The Fourier transform pair is derived and various conventions in its definition discussed. It is shown how to obtain forward and inverse Fourier transforms for specific functions, which results in the completeness relation being formally proven. The basic properties of the Fourier transform are derived which include the symmetry properties of the real and imaginary parts, the shifting property, the stretching property, the differentiation property, Parseval’s theorem, the convolution theorem, and the integral-moment relations. The Fourier transform pair is then used to derive the two most important theorems of probability theory: the central-limit theorem and the law of large numbers. The Fourier transform is then used to solve various initial-value problems involving the diffusion and wave equation. The chapter concludes with the way Fourier analysis is key to performing time-series analysis of recorded data, which includes both filtering of the data and topics related to the data being recorded at discrete time intervals.

Readers are presented with achievable reforms of laws and policies discussed in earlier chapters.

This chapters traces the evolution of the Nova Holanda gang’s governance practices from the mid-1990s until the occupation of Maré by the Brazilian Military in April 2014 through the analysis of newspaper archives, oral histories with residents and gang members, and a dataset of anonymous gang denunciations. Following its integration into the Comando Vermelho faction, CVNH maintained a benevolent dictator regime, combining high levels of coercion with responsive benefits, until several years of warfare with their primary rival led to the use of extreme forms of coercion against residents as disorder prevailed. By 2004, the war between CVNH and Terceiro Comando Puro (TCP) had ended though enforcement continued to be active and frequent, leading to a social bandit regime, in which the gang offered significant benefits and engaged in low levels of coercion. Then, following the resurgence of TCP in 2009 until the arrival of the Brazilian military, CVNH can be considered a benevolent dictator gang once again. They ramped up their coercive behavior in response to TCP’s more aggressive posture while providing significant benefits to avoid frequent police enforcement efforts.

In the previous chapters we introduced the concept of valuation, which involved converting cash flows that are expected to happen in the future into today’s terms, and we learned about the returns on various assets and how to analyze the past performance of financial instruments to inform investment decisions. However, the future is not known for sure. The cash flows that occur may be different from what we initially expect, and the value (and rates of return) of financial instruments change over time. In this chapter, we introduce a fundamental concept in finance: Uncertainty about the future can affect valuation and decision making.

We begin by defining what risk is in finance, and how it affects financial decisions. We then dive into how risk can be managed, which includes identifying relevant risks, assessing how they can affect one’s financial situation, and then determining appropriate techniques that can be used to reduce these risks.

Before proceeding with our first steps in valuation, we need to introduce some tools and define some notation that will be used here and throughout the book when valuing assets.

At a fundamental level, the value of an asset comes from the cash flows that are associated with it—that is, from the amounts of money that the owner either receives or pays at various points in time. An essential tool in analyzing cash flows from any financial decision is a diagram known as a timeline, a linear representation of cash outflows and inflows over a period of time. A negative sign in front of a cash flow means that you are paying that amount of money (it’s a cash outflow from you). No sign means that you are receiving an amount of money (it’s a cash inflow to you).

Anaesthetists working in paediatric settings may care for patients ranging in age from preterm neonates to teenagers, some of whom will be undergoing relatively simple procedures for isolated conditions whereas others will have extremely complex needs and will be undergoing complicated, high-risk procedures. What all of these patients will have in common, however, is the need for developmentally appropriate communication from and with the professionals caring for them. Alongside an understanding and knowledge of the anatomical, physiological and pharmacological issues relevant to the care of the paediatric patient, anaesthetists also need an understanding of the developmental, communication, emotional and behavioural issues relevant to their paediatric patient. This chapter summarises some of the key theories of cognitive and psychosocial development, including beliefs about illness, and how these are relevant to the child undergoing anaesthesia. Effective communication with children and their families is central to the delivery of high-quality care, and this is discussed alongside the role of preparation and behavioural and psychological techniques in optimising experiences and outcomes for the child, family and anaesthetist.

The availability of data is a condition for the development of AI. This is no different in the context of healthcare-related AI applications. Healthcare data are required in the research, development, and follow-up phases of AI. In fact, data collection is also necessary to establish evidence of compliance with legislation. Several legislative instruments, such as the Medical Devices Regulation and the AI Act, enacted data collection obligations to establish (evidence of) the safety of medical therapies, devices, and procedures. Increasingly, such health-related data are collected in the real world from individual data subjects. The relevant legal instruments therefore explicitly mention they shall be without prejudice to other legal acts, including the GDPR. Following an introduction to real-world data, evidence, and electronic health records, this chapter considers the use of AI for healthcare from the perspective of healthcare data. It discusses the role of data custodians, especially when confronted with a request to share healthcare data, as well as the impact of concepts such as data ownership, patient autonomy, informed consent, and privacy and data protection-enhancing techniques.

This chapter takes its lead from Islamic poetry, which was practiced for centuries in Arabic, Persian, Ottoman-Turkish, and Urdu, in a geography extending from the Middle East to South Asia. Within that cultural universe, it focuses on the relation of the Ottoman lyric tradition to the environment. I address this tradition as the ‘last ring’ encircling a common Islamicate civilisation, after the Turkish critic Ahmet Hamdi Tanpınar’s arboreal tropology, which represents the stages of ‘Muslim Orient’s’ literary-cultural history as encircling each other like tree-rings. While surveying the greenery of the Middle Eastern literatures with an eye on the relationship to the environment they articulate or enable, this article also tests the suggestion that ‘[t]he “Middle East” is euphemism for what was the Ottoman Empire’.

This chapter looks at the Department of Child Safety and the criminal justice system. Child Safety often didn’t understand that a young person had a cognitive disability. Sometimes young people with cognitive disability were abused while they were in Child Safety. Young people with cognitive disability often did not get much help when they left Child Safety. Parents with cognitive disability often had their children removed from them by Child Safety. Some young people were abused by police. Young people with cognitive disability who went to prison didn’t get much help. They also found it hard when they left prison.

Anaesthesia for ENT surgery in children is varied, interesting and challenging. It ranges from grommet insertion and adenotonsillectomy, some of the most commonly conducted procedures in children, to the rare and evolving fields of airway reconstruction and EXIT procedures. Excellent teamwork and situational awareness are crucial to be safe and effective. This is particularly important in airway surgery given the small size of the paediatric airway, which is shared and often crowded with instruments, the sensitive physiology of small children and their frequent and complex comorbidities. Multidisciplinary team meetings and shared decision-making is increasingly important for these complex procedures and also on occasion for commonly conducted ENT procedures where there is a paucity of data around central issues such as postoperative admission criteria in children with obstructed sleep apnoea (OSA) and analgesia after tonsillectomy. Ultimately agreed local guidance should be followed as further investigations continue. An area of particular interest is the development of more effective modes of oxygenation such as high-flow oxygen delivery.

Artificial intelligence (AI) is increasingly adopted in society, creating numerous opportunities but at the same time posing ethical challenges. Many of these are familiar, such as issues of fairness, responsibility, and privacy, but are presented in a new and challenging guise due to our limited ability to steer and predict the outputs of AI systems. This chapter first introduces these ethical challenges, stressing that overviews of values are a good starting point but often fail to suffice due to the context-sensitivity of ethical challenges. Second, this chapter discusses methods to tackle these challenges. Main ethical theories (such as virtue ethics, consequentialism, and deontology) are shown to provide a starting point, but often lack the details needed for actionable AI ethics. Instead, we argue that mid-level philosophical theories coupled to design-approaches such as “design for values”, together with interdisciplinary working methods, offer the best way forward. The chapter aims to show how these approaches can lead to an ethics of AI that is actionable and that can be proactively integrated in the design of AI systems.

This chapter explains principles of safeguarding, the relevant law and statutory framework, the role of the anaesthetist in safeguarding, specific forms of abuse, the safeguarding process for children when concerns arise and the investigation process when a child dies.

This conversation brings together national and international policymakers to discuss the impact of digitalisation on access to justice. The background of the discussion is provided by the United Nation’s Global Goal 16 to ‘provide access to justice for all’. The policymakers contributing to this conversation represent the ministries of justice of Germany and Japan, the Organisation for Economic Co-operation and Development (OECD), the International Institute for the Unification of Private Law (UNIDROIT) and the Pathfinders for Peaceful, Just and Inclusive Societies. The discussants explore the potential of technology to provide meaningful access to law and justice. They do so within the context of their organisation’s policy initiatives such as digitalising courts and other justice institutions. Referring to reform experiences, they pay attention to facilitators and barriers of technological change. The policymakers also consider the risks of technology for access to justice and emphasise the need to keep digital vulnerability in mind.