialized distinctions. Yet in many ways the ILO was, for better or worse, at the vanguard of international legal ordering throughout this period, and highly influential on the international order that emerged after the Second World War.

We are interested in discrete structures like graphs, hypergraphs, and simplicial complexes, and we want to study them via spectral properties of Laplace type operators defined on them. These operators perform some kind of local averaging. The eigenvalues and eigenfunctions of such operators can be obtained as critical values and points of Rayleigh quotients. Symmetry groups of the underlying structures have representations on eigenspaces.

This chapter explores the shift from viewing languages as fixed, bounded systems to understanding languaging as a fluid, creative, and relational process of meaning-making. It presents languaging as an embodied and affective act that embodies both agency and vulnerability. The concept of “playful voices” captures the ways language users draw on their diverse linguistic repertoires to navigate, challenge, and reimagine power structures that privilege certain ways of speaking. Yet, these playful acts unfold on “precarious grounds,” where speakers’ linguistic creativity is frequently surveilled, corrected, and devalued. The chapter positions languaging as a space of both empowerment and risk – a means through which individuals negotiate identity, belonging, and resistance within unequal social orders. Ultimately, it argues that moving from languages to languaging transforms our understanding of communication, highlighting it as a living, dynamic practice shaped by both playfulness and precarity.