We show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph. To this end, define the underlying treewidth of a graph class $\mathcal{G}$ to be the minimum non-negative integer $c$ such that, for some function $f$, for every graph $G \in \mathcal{G}$ there is a graph $H$ with $\textrm{tw}(H) \leqslant c$ such that $G$ is isomorphic to a subgraph of $H \boxtimes K_{f(\textrm{tw}(G))}$. We introduce disjointed coverings of graphs and show they determine the underlying treewidth of any graph class. Using this result, we prove that the class of planar graphs has underlying treewidth $3$; the class of $K_{s,t}$-minor-free graphs has underlying treewidth $s$ (for $t \geqslant \max \{s,3\}$); and the class of $K_t$-minor-free graphs has underlying treewidth $t-2$. In general, we prove that a monotone class has bounded underlying treewidth if and only if it excludes some fixed topological minor. We also study the underlying treewidth of graph classes defined by an excluded subgraph or excluded induced subgraph. We show that the class of graphs with no $H$ subgraph has bounded underlying treewidth if and only if every component of $H$ is a subdivided star, and that the class of graphs with no induced $H$ subgraph has bounded underlying treewidth if and only if every component of $H$ is a star.

Diapycnal mixing plays a key role in the thermohaline circulation of the deep ocean. Field observations have suggested that this mixing is intensified over the rough topography along the boundaries of the ocean. In this study, we experimentally explore the transport of salinity and tracer in a horizontally stirred, stratified fluid with a steady vertical buoyancy flux. The mechanical mixing occurs either uniformly across the tank or near a sidewall. To compare uniform and boundary mixing, first we explore the steady state dynamics and find that, in both cases, the surfaces of constant density are horizontal. With uniform mixing, vertical transport of buoyancy occurs uniformly throughout the tank while, with boundary mixing, transport is confined to the turbulent region and the interior space remains quiescent and does not mix or have any net movement. We then explore the transient evolution of the stratification when the source of buoyancy is removed from the base of the system. In the boundary mixing case, the resulting divergence of the turbulent diffusive flux in the boundary region leads to a reduction in the buoyancy of the fluid in the boundary region, and a net upflow develops in the boundary region. In turn, this drives a downwelling in the interior. Vertical gradients in the rate of downwelling lead to stretching of isopycnals and, together, these processes enable the interior stratification to evolve. The experiments highlight that, with boundary mixing, the main transport of buoyancy occurs near the boundaries even though the interior is stratified; independent measurements of tracer mixing in the interior show that this fluid may be quiescent and stratified even though there is a large flux being transported in the boundary region. This has important implications for the interpretation of mixing data in the ocean. In a companion paper, (Li and Woods Part 2), we explore the interaction of a net upwelling with such boundary mixing.

This study examined physicians’ reasoning about obtaining transesophageal echocardiography (TEE) in cases of Staphylococcus aureus bacteremia (SAB). In 221 cases of SAB over 5 years, the most common reasons for not performing TEE were clinical response to antibiotics, negative TTE results, and the expectation that TEE would not change management.

Radiocarbon dates on charred plant remains are often used to define the chronology of archives such as lake cores and fluvial sequences. However, charcoal is often older than its depositional context because old-wood can be burnt and a range of transport and storage stages exist between the woodland and stream or lake bed (“inherited age”). In 1978, Blong and Gillespie dated four size fractions of charcoal found floating or saltating in the Macdonald River, Australia. They found larger fragments gave younger age estimates, raising the possibility that taphonomic modifications could help identify the youngest fragments. In 1978 each date required 1000s charcoal fragments. This study returns to a sample from the Macdonald River to date individual charcoal fragments and finds the inherited age may be more than 1700 years (mode 250 years) older than the collection date. Taphonomic factors, e.g., size, shape or fungal infestation cannot identify the youngest fragments. Only two fragments on short-lived materials correctly estimated the date of collection. In SE Australia, this study suggests that wood charcoal will overestimate the age of deposition, taphonomic modifications cannot be used to identify which are youngest, and multiple short-lived materials are required to accurately estimate the deposition age.

Accelerator mass spectrometry (AMS) radiocarbon (14C) dating is central to the development of robust chronologies in archaeological and paleoenvironmental contexts spanning the last 50,000 years. For dates to be accurate, samples must be free of exogenous carbon contamination. At the Oxford Radiocarbon Accelerator Unit (ORAU), considerable advancements in the dating of bone collagen have been made through the development of a high performance liquid chromatography (HPLC) method for the dating of the amino acid hydroxyproline, which can mitigate the effects of carbon contamination. However, recent changes in ligand manufacturing methods for the mixed-mode column used in the ORAU protocol (Primesep A, SIELC Technologies; IL, USA) have resulted in unacceptably high analytical backgrounds. Prior to the manufacturing change, backgrounds of > 50k BP were achievable. Since the manufacturing change, a mean background of 32.5k BP has been measured. Due to column bleed, the Primesep A is therefore no longer suitable for 14C measurement of hydroxyproline from older material. Here, we present background data and the chromatography conditions used to isolate hydroxyproline using an alternative column, a preparative-scale Newcrom AH, which shows promising potential as an alternative for the routine isolation and AMS dating of hydroxyproline—especially approaching the age and mass limits of the method.

Many geological layers include cross bedding, which leads to different values for permeability along and across the bedding planes. We explore how such cross bedding impacts buoyancy-driven flow through an inclined aquifer. For each bedding angle and ratio of the permeability along and across the bedding, a free buoyancy-driven plume rises at a particular angle to the horizontal. If the angle of inclination of the aquifer to the horizontal is smaller than this angle, then the plume rises along the upper boundary, otherwise, somewhat surprisingly, the buoyant plume rises along the lower boundary of the aquifer. We present new laboratory experiments to support these predictions. We also test a model for the effective permeabilities which control the speed and the rate of spread of the plume along one or other boundary of the aquifer. We consider the impact of our results for modelling geological storage of ${\rm CO}_2$ or aquifer thermal energy storage.

The Nama Group, Namibia (≥550.5 to <538 million years ago, Ma), preserves one of the most diverse metazoan fossil records of the terminal Ediacaran Period. We report numerous features that may be biological in origin from the shallow marine, siliciclastic, lowermost Mara Member (older than ca. 550.5 Ma) from the Tsaus Mountains. These include forms that potentially represent body fossils, Beltanelliformis and an indeterminate juvenile uniterminal rangeomorph or arboreomorph frond, plug trace fossils, Bergaueria, as well as sedimentary surface textures, which are possibly microbially induced. These are the oldest documented macrofossils in the Nama Group. They represent taxa that persist from the Avalon or White Sea assemblages prior to the later appearance of new biota, including calcified metazoans, calcified and soft-bodied tubular taxa including all cloudinids, as well as more complex trace fossils.

Using a new age model that allows more accurate stratigraphic placement of major Ediacaran macrofossil morphogroups and taxa, we propose a re-definition of the Nama Assemblage following the practice for Phanerozoic evolutionary faunas to include only new morphogroups of soft-bodied tubular, calcified taxa and complex trace fossils, defined by first appearance of Cloudina, which postdates deposition of the Kanies and lower Mara members and first appears ca. 550 Ma and persists until at least 539 Ma.

Finally, the Tsaus Mountain environment is pristine, unspoilt by geologists and naturalists. Following World Heritage Convention, we suggest a pledge of non-destructive excavation that all future scientists should be able to make in publications of work that involve research in this area.

A total of 235 vials of nematodes held in the Australian Helminthological Collection of the South Australian Museum from 125 individuals of Isoodon macrourus were examined. The nematode assemblage of I. macrourus, comprising 12 families, including 16 genera and 23 identified species, was compared with the sympatric bandicoot species Perameles nasuta, 20 identified species (Sorensen’s index of similarity 0.56) and P. pallescens, 12 identified species (Sorensen’s index 0.51). Sprattellus cassonei n. sp. is distinguished from its congeners by having a synlophe with 7–8 ridges with the anterior ventral ridges interrupted, the morphology of the dorsal ray and the branching of the spicule tips. A single male specimen identified as Linstowinema sp. 1. is characterised by seven circles of body hooks, the oesophagus terminating at the level of the seventh circle and robust scale-like spines on the posterior ventral body. A complete description of the species will require additional material, including females. Difficulties in identifying individuals of the genus Mackerrastrongylus to species level are discussed. Overall similarities in the nematode assemblages of the three bandicoot hosts are likely due to shared relationships and similar behaviours.

A series of laboratory experiments are reported in which a continuous stream of bubbles rise from a small source at the base of a tank of water. Using different nozzles, bubble sizes $d$ ranging from 1.2 to 11.6 mm were produced for a number of gas volume fluxes, $Q_b$, ranging between 1.1 and $21.1\times 10^{-6}\ {\rm m}^3\ {\rm s}^{-1}$. Within a small distance from the source, the slip speed of these bubbles exceeds the speed of the equivalent single-phase plume with the same buoyancy flux, leading to formation of what we refer to as the ‘slip plume’ regime. Through a combination of high-speed photography, coupled with flow visualisation in the plume and the ambient fluid using dye, we find that the bubble speed and the fluid speed remain nearly constant with height, with the maximum fluid speed being of order $0.30\pm 0.03$ of the bubble speed. Using the filling box method, we also find that the net fluid volume flux in the slip plume increases linearly with distance from the source at a rate $Q_l = \lambda Bz/v_s^2$, where $B$ is the buoyancy flux of the gas, $v_s$ the rise speed of the gas bubbles, $z$ the distance above the source and $\lambda$ is a constant related to the dimensionless volume of fluid in the wake of each bubble. This slip-dominated flow regime can be understood in terms of kinetic energy imparted to the fluid as the bubbles rise and release potential energy. Further experiments with particle-laden plumes illustrate similar scalings for the volume flux in a particle-driven slip plume once the slip speed of the particles exceeds the bulk speed of the equivalent single-phase buoyant plume with the same buoyancy flux. Near the source the slip speed may be smaller than the plume speed, and the flow follows the classical model for a turbulent buoyant plume, with the transition to the slip regime occurring at a distance $z^*\approx (32\pm 5)\lambda ^{3/2} B/v_s^3$ from the source, where the dimensionless parameter $\lambda$ relates to the dimensionless volume of the fluid wake, which we find varies with the Reynolds number of the particles.

Background: Respiratory cultures are commonly obtained from patients with suspicion for ventilator-associated infections (VAIs). In the absence of specimen ordering and collection guidelines, management practices may differ. We characterized current respiratory culture collection practices and perceptions and identified potential barriers to changing practices among a national collaborative of pediatric intensive care units (PICUs). Methods: We conducted an electronic survey of PICU physicians, advanced practice providers (APPs), respiratory therapists (RTs), and nurses at 16 US academic pediatric hospitals across the United States. Positive Likert-scale responses (eg, “agree” and “strongly agree”) were grouped. To account for varying hospital representation, we analyzed the results as the median proportion of participants with that response across the hospitals. Results: After excluding incomplete responses, 568 (44%) of 1,301 invited participants responded (range, 16–107 per site); the median hospital response rate was 60% (range, 17%–83%). Roles included physicians (35%), APPs (10%), RTs (24%), and nurses (31%). Moreover, 44% of the participating units cared for cardiac surgery patients. Across hospitals, specimens are often collected by RTs, followed by nurses, typically via inline endotracheal aspirate for either endotracheal tubes or tracheostomies. Saline lavage is a common practice, but only 4% reported a standardized approach. Examining the likeliness to obtain cultures for different clinical symptoms, the widest variation in responses were for fever and inflammatory markers without respiratory symptoms (median proportion, 68%; IQR, 54%–79%), isolated change in secretion characteristics (67%; IQR, 54%–78%), isolated increased secretions (55%; IQR, 40%–65%), isolated inflammatory markers (49%; IQR, 38%–57%) or isolated fever (49%; IQR, 38%–61%). Overall, 75% (IQR, 70%–86%) of reported respiratory cultures were likely to be obtained as a “pan culture.” Most respondents (median proportion, 69%) felt confident about the indications to obtain cultures, but 60% felt that clinicians had a low threshold, and 84% reported clinical practice variation. Barriers to change included reluctance to change (70%), opinion of consultants (64%), and fear of missing a diagnosis of VAI (62%). Respondents agreed that they would find clinical decision support (CDS) tools helpful (79%). In addition, 83% expected that they would follow CDS, and 82% thought that CDS would help align ICU and/or consulting teams. Conclusions: Among 16 participating hospitals, we detected a lack of standardized respiratory-culture specimen collection and ordering practices. Most respondents agreed that CDS tools would be helpful. Diagnostic stewardship of respiratory cultures using CDS must account for potential reluctance to change and needs to address stakeholder perspectives, including fear of missing infections.

Disclosure: None

We prove that for every tree $T$ of radius $h$, there is an integer $c$ such that every $T$-minor-free graph is contained in $H\boxtimes K_c$ for some graph $H$ with pathwidth at most $2h-1$. This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and $2h-1$ is the best possible bound.

With a modified formalization of Heckscher–Ohlin theory as the basis of a novel econometric specification, this paper uses worldwide data over three decades to estimate how the effects of greater openness on industrialization vary among countries with differing endowments of land relative to labour. The results confirm the theoretical prediction that greater openness reduces manufactured output shares in land-abundant countries, while increasing them in land-scarce countries. The implications of these results for trade and development policy are debatable.

This paper develops a Heckscher−Ohlin model in which the effects on production structure of endowments and changes in trade policies depend in a continuous way on a country's degree of openness to trade. Its main contribution is to show semi-formally how the introduction of product differentiation causes the elasticities of output with respect both to factor endowments and to sectoral trade barriers to vary with import penetration (the share of foreign firms in home markets) and export orientation (the share of foreign markets in home-firm sales).