This chapter covers basic theory and constructions of randomized hash functions. Then it presents several applications in complexity theory, including isolation of witnesses, approximate counting and sampling of witnesses, randomness-efficient amplification, and streaming algorithms.

The Old English exile elegies attempt to recuperate loss by reiterating an inverted set of social and physical landmarks, mapping the past onto the present. The familiar imagery of the hall, the lord, and the voices of other human beings – the relationships that constitute community – are not absent in exile: instead, in the absence of the “real thing,” each exile must reconstruct and reiterate a set of replacement landmarks to understand their current situation. Similarly, The Ruin navigates the loss of living memory by imagining the past context necessary to fit its subject back into the fabric of a living world. The frequent depiction of the exile elegies as nostalgic, repetitive, or static is not an incidental formal element, but a core response to the loss of relational landmarks. In exile, alienation from the past—the spoliation of memory as well as the loss of community—suspends the relational self in time. Yet the Old English exiles continue to navigate inverted relational landmarks of identity. The solution is not to abandon relational reiteration; it is instead to seek a new point of departure when familiar points of reference are lost.

This chapter examines the often harmful consequences of the deliberate anthropomorphizing of generative AI (GenAI) chatbots by tech companies. Developers intentionally fine-tune systems to be human-like and accommodating, employing strategies like personalization, fostering dependency, offering excessive empathy (sycophancy), adopting a servility model, and promoting endless conversationality, all to maximize user engagement and monetization.

The chapter details how this strategy prioritizes profit over user welfare, leading to unintended and severe consequences, including psychological harm, increased social isolation, and the spread of dangerous misinformation, particularly in fields involving highly vulnerable people, such as mental health and education. The analysis criticizes the lack of accountability from AI companies, which often disclaim responsibility for the harms their products cause.

The fields of human rights and public health intersect in important and interesting ways. Building upon advances in the Health and Human Rights movement in the late twentieth century, practitioners and educators in public health increasingly address the ways in which population health can be advanced and strengthened through an explicitly rights-based approach. Public health, which focuses primarily on community-level prevention, utilizes an interdisciplinary approach in research and teaching to ensure awareness of and respect for human rights. The Right to Health is essential for population well-being, but operationalizing this right has proven challenging and controversial. The need to take a more holistic view of health requires attention to the broader social determinants of health. Public health educators and researchers have started to utilize theoretical and methodological approaches drawn from the natural sciences, social sciences, law, and humanities to address key issues related to health and human rights in a global context.

This chapter integrates empirical research on the pains of imprisonment with psychological and neuroscientific insights into the nature, sources, and effects of social pain, including its connection to the fundamental human need to belong. It argues that social pain provides a comprehensive framework for situating the pains of imprisonment – outlined in Chapter 3– within a unified conceptual construct. This argument rests on three interrelated premises. First, the contexts of exclusion that elicit social pain – social isolation, rejection, and ostracism – closely mirror the layers of exclusion that define the various domains of prison life. Second, the effects of social pain – particularly when pervasive or prolonged – on psychological well-being, behavior, and health significantly overlap with those documented among incarcerated individuals, both during and after imprisonment. Third, the psychological mechanisms that lead people to cause social pain in others, while underestimating its consequences, similarly underpin the logic of punishment, including the tendency to minimize the actual harms of the prison experience. Building on these premises, the chapter develops the book’s central claim: that the real pain of carceral punishment ultimately resides in the systematic threat to the fundamental human need to belong.

The chapter describes the case of a 45-year-old male with stage 3 HIV who presents to the ED with fever, shortness of breath, pleuritic chest pain, and nonbloody diarrhea. The patient exhibits tachycardia, hypoxia, and a warm, diaphoretic appearance. Initial actions include oxygen supplementation, IV fluids, and labs. The patient is diagnosed with HIV pneumonia, likely Pneumocystis jirovecipneumonia (PCP), and is treated with antibiotics and steroids. Early recognition of fever and hypoxia, along with respiratory isolation, is critical to prevent sepsis. Tests ordered should include CBC, electrolytes, liver function tests, urinalysis and culture, blood cultures, and CXR. Focal infiltrates suggest bacterial pneumonia, while a diffuse interstitial or perihilar, granular pattern on CXR is associated with PCP. Steroids should be given to patients with a partial pressure of arterial oxygen <70 mmHg or an alveolar–arterial gradient of >35 mmHg.

This chapter describes a case of a 45-year-old male with stage 3 HIV who presented to the ED with fever, shortness of breath, pleuritic chest pain, and nonbloody diarrhea. The patient was diagnosed with HIV pneumonia, likely Pneumocystis jiroveci pneumonia(PCP), and was treated with antibiotics, steroids, oxygen supplementation, and IV fluids. The chapter emphasizes the importance of recognizing the symptoms of pneumonia in HIV patients and providing early treatment to prevent sepsis. The chapter also provides guidelines for diagnostic tests and highlights the significance of CD4 counts in the development of pulmonary disorders in HIV patients.

Social network ties represent an important and complex confluence of sundry social processes and their consequences. It is an enduring fact of life that the more socially connected a person is, the better off they are. This goes for well-being, for health, for social stature, for popularity and prestige, for social mobility, and for access to material resources. Social connections give people power. They plug people into a switchboard of opportunities and resources, making them part of a resource-rich social system. Social connections liberate people from the stringencies of what might otherwise be stultifying conditions of everyday life. They create trust and produce the capacity for collective action to deal with local and regional social problems. They help people live longer lives. And social connections generally make life more fun, and richer, in every sense of those terms. It is a bundle of benefits that cannot be unwound. This introductory chapter lays out the primary motivation behind this book, which is an attempt to understand whether everyone has equal access to these valuable social resources, and whether they are so potent as to substitute for other valuable resources, such as wealth and prestige, in shaping people’s life chances.

The overarching question that guides this chapter is: Are social ties, and the resources they represent, equally distributed throughout society? That is, are these connections so free and abundant that they transcend the relentless constraints that people face in obtaining other forms of capital? In particular, do people from disadvantaged backgrounds enjoy the same level of access to such ties as wealthy people? This requires close examination of factors such as people’s connectedness to friends and family; the number of such ties they have and how often they engage them; how much turnover and instability there is in people’s networks; the internal wiring of the networks in which they are embedded, and how that relates to dense connections and brokerage potential; the status and wealth of their contacts; involvement in exchange processes; and connections to community organizations. This chapter navigates the thicket of findings regarding the distribution of these various forms of social capital by first walking through analyses of personal, micro-level connections, and then proceeding upward to more macro-level, organization-oriented indicators. This set of analyses reveals some latent, surprising, and fateful truths about how universally bountiful and reachable these valuable social resources really are.

Chapter 10 examines a different type of long-run consequence. Various counties spent different amounts of time “on the frontier” and had different levels of absolute and relative homesteading.

Both Ibn Bājja and Ibn Ṭufayl – readers of al-Fārābī in the Islamic West – subscribe to the broad strokes of al-Fārābī’s ideas about humanity. However, in their works on the individual’s mystical journey, they take the gulf between the few and the many so seriously that they ponder whether and how a shared social life between those of excellent and deficient fiṭra is possible or desirable. They both agree with al-Fārābī that human beings share some form of a basic, created nature, or fiṭra; and, broadly speaking, they agree that humans’ fiṭar can be better or worse, which mostly influences people’s access to knowledge. However, they call into question the ability of those of excellent fiṭra to guide or live among those of lesser ones as al-Fārābī had envisioned. As part of this shift in interest, they zoom in on larger, social and political questions. These two Andalusian thinkers powerfully underscore the contested and copious nature of fiṭra and how engagement with fiṭra is part of larger questions about the necessity or possibility of human sociality and the nature of power relations.