Binomial edge ideals and rational normal scrolls

Let $X$ be the Hankel matrix of size $2\times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_G\subset K[x_1,\ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaulay. We find the minimal primes of $I_G$ and show that $I_G$ is a set theoretical complete intersection. Moreover, a sharp upper bound for the regularity of $I_G$ is given

A new method for the synthesis of pyrazolidines.

Fully protected pyrazolidines can be readily obtained by acid-catalysed cyclisations of the corresponding allylic hydrazines by carbenium ion generation using concentrated sulfuric acid in dichloromethan

Role of CXR and HRCT in diagnosing COVID-19, a descriptive cross-sectional study, at a tertiary care hospital in Pakistan

ABSTRACT Objectives: Objectives of this study are to do the analysis of chest X-ray and High-resolution CT scan findings in patients who are clinical suspects of COVID-19 infection. The other objective is to classify the radiological findings in mild, moderate or severe diseases according to BSTI criteria for chest X-ray and CTSS for high-resolution CT scan. Methods: This is a cross-sectional descriptive study. A group of 50 patients who were clinically suspected cases of COVID-19 infection, presented to Corona flu filter clinic of Holy Family Hospital (HFH) or admitted to corona isolation wards were included. The time duration of the study was from 15 May 2020 to 15 June 2020. Patients labelled as clinically suspected cases were having positive contact with confirmed positive (based upon positive PCR) patients. Recent travel history from the area having an outbreak. They were having clinical signs/symptoms of fever, cough, and shortness of breath, lethargy and loss of sense of smell or taste. CXR and HRCT was the investigation of choice for all the 50 patients.  I also did PCR to make a correlation with the other two tests. All radiological findings were analyzed based upon Fleischner society glossary of terms for thoracic imaging. Two radiologists then assessed CXRs findings based upon BSTI criteria. They marked those CXR findings as low, moderate and high probability for COVID-19 infection. HRCT findings were analyzed using CT-SS, and researchers labelled outcomes as mild, moderate and severe disease.  Results: Out of 50 patients, 33(66%) were males, and 17(34%) were females. Mean age was 51 with ages ranging from 30-72 years. Presenting complaints were fever in 42(84%) patients, cough in 37(74%), lethargy in 33(66%), shortness of breath in 41(82%) and loss of sense of smell and taste in 21(42%) patients. Out of these 50, 32(72%) were having positive PCR for COVID-19 infection. On CXR 5(10%) patients showed classic findings which were highly probable for COVID-19. 19(38%) patients showed intermediate results for COVID-19, 7(14%) patients had a low probability of COVID-19 infection on CXRS. Out of 50, 19(38%), patients showed normal CXR with no evidence of COVID-19 infection. We did HRCT of the same patients on the same day; it showed 21(42%)patients with mild disease,23(46%)patients with moderate disease and 6(12%)patients with the severe disease according to CTSI.HRCT of 3(6%)patients was ok with no evidence of illness in bilateral lungs.    Conclusion: The role of radiology is crucial in the diagnosis of this viral illness. CXR, with its ability to detect changes of COVID-19 in lungs, should be used as a first-line imaging modality in clinically suspected patients. Moreover, it should also be used for follow up of patients with COVID-19. HRCT is very sensitive in the diagnosis of COVID-19 infection in its milder forms. Due to lack of its widespread availability in countries with inadequate medical facilities, it was not the primary imaging tool/screening tool. Due to risk of infection to radiological staff as well as non-covid-19 patients due to surface contact, due to reduced infection control issues, due to increased burden of ionizing radiations in patients. All these factors limit the role of HRCT as a primary imaging modality for COVID-19 infectio

Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel

This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractional order model. Additionally, stability is evaluated, along with the local and global effects of the virus that causes Ebola. Using the fractional order model of Ebola virus infections, the existence and uniqueness of solutions, as well the posedness and biological viability and disease free equilibrium points are confirmed. Many applications of fractional operators in modern mathematics exist, including the intricate and important study of symmetrical systems. Symmetry analysis is a powerful tool that enables the creation of numerical solutions for a given fractional differential equation very methodically. For this, we compare the results with the Caputo derivative operator to understand the dynamic behavior of the disease. The simulation demonstrates how all classes have convergent characteristics and maintain their places over time, reflecting the true behavior of Ebola virus infection. Power law kernel with the two step polynomial Newton method were used. This model seems to be quite strong and capable of reproducing the issue’s anticipated theoretical conditions.Basque Government:Grant IT1555-22 Basque Government: Grant KK-2022/00090 MCIN/AEI 269.10.13039/501100011033/FEDER,UE: Grant PID2021-1235430B-C21 MCIN/AEI 269.10.13039/501100011033/FEDER,UE: Grant PID2021-1235430B-C22

1,3-Diphenyl-1H-pyrazole-4-carbaldehyde

There are four mol­ecules in the asymmetric unit of the title compound, C16H12N2O. The dihedral angle between the phenyl rings in the mol­ecules are 22.2 (2), 22.4 (2), 25.1 (3) and 41.9 (2)°. In the crystal, mol­ecules form dimers due to inter­molecular C—H⋯O hydrogen bonds, which result in one R 2 2(10) and two R 2 1(7) ring motifs. Weak aromatic π–π stacking [centroid–centroid separation = 3.788 (3) Å] and C—H⋯π inter­actions may also consolidate the packing

Global prevalence and genotype distribution of hepatitis C virus infection in 2015 : A modelling study

Publisher Copyright: © 2017 Elsevier LtdBackground The 69th World Health Assembly approved the Global Health Sector Strategy to eliminate hepatitis C virus (HCV) infection by 2030, which can become a reality with the recent launch of direct acting antiviral therapies. Reliable disease burden estimates are required for national strategies. This analysis estimates the global prevalence of viraemic HCV at the end of 2015, an update of—and expansion on—the 2014 analysis, which reported 80 million (95% CI 64–103) viraemic infections in 2013. Methods We developed country-level disease burden models following a systematic review of HCV prevalence (number of studies, n=6754) and genotype (n=11 342) studies published after 2013. A Delphi process was used to gain country expert consensus and validate inputs. Published estimates alone were used for countries where expert panel meetings could not be scheduled. Global prevalence was estimated using regional averages for countries without data. Findings Models were built for 100 countries, 59 of which were approved by country experts, with the remaining 41 estimated using published data alone. The remaining countries had insufficient data to create a model. The global prevalence of viraemic HCV is estimated to be 1·0% (95% uncertainty interval 0·8–1·1) in 2015, corresponding to 71·1 million (62·5–79·4) viraemic infections. Genotypes 1 and 3 were the most common cause of infections (44% and 25%, respectively). Interpretation The global estimate of viraemic infections is lower than previous estimates, largely due to more recent (lower) prevalence estimates in Africa. Additionally, increased mortality due to liver-related causes and an ageing population may have contributed to a reduction in infections. Funding John C Martin Foundation.publishersversionPeer reviewe

Effect of early tranexamic acid administration on mortality, hysterectomy, and other morbidities in women with post-partum haemorrhage (WOMAN): an international, randomised, double-blind, placebo-controlled trial

Background Post-partum haemorrhage is the leading cause of maternal death worldwide. Early administration of tranexamic acid reduces deaths due to bleeding in trauma patients. We aimed to assess the effects of early administration of tranexamic acid on death, hysterectomy, and other relevant outcomes in women with post-partum haemorrhage. Methods In this randomised, double-blind, placebo-controlled trial, we recruited women aged 16 years and older with a clinical diagnosis of post-partum haemorrhage after a vaginal birth or caesarean section from 193 hospitals in 21 countries. We randomly assigned women to receive either 1 g intravenous tranexamic acid or matching placebo in addition to usual care. If bleeding continued after 30 min, or stopped and restarted within 24 h of the first dose, a second dose of 1 g of tranexamic acid or placebo could be given. Patients were assigned by selection of a numbered treatment pack from a box containing eight numbered packs that were identical apart from the pack number. Participants, care givers, and those assessing outcomes were masked to allocation. We originally planned to enrol 15 000 women with a composite primary endpoint of death from all-causes or hysterectomy within 42 days of giving birth. However, during the trial it became apparent that the decision to conduct a hysterectomy was often made at the same time as randomisation. Although tranexamic acid could influence the risk of death in these cases, it could not affect the risk of hysterectomy. We therefore increased the sample size from 15 000 to 20 000 women in order to estimate the effect of tranexamic acid on the risk of death from post-partum haemorrhage. All analyses were done on an intention-to-treat basis. This trial is registered with ISRCTN76912190 (Dec 8, 2008); ClinicalTrials.gov, number NCT00872469; and PACTR201007000192283. Findings Between March, 2010, and April, 2016, 20 060 women were enrolled and randomly assigned to receive tranexamic acid (n=10 051) or placebo (n=10 009), of whom 10 036 and 9985, respectively, were included in the analysis. Death due to bleeding was significantly reduced in women given tranexamic acid (155 [1·5%] of 10 036 patients vs 191 [1·9%] of 9985 in the placebo group, risk ratio [RR] 0·81, 95% CI 0·65–1·00; p=0·045), especially in women given treatment within 3 h of giving birth (89 [1·2%] in the tranexamic acid group vs 127 [1·7%] in the placebo group, RR 0·69, 95% CI 0·52–0·91; p=0·008). All other causes of death did not differ significantly by group. Hysterectomy was not reduced with tranexamic acid (358 [3·6%] patients in the tranexamic acid group vs 351 [3·5%] in the placebo group, RR 1·02, 95% CI 0·88–1·07; p=0·84). The composite primary endpoint of death from all causes or hysterectomy was not reduced with tranexamic acid (534 [5·3%] deaths or hysterectomies in the tranexamic acid group vs 546 [5·5%] in the placebo group, RR 0·97, 95% CI 0·87-1·09; p=0·65). Adverse events (including thromboembolic events) did not differ significantly in the tranexamic acid versus placebo group. Interpretation Tranexamic acid reduces death due to bleeding in women with post-partum haemorrhage with no adverse effects. When used as a treatment for postpartum haemorrhage, tranexamic acid should be given as soon as possible after bleeding onset. Funding London School of Hygiene & Tropical Medicine, Pfizer, UK Department of Health, Wellcome Trust, and Bill & Melinda Gates Foundation