A Pell–Abel equation is a functional equation of the form $P^{2}-DQ^{2} = 1$, with a given polynomial $D$ free of squares and unknown polynomials $P$ and $Q$. We show that the space of Pell–Abel equations with the degrees of $D$ and of the primitive solution $P$ fixed is a complex manifold. We describe its connected components by an efficiently computable invariant. Moreover, we give various applications of this result, including to torsion pairs on hyperelliptic curves and to Hurwitz spaces, and a description of the connected components of the space of primitive $k$-differentials with a unique zero on genus $2$ Riemann surfaces.

Although manuscripts are, literally, old media, they are also breaking news. This article reports from a study of scholars of ancient religions’ experiences with media engagement concerning manuscript finds and forgeries. Inspired by a mediatization-of-science perspective, the study explores the motivations for and involvement in public-facing scholarship, as well as the experienced effects of and reactions to their media exposure. Focusing on the challenges of media publicity in particular, the study discusses how the current impact and publicity agenda of contemporary universities affects individual academics.

The findings of this article are based on interviews with a sample of experts who, during the last twenty-five years, have shared their expertise in public-facing media outlets about the Gospel of Judas, the Hazon Gabriel tablet, the Jehoash inscription, the post-2002 Dead Sea Scrolls-like fragments, the so-called Gospel of Jesus’s Wife, the Sappho papyri, and the manuscript purchases of the Museum of the Bible in Washington, D.C.

Guaman Poma does not need to be presented as a superhero to highlight his place in history as the author of a codex containing a protest, a proposal, and a history of the Andes. Indeed, the case of Guaman Poma must be understood in its historical context, as it has been studied since its publication in Paris almost a century ago, in 1936. Thanks to rigorous studies by scholars from many countries, we are increasingly learning more about the author and his work, concluding that this is a completely plausible case—a product of the circumstances in which he lived, was formed, and developed over several decades during the consolidation of the colonial regime in the Andes.

We compute the $\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree d over any algebraically closed field of characteristic different from two, three and coprime to d. We achieve this result by computing the low-degree cohomological invariants of these stacks. As a corollary, we are additionally able to compute the $\ell$-primary torsion of the Brauer group of the moduli stack of principally polarized abelian varieties of dimension three over any field of characteristic different from two.

The tiger Panthera tigris is an apex predator categorized as Endangered on the IUCN Red List. The availability of sufficient prey is a key requirement for its survival. The tiger diet landscape refers to a dynamic ecological picture of the diverse prey species consumed by tigers in a specific region, reflecting the complex relationships between tiger populations and their prey. It can provide information on the tiger’s preferred prey as well as the conservation status of prey species across boundaries. To draw up a road map for the conservation and management of tigers across the Indian subcontinent, where the Bengal tiger Panthera tigris tigris occurs, we identified which prey species make up the majority of the tiger’s diet and answered questions relating to prey density, distribution and conservation status. We reviewed 48 studies published over 30 years (1992–2022) on tiger diet and prey availability. We recorded c. 30 mammalian prey species, with chital Axis axis, sambar Rusa unicolor, wild boar Sus scrofa, Tarai gray langur Semnopithecus hector, northern red muntjac Muntiacus vaginalis and domestic livestock contributing c. 90% of the total relative biomass consumed. Nearly half of the prey species are of conservation concern (categorized as Near-Threatened, Vulnerable or Endangered on the IUCN Red List), and 11 prey species are listed on CITES Appendix I. As part of a sustainable tiger conservation road map, we suggest that the tiger’s major prey species should be incorporated into government protection schemes.

Unlike in other contexts and regions in India, servants/slaves in Goan homes (in the sixteenth to eighteenth centuries) received inordinate attention from European non-Portuguese travellers. They provided disturbing descriptions of Goan households and the violence inflicted on the subalterns. Slave ownership in the Portuguese empire was both an economic imperative and a problem for moral theology in Europe and overseas. Although slavery was not at the centre of the debate, it contributed to the construction of the ‘Black Legend’ of Portuguese colonialism in Asia. It nourished the complaint regarding moral dissoluteness due to the mixing of population and economic corruption of the Portuguese imperial institutions. The argument was that the Portuguese intermarried and consequently started closely resembling gentiles, some of whom they first enslaved. By looking into three types of archival documents, I discuss slavery/servitude in Goan households: 1) in the legal and moral framework for the ‘just’ slave society debated by ecclesiastics, 2) as it was seen and represented by foreign travellers, 3) and in the seventeenth-century history rewriting of elite Goan Christian theologians obsessed with the purity of blood of their ancestors.

Exploring the minimum wage policy discontinuities at county borders, we find that minimum wage hikes induce industrial firms to pollute more and reduce their abatement efforts. State ownership mitigates these negative effects, suggesting its role in addressing externality. The adverse environmental impacts are attenuated by the staggered increase in pollution discharge fees across provinces. These effects are stronger for firms with higher minimum wage sensitivity, lower market power, and greater financial constraints, and for firms that are the subsidiaries of nonlisted companies. Overall, our findings highlight the unintended environmental consequences of labor market policies.

Archaeologists have long investigated the rise of inequality in prehistoric Europe. I argue that images of steadily increasing inequality are usually based on cherry-picking outstanding cases and selectively interpreting the results. Based on a large-scale qualitative assessment of the Central Mediterranean, I make two claims. First, a broad review of evidence suggests that social inequality was not a major organizing principle of most prehistoric societies. Instead, throughout prehistory, inequality formed part of a heterogeneous, heterarchical social order. Second, this was not simply due to historical chance or stagnation. As my outline of the “people’s history” of prehistoric Europe suggests, many of the archaeologically most visible developments in every period were actively aimed at undermining, encapsulating, or directing the potential development of hierarchy. In this sense, Europe’s long prehistory of limited and ambiguous hierarchy does not represent a failure of social evolution but rather widespread success in developing tactics for maintaining equality.

Distributionally robust optimization (DRO) studies decision problems under uncertainty where the probability distribution governing the uncertain problem parameters is itself uncertain. A key component of any DRO model is its ambiguity set, that is, a family of probability distributions consistent with any available structural or statistical information. DRO seeks decisions that perform best under the worst distribution in the ambiguity set. This worst case criterion is supported by findings in psychology and neuroscience, which indicate that many decision-makers have a low tolerance for distributional ambiguity. DRO is rooted in statistics, operations research and control theory, and recent research has uncovered its deep connections to regularization techniques and adversarial training in machine learning. This survey presents the key findings of the field in a unified and self-contained manner.

Now mostly derided as a musical vandal, the cellist Friedrich Grützmacher (1832–1903) was seen during his lifetime as a noble and serious artist, highly respected as a performer and sought-after as a teacher. His numerous and heavily annotated performing editions – and in particular his pedagogical editions of older works – represent his attempt to preserve and disseminate a style of playing that was referred to at the time as ‘classical’ (classisch or klassisch). While the concept of classic works, as it developed in the nineteenth century, has been studied in depth by Lydia Goehr, William Weber and others, the related yet distinct concept of classical musicianship is relatively unexplored. This chapter traces the cultural resonances of the term ‘classisch’ as it was used in the German-speaking press over the course of Grützmacher’s lifetime, arguing that it represents a complement or parallel to the idea of classic works, with an independent connection to Romantic Idealism and Hellenism. The chapter then examines the performance practice implications of classical musicianship through the lens of Grützmacher’s editions, with a particular focus on a disciplined sense of tempo, a grand and tranquil physical presence, and a highly nuanced use of the bow in the service of musical character. Viewing classical musicianship in this way clears Grützmacher’s editions of the charge of vandalism by challenging us to reconsider the ideal relationship between composer and performer, as well as the fundamental purpose of an edition.

Case-control studies can provide attribution estimates of the likely sources of zoonotic pathogens. We applied a meta-analytical model within a Bayesian estimation framework to pool population attributable fractions (PAFs) from European case-control studies of sporadic campylobacteriosis and salmonellosis. The input data were obtained from two existing systematic reviews, supplemented with additional literature searches, covering the period 2000–2021. In total, 12 studies on Campylobacter providing data for 180 PAFs referring to 5983 cases and 13213 controls, and five studies on Salmonella providing data for 75 PAFs referring to 2908 cases and 5913 controls, were included. All these studies were conducted in Western or Northern European countries. Both pathogens were estimated as being predominantly linked to food- and waterborne transmission, which explained nearly half of the cases, with Campylobacter being mainly attributable to poultry (meat), and Salmonella to poultry (eggs and meat) and pig (meat), as specific foodborne exposures. When also considering contact with animals, around 60% of cases could be explained by the larger group of zoonotic transmission pathways. While environmental transmission was also sizeable (around 10%), about a quarter of cases could be explained by factors such as travel, underlying diseases/medicine use, person-to-person transmission and occupational exposure.