We identify the size of the largest connected component in a subcritical inhomogeneous random graph with a kernel of preferential attachment type. The component is polynomial in the graph size with an explicitly given exponent, which is strictly larger than the exponent for the largest degree in the graph. This is in stark contrast to the behaviour of inhomogeneous random graphs with a kernel of rank one. Our proof uses local approximation by branching random walks going well beyond the weak local limit and novel results on subcritical killed branching random walks.

Manes (1998). Implementing Collection Classes with Monads. Mathematical Structures in Computer Science 8 (231–276) introduced the notion of a collection monad on the category of sets as a suitable semantics for collection types. The canonical example of collection monad is the finite powerset monad. In order to account for the algorithmic aspects, the category of sets should be replaced with categories whose arrows are maps computable by low-complexity algorithms. Inspired by realizability, we give a systematic way for constructing categories of small sets and low-complexity functions and define an analogue of collection monads on such categories.

Thought reform campaigns aimed at the psychological transformation of captives have long been tools to enhance national security and political legitimacy in East Asia. Fusing Soviet concepts of human perfectibility and Confucian ideals of transformation through education, sophisticated systems have evolved to convert political opponents. Whether labelled as tenkō in Japan, ‘self-renovation’ in Nationalist China, or ‘new learning’ in the People’s Republic of China, these programmes shared the fundamental goal of pressuring individuals to renounce previous beliefs and adopt state-sanctioned ideologies. This article examines how Japanese war crimes prisoners, political dissidents, and former Chinese Nationalist officers experienced these campaigns. Despite differences in implementation, each regime used confession, group study, and psychological coercion. This historical perspective is particularly relevant today as China’s leadership continues to weaponise historical narratives – including the ‘correct’ understandings of WWII history – with implications for contemporary tensions between China and Taiwan.

A despairing agent might object to climate obligations by framing them as too demanding to be morally required because they give rise to burdensome consequences of despair, like depression. This objection can be refuted on the grounds that it is morally wrong. However, when it is understood as symptomatic of moral injury, an alternative response prioritizing moral repair is illuminated. I consider how the virtue of epistemic humility can promote tasks for repair, like attentiveness to symptoms of moral injury. I see this virtue as a basis for an active form of care for others and the self that resists temptations to refer to this objection.

The main result of this article is the construction of a new class of weight shifting operators, similar to the theta operators of de Shalit and Goren (2019, Algebra Number Theory, 13, 1829–1877), Eischen et al. (2021, Algebra Number Theory, 15, 1469–1504), and others, which are defined on the lower Ekedahl–Oort strata of the geometric special fiber of unitary Shimura varieties of signature $(n-1, 1)$ at a good prime p, split in the reflex field E, which we assume to be quadratic imaginary. These operators act on certain graded sheaves which are obtained from the arithmetic structure of the EO strata, in particular the p-rank on each stratum. We expect these operators to have applications to the study of Hecke-eigensystems of $({\mathrm {mod}}\, p)$ modular forms and generalizations of the weight part of Serre’s conjecture.

Democracy is anchored by communication, grounded in a commitment to factual truth. This is an ideal historically captured by the ancient Athenian concept of parrhesia (frankness) and, in contemporary deliberative theory, by sincerity. This essay argues that the US far right has hijacked this democratic ideal, weaponizing it to create a post-truth environment and fuel a form of demagogic propaganda. The essay traces the historical evolution of the truth-telling ideal, noting how sincerity can morph into an antirhetorical style of “hyper-sincerity,” which performs shamelessness for a citizenry sidelined by massive economic inequality and corporate power. Drawing on Jason Stanley’s work, the essay then argues that this rhetorical style has become a form of fascist demagoguery, a rhetorical style that poses a threat to the very possibility of democratic politics. The final section explores the possibilities for irony as an antidote to hyper-sincerity. It reveals that the far right has also hijacked irony to create a mode of “fascist irony.” The paper concludes by calling for a “civic irony” rooted in a commitment to democratic values.

The letters exchanged between Ignatius Sancho and Laurence Sterne in 1766 have encountered considerable attention, as have those passages in Sterne’s works that seemingly engage with antislavery discourse. Some critics suggest these passages fail to address slavery directly; Sterne, in turn, has been viewed as readily capitalizing on his connection with Sancho to promote a philanthropic image that his writings do not support, and even to exploit it for financial gain. This article suggests a recalibration, partly based on the chronology of this exchange and its first public appearance in 1775. It argues that a richer understanding of Sancho’s and Sterne’s reception histories, and especially the role played by the eighteenth-century press in recirculating reviews of and excerpts from this exchange, helps to establish a more nuanced approach toward how the public image and the texts of both writers were subsequently incorporated into antislavery and Abolitionist debates.

In this paper, we consider the time-dependent Born–Oppenheimer approximation (BOA) of a classical quantum molecule involving a possibly large number of nuclei and electrons, described by a Schrödinger equation. In the spirit of Born and Oppenheimer’s original idea, we study quantitatively the approximation of the molecular evolution. We obtain an iterable approximation of the molecular evolution to arbitrary order, and we derive an effective equation for the reduced dynamics involving the nuclei equivalent to the original Schrödinger equation and containing no electron variables. We estimate the coefficients of the new equation and find tractable approximations for the molecular dynamics going beyond the one corresponding to the original Born and Oppenheimer approximation.

Archaeology is not new to public education. However, scholars of archaeology education have noted the lack of a systematic approach to the field in the last two decades. In our case study of the Trowels to Teaching Workshop, a five-day professional development program for Maryland K-12 educators conducted in 2025 through the Baltimore Community Archaeology Lab at Towson University, we offer a model for embedding archaeology education in existing applied archaeology programs in the academy. The workshop combined hands-on field and laboratory training, collaboration with Indigenous representatives from the Piscataway Conoy Tribe and the Pocomoke Indian Nation, and active participation by undergraduate student employees who both learned and taught archaeological skills. Formal pre- and post-assessments demonstrated significant learning gains among participating teachers, including increases in archaeological knowledge, confidence in lesson design, and awareness of descendant perspectives. The outcomes highlight how applied archaeology programs in universities can integrate teacher professional development into existing research, provide undergraduates with transformative teaching experiences, and deepen collaborations with descendant communities.

Breastfeeding is a critical component of infant nutrition, and breastfed infants are less likely to become stunted or obese reducing the risk of non-communicable diseases in adult life. Optimal breastfeeding practices remain a challenge worldwide; as adolescents are the mothers and fathers of tomorrow, integrating DOHaD-informed knowledge into school curricula is called for. However, research indicates adolescents have low awareness of the importance of the first 1000 days of life, only see specific elements as relevant to them, and gender-related differences exist in their comprehension. This study evaluated the impact on adolescents of an in-class presentation on parenting and the benefits of breastfeeding in high schools in 5 African countries. Pre- and post-intervention questionnaires were completed by 345 pupils (182 girls, 163 boys, mean age 17.9 years). Analysis indicated the education session impacted pupils’ perceptions of parenting and changed which aspects of breastfeeding they viewed as most and least interesting. A statistically significant difference was evident between genders on the importance of cost-benefits; more boys saw relevance for fathers that no cost is incurred for formula. Boys also ranked the potential to reduce diabetes healthcare costs in adult life higher than girls. Girls preferentially ranked breastfed babies crying less, being easier to feed at night, and diaper changing being less gross as benefits for fathers. School-based education can engage adolescents and impact knowledge and attitudes about breastfeeding. Awareness of differences in girls’ and boys’ perceptions of relevance will enable educational content to be targeted to attract and inform both genders.

Recent years have witnessed an increase in white Americans’ support for the Great Replacement Theory (GRT), the xenophobic conspiracy theory that posits that political elites are embracing permissive immigration policies to bring in “obedient” voters who will vote for them and who will eventually replace native white citizens. This conspiracy theory has been publicly endorsed by several conservative political figures and prominently featured in conservative media outlets, most notably Fox News. This article uses the American Multiracial Panel Study to investigate whether exposure to Fox News is associated with support for the GRT. We find clear and consistent evidence that whites who receive their political news from Fox News are significantly more likely to support core tenets of the GRT than those who do not. We consider our results as evidence of the continued influence of elite rhetoric on public opinion and the unique impact of Fox News on the nature and origins of white public opinion about immigration and the nation’s demographic future.

Increased occurrence of high melt summers across Arctic ice caps and the Greenland Ice Sheet creates thicker, more numerous ice layers within the near surface snow and firn of their accumulation zones. Ice layers may reduce vertical percolation of surface meltwater, promote lateral runoff, reduce refreezing at depth in underlying snow and firn promoting a positive feedback towards more negative surface mass balance. Despite their significance for ice sheet mass balance, controls on ice layer permeability are poorly understood. Here, we explore ice layer permeability using cold-laboratory snowpack experiments with predefined thermal regimes and ice layer thicknesses. We found that in a cold thermal regime (−3°C), ice layers (5–20 mm thick) within the snowpack are impermeable. Meltwater runs off laterally or ponds and subsequently refreezes within 3 h. With temperate conditions (0°C), meltwater ponds over ice layers (10–60 mm thick) without freezing. Temperate ice layers are permeable over timescales of ∼4 to 18 h. We propose that permeability of refrozen ice layers is primarily a function of thermal regime and that ice layer thickness is a secondary control. Our findings pave the way for improved snow and firn model parameterizations of ice layer permeability and ice sheet mass loss projections.

The Khaderpet carbonatite (15°58′N, 77°33′E) occurs as a small plug-like intrusion (45 m × 60 m) within altered ultramafic volcaniclastic breccia of unknown parentage. Both the carbonatite and its host rock contain crustal xenoliths of granite and quartz monzonite. Although the absence of primary silicate and oxide phases obscures its direct genetic link with the host rocks, the carbonatite preserves clear evidence of magmatic crystallization subsequently overprinted by hydrothermal alteration, crustal assimilation and supergene oxidation. The rock is dominated by calcite, which occurs in three distinct generations. Early Sr-Ba-rich calcite-1 (0.8–2.1 wt.% SrO and 0.4–2.2 wt.% BaO) phenocrysts co-crystallized with rounded fluorite at temperatures above ∼600°C, and are hosted within a Ba-Sr-poor calcite-2 matrix. Mantle-like bulk-rock δ13C values (–4.21 to –4.62 ‰, VPDB), together with (La/Yb)Cn (>1–100) and Y/Ho (24–34) ratios in calcite-1 and calcite-2, support a primary magmatic origin. Evidence for crustal assimilation includes REE-Si enrichment in apatite (up to 1.3 wt.% SiO2) by a britholite-type substitution, increased allanite abundance near xenolith contacts, Si-rich pyrochlore and interstitial quartz. Coarse calcite-3 veins crosscut the calcite-2 matrix and comprise Mn-Fe-Mg-rich bright calcite-3a cores and nearly pure, dark calcite-3b peripheries. Elevated Mn-Fe-Mg contents and high Y/Ho ratios (up to 64) in calcite-3a reflect rapid crystallization during waning hydrothermal stages. High δ18O values (+9.17 to +11.54 ‰ VSMOW) indicate low-temperature H2O-rich, CO2-poor meteoric fluid alteration. Negative Ce anomalies in apatite (Ce/Ce*: 0.8–0.3) and calcite (Ce/Ce*: 0.8–0.4), most pronounced in calcite-3b (Ce/Ce*: 0.2–0.6), together with apatite trace element compositions, indicate supergene alteration. Textural evidence of supergene alteration includes replacement of pyrochlore-1 by pyrochlore-2, pyrochlore-1 and pyrite by goethite, allanite-(La) by ferriallanite-(Ce), and late precipitation of baryte, REE-fluorocarbonates and vanadinite, indicating involvement of F–, SO42–, Pb and V in oxidizing hydrothermal fluids.

This article overturns the assumption that early modern ballads include too much godly, moralizing content to be considered part of news culture. It uses a wide range of sixteenth- and seventeenth-century English ballads in print and manuscript to demonstrate that one of the news ballad’s most significant features was the inclusion of providence – the ongoing supernatural workings of God in the material world. Placing these songs in the context of other cheap print genres and drawing on research into the role of religion in everyday life, the article shows that rather than undermining the ballad’s role in news culture, providence defined it. Moreover, the early modern distinction between God’s overall plan and specific examples of his intervention in earthly affairs helps to subdivide the genre into those where providence forms an editorial line and those where providence itself provides the story. This second type has traditionally been seen as godly rather than ‘newsy’. Understanding providence shows that those ballads which have been dismissed as more moralistic than topical in fact shared the most important news people could hear.