This chapter examines the horse trade at the Hengshan borderlands garrison, focusing on the 12th century Sino-Vietnamese borderlands. Interactions with indigenous Tai-speaking communities and neighboring upland kingdoms significantly shaped the salt and horse trade, thereby influencing regional dynamics and economic exchange. The study explores the roles of these local communities, contrasts overland and maritime trade routes, and investigates the efforts of the Southern Song and Lý courts to control the borderlands settlements. By examining trade and political undercurrents along the trade route known as the Ancient Road of the One Hundred Yue, the chapter highlights the interconnectedness of the borderland’s communities and their strategic importance for salt and horse trade. These interactions are crucial for understanding the broader historical and economic context of the region during the 12th century. By providing insights into everyday life at the Hengshan borderlands garrison, the chapter underscores the significance of the salt and horse trade in shaping the historical trajectory of the Sino-Vietnamese frontier in this period.

Partially ordered sets are fundamental objects ubiquitous in many parts of mathematics; they are also used to model various structures and phenomena in other areas like computer science, biology, and beyond. In this short chapter, we study the basic theory and properties of partially ordered sets from an extremal combinatorics perspective.

Chapter 7 returns to a key issue from the previous chapter: should Cantor’s diagonal construction (CD) be considered a genuine real number? To answer, we need first to clarify the distinction underlying Wittgenstein’s take on Cantor’s proof, between ‘intensionalism’ and ‘extensionalism.’ The main message here is, again, ultimately therapeutic-liberatory, and not revisionist (only reluctantly so): we are not forced to accept that CD is a genuine real, and hence to say that there are more reals than naturals. We may say this, and introduce a new concept of a real, but we don’t have to. That CD is a genuine irrational is not an epochal discovery, but an invention, a technical stipulation. A background difficulty in this chapter concerns the overarching philosophical problem Wittgenstein grapples with in RFM II. I propose that this is the question, ‘What is the significance of Cantor’s discovery of the hierarchy of infinities?’ – and I argue that he saw it as ill-posed. Since mathematicians are inventors and not discoverers (RFM I-168), Cantor did not discover anything; so, the question is based on a confused presupposition and should be discarded.

This chapter shifts focus inward, analyzing how teams, leadership, and organizational psychology shape AI development outcomes. Through examples like Tesla’s safety controversies and Meta’s Galactica failure, it demonstrates that many AI failures stem not from technical flaws but from poor team dynamics, leadership gaps, and cognitive biases. The chapter draws on research in organizational psychology and decision-making to stress the importance of psychological safety, inclusive leadership, and diverse team composition. It warns against techno-optimism, novelty-seeking, and sunk-cost bias, urging organizations to integrate human judgment with machine intelligence in thoughtful, accountable ways.

This chapter includes three parts. The first part provides a brief introduction to rural China during the Song period. This is followed by a focused discussion on the spatial and administrative organization of Changshu County (in Jiangsu) near Lake Tai. Part three presents a case study of another county, Shanyin (Shaoxing, Zhejiang) in the southeast, aiming to illustrate the various aspects of rural life for both elites and ordinary people during the Southern Song.

This chapter explores the provisions of the Treaty on the Functioning of the European Union (TFEU) relevant to company law. It examines the legal basis for EU action in this area, focusing on Articles 49–54 TFEU, which underpin the freedom of establishment and the mutual recognition of companies across Member States. The chapter discusses key principles such as non-discrimination, cross-border mobility and the harmonization of company law. It also considers the evolving role of the European Court of Justice in shaping company law through its interpretation of TFEU provisions and highlights future challenges in legal convergence and enforcement.

This chapter is devoted to degenerate or bipartite Turán problems, a topic that is concerned with extremal numbers for bipartite graphs. We cover the Kővari– Sós–Turán Theorem and it strengthenings, the Zarankiewicz problem and norm graphs, the asymptotics of the Turán number for K3,3, constructions from finite geometry, the method of dependent random choice, and relative Turán problems.

Understanding systems behaviour through experimentation is at the heart of modern Behavioural Data Science. While earlier chapters have explored the analysis of human and algorithmic behaviour, this chapter centres on the dynamic and often non-linear processes that emerge when individual components – human agents, algorithms, environments – interact within a system. These systems can span sectors, from health and mobility to climate and governance, and are characterised by emergent properties that defy reductionist interpretations. This chapter elaborates on how experimental paradigms, including in silico simulations, real-world interventions and digital twin testbeds, facilitate insight into the adaptive behaviour of complex systems. Anchored in the frameworks of complex adaptive systems, cybernetics and socio-technical experimentation, we articulate the distinct role of Behavioural Data Science in producing actionable knowledge through systems-level interventions. The chapter also interrogates the ethical, epistemological and methodological dilemmas associated with manipulating complex systems and proposes principles for the responsible design of system-wide experiments.

Painful as it is for a Remain campaigner like me to admit, the EU has always been dire when it comes to policies for supporting innovation and technology. Even more painfully, things have worsened over the past ten years. Longstanding structural weaknesses in EU innovation policy date from well before the Brexit referendum in 2016. The European Union had dismally failed to create a regulatory environment conducive to technological innovation. As I found whenever I visited to Brussels as a No. 10 adviser under David Cameron, the policy instincts of European Commission officials were overwhelmingly rooted in market stability and risk avoidance – values that, while defensible in themselves, often produced unintended consequences for fast-moving sectors such as digital technology and life sciences. Take the EU’s data privacy rules, which were debated and developed for years before being finally implemented in 2018. As Cameron’s team repeatedly warned at the time, the compliance costs fell disproportionately on small and early-stage firms. Even before fines or litigation, the administrative burden for smaller organisations typically ran into tens of thousands of pounds.

In 1802, the German physicist Ernst Chladni published Die Akoustik, a groundbreaking textbook expanding upon his earlier research on patterns of tonal vibration to further explore the psychophysical function of the human ear in perceiving them. This chapter puts Chladni’s acoustic experiments into conversation with the writing of William Wordsworth and Samuel Taylor Coleridge. Drawing from Wordsworth’s The Prelude (1805) as well as his 1802 ‘Preface’ to Lyrical Ballads and Coleridge’s ‘The Eolian Harp’ along with sections of his notebooks, it examines how the idea of aurality plays important roles in both poets’ theories of the creative imagination. Altogether, placing Romantic poetic explorations of listening next to contemporaneous writing on vibrational physics helps to reveal how emergent acoustic information prompted new ways of thinking about the affordances of the ear – in corporeal and metaphysical senses – as a point of resonant contact with the sensible world.

This chapter focuses on the communicative systems for the Deaf and Blind communities: sign language and braille. Starting from the crucial point that sign languages are fully-fledged natural languages, it describes the history and regional varieties of sign language in China, and the major linguistic features of Chinese Sign Language. The development of Chinese Braille and its linguistic and structural features are also described.

Replacing immersions to smooth schemes by exact immersions to log smooth schemes, we define a logarithmic variant of the filtration by upper ramification subgroups. As a preliminary, we prepare basic facts on log smooth schemes. The logarithmic variant coincides with the non-logarithmic one after taking a log smooth base extension. For abelian extensions in characteristic p, the filtration is given by Brylinski's filtration on the Witt vectors. The proof is based on a computation of Witt vectors with respect to dilatations.

This chapter traces the recent history of Chinese writing, examining the 20th-century simplification of Chinese characters on the mainland in the context of the language reform movement. It describes transcriptions and romanizations of Chinese, with a focus on five key examples from the last 150 years. “Dialect writing”, notably Cantonese, is described and analyzed.

We present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Scandinavia, beginning with its origins: the formative people, places, and various intellectual schools of thought. Writing about the current state of the topic, we reflect on influential factors that are either facilitating or inhibiting the study of PoR, including publication options, topical emphases, practitioners, orientations, methodologies, and professional organizations.

We offer opinions concerning future development topics that are emerging as important in the immediate future and/or are perennially important in order to stimulate creative and useful research including Western theoretical relevance, the extent to which Western PoR theories may or may not contain reasonable expectations and concepts for this region, contextual nuances, Indigenous theoretical concerns, collaborative research opportunities, and common faux pas – reflections on what people unfamiliar with this region commonly and incorrectly assume about conducting PoR work in this context.