Chapter 2 explores the fundamental concept of least squares, covering its geometric, algebraic, and numerical aspects. The chapter begins with a review of vector spaces and matrix inverses, then introduces the geometry of least squares through orthogonal projections. It presents the QR decomposition and Householder transformations as efficient methods for solving least-squares problems. The chapter concludes with an application to regression analysis, demonstrating how to fit linear and polynomial models to data. Key topics include the normal equations, orthogonal decomposition, and the Gram–Schmidt algorithm. The chapter also addresses the issue of overfitting in polynomial regression, highlighting the importance of model selection in data analysis. The chapter includes practical Python implementations and numerical examples to reinforce the theoretical concepts.

The goal of this chapter is to introduce anti-Asian racism and the COVID-19 pandemic. It begins with the story of Kristina Arevalo, an Asian American scholar pursuing a PhD in developmental psychology in New York City who experienced racial discrimination during the COVID-19 pandemic. This is consistent with the history of racial scapegoating in the US, a strategy of blaming Asian Americans for health and economic crises, as well as wars, that relies on fear and hate to justify violence against them. This chapter is informed by Asian critical race theory (AsianCrit), discusses who are Asian Americans, Native Hawaiians, and Pacific Islanders, some popular myths about them, and their place in a racial position model. It examines how anti-Asian racism is supported by the model minority myth, the Yellow Peril racist trope, the perpetual foreigner stereotype, and Orientalism. The chapter includes a Food for Thought section on the Delano grape strike and linked fate. It ends with a discussion of Kristina Arevalo and rethinking who is considered a “Real American.”

This chapter introduces the foundational mathematical concepts behind neural networks, backpropagation, and stochastic gradient descent (SGD). It begins by generalizing the Chain Rule and providing a brief overview of automatic differentiation, which is essential for efficiently computing derivatives in machine learning models. The chapter then explains backpropagation within the context of multilayer neural networks, specifically focusing on multilayer perceptrons (MLPs). It covers the implementation of SGD, highlighting its advantages in optimizing large datasets. Practical examples using the PyTorch library are provided, including the classification of images from the Fashion-MNIST dataset. The chapter provides a solid foundation in the mathematical tools and techniques that underpin modern AI.

The goal of this chapter is to introduce xenophobia against Latinx immigrants. It begins with the story of Carlos Gregorio Hernández Vásquez, a boy from an Indigenous Maya village in Guatemala, an exceptional student who migrated to the US with his sister, was separated from her, and died in custody of US Border Patrol in 2019. The story of family separation of Carlos illustrates anti-immigration policies and xenophobia against asylum seekers, refugees, and undocumented immigrants in the US. Informed by Latinx critical race theory (LatCrit), this chapter discusses who are Latinx people, some popular myths about them, and how they are treated in the US under laws such as Arizona SB 1070 that criminalized undocumented immigrants. It examines the differences between internal and international migration, voluntary and involuntary migration, and emigration and immigration. The chapter includes a Food for Thought section on 9/11, the War on Terror, and Islamophobia. It ends with a discussion of Carlos Hernández and the need for immigration reform.

Critical Security Studies (CSS) is a diverse and multidisciplinary field that approaches traditional security studies through a critical lens and examines the ways in which security discourses and practices reify and reinforce existing power relations and contribute to the marginalization, oppression, and precarity of various groups of people. CSS scholars ask whose security we center when we talk “Security,” and whose security we neglect or sacrifice, what issues are present/absent, who is afforded agency, and who appear only as voiceless victims. They examine the ways in which security and power are intertwined so that evoking security can generate power, enable various kinds of interventions, perpetuate relations of domination and subjugation, and reproduce social hierarchies. Many CSS scholars adopt an interpretivist methodology and normative approach to scientific knowledge; they are interested in analysis not just for the sake of it but for bringing about change to the status quo.

While the UK may not have a single, codified constitution or Bill of Rights instrument, it nevertheless has a long history of rights protection under the common law and through various legislative enactments including, most notably, the Human Rights Act 1998 which gives effect in domestic law to the core rights enshrined in the ECHR. In this chapter, we examine how rights are protected (including their enforcement) in domestic law in the UK, paying particular attention to the principle of legality and the powers conferred on the courts under the Human Rights Act 1998. Common law rights continue to develop and evolve alongside the Human Rights Act and they still act as a vehicle to protect rights and fundamental values.

To link the economic sphere of international relations to the security sphere of international politics in this chapter, we treat economics as a function of politics and security. While controversial in some circles, this need not be so. Economists, historians, and political scientists have distinct answers to questions concerning the economy. That they differ in scope, interest, and focus should be viewed as alternatives for assessing the empirical world, not mutually exclusive representations of it. This is fundamental to the interdisciplinary approach of International Security. It should be no surprise that the vastness and complexity of the global economic system intersect with realms outside the purview of economics. Security is an arena in which the politics of economic decision-making are felt most intensely.

This chapter considers the nature of human rights and its critiques. The language of human rights has become the common lexicon of social justice and the critical standard for assessing political institutions. Yet, whilst human rights law occupies a central place in our moral and legal discourse, there are many aspects of the human rights project which are contested. This chapter introduces the key debates as to the origins of human rights rights and the justifications advanced for the existence of human rights. This includes examining institutional critiques which focus on how rights should be enforced; as well as ideological critiques, which argue that the gaps in what is protected and who is protected mean that human rights law is itself part of the problem.

Freedom to protest is important for similar reasons to freedom of expression, it is, after all, a core form of political expression. Yet while protest is important, protests can also be disruptive, annoying, offensive, harmful and violent. In a rights-based system we thus have to consider where lines should be drawn between competing rights and interests and by whom. This chapter examines how the domestic and ECtHR case law reflects these tensions, with some cases leaning towards a more deferential approach and others establishing a more robust role for the courts. This chapter primarily examines Article 11 the right to freedom of association and assembly, but it also highlights the ways in which many of the other Convention rights safeguard the freedom to protest. In respect of domestic law, this chapter observes that the post-HRA period has also seen the enactment of far wider legislative restrictions than existed previously. There are also concerns about the growing use of surveillance, police brutality and increased restrictions on access to land.

The goal of this chapter is to introduce accessibility, democracy, and the need to confront ableism. It begins with the story of Alice Wong, an Asian American disabled activist and bestselling author who wrote about the barriers to vote faced by People with Dis/abilities like her during the COVID-19 pandemic. The story of Alice illustrates the challenges with voting in the US, a country that is now considered a flawed democracy and facing many institutional barriers, including voter suppression laws. Informed by dis/ability critical race studies (DisCrit), this chapter examines who are People with Dis/abilities, some popular myths about them, and how they are treated in the US when it comes to voting. Ableism, a system that treasures able-bodiedness and imposes it as the norm in society, is discussed as harmful to US democracy. To confront ableism and improve democracy we need accessibility, satisfying needs to allow full participation in a space or action. The chapter includes a Food for Thought section on interdependence and solidarity, from San Francisco to Gaza. It ends with a discussion of Alice Wong and the disability justice movement.

This chapter examines the role of human rights law in tackling modern slavery and human trafficking. It begins with Article 4 ECHR, which expressly prohibits slavery, servitude and forced or compulsory labour. It considers how each of those concepts has been defined by the ECtHR, how the ECtHR expanded Article 4 ECHR to include human trafficking, and why this was contested. Having examined the conceptual ambit of Article 4 ECHR it then considers the obligations associated with that right. Finally, it looks at how the UK seeks to satisfy its obligations through the NRM and the MSA. In this regard we will see that amendments made by the NBA and the IMA have starkly exposed growing tensions over, and resistance to, human rights law where it gives rise to obligations to those that have crossed a State’s border. Overall, this chapter thus highlights fundamental differences between the direction of travel in domestic law as compared with the direction of travel on the international plane.

This chapter focuses on the core concepts of optimization theory and its application in data science and AI. It begins with a review of differentiable functions of several variables, including the gradient and Hessian matrices, and key results like the Chain Rule and the Mean Value Theorem. The chapter then introduces optimality conditions for unconstrained optimization, explaining first-order and second-order conditions, and the role of convexity in ensuring global optimality. A detailed discussion of the gradient descent algorithm is provided, including its convergence analysis under different assumptions. The chapter concludes with an application to logistic regression, demonstrating how gradient descent is used to optimize the cross-entropy loss function in a supervised learning context. Practical Python examples are integrated throughout to illustrate the theoretical concepts.