In this chapter, we begin our dive into the fundamentals of network data. We delve deep into the strange world of networks by considering the friendship paradox, the apparently contradictory finding that most people (nodes) have friends (neighbors) who are more popular than themselves. How can this be? Where are all these friends coming from? We introduce network thinking to resolve this paradox. As we will see, It is due to constraints induced by the network structure: pick a node randomly and you are much more likely to land next to a high-degree node than on a high-degree node because high-degree nodes have many neighbors. This is unexpected, almost profoundly so; a local (node-level) view of a network will not accurately reflect the global network structure. This paradox highlights the care we need to take when thinking about networks and network data mathematically and practically.

Network studies follow an explicit form, from framing questions and gathering data, to processing those data and drawing conclusions. And data processing leads to new questions, leading to new data and so forth. Network studies follow a repeating lifecycle. Yet along the way, many different choices will confront the researcher, who must be mindful of the choices they are making with their data and the choices of tools and techniques they are using to study their data. In this chapter, we describe how studies of networks begin and proceed, the life-cycle of a network study

This chapter explores the relationship between climate distress – particularly fear and sadness about climate change – and clinical-level psychiatric symptoms in children and young people, focusing on pediatric anxiety and depression. In response to societal tendencies to under- or overplay the mental health risks of climate emotional impacts, it describes the spectrum of healthy and unhealthy pediatric anxiety and depression, the role that chronic stress and direct climate impacts play on child and adolescent brain development and clinical syndromes, and the ways that responding emotionally to climate change can influence youth identity development and emotional strength. The chapter provides a template for how to assess young people’s climate emotions clinically, offering several detailed case descriptions to illustrate how stress, psychopathology, psychological and brain development, and climate emotions can weave together to influence the sum of a young person’s presentation. As parents’ and other adults’ responses play a key role in whether these emotions evolve to a clinical level, it also suggests some best practices for interacting with climate-distressed youth to minimize poor clinical outcomes.

Water shapes the planet and all life upon it. Breaking down traditional disciplinary barriers, this accessible, holistic introduction to the role and importance of water in Earth’s physical and biological environments assumes no prior knowledge. It provides the reader with a clear and coherent explanation of the unique properties of water and how these allow it to affect landscapes and underpin all life on Earth. Contemporary issues surrounding water quality – such as the rise of microplastics and climate change – are highlighted, ensuring readers understand current debates. Giving all of the necessary background and up-to-date references, and including numerous examples and illustrations to explain concepts, worked mathematical calculations, and extensive end-of-chapter questions, this is the ideal introductory textbook for students seeking to understand the inextricable links between water and the environment.

In addition to knowledge of information (details and organising ideas), students also need to develop the skills and processes needed to complete mental tasks, for example, how to do long division, how to read a map and how to write in a specific genre. This domain of knowledge is called mental procedures. Mental procedures are learned through practice and are executed when needed to complete a task. Mental procedures occur inside a person’s brain. Educators use pedagogies to help students to learn these procedures and, once learned, to activate and facilitate this mode of thinking. This chapter will focus on how digital technologies can be used to support these pedagogies while also exploring some new opportunities.

This chapter begins by explaining mental procedures domain of knowledge. After using the TPACK model (see Chapter 3) to highlight the importance of intentionally using digital technologies, it then explores how they can be used to develop mental procedures and to guide student’s when using mental procedures.

Problems with calculations of Berry properties in real and reciprocal spaces and physical characteristics involving manifestations of Berry properties are included.

This chapter presents the Laplace transform, which is as fundamental to continuous-time systems as the z-transform is to discrete-time systems. Several properties and examples are presented. Similar to the z-transform, the Laplace transform can be regarded as a generalization of the appropriate Fourier transform. In continuous time, the Laplace transform is very useful in the study of systems represented by linear constant-coefficient differential equations (i.e., rational LTI systems). Frequency responses, resonances, and oscillations in electric circuits (and in mechanical systems) can be studied using the Laplace transform. The application in electrical circuit analysis is demonstrated with the help of an LCR circuit. The inverse Laplace transformation is also discussed, and it is shown that the inverse is unique only when the region of convergence (ROC) of the Laplace transform is specified. Depending on the ROC, the inverse of a given Laplace transform expression may be causal, noncausal, two-sided, bounded, or unbounded. This is very similar to the theory of inverse z-transformation. Because of these similarities, the discussion of the Laplace transform in this chapter is brief.

This chapter argues that in the period under review, Australia’s foreign-policymaking faced a number of challenges, most notably in its handling of bilateral relations with China, which took a significant turn for the worse. Unfortunately, this was also a time when Australians of Chinese heritage made little contribution to foreign policy. Despite Australia’s multicultural identity and a professed embrace of the strength and diversity of its growing migrant populations, low numbers of Chinese Australians were working in government and politics. By drawing on data from the 2019 Lowy Institute Poll on Australian attitudes towards the world, this chapter argues that Asian Australians had different views on foreign policy compared to those born in Australia. If Australia is to truly embrace its growing migrant population to engage confidently with its Asian neighbours, the chapter concludes, the views of Asian Australians in political debates and policymaking matters need to be formally recognised through greater representation.

Violence is common and is a public health issue. Forensic psychiatrists offer treatment for the small amount of violence that is due to mental disorder. It is essential to distinguish between meaningful explanations and causes. Violence is not a unitary concept. Evidence for the specific causal associations between mental illness and violence is reviewed. Anger, anxiety, moral and amoral actions are reviewed including intoxication and withdrawal, deception, antisocial personality and psychopathy, and a range of mental illnesses and developmental disorders. Social and developmental factors are also important. Memes, media and social contagion influence the forms of violence. Court reports and treatments are considered critically in relation to violence.

Water shapes the planet and all life upon it. Breaking down traditional disciplinary barriers, this accessible, holistic introduction to the role and importance of water in Earth’s physical and biological environments assumes no prior knowledge. It provides the reader with a clear and coherent explanation of the unique properties of water and how these allow it to affect landscapes and underpin all life on Earth. Contemporary issues surrounding water quality – such as the rise of microplastics and climate change – are highlighted, ensuring readers understand current debates. Giving all of the necessary background and up-to-date references, and including numerous examples and illustrations to explain concepts, worked mathematical calculations, and extensive end-of-chapter questions, this is the ideal introductory textbook for students seeking to understand the inextricable links between water and the environment.