The fourth chapter introduces the singular value decomposition (SVD), a fundamental matrix factorization with broad applications in data science. The chapter begins by reviewing key linear algebra concepts, including matrix rank and the spectral theorem. It then explores the problem of finding the best low-dimensional approximating subspace to a set of data points, leading to the formal definition of the SVD. The power iteration method is presented as an efficient way to compute the top singular vectors and values. The chapter then demonstrates the application of SVD to principal components analysis (PCA), a dimensionality reduction technique that identifies the directions of maximum variance in data. Further applications of the SVD are discussed, including low-rank matrix approximations and ridge regression, a regularization technique for handling multicollinearity in linear systems.

Immigration is one of the most politically charged aspects of human rights law. This chapter examines the application of Article 8 ECHR in cases where migrants face deportation and where family members seek entry to the Contracting State. In practice few applicants succeed in using Article 8 ECHR to resist deportation even in cases where they were born or lived almost their entire life in the State. This has led to the criticism that the ECtHR prioritises State sovereignty, above migrants, rendering the rights virtually meaningless and legitimising States’ practices. An opposing perspective is that the process of having to justify deportation to an international human rights court is an incursion into State sovereignty that exceeds the limits of the ECtHR’s role. The case law on family reunification is equally contested by both those that believe the ECtHR is exceeding its legitimate function and those that believe the ECtHR is averting its eyes to the hardship and suffering of migrants. The final part of this chapter examines the ways in which Article 8 ECHR has been shaped by domestic immigration law and the driving forces behind the interpretation and application of rights.

The goal of this chapter is to introduce systemic racism and critical race theory. It begins with the story of Breonna Taylor, a successful health-care professional and twenty-six-year-old Black woman who was killed in her home in Louisville, Kentucky, by plainclothes White police officers in 2020. It galvanized the Black Lives Matter movement against systemic racism, the approach to racism that recognizes that all institutions and persons play a role in it, including us. This chapter reviews the history of police violence in the US, the defining features of systemic racism and popular myths about it, and some major themes in critical race theory, a framework that can help us see why race and racism were invented and why they persist despite reform. Colorblind racial ideology, multiculturalism, and anti-racism are discussed as strategies that deal with racism. The chapter includes a Food for Thought section on Nikole Hannah-Jones and the 1619 Project. It ends with a discussion of anti-racism, police violence, and justice for Breonna Taylor.

This chapter examines the human rights implications of the UK’s legal response to terrorism, focusing on the ECHR. It explores the significant body of terrorism legislation that has evolved over the past three decades, considering also the legacy of The Troubles. There are myriad rights that may be impacted by terrorism legislation including the right to life, freedom from ill-treatment, right to liberty, right to a fair trial, freedom of religion, freedom of expression, freedom of association and the right to enjoy such rights free from discrimination. Having regard to the evolving nature of terrorist threats including, for instance, inceldom and right-wing extremism, and the increasing role of online modes of communication, the chapter examines the potential limitations of the existing legal framework in responding to terrorism. The chapter further explores the role of the derogation power under Article 15 ECHR in the counter-terrorism context and the potential for a progressive dilution of rights as courts are called upon to accommodate within the existing rights rubric increasingly restrictive terrorism legislation.

International law arose in the mid nineteenth century when European powers determined to codify and formalize customary law, to restrain the use of violence in armed conflict, and to create certain protected categories of people. The Hague and Geneva Conventions formed the core of the emerging laws of war and international humanitarian law. While the Conventions have been breached at times, they still form one of the most widely accepted and long-standing aspects of international law. International humanitarian law and laws of war clarify and formalize the differentiation between civilians and combatants, regular and irregular forces, lawful and unlawful combatants. While international laws attempt to make the demarcation of these boundaries as precise as possible, the realities of war always undermine and undo such delineation efforts. Recently, there have been increasing efforts to regulate these gray areas and create international laws and agencies to regulate groups that elude classification.

The goal of this chapter is to introduce the Black maternal mortality crisis and intersectionality. It begins with the story of Kira Johnson, an accomplished Black businesswoman, mother, and wife living in Los Angeles, California. Kira died due to medical neglect after giving birth to her second son, Langston, in 2016 and her death illustrates the Black maternal mortality crisis in the US, the highest among rich countries in the world. This chapter reviews the concept and popular myths on gendered racism, how sexism and racism intersect and combine in the experience of Black women, girls, and femmes. It introduces intersectionality, a valuable tool to understand and dismantle gendered racism driving this Black maternal health crisis, and other intersecting systems of power. Intersectionality is discussed as a field of study, an analytical approach, and as critical action. The chapter includes a Food for Thought section on the Page Act of 1875 and the Atlanta spa shootings of 2021. It ends with a discussion of Kira Johnson and reproductive justice.

The goal of this chapter is to introduce dehumanization and humanness. It begins with the story of Carmelita Torres, a seventeen-year-old adolescent girl from Juárez, Mexico. In January 1917, she was asked to get naked, shave her hair, and take a kerosene bath by US immigration authorities when she was coming to work as a maid in El Paso, Texas. The story of Carmelita illustrates dehumanization, the denial of people’s full humanity. This chapter examines popular myths and different forms of dehumanization, such as treating people like animals (animalistic dehumanization), objects (mechanistic dehumanization), and supernatural beings (mystic dehumanization). To confront dehumanization, we need to affirm our humanness, the dignity and wholeness of all human beings that makes them unique, free, and entitled to rights. Carmelita and others affirmed their humanness by protesting in the 1917 Bath Riots. The chapter includes a Food for Thought section on Halloween, blackface, and redface. It ends with a discussion of Carmelita Torres and the affirmation of our humanity.

Are there objective criteria that we can use to discern if an act of violence constitutes terrorism, or is such labeling always a subjective and political decision? Wherein lies the boundary between domestic versus international terrori and is that a meaningful distinction to make? How do individuals get radicalized, and how do they reach the point of committing violent acts? In this chapter, we tackle these questions (and others) and the issue of terrorism in international security. There are no easy, agreed upon answers to most of them, and terrorism continues to be a highly contested and politically charged concept, while constituting a very real and pressing security threat in many countries around the world. But that is even more reason to look closely at the controversies surrounding its definition, its historical evolution and patterns, and its contemporary manifestations in the twenty-first century as well as approaches to countering terrorism and attempts at international cooperation.

The goal of this chapter is to introduce the concepts of the American nightmare and Whiteness as property, supremacy, and violence. It begins with the case of Melvin Davis and Licurtis Reels, two Black brothers from North Carolina who lost their land in 2011 but refused to leave it. Black involuntary land loss is important for Justice, Equity, Diversity, and Inclusion in the US because it is a major driver of racial wealth inequities. This can be explained, in part, by Whiteness, a system built on antiblackness and anti-Indianism that creates and is created to put White people at the top of the US racial hierarchy through legal, cultural, and material means, such as property. This chapter examines some key facts about Black Americans, the meaning of the American nightmare, the defining features and popular myths about Whiteness, and how it was invented, and is justified, and defended. The chapter includes a Food for Thought section on Black prosperity and White riots. It ends with a discussion of two equities for reclaiming the American Dream.

Constructivism emphasizes the role of ideas, identities, and norms in shaping state behavior and international politics, as well as the intersubjective and relational nature of these ideational factors. Social relations “make or construct people – ourselves – into the kinds of beings that we are. Conversely, we make the world what it is, by doing what we do with each other and saying what we say to each other” (Onuf, 1998, 59). Constructivism therefore highlights the intangible yet relational aspects of our reality: a world in which the meaning of objects and actions is not fixed but socially constructed through our interactions; states are held together by collective belief and actively participate in the social construction of anarchy. Norms play a significant role by defining appropriate behavior and enabling action by providing a framework for actors to understand and interact with the world.