What proportion of integers $n \leq N$ may be expressed as $x^2 + dy^2$ for some $d \leq \Delta $, with $x,y$ integers? Writing $\Delta = (\log N)^{\log 2} 2^{\alpha \sqrt {\log \log N}}$ for some $\alpha \in (-\infty , \infty )$, we show that the answer is $\Phi (\alpha ) + o(1)$, where $\Phi $ is the Gaussian distribution function $\Phi (\alpha ) = \frac {1}{\sqrt {2\pi }} \int ^{\alpha }_{-\infty } e^{-x^2/2} dx$.

A consequence of this is a phase transition: Almost none of the integers $n \leq N$ can be represented by $x^2 + dy^2$ with $d \leq (\log N)^{\log 2 - \varepsilon }$, but almost all of them can be represented by $x^2 + dy^2$ with $d \leq (\log N)^{\log 2 + \varepsilon}\kern-1.5pt$.

I will start this review with a major development for the study of ancient Greek history: the publication of the first volume of the Oxford History of the Archaic Greek World (OHAGW), edited by Paul Cartledge and Paul Christesen. The range of the available evidence can no longer keep pace with the theoretical frameworks and the syntheses of individual scholars. A huge part of the evidence remains known to a few specialists, while wider interpretative frameworks rarely make the effort to incorporate the diversity and complexity of the evidence. Big data digital projects are certainly one way forward; the editors of OHAGW have chosen an alternative path: to offer a collection of syntheses on the archaic history of thirty Greek communities for which the available evidence makes this possible. The adoption of a common format for all local syntheses will make possible the focused comparison between individual cases; alongside the serious effort to systematically combine archaeology and history, which OHAGW editors call ‘archaeohistory’, this project has the potential to revolutionise Greek history.

While the reception of Greek tragedy is by now well-trodden terrain for the classical reception scholar, responses to Old Comedy are still harder to come by. Peter Swallow's study of the reception of Aristophanes in Britain in the Long Nineteenth Century examines the playwright's appearance, following a period in which there had been ‘few translations, and no commentaries’ in English, and his obscure contemporary references proved irksome to Hellenists (23). As a result, while the political – or intentionally apolitical – dimensions of his case studies are a consistent topic throughout the study, we also see Swallow unpick some more subtle or ‘subterranean’ receptions among their more explicit companions. This is particularly the case in the chapter on W. S. Gilbert (1836–1911), who, although known as the ‘English Aristophanes’ (4), showed little in the way of direct acknowledgement of his Attic predecessor. However, characterizing Gilbert as a beloved, but moderate humourist, Swallow identifies several modes of Aristophanic reception across a number of his works. For example, his burlesque Thespis (1871) not only has similar plot points to those found in Birds but also shares with the Aristophanic Jacques Offenbach, whose ‘influence on the British tradition is impossible to overstate’ (98), a cheeky attitude towards the gods. Gilbert's body of work and attitude to classical sources is contextualized with reference to the work of J. R. Planché (1796–1880), in whom classical reception scholarship has already shown a significant amount of interest and who appears throughout this book, even having his own chapter. Here, Swallow helps to fill in some notable gaps in the history of Victorian burlesque and related performance forms.

Since the outbreak of the COVID-19 pandemic, scholars have debated whether digital fieldwork can effectively substitute for on-site field research. The prevailing view is that digital fieldwork is a last resort when in-person access is limited. Reflecting on my recent field research in Vietnam and Malaysia, I advocate for integrating digital and on-site fieldwork as complementary components of the research process. This approach is particularly valuable for scholars who are unable to spend extended periods in the field. The integrative approach helps researchers (a) prepare effectively for on-site fieldwork, (b) adapt the data collection process flexibly while in the field, and (c) continue data collection and maintain working relationships with local networks after leaving the field. Through this reflection, I encourage researchers to normalize the integration of both methodologies to leverage the strengths of each approach.

The political status of Washington, D.C., is a longstanding question in American political thought. Intervening in that debate, I argue that Washington, D.C. deserves democratic equality. Democratic equality entails that, at a minimum, D.C. residents should have the power to vote for representatives in national and local legislatures (like residents of the several states), that their vote should have equal weight to others, and that D.C.’s elected legislative representatives should have power to vote on what the law is. This ideal of democratic equality for D.C. is only possible via D.C. statehood. Drawing on original archival research, the article provides a historical overview of D.C.’s democratic disenfranchisement, outlines three principal forms of democratic inequality faced by D.C. residents, and imagines what democratic equality for D.C. might look like. It concludes by sketching a broader research agenda about the democratic injustices accorded to those Americans living outside the several states.

DNA barcoding approaches have been successfully applied for estimating diet composition. However, an accurate quantification in the diets of herbivores remains to be achieved. In the current study, we present a novel methodology that reveals the relationship between the actual proportions (by mass) of each herbage species in the diets and the relative proportions of the ITS2 gene sequences obtained from faecal samples to evaluate the diet composition of sheep in a meadow steppe. Nine common and 12 rare species of plants were employed for formulating 6 diets, along with the addition of feed supplements for improving the growth performance of sheep. Faecal samples were collected for DNA analysis over the period spanning days 7–12. A significant positive correlation (Spearman’s ρ = 0.389) was obtained between the actual proportions (by mass) of the herbage in the diet provided and the relative abundance of ITS2 sequences obtained from the faecal samples. A significant regression coefficient was found between the relative abundance of all common species and their respective herbage mass proportions. The accuracy of the relation equations, evaluated by utilizing the similarity coefficient, showed 84.69% similarity between the actual diet composition and the correct percentage. Taken together, the current study has provided empirical evidence for the accuracy and applicability of ITS2 as a DNA barcode for obtaining quantitative information about the diet composition of sheep grazing in species-rich grasslands.

‘There is no well-known individual in all Greek mythology except Alcestis [original emphasis] who dies and is returned to human life without cosmic repercussions which are soon remedied’ (John Heath). The ineluctability of death is not just a feature of Greek myth in general but is also one of the most prominent themes in Euripides’ version of the story in his play Alcestis (438 bc). A further problem is that Greek tragedy is a basically realistic genre which is not hospitable to violations of the laws of nature. Euripides thus set himself a remarkable challenge in Alcestis, to present an event which violates a law of nature which is so unbreakable that it is on the whole observed throughout Greek mythology as well as being repeatedly affirmed in the play. This article will examine how he succeeds in doing so in a way which is dramatically convincing.

We describe the structure of regular codimension $1$ foliations with numerically projectively flat tangent bundle on complex projective manifolds of dimension at least $4$. Along the way, we prove that either the normal bundle of a regular codimension $1$ foliation is pseudo-effective, or its conormal bundle is nef.

In my last review I discussed Mark Usher's How to Care About Animals, one of Princeton University Press’ volumes of Ancient Wisdom for Modern Readers. The series’ rapidly growing roster now includes Sarah Nooter's book How To Be Queer: An Ancient Guide to Sexuality. Nooter selects, translates, and introduces a range of texts from Sappho and Plato (most heavily featured) to Homer, Pindar, Alcman, Anacreon, Theognis, and Theocritus (to name just a selection of the selection). There is an important ‘nothing new under the sun’ ethos to this volume, as is the case with many in the series. As Nooter puts it, ‘The past decade has seen a revolution in sexuality… sexual fluidity is now mainstream… And yet the Greeks got there long ago.’ (vii) The Greeks wrote about sexuality ‘with little angst and much wit’, and it is this that Stephen Fry picks up on in his endorsement of the book: ‘our ancestors often had clearer, less guilt-ridden, confused, prurient, and prudish attitudes to the rainbow of sexualities we wrongly think unique to our age’.

C-type lectins (CTLs), a diverse family of pattern recognition receptors, are essential for immune recognition and pathogen clearance in invertebrates. TcCTL17 contains one carbohydrate recognition domain and three scavenger receptor Cys-rich domains. Spatial and temporal expression analysis revealed that TcCTL17 is highly expressed in early pupa, early adult stages, and the larval gut at 20 days. The recombinant TcCTL17 exhibited dose-dependent binding to lipopolysaccharides and peptidoglycans, Ca2+-dependent binding and agglutination of bacteria in vitro. Knocking down TcCTL17 before bacterial exposure reduced survival rates and increased bacterial loads in T. castaneum larvae, accompanied by decreased antimicrobial peptide expression and haemolymph phenoloxidase activity. Additionally, TcCTL17 RNA interference caused developmental abnormalities, affecting metamorphosis and fecundity, possibly by influencing the 20E, JH, and vitellogenin pathways. These findings underscore dual functions of TcCTL17 in immunity and development, making it a potential target for pest management.