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

Seismic Category I Structures Program

With the use of different size scale models, the Seismic Category I Structures Program has demonstrated consistent results for measured values of stiffness at working loads. Furthermore, the values are well below the theoretical stiffnesses calculated from an uncracked strength-of-materials approach. The scale model structures, which are also models of each other, have demonstrated scalability between models. The current effort is to demonstrate that the use of microconcrete and other modeling effects do not introduce significant distortions that could drastically change conclusions regarding prototype behavior for these very stiff, shear-dominated structures. Working closely with the technical review group (TRG) for this program, structures have been designed and tests have been planned that will help to resolve issues surrounding the use of microconcrete scale models

The Seismic Category 1 Structures Program

The Seismic Category I Structures Program entered a new phase at the end of FY 1984. During the prior fiscal years, tests on microconcrete scale model shear deformation dominated structures were completed. The results indicated that these structures responded to seismic excitations with frequencies that were reduced by factors of two or more over those calculated based on an uncracked cross section strength-of-materials approach. This reduction implies that stiffness associated with seismic working loads (loads resulting from an operating basis earthquake up to and including a safe shutdown earthquake) are down by a factor of four or more. These reductions were also consistent with those measured during quasistatic tests to an equivalent level of loading. Furthermore, though the structures themselves were shown to have sufficient reserve margin, the equipment and piping are designed to response spectra that are based on uncracked cross sectional member properties, and these spectra may not be appropriate for actual building responses

Latest results from the Seismic Category I Structures Program

With the use of scale models, the Seismic Category I Structures Program has demonstrated consistent results for measured values of stiffness at working loads. Furthermore, the values are well below the theoretical stiffnesses calculated from an uncracked strength-of-materials approach. The scale model structures, which are also models of each other, have demonstrated scalability between models. The current effort is to demonstrate that the use of microconcrete and other modeling effects do not introduce significant distortions that could drastically change conclusions regarding prototype behavior for these very stiff, shear dominated structures. 3 refs., 3 figs., 1 tab

Static load cycle testing of a low-aspect-ratio four-inch wall, TRG-type structure, TRG-5-4 (1. 0, 0. 56)

This report is the second in a series of test reports that details the quasi-static cyclic testing of low height-to-length aspect ratio reinforced concrete structures. The test structures were designed according to the recommendations of a technical review group for the US Nuclear Regulatory Commission sponsored Seismic Category I Structures Program. The structure tested and reported here had 4-in.-thick shear and end walls, and the elastic deformation was dominated by shear. The background of the program and previous results are given for completeness. Details of the geometry, material property tests, construction history, ultrasonic testing, and modal testing to find the undamaged dynamic characteristics of the structures are given. Next, the static test procedure and results in terms of stiffness and load deformation behavior are given. Finally, results are shown relative to other known results, and conclusions are presented. 33 refs., 140 figs., 13 tabs

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

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