We study covering numbers of subsets of the symmetric group $S_n$ that exhibit closure under conjugation, known as normal sets. We show that for any $\epsilon>0$, there exists $n_0$ such that if $n>n_0$ and A is a normal subset of the symmetric group $S_n$ of density $\ge e^{-n^{2/5 - \epsilon }}$, then $A^2 \supseteq A_n$. This improves upon a seminal result of Larsen and Shalev (Inventiones Math., 2008), with our $2/5$ in the double exponent replacing their $1/4$.

Our proof strategy combines two types of techniques. The first is ‘traditional’ techniques rooted in character bounds and asymptotics for the Witten zeta function, drawing from the foundational works of Liebeck–Shalev, Larsen–Shalev, and more recently, Larsen–Tiep. The second is a sharp hypercontractivity theorem in the symmetric group, which was recently obtained by Keevash and Lifshitz. This synthesis of algebraic and analytic methodologies not only allows us to attain our improved bounds but also provides new insights into the behavior of general independent sets in normal Cayley graphs over symmetric groups.

Despite chronicles from the 16th century describing fertile alluvial plains and densely populated wetlands, archaeology in western Mexico has been little studied. The Directorate of Archaeological Salvage (DSA) of National Institute of Anthropology and History (INAH) has initiated a study of two sites in Costa Canuva, at the southern part of Nayarit state: Becerros and Naranjos. Thirty charcoal and shell samples were radiocarbon (14C) dated to determine occupation history. A Bayesian approach was used to build a chronological modeling from charcoal samples. Charcoal and shell samples found in the same context allowed us to calculate the ΔR values of marine offset for this period. In general, the archaeological sites of this area are divided into three major periods: Formative, Classic, and Postclassic. The 14C dating of Becerros recovered materials provided a chronological framework for the site’s occupation, from cal AD 169–1025, corroborating the ceramic studies in the sense that human settlement activities date from the Formative (300 BC–AD 600) to the Early Postclassic (AD 900–1200). Naranjos started in the Classic period and reached its occupancy peak in the Late Classic. The site’s occupation may have persisted for at least two centuries after the conquest of the Altiplano in 1521. The comparison of charcoal dates and associated shell samples from the Naranjos Unit gave a probability distribution for ΔR, that ranged from 118.5 to 199.5 with a mean value of 159 ± 4, slightly higher than other values obtained at nearby sites.

To determine the semantic importance of certain features has been a topic of interest for many semantic memory models. Diverse measures have been proposed in the last years. Semantic significance, the latest measure proposed by Montefinese and colleagues, is both sophisticated and comprehensive. Given the cultural and linguistic variability of semantic measures, this study presents values of significance and relative weight for the Spanish-speaking population corresponding to 400 concrete concepts. First, we presented data for both young and older adults. Second, we assessed the effect of significance on response times in two speeded feature verification tasks. Third, we compared significance values with the existing Italian significance norms. To evaluate the effect of significance to predict response times, two speeded verification tasks (Experiment 1 and 2) were carried out, selecting a total of a 130 concepts for analysis. In Experiment 1, subjects were presented with a feature followed by a concept, while in Experiment 2, the order of stimulus presentation was reversed (i.e., the concept was presented before the feature). An independent linear mixed model showed that significance was a good predictor of response latencies in Experiments 1 and 2. Moreover, results revealed a strong positive correlation between the Spanish and Italian significance values. Findings are discussed in terms of recent theories of semantic cognition.

Pollen analysis was carried out on the infilling succession of the Fossa San Vito sinkhole, at the NE foothills of the Sarno Plain (Italy). Four 14C dates and six tephra layers constrain the pollen sequence between ca. 6000 and 500 cal yr BP. A forested environment, with a few signs of human activities, characterizes the pre-protohistoric period (ca. 6000–2750 yr BP). Stability of the arboreal pollen grains to non-arboreal pollen grains (AP/NAP) curve is due to climate-related opposite oscillations of deciduous and evergreen forest. In this period, the pyroclastic products from Neapolitan volcanoes that reached the upper Sarno Plain seem to have affected neither vegetation nor human activities. In the archaic and classic periods (ca. 2750–1500 yr BP), intensive deforestation and increase in anthropogenic indicators indicate the occurrence of grazing and crop activities managed by the main urban centers located in the plain: Pompeii, Stabiae, and Nuceria. After the Pompeii eruption in CE 79, a rapid re-afforestation and decline in all anthropogenic indicators testify to the temporary abandonment of the area, linked to the disastrous demise of the main economic centers. The upper plain was repopulated and exploited in the Late Ancient and Middle Ages (ca. 1700–500 yr BP), as indicated by the increase in all crop and grazing indicators.

The purpose of this study was to examine the potential for sustained almond consumption to reduce HbA1c concentrations among individuals with elevated values. A 16-week randomized, parallel-arm, controlled trial was conducted. Eighty-one adults with elevated HbA1c concentrations (>5.7%) were randomly assigned to incorporate 2 oz of raw almonds (A: n=39) or energy-matched snacks (C: n=42) into their daily diets. Body weight, body composition, plasma lipids, HbA1c, plasma vitamin E, glycemia (by meal tolerance test and continuous glucose monitoring), dietary intake, and hedonic responses to test foods were measured at stipulated time points. Participants consuming almonds ingested 253 kcal/d more than participants in the control group (P=0.02), but this did not result in a significant difference in body weight. No statistically significant differences were observed in HbA1c concentrations, blood chemistries, body composition, or glycemia over time or between groups. However, Healthy Eating Index scores improved within the almond group as compared to the control group (P<0.001). Additionally, the hedonic rating of almonds within the almond group did not decline as markedly as the control group’s reduced liking of the pretzel snack. Alpha-tocopherol increased significantly, and gamma tocopherol tended to decrease in the almond group, indicating compliance with the dietary intervention. Overall, daily ingestion of 2oz of raw almonds in a self-selected diet for 16 weeks did not alter short-term or longer-term glycemia or HbA1c concentrations in adults with elevated HbA1c concentrations, but they were well-tolerated hedonically and improved diet quality without promoting weight gain.

Seahorses Hippocampus spp. are commercially and culturally important to many communities. Although seahorses are widely used in traditional medicine, as curios and as aquarium fishes in Southeast Asia, documentation on the current nature and extent of culturally motivated seahorse uses in Malaysia is lacking. To examine how ethnicity and other socio-demographic drivers shape traditional medicinal use and underlying cultural beliefs involving seahorses, we administered a questionnaire-based survey during March 2021–April 2022 to members of the general public and fishers in Malaysia. Approximately one-fifth (21.0%) of respondents reported consuming seahorses (34.4% of these used seahorses for medicinal purposes, 55.2% for other non-medicinal uses and 10.4% for both types). Consumers of seahorses were from all ethnic groups except for Indigenous groups. In the general public group, medicinal use was more common amongst the Chinese respondents, whereas in the fisher group, other uses were more common amongst the Malay respondents. Amongst the threats facing seahorses, which include overfishing, habitat destruction, bycatch and ocean plastic pollution, only bycatch was perceived as a major threat by most of the general public and fisher respondents. The relatively low prevalence of reported seahorse use amongst Malaysians is an encouraging finding from a conservation perspective. However, the high proportion of non-medicinal uses indicates the need to focus on such other uses to ensure the sustainability of seahorse use in Malaysia.

The policy-making process for health financing in most places lacks equity, failing to adequately consider the voices of ordinary citizens, residents, and especially those facing significant disadvantage. Procedural fairness is about addressing this imbalance, which requires a recalibration of power dynamics, ensuring that decision-making incorporates a more diverse range of perspectives. In this comment, we highlight the important contributions made by the report ‘Open and inclusive: Fair processes for financing universal health coverage’ in furthering the understanding and importance of procedural fairness in health financing decision-making especially as it relates to the three sub-functions of financing – revenue raising, pooling, and purchasing. We also argue for the importance of conceptual clarity – especially as to the added value of procedural fairness vis-à-vis accountability – and critically review the proposed framework for procedural fairness, emphasising the role of voice as the linchpin to advancing equity in influence.

Characterised by the extensive use of obsidian, a blade-based tool inventory and microblade technology, the late Upper Palaeolithic lithic assemblages of the Changbaishan Mountains are associated with the increasingly cold climatic conditions of Marine Isotope Stage 2, yet most remain poorly dated. Here, the authors present new radiocarbon dates associated with evolving blade and microblade toolkits at Helong Dadong, north-east China. At 27 300–24 100 BP, the lower cultural layers contain some of the earliest microblade technology in north-east Asia and highlight the importance of the Changbaishan Mountains in understanding changing hunter-gatherer lifeways in this region during MIS 2.