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

Polymorphic variants of genes involved in homocysteine metabolism in celiac disease

Celiac disease (CD) is a polygenic chronic enteropathy conferring an increased risk for various nutrient deficiency states. Hyperhomocysteinemia is a frequent finding in CD and may be related to the development of venous thrombosis, cardiovascular disease, and stroke in untreated CD patients. Recently, a possible excess in the frequency of the MTHFR c.677C>T (rs1801133) gene variant in CD patients was reported. The purpose of this study was to determine if there exist differences in the distribution of polymorphic variants of genes involved in homocysteine/methyl group metabolism between CD patients and the general population. A set of 10 gene polymorphisms (MTHFR rs1801133, MTR rs1805087, MTHFD1 rs2236225, MTRR rs1801394, CBS 844ins68, BHMT1 rs7356530 and rs3733890, BHMT2 rs526264 and rs625879, and TCN2 rs1801198) was tested in 134 patients with CD and 160 matched healthy controls. The frequency of the MTR rs1805087 GG genotype in CD patients was lower than in controls (0.01 and 0.06, respectively), although statistical significance was not achieved (P = 0.06). For the other analyzed polymorphisms, there was no evidence of difference in both allelic and genotypic distribution between cases and controls. The exhaustive Multifactor Dimensionality Reduction analysis revealed no combination of interactive polymorphisms predicting the incidence of CD. In contrast to the well-documented clinical observations of increased risks of vascular disease in patients with longstanding untreated CD, in our group of patients no significant association with CD was found for all tested polymorphic variants of genes involved in homocysteine metabolism. These findings should be replicated in studies with a larger sample size

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

The Role of Citizen Science and Crowdsourcing Tools in Supporting Systems Analysis at IIASA

The involvement of citizens in scientific activities from data collection to hypothesis generation is referred to as citizen science. The majority of citizen involvement tends to be on the data collection side, where numerous crowdsourcing platforms have been built to involve citizens in image interpretation, online mapping and other micro-tasks that would not otherwise have been possible. There has been increasing attention directed towards how citizen-contributed data can be used for improved calibration and validation of satellite-derived products, such as land cover, as well as data for modeling purposes. This poster will provide examples of tools and applications in the area of citizen science and crowdsourcing within the Earth Observation Systems group of the IIASA Ecosystem Services Program. These tools include Geo-Wiki, mobile gaming apps such as Cropland Capture and Picture Pile, and other high-frequency mobile data collection tools. Some of the crowdsourced data have led to improved global maps of cropland, crop-type distributions and forest cover, information which is needed by economic land-use models such as the Global Biosphere Management Model and crop-growth models such as the Environmental Policy Integrated Model. Other data have the potential to help calibrate and validate these models, for example, through information on farm-level crop types and management information. These various activities, and their linkages to systems analysis work at IIASA, will be showcased on the poster

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

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