In this paper, we investigate finite solvable tidy groups. We prove that a solvable group with order divisible by at least two primes is tidy if all of its Hall subgroups that are divisible by only two primes are tidy.

Let G be a p-group for some prime p. Recall that the Hughes subgroup of G is the subgroup generated by all of the elements of G with order not equal to p. In this paper, we prove that if the Hughes subgroup of G is cyclic, then G has exponent p or is cyclic or is dihedral. We also prove that if the Hughes subgroup of G is generalised quaternion, then G must be generalised quaternion. With these results in hand, we classify the tidy p-groups.

Background: Emerging evidence supports the use of billing data to identify stewardship targets in primary care. Standardizing an approach to antibiotic prescribing rate (APR) calculations could facilitate external benchmarking. Methods: Using methodology and an ICD-10 dictionary validated in urgent care clinics,1 we created an expanded ICD-10 dictionary to incorporate additional ICD-10 codes from primary care associated with antibiotic prescriptions (Fig. 1). We then compared antibiotic prescribing rates using the urgent care and expanded dictionaries. We included all primary care visits from 2019 to 2020 and extracted ICD-10 codes and antibiotic order data. Using the urgent care and expanded ICD-10 dictionary, we classified each encounter by prescribing tier based on whether antibiotics are almost always (tier 1), sometimes (tier 2), or almost never (tier 3) indicated. For encounters with ICD-10s in multiple tiers, we chose the lowest tier. For multiple ICD-10 codes within the same tier, we chose the first extracted ICD-10 code. We calculated antibiotic prescribing rates as the proportion of encounters associated with ≥ 1 antibacterial prescription. This quality improvement project was deemed non–human subjects research by the Stanford Panel on Human Subjects in Medical Research. Results: The urgent care dictionary has 1,400 ICD-10 codes. We added 1,439 ICD-10 codes derived from primary care encounters to create the expanded ICD-10 dictionary (8.5% tier 1, 9.1% tier 2, and 82.4% tier 3) (Fig. 1). We identified 177,531 encounters; 74% had ≥ 2 associated ICD-10 codes (Fig. 2). In total, 147,085 encounters (82.9%) were classified into a tier using the urgent care dictionary. An additional 22,039 encounters were classified with the expanded dictionary (Table 1). Most added encounters were tier 3 with low 0.7% APR (Tables 1 and 3). In total, 41,473 (28.2%) encounters were classified differently depending on the ICD-10 dictionary used, most commonly changing from tier 3 to tier 2 without an increase in overall tier 2 antibiotic prescribing rate (Tables 2 and 3). Overall antibiotic prescribing rates were similar when using either the urgent care or expanded ICD-10 dictionary (Table 2). Conclusions: The expanded ICD-10 dictionary allowed for classification of more encounters in primary care; however, it did not meaningfully change antibiotic prescribing rates. Antibiotic prescribing rates were likely diluted by classifying more encounters without identifying an associated increase in antibiotic prescribing. A more sophisticated classification system may help to accommodate the diversity and volume of ICD-10 codes used in primary care.

1. Stenehjem E, et al. Clin Infect Dis 2020;70:1781–1787.

Funding: None

Disclosures: None

The Variables and Slow Transients Survey (VAST) on the Australian Square Kilometre Array Pathfinder (ASKAP) is designed to detect highly variable and transient radio sources on timescales from 5 s to $\sim\!5$ yr. In this paper, we present the survey description, observation strategy and initial results from the VAST Phase I Pilot Survey. This pilot survey consists of $\sim\!162$ h of observations conducted at a central frequency of 888 MHz between 2019 August and 2020 August, with a typical rms sensitivity of $0.24\ \mathrm{mJy\ beam}^{-1}$ and angular resolution of $12-20$ arcseconds. There are 113 fields, each of which was observed for 12 min integration time, with between 5 and 13 repeats, with cadences between 1 day and 8 months. The total area of the pilot survey footprint is 5 131 square degrees, covering six distinct regions of the sky. An initial search of two of these regions, totalling 1 646 square degrees, revealed 28 highly variable and/or transient sources. Seven of these are known pulsars, including the millisecond pulsar J2039–5617. Another seven are stars, four of which have no previously reported radio detection (SCR J0533–4257, LEHPM 2-783, UCAC3 89–412162 and 2MASS J22414436–6119311). Of the remaining 14 sources, two are active galactic nuclei, six are associated with galaxies and the other six have no multi-wavelength counterparts and are yet to be identified.

Recovering the agency, skill and innovation of archaeological field assistants from historical encounters is essential to interrogating processes of knowledge production, but is often hampered by access to appropriate archival sources and methods. We detail a field project from early twentieth-century Basutoland (modern-day Lesotho) that is unique both for its aim to salvage details of rock-art production as a dying craft and for its archive chronicling the project's intellectual journey from experiment to draft manuscripts to published work over more than three decades. We argue that critical historiographic attention to this archive offers a guide for examining the intimate dynamics of fieldwork and the effects of these micropolitics on the archaeological canon. We demonstrate how sustained attention to long processes of knowledge production can pinpoint multiple instances in which the usability of field assistants’ scientific knowledge is qualified, validated, or rejected, and in this case how an African assistant is transformed into an ethnographic interlocutor. For rock-art studies especially, this represents a need for interrogating the epistemic cultures—not just the content—of foundational historical data.

Morgan and Parker proved that if G is a group with ${\textbf{Z}(G)} = 1$ , then the connected components of the commuting graph of G have diameter at most $10$ . Parker proved that if, in addition, G is solvable, then the commuting graph of G is disconnected if and only if G is a Frobenius group or a $2$ -Frobenius group, and if the commuting graph of G is connected, then its diameter is at most $8$ . We prove that the hypothesis $Z (G) = 1$ in these results can be replaced with $G' \cap {\textbf{Z}(G)} = 1$ . We also prove that if G is solvable and $G/{\textbf{Z}(G)}$ is either a Frobenius group or a $2$ -Frobenius group, then the commuting graph of G is disconnected.

A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson’s strong negation.

Proglacial environments are ideal for studying the development of soils through the changes of rocks exposed by glacier retreat to weathering and microbial processes. Carbon (C) and nitrogen (N) contents as well as soil pH and soil elemental compositions are thought to be dominant factors structuring the bacterial, archaeal and fungal communities in the early stages of soil ecosystem formation. However, the functional linkages between C and N contents, soil composition and microbial community structures remain poorly understood. Here, we describe a multivariate analysis of geochemical properties and associated microbial community structures between a moraine and a glaciofluvial outwash in the proglacial area of a High Arctic glacier (Longyearbreen, Svalbard). Our results reveal distinct differences in developmental stages and heterogeneity between the moraine and the glaciofluvial outwash. We observed significant relationships between C and N contents, δ13Corg and δ15N isotopic ratios, weathering and microbial abundance and community structures. We suggest that the observed differences in microbial and geochemical parameters between the moraine and the glaciofluvial outwash are primarily a result of geomorphological variations of the proglacial terrain.

In this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the syntax of First Order Logic with equality and the semantics of Quantified Equilibrium Logic with evaluable functions (${\rm QEL}^=_{\cal F}$). Then, we proceed to incorporate a new kind of logical term, intensional set (a construct commonly used to denote the set of objects characterised by a given formula), and to extend ${\rm QEL}^=_{\cal F}$ semantics for this new type of expression. In our extended approach, intensional sets can be arbitrarily used as predicate or function arguments or even nested inside other intensional sets, just as regular first-order logical terms. As a result, aggregates can be naturally formed by the application of some evaluable function (count, sum, maximum, etc) to a set of objects expressed as an intensional set. This approach has several advantages. First, while other semantics for aggregates depend on some syntactic transformation (either via a reduct or a formula translation), the ${\rm QEL}^=_{\cal F}$ interpretation treats them as regular evaluable functions, providing a compositional semantics and avoiding any kind of syntactic restriction. Second, aggregates can be explicitly defined now within the logical language by the simple addition of formulas that fix their meaning in terms of multiple applications of some (commutative and associative) binary operation. For instance, we can use recursive rules to define sum in terms of integer addition. Last, but not least, we prove that the semantics we obtain for aggregates coincides with the one defined by Gelfond and Zhang for the ${\cal A}\mathit{log}$ language, when we restrict to that syntactic fragment.

Current understanding of climate change impacts, adaptation and vulnerability among Inuit in the Arctic is relatively static, rooted in the community and time that case studies were conducted. This paper captures the dynamism of Inuit–climate relationships by applying a longitudinal approach to assessing vulnerability to climate change among Inuit in Ulukhaktok, Northwest Territories, Canada. Data were collected in 2005 and 2016 following a consistent methodology and analytical framework. Findings from the studies are analysed comparatively together with longitudinal datasets. The data reveal that many of the climatic changes recorded in 2005 that adversely affected hunting activities have been observed to be persisting or progressing, such as decreasing sea ice thickness and extent, and stronger and more consistent summer winds. Inuit are responding by altering travel routes and equipment, taking greater pre-trip precautions, and concentrating their efforts on more efficient and accessible hunts. Increasing living and subsistence costs and time-constraints, changes in the generation and transmission of environmental knowledge and land skills, and the concentration of country food sharing networks were identified as key constraints to adaptation. The findings indicate that the connections between subsistence activities and the wage economy are central to understanding how Inuit experience and respond to climate change.

Rock art worldwide has proved extremely difficult to date directly. Here, the first radiocarbon dates for rock paintings in Botswana and Lesotho are presented, along with additional dates for Later Stone Age rock art in South Africa. The samples selected for dating were identified as carbon-blacks from short-lived organic materials, meaning that the sampled pigments and the paintings that they were used to produce must be of similar age. The results reveal that southern African hunter-gatherers were creating paintings on rockshelter walls as long ago as 5723–4420 cal BP in south-eastern Botswana: the oldest such evidence yet found in southern Africa.

The Numeniini is a tribe of 13 wader species (Scolopacidae, Charadriiformes) of which seven are Near Threatened or globally threatened, including two Critically Endangered. To help inform conservation management and policy responses, we present the results of an expert assessment of the threats that members of this taxonomic group face across migratory flyways. Most threats are increasing in intensity, particularly in non-breeding areas, where habitat loss resulting from residential and commercial development, aquaculture, mining, transport, disturbance, problematic invasive species, pollution and climate change were regarded as having the greatest detrimental impact. Fewer threats (mining, disturbance, problematic native species and climate change) were identified as widely affecting breeding areas. Numeniini populations face the greatest number of non-breeding threats in the East Asian-Australasian Flyway, especially those associated with coastal reclamation; related threats were also identified across the Central and Atlantic Americas, and East Atlantic flyways. Threats on the breeding grounds were greatest in Central and Atlantic Americas, East Atlantic and West Asian flyways. Three priority actions were associated with monitoring and research: to monitor breeding population trends (which for species breeding in remote areas may best be achieved through surveys at key non-breeding sites), to deploy tracking technologies to identify migratory connectivity, and to monitor land-cover change across breeding and non-breeding areas. Two priority actions were focused on conservation and policy responses: to identify and effectively protect key non-breeding sites across all flyways (particularly in the East Asian- Australasian Flyway), and to implement successful conservation interventions at a sufficient scale across human-dominated landscapes for species’ recovery to be achieved. If implemented urgently, these measures in combination have the potential to alter the current population declines of many Numeniini species and provide a template for the conservation of other groups of threatened species.