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 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.

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.

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.

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.

A central notion in extremal set theory is the shadow of a family H of k-element subsets of an n-element set. It consists of all the k − 1-element subsets that are contained in some set of H. A matching of H is a collection of pairwise disjoint sets in H, and the matching number of H is the largest size of a matching in H. In this chapter, we discuss the basic problems surrounding shadows and matchings in hypergraphs.

Logic simplifies and clarifies ordinary language and thereby improves communication by reducing or eliminating errors of interpretation. While English and other languages offer many ways of saying things, logic uses simple structures whose meanings are always clear because they are stated using only a few well-known forms. This chapter considers sentential logic in which every sentence may be either true or false but not both or of unknown truth value. Such logic simplifies communication from the uncertainty that is common in ordinary language. Negation, conjunction, disjunction and implication (or conditionals) are illustrated by truth tables. All are valuable in theory development and enable the prediction of outcomes from premises.

We present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Argentina, 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.

We present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Nigeria, 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.

We define filtration by upper ramification subgroups. Using the geometric construction in the previous chapter, we construct a filtration on the fiber functor. The proof of the fact that this filtration defines the subgroups is based on the going down theorem. We prove that the first steps of the filtration are in fact the inertia group and the wild inertia group, using the computation in the monogenic case. We also prove semi-continuity. The proof relies on the stable reduction theorem and a general version of the reduced fiber theorem.

We present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Turkey, 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.

The essays in this volume were commissioned to address how British literature developed in the first decade of the nineteenth century, as seen from our current vantage, one-quarter of the way through the twenty-first. They examine the literary forms and cultural formations that emerged during this paradoxical era of aftermath and new beginnings. As with the other volumes in the Nineteenth-Century Literature in Transition series, a decadal ‘cut’ into literary history lends each of the chapters its frame. Our collective goal has been to re-examine a period within the Romantic period, and within the larger context of the nineteenth century. This introduction offers a brief summary of the fourteen chapters that comprise the volume and draws connections among them.