After introducing basic notions on finite extensions of local fields, including tamely ramified extensions, inertia groups, and so on, we define the main subject, lower ramification subgroups. We also define log monogenic extensions and extend the classical equalities, including the conductor-discriminant formula, to this type of extension. Finally, we study the norm map of the multiplicative groups and its relation with ramification of the extension. As a preliminary to the definition of Henselian local rings, some general results on etale morphisms of rings are studied at the beginning of the chapter.

Although extremal set theory began with Sperner’s theorem from 1928, most of the subject has centered around so-called intersection theorems initiated by Erdős–Ko–Rado, and developed by Kleitman, Katona, Frankl, Füredi, and others. This chapter discusses some of these early developments.

This book argues that news, as a transatlantic commodity, was just as valuable as sugar, tobacco, or cotton. It does so by focusing on news reports and storylines from the Atlantic world in printed newspapers, and the ways in which metropolitan and colonial authorities subsequently managed public communications. The book investigates how newspapers – ‘new media’ at the time – covered distant but urgent transoceanic conflicts with a weekly periodicity, using primary sources from Atlantic societies like Spain, Portugal, France, the Low Countries, and the British Isles, from so-called second-row Atlantic states such as Italy and the Holy Roman Empire that do not currently feature in the field’s predominant discourse of empire, and from emerging colonial societies in North and South America. It reveals the idiosyncratic rhythm of communications in the Atlantic world, which challenged news writers to navigate judiciously between speculation and confirmation, and demonstrates that the circulation of information was underlying all other transatlantic exchanges – of people, commodities, values, and ideas – that have been the staple of Atlantic history.

The most famous geometric application of ramification groups is the Grothendieck–Ogg–Shafarevich (GOS) formula that computes the Euler–Poincaré characteristic of an étale sheaf on a curve over a field of characteristic p. The GOS formula is deduced from the Lefschetz trace formula, which is a consequence of the Poincaré duality. We recall briefly the basic constructions on étale cohomology such as the cycle class of divisors, trace mapping, and so on.

I present historical background, contemporary status, and potential future development of the psychology of religion (PoR) in Greece, beginning with its origins: the formative people, places, and various intellectual schools of thought. Writing about the current state of the topic, I 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.

I 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.

This chapter examines the rise of government-run pharmacies during the Song dynasty as a lens through which to explore the state’s active role in shaping the healing marketplace and medical literature. These pharmacies not only sold pre-prepared prescriptions but also published self-help manuals. These manuals cataloged the full range of prescriptions available at the government-sponsored drugstores, along with the symptoms they were intended to treat. By promoting ready-made, prepackaged medications accessible directly to the public, the Pharmacy Formulary helped pioneer a new genre of self-help medical treatises. This development enabled patients to bypass physicians altogether, threatening physicians’ livelihoods and intensifying competition in an already crowded medical marketplace. In response, many learned physicians sought to defend the value of their expertise by emphasizing the nuanced skill required to match even standardized drugs to individual patients’ bodily conditions and disease progressions. This emphasis on diagnostic and therapeutic sophistication became a recurring theme in medical writings for centuries to come.

This chapter establishes the relation between pseudorandom graphs and Ramsey theory, using a variety of constructions, including superline graphs and random block constructions. A particular focus is on off-diagonal Ramsey numbers, and the asymptotics of the Ramsey number r (4, t), as well as the general transference theorem from extremal graph theory to Ramsey numbers r (F, t).

This chapter explores how fashion journalism shaped the development of the realist novel in nineteenth-century France. Drawing on scholarship that explores the interdependence of these forms of writing, it notes that both fashion journalists and novelists including Honoré de Balzac, Gustave Flaubert, and Emile Zola seek to create what Roland Barthes described as the “reality effect” – in which the inclusion of particular details generates in the reader the sense that a text describes the real world. Ultimately, this chapter argues, the fantasy of fashion lies at the heart of the fantasy of realism as a way of representing the word, from fictional depictions of the values and mores of different social worlds to attempts to capture the experience of urban modernity. Hence fashion and femininity – though often dismissed or diminished by male realist novels – are at the heart of their literary innovations.

Young people are often excluded from placemaking decisions, despite being among the most affected by changes to local environments. This chapter examines Design Your Neighborhood (DYN), a place-based action civics curriculum implemented in middle schools in Nashville, Tennessee. DYN introduces students to urban design and engages them in participatory community development and decision-making. Drawing on qualitative data from eight focus groups across seven schools, the chapter explores how young people perceive and relate to their communities. Guided by sense of place theory, the analysis highlights students’ values, including community connectedness, safety, inclusivity, accessibility, and housing security. Students also identified ideas for improving their neighbourhoods, reflecting their aspirations in the context of Nashville’s rapidly changing built environment. The findings suggest that incorporating young people’s perspectives not only strengthens their sense of place but also provides valuable insights for cities seeking more inclusive, resilient, and equitable approaches to urban development.

This chapter theorizes and puts into practice the use of fashion in feminist historiography. It does so by charting two histories of the modernist poet and artist Mina Loy. One is narrated via Loy’s 1940s designs for a “corselet,” intended to correct curvature of the spine in a woman’s middle age. The other is via the poetic series Loy wrote at the same time, “Compensations of Poverty,” in which she identifies with a group of outcast people in fashion contexts. These histories augur different versions of Loy, with different temporalities: one capitalist, teleological and individualist, based on the opportunities offered by new plastic materials; the other intersubjective, cyclical and, this chapter argues, sustainable. Ultimately the chapter asks: which of these Loys do we want, now, in the context of climate catastrophe and persistent sexism? How can fashion help us write the feminist history we need?

Between 2010 and 2012, a catastrophic earthquake sequence devastated Christchurch, a colonial city built on Ngāi Tahu ancestral land in Canterbury, New Zealand. This chapter explores how government agencies, including public health services, collaborated with mana whenua (Ngāi Tahu, the local Māori tribe) to rebuild Ōtautahi Christchurch in ways that respect its colonial past while looking to a climate-challenged future. The rebuild sought to integrate natural environmental features and symbolic markers significant to mana whenua, while also promoting health, wellbeing, and a renewed sense of place for all residents. Writing as three Tangata Tiriti (settler-colonial) women, we draw on our professional roles in public health, urban design, landscape architecture, and strategic planning. We reflect on our involvement in planning and policy implementation, considering what worked well, what fell short, and our hopes for a future city that fosters resilience, inclusivity, and belonging.

Machines are becoming more autonomous and intelligent, capable of making decisions and interacting with their environment. As they become more ubiquitous in our daily lives, it becomes increasingly important to understand and model their behaviour. This chapter will discuss the concept of machine behaviour and its importance in various fields, including artificial intelligence, robotics and human–computer interaction. The chapter starts by defining machine behaviour and providing an overview of its key characteristics. It will then explore the different approaches to modelling and understanding machine behaviour, including rule-based systems, statistical models and deep learning techniques. The chapter also covers the challenges and limitations of modelling machine behaviour, including the black box problem, interpretability and ethics. It also focuses on the applications of machine behaviour in various domains, such as autonomous vehicles, robotics and cybersecurity. The chapter will highlight how machine behaviour models can help in improving the performance, safety and security of these systems. The chapter discusses the future of machine behaviour and its potential impact on society. The chapter will explore the ethical implications of autonomous machines, including issues of responsibility, accountability and transparency. It will also discuss the need for interdisciplinary research in machine behaviour.

On the surface, behavioural data science and physics seem to be two disparate fields of research. However, a closer examination of problems solved by them reveals that they are uniquely related to one another. Exemplified by the theories of quantum mind, cognition and decision-making, this unique relationship serves as the topic of this chapter. Surveying the current academic journal papers and scholarly monographs, we present an alternative vision of the role of quantum mechanics in the modern studies of human perception, behaviour and decision-making. To that end, we mostly aim to answer the ‘how’ question, deliberately avoiding complex mathematical concepts but developing a technically simple computational code that the readers can modify to design their own quantum-inspired models. We also present several practical examples of the application of the computation code and outline several plausible scenarios, where quantum models based on the proposed do-it-yourself model kit can help understand the differences between the behaviour of individuals and social groups.

This chapter provides a collective portrait of the women in the family of the Northern Song statesman, Han Qi, based on Han’s funerary biographical work. Part one introduces Han the biographer and provides an overview of the women he recorded. This is followed by an examination of the Han women as female prototypes and individuals of unique talents and distinctive personalities. While these women were depicted as feminine exemplars, none of them appeared “faceless,” nor were they lauded for simply performing their designated domestic tasks. In addition to fulfilling their familial roles and duties, each woman navigated unique circumstances and showcased a diverse range of talents and personalities. Han Qi the biographer showed no reservations in expressing his affection for these women, acknowledging their contributions to the family, admiring their abilities and accomplishments, and mourning their loss. In addition to offering a close look at three generations of women in one scholar-official family, this chapter delves into Han Qi’s representation of female virtue and ability in the context of his emotional life and family preservation project.

‘Liveability’ is an important and well-recognised term applied across large cities worldwide and highly relevant to key international policy agendas including the United Nations Sustainable Development Goals. However, the application of urban or city-centric liveability in regional and rural communities remains contested. This chapter will explore the understanding of liveability in regional and remote contexts across Australia, focusing on the development of new spatial methods to measure and assess liveability in regional and rural towns across the state of Victoria in south-eastern Australia. The chapter will explain the research context, partnership development, spatial methodologies, and indicators developed and applied to measure liveability, knowledge translation, and lessons learned from the research. This work has become increasingly relevant post-COVID-19 with a surge in ‘tree-change’ and ‘sea-change’ migration to regional Victoria and elsewhere across Australia. Data for mapping rural and regional liveability are urgently needed to inform policies to protect regional amenity and character

Coming in the wake of the ‘heroic’ 1790s, the 1800s may seem the ‘fen of stagnant waters’ described in William Wordsworth’s ‘London 1802’. This essay instead treats the decade as one of political abeyance, a pause of sorts when inchoate forces that would come to shape the liberal politics of the nineteenth century were gathering beneath the surface. Its title draws upon a letter William Roscoe wrote supporting Catholic Emancipation in 1805, one of many emergent causes that did not succeed until the late 1820s. From this perspective, the essay reassesses the familiar story of the re-orientation of Wordsworth and Coleridge, the re-invigoration of London radicalism, and the less-remarked emergence of the poet and publisher James Montgomery, whose case history testifies to the new energies of English provincial opinion that opposed the government’s war policy, supported the abolition of the slave trade, and fostered the talents of women writers.