Connectivity and tree structure in finite graphs

Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we determine conditions under which such a separation system contains a nested subsystem that still separates those sets and is invariant under the automorphisms of the graph. As an application, we show that the $k$-blocks -- the maximal vertex sets that cannot be separated by at most $k$ vertices -- of a graph $G$ live in distinct parts of a suitable tree-decomposition of $G$ of adhesion at most $k$, whose decomposition tree is invariant under the automorphisms of $G$. This extends recent work of Dunwoody and Kr\"on and, like theirs, generalizes a similar theorem of Tutte for $k=2$. Under mild additional assumptions, which are necessary, our decompositions can be combined into one overall tree-decomposition that distinguishes, for all $k$ simultaneously, all the $k$-blocks of a finite graph.Comment: 31 page

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.Comment: 13 page

An update on vitamin B12-related gene polymorphisms and B12 status.

Vitamin B12 is an essential micronutrient in humans needed for health maintenance. Deficiency of vitamin B12 has been linked to dietary, environmental and genetic factors. Evidence for the genetic basis of vitamin B12 status is poorly understood. However, advancements in genomic techniques have increased the knowledge-base of the genetics of vitamin B12 status. Based on the candidate gene and genome-wide association (GWA) studies, associations between genetic loci in several genes involved in vitamin B12 metabolism have been identified. The objective of this literature review was to identify and discuss reports of associations between single-nucleotide polymorphisms (SNPs) in vitamin B12 pathway genes and their influence on the circulating levels of vitamin B12. Relevant articles were obtained through a literature search on PubMed through to May 2017. An article was included if it examined an association of a SNP with serum or plasma vitamin B12 concentration. Beta coefficients and odds ratios were used to describe the strength of an association, and a  < 0.05 was considered as statistically significant. Two reviewers independently evaluated the eligibility for the inclusion criteria and extracted the data. From 23 studies which fulfilled the selection criteria, 16 studies identified SNPs that showed statistically significant associations with vitamin B12 concentrations. Fifty-nine vitamin B12-related gene polymorphisms associated with vitamin B12 status were identified in total, from the following populations: African American, Brazilian, Canadian, Chinese, Danish, English, European ancestry, Icelandic, Indian, Italian, Latino, Northern Irish, Portuguese and residents of the USA. Overall, the data analyzed suggests that ethnic-specific associations are involved in the genetic determination of vitamin B12 concentrations. However, despite recent success in genetic studies, the majority of identified genes that could explain variation in vitamin B12 concentrations were from Caucasian populations. Further research utilizing larger sample sizes of non-Caucasian populations is necessary in order to better understand these ethnic-specific associations

Discovery And Confirmation Of The Shortest Gamma-Ray Burst From A Collapsar

Gamma-ray bursts (GRBs) are among the brightest and most energetic events in the Universe. The duration and hardness distribution of GRBs has two clusters(1), now understood to reflect (at least) two different progenitors(2). Short-hard GRBs (SGRBs; T-90 \u3c 2 s) arise from compact binary mergers, and long-soft GRBs (LGRBs; T-90 \u3e 2 s) have been attributed to the collapse of peculiar massive stars (collapsars)(3). The discovery of SN 1998bw/GRB 980425 (ref. (4)) marked the first association of an LGRB with a collapsar, and AT 2017gfo (ref. (5))/GRB 170817A/GW170817 (ref. (6)) marked the first association of an SGRB with a binary neutron star merger, which also produced a gravitational wave. Here, we present the discovery of ZTF20abwysqy (AT2020scz), a fast-fading optical transient in the Fermi satellite and the Interplanetary Network localization regions of GRB 200826A; X-ray and radio emission further confirm that this is the afterglow. Follow-up imaging (at rest-frame 16.5 days) reveals excess emission above the afterglow that cannot be explained as an underlying kilonova, but which is consistent with being the supernova. Although the GRB duration is short (rest-frame T-90 of 0.65 s), our panchromatic follow-up data confirm a collapsar origin. GRB 200826A is the shortest LGRB found with an associated collapsar; it appears to sit on the brink between a successful and a failed collapsar. Our discovery is consistent with the hypothesis that most collapsars fail to produce ultra-relativistic jets

Development of a Management Algorithm for Post-operative Pain (MAPP) after total knee and total hip replacement: study rationale and design.

BACKGROUND: Evidence from clinical practice and the extant literature suggests that post-operative pain assessment and treatment is often suboptimal. Poor pain management is likely to persist until pain management practices become consistent with guidelines developed from the best available scientific evidence. This work will address the priority in healthcare of improving the quality of pain management by standardising evidence-based care processes through the incorporation of an algorithm derived from best evidence into clinical practice. In this paper, the methodology for the creation and implementation of such an algorithm that will focus, in the first instance, on patients who have undergone total hip or knee replacement is described. METHODS: In partnership with clinicians, and based on best available evidence, the aim of the Management Algorithm for Post-operative Pain (MAPP) project is to develop, implement, and evaluate an algorithm designed to support pain management decision-making for patients after orthopaedic surgery. The algorithm will provide guidance for the prescription and administration of multimodal analgesics in the post-operative period, and the treatment of breakthrough pain. The MAPP project is a multisite study with one coordinating hospital and two supporting (rollout) hospitals. The design of this project is a pre-implementation-post-implementation evaluation and will be conducted over three phases. The Promoting Action on Research Implementation in Health Services (PARiHS) framework will be used to guide implementation. Outcome measurements will be taken 10 weeks post-implementation of the MAPP. The primary outcomes are: proportion of patients prescribed multimodal analgesics in accordance with the MAPP; and proportion of patients with moderate to severe pain intensity at rest. These data will be compared to the pre-implementation analgesic prescribing practices and pain outcome measures. A secondary outcome, the efficacy of the MAPP, will be measured by comparing pain intensity scores of patients where the MAPP guidelines were or were not followed. DISCUSSION: The outcomes of this study have relevance for nursing and medical professionals as well as informing health service evaluation. In establishing a framework for the sustainable implementation and evaluation of a standardised approach to post-operative pain management, the findings have implications for clinicians and patients within multiple surgical contexts

Discovery and confirmation of the shortest gamma ray burst from a collapsar [Author Correction to: Nature Astronomy https://doi.org/10.1038/s41550-021-01428-7,]

Gamma-ray bursts (GRBs) are among the brightest and most energetic events in the universe. The duration and hardness distribution of GRBs has two clusters, now understood to reflect (at least) two different progenitors. Short-hard GRBs (SGRBs; T90 2 s) have been attributed to the collapse of peculiar massive stars (collapsars). The discovery of SN 1998bw/GRB 980425 marked the first association of a LGRB with a collapsar and AT 2017gfo/GRB 170817A/GW170817 marked the first association of a SGRB with a binary neutron star merger, producing also gravitational wave (GW). Here, we present the discovery of ZTF20abwysqy (AT2020scz), a fast-fading optical transient in the Fermi Satellite and the InterPlanetary Network (IPN) localization regions of GRB 200826A; X-ray and radio emission further confirm that this is the afterglow. Follow-up imaging (at rest-frame 16.5 days) reveals excess emission above the afterglow that cannot be explained as an underlying kilonova (KN), but is consistent with being the supernova (SN). Despite the GRB duration being short (rest-frame T90 of 0.65 s), our panchromatic follow-up data confirms a collapsar origin. GRB 200826A is the shortest LGRB found with an associated collapsar; it appears to sit on the brink between a successful and a failed collapsar. Our discovery is consistent with the hypothesis that most collapsars fail to produce ultra-relativistic jets

Affordances guiding Forest School practice: The application of the Ecological Dynamics approach

Forest School focuses on child development underlining nature-connection and play pedagogy. Practitioners facilitate child-led learning through a deep observation approach. However, challenges and assumptions exist in such approaches. Additionally, a critical examination of the practice reveals that it may be lacking a solid theoretical underpinning that can respond to diverse contexts and participants while escaping a one-size-fits-all approach encouraged by commercialisation. Ecological Dynamics offers a theoretical framework that has the potential to guide Forest School practice and clarify its effectiveness. Specifically, notions of affordances combined with analysis at the level of person-environment relationships could guide future design and implementation of activities. Benefits could include realising and attuning to affordances which have sociocultural and individual connotations, thereby respecting local cultures and their community resources. The role of the Forest School practitioner becomes one of facilitating diverse populations in their perception of affordances in nature for individualised benefits, including well-being

In Search of Short Gamma-Ray Burst Optical Counterparts with the Zwicky Transient Facility

The Fermi Gamma-ray Burst Monitor (GBM) triggers on-board in response to ∼40 short gamma-ray bursts (SGRBs) per year; however, their large localization regions have made the search for optical counterparts a challenging endeavour. We have developed and executed an extensive program with the wide field of view of the Zwicky Transient Facility (ZTF) camera, mounted on the Palomar 48 inch Oschin telescope (P48), to perform target-of-opportunity (ToO) observations on 10 Fermi-GBM SGRBs during 2018 and 2020-2021. Bridging the large sky areas with small field-of-view optical telescopes in order to track the evolution of potential candidates, we look for the elusive SGRB afterglows and kilonovae (KNe) associated with these high-energy events. No counterpart has yet been found, even though more than 10 ground-based telescopes, part of the Global Relay of Observatories Watching Transients Happen (GROWTH) network, have taken part in these efforts. The candidate selection procedure and the follow-up strategy have shown that ZTF is an efficient instrument for searching for poorly localized SGRBs, retrieving a reasonable number of candidates to follow up and showing promising capabilities as the community approaches the multi-messenger era. Based on the median limiting magnitude of ZTF, our searches would have been able to retrieve a GW170817-like event up to ∼200 Mpc and SGRB afterglows to z = 0.16 or 0.4, depending on the assumed underlying energy model. Future ToOs will expand the horizon to z = 0.2 and 0.7, respectively

VERTEX CUTS

We generalise structure tree theory, which is based on removing finitely many edges, to removing finitely many vertices. This gives a significant generalization of Tutte’s tree decomposition of 2-connected graphs into 3-connected blocks. For a finite graph there is a structure tree that contains information about k-connectivity for any k. The theory can also be applied to infinite graphs that have more than one vertex end, i.e. ends that can be separated by removing a finite number of vertices. This gives a generalization of Stallings’ structure theorem for groups with more than one end