This chapter discusses nonuniformity, which means using different algorithms for different input sizes. First, the chapter presents evidence that nonuniformity is unlikely to help solve NP-complete problems efficiently. Then the models of logic circuits and branching programs are introduced, elaborated, and shown to capture nonuniform time and space complexities, respectively.

This chapter is about parallel computation, in which many processors collectively perform a lot of work simultaneously in each time step. Fast parallel algorithms for arithmetic are presented. Then the chapter shows close relationships between space, parallel time, and logic formulas. The chapter concludes with a surprising equivalence between parallel time and narrow branching programs.

This chapter covers techniques for lower bounding the size of circuits and formulas. This includes gate elimination, polynomial approximation, the switching lemma, formula shrinkage, communication complexity, and monotone circuit lower bounds. The chapter concludes with the natural proofs barrier, which shows that known types of circuit lower bound techniques are inherently insufficient to separate P from NP.

Chapter 7: Crucial to any legal system is the plaintiff’s ability to get the defendant into court, and the supervision of the process in civil suits. In Rome the praetor decided if there was a case to answer, and presented a formula to the judge outlining the main issues. The formulary system was gradually superseded in the first century ad by cognitio, in which there was only one stage, before a magistrate, who heard the case himself and reached a judgement. Criminal cases were heard in public jury courts, and the charge was brought by a private individual (delator). Roman society was litigious, and it is useful to examine the experience of appearing in court, the place of the litigant, the availability and role of advocates, and the extent to which the state could ensure fairness in a system weighted in favour of the wealthy and the socially advantaged. State and citizen came in contact through the legal process and the courts.

The foundations of modern probability theory are briefly presented and discussed for both discrete and continuous stochastic variables. Without daring to give a rigorous mathematical construction – but citing different extremely well-written handbooks on the matter – the axiomatic theory of Kolmogorov and the concepts of joint, conditional, and marginal probability are introduced, along with the operations of union and intersection of generic random events. Eventually, Bayes’ formula is put forward with some examples. This will be at the cornerstone of statistical inference methods reported in Chapters 5 and 6.

The concept of a ‘formula’ (Formel) plays an important, if complicated, role in Kant’s ethics, especially in the Groundwork. The concept of a formula also plays an important role in Stoic accounts of moral reasoning in the Latin sources, Cicero and Seneca. This chapter explores the place and function of this concept in Stoic ethics and its origins in Roman legal theory and practice. It then raises the question of the relationship between the Kantian and Stoic uses of the concept, asking whether this is a case of direct influence of Stoicism on Kant’s moral philosophy. The chapter comes to no definite conclusion on the question, but aims to provide comparative materials that may help others to address the question.

The prevalence of direct speech in Homeric epic plays a key role in fostering audience engagement with the poems. The speeches in the Homeric epics include some features that closely resemble those found in ordinary spoken speeches and conversations, and others that are evidently stylized for the artistic medium of oral poetry.

This essay gives an overview of Milman Parry’s pioneering contributions, through fieldwork and scholarship, to the study of the Homeric epics as oral poems composed in performance.

Chapter eight, “Infectious Intestinal Disease and Global Public Health,” explores the major challenges to and advances in the control of infectious intestinal diseases since 1970s, when new sets of actors took up the crusade against diarrheal diseases. Physicians and activists organized in response to a spike in infant deaths in the Global South linked to bottle-feeding. Nongovernmental agencies and national politicians encouraged behavioral change to end open defecation. Biomedical scientists developed additional vaccines against poliovirus and rotavirus. Epidemiologists threw new light on the global prevalence of diarrheal diseases and regional disparities in childhood survival rates. The new focus on biomedical interventions and programs of community- or national-level behavioral change constituted a new era in the control of infectious intestinal disease.

Deals with the perceived conventional and formulaic aspects of the style, starting with a discussion (and defence) of convention itself. I show how through various forms of distortion and contextual manipulation, conventions and formulas may be renewed. One such convention is the grammatical essential of the cadence, which is often refreshed when a simple, understated cadential formulation appears to undercut a preceding passage of a brilliant or emotionally heated nature. I consider how this and other such patterns demonstrate a taste for reduction, ‘to say more with less’, showing a creative distrust of a certain kind of rhetorical eloquence. Another way of understanding such manoeuvres is that they compel the attention of the listener, and this term is found frequently in writings on music of the time. Its opposite state, boredom, is, I argue, ‘written into’ some music in the form of distractions and non sequiturs. A further type of renewal of attention can be achieved by mixing up or conflating the three formal functions of beginning, middle and ending, and the final portion of the chapter considers the handling of such functional signs.

This chapter is dedicated to showing the technique used by John to portray himself as an eyewitness: description. This description, in the classical rhetorical tradition of ante oculos ponere, engages the audience in the narrative by giving them the opportunity to visualize what John himself saw. For example, descriptions introduced by the phrase ?a? e?d?? are rendered as though they formed part of a transcription of a vision made at the very moment it occurred. This is why they appear in the text ex abrupto, marked only by the introductory sign ?a? e?d??, a device habitually used to signal the reader/listener that a given vision has occurred unexpectedly. The ?a? e?d?? structure mimics the mechanics of sight. However, the descriptive forms employed in the book of Revelation are not limited to the use of this ?a? e?d?? pattern. On the contrary, throughout the text John employs six other kinds of descriptions: 1) ????sa ?a? e?d?? descriptions, or ecphrasis; 2) e?d??-????? descriptions; 3) t? p???e??µe?a descriptions; 4) ?a? e?d?? ???e??? descriptions; 5) ?? t? d????se? descriptions; 6) t?p?? or t?p???af?a descriptions.

If description facilitates the effect of ante oculos ponere, one can also state (echoing Cicero) that direct speech confers upon John the power ad aures ponere, allowing him simultaneously to appear as a mere spectator and aural witness to what he has heard. This explains the recurrent use of the lexeme ????sa throughout the entire account. As we know, direct speech facilitates the momentary concealment of the narrator. John deftly uses this device to shift the protagonist role to the voices that he hears. To recreate the dramatic action, the author of the book of Revelation borrows various techniques from tragedy: the chorus; a frequent recourse to deixis; the use of dialogue to indicate movement; and messenger speeches. As though these theatrical devices were not sufficient to express what the narrator heard, the author also makes use of the dramatized epistolary form. In addition, we must remember that John also witnessed an aural environment replete with celestial chanting, the sound of trumpets, etc. Through language, the audience is immersed in the revelation’s aural context. Finally, John is aware that his text will be read aloud; this explains the use of the oral style.