A new proof of Stanley's theorem on the strong Lefschetz property

A standard graded artinian monomial complete intersection algebra $A=\Bbbk[x_1,x_2,\ldots,x_n]/(x_1^{a_1},x_2^{a_2},\ldots,x_n^{a_n})$, with $\Bbbk$ a field of characteristic zero, has the strong Lefschetz property due to Stanley in 1980. In this paper, we give a new proof for this result by using only the basic properties of linear algebra. Furthermore, our proof is still true in the case where the characteristic of $\Bbbk$ is greater than the socle degree of $A$, namely $a_1+a_2+\cdots+a_n - n$

Assessing Spatiotemporal Drought Dynamics and Its Related Environmental Issues in the Mekong River Delta

Drought is a major natural disaster that creates a negative impact on socio-economic development and environment. Drought indices are typically applied to characterize drought events in a meaningful way. This study aims at examining variations in agricultural drought severity based on the relationship between standardized ratio of actual and potential evapotranspiration (ET and PET), enhanced vegetation index (EVI), and land surface temperature (LST) derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) platform. A new drought index, called the enhanced drought severity index (EDSI), was developed by applying spatiotemporal regression methods and time-series biophysical data derived from remote sensing. In addition, time-series trend analysis in the 2001–2018 period, along with the Mann–Kendal (MK) significance test and the Theil Sen (TS) slope, were used to examine the spatiotemporal dynamics of environmental parameters (i.e., LST, EVI, ET, and PET), and geographically weighted regression (GWR) was subsequently applied in order to analyze the local correlations among them. Results showed that a significant correlation was discovered among LST, EVI, ET, and PET, as well as their standardized ratios (|r| > 0.8, p 0.7 and a statistical significance p < 0.01. Besides, it was found that the temporal tendency of this phenomenon was the increase in intensity of drought, and that coastal areas in the study area were more vulnerable to this phenomenon. This study demonstrates the effectiveness of EDSI and the potential application of integrating spatial regression and time-series data for assessing regional drought conditions

Association between vitamin D insufficiency and tuberculosis in a vietnamese population

<p>Abstract</p> <p>Background</p> <p>Recent <it>in vitro </it>evidence suggests a link between vitamin D status and the risk of tuberculosis (TB). This study sought to examine the association between vitamin D status, parathyroid hormone (PTH) and the risk of TB in a Vietnamese population.</p> <p>Methods</p> <p>The study was designed as a matched case-control study, which involved 166 TB patients (113 men and 53 women), who were age-and-sex matched with 219 controls (113 men and 106 women). The average age of men and women was 49 and 50, respectively. TB was diagnosed by the presence of acid-fast bacilli on smears from sputum, and the isolation of <it>M. tuberculosis</it>. All patients were hospitalized for treatment in a TB specialist hospital. Controls were randomly drawn from the general community within the Ho Chi Minh, Vietnam. 25-hydroxyvitamin D [25(OH)D] and PTH was measured prior to treatment by an electrochemiluminescence immunoassay (ECLIA) on a Roche Elecsys. A serum level of 25(OH)D below 30 ng/mL was deemed to be vitamin D insufficient.</p> <p>Results</p> <p>The prevalence of vitamin D insufficiency was 35.4% in men with TB and 19.5% in controls (<it>P </it>= 0.01). In women, there were no significant differences in serum 25(OH)D and serum PTH levels between TB patients and controls. The prevalence of vitamin D insufficiency in women with TB (45.3%) was not significantly different from those without TB (47.6%; <it>P </it>= 0.91). However, in both genders, serum calcium levels in TB patients were significantly lower than in non-TB individuals. Smoking (odds ratio [OR] 1.25; 95% confidence interval [CI] 1.10 - 14.7), reduced 25(OH)D (OR per standard deviation [SD]: 1.14; 95% CI 1.07 - 10.7) and increased PTH (OR per SD 1.13; 95% CI 1.05 - 10.4) were independently associated with increased risk of TB in men.</p> <p>Conclusion</p> <p>These results suggest that vitamin D insufficiency was a risk factor for tuberculosis in men, but not in women. However, it remains to be established whether the association is a causal relationship.</p

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment

Implicating genes, pleiotropy, and sexual dimorphism at blood lipid loci through multi-ancestry meta-analysis

Publisher Copyright: © 2022, The Author(s).Background: Genetic variants within nearly 1000 loci are known to contribute to modulation of blood lipid levels. However, the biological pathways underlying these associations are frequently unknown, limiting understanding of these findings and hindering downstream translational efforts such as drug target discovery. Results: To expand our understanding of the underlying biological pathways and mechanisms controlling blood lipid levels, we leverage a large multi-ancestry meta-analysis (N = 1,654,960) of blood lipids to prioritize putative causal genes for 2286 lipid associations using six gene prediction approaches. Using phenome-wide association (PheWAS) scans, we identify relationships of genetically predicted lipid levels to other diseases and conditions. We confirm known pleiotropic associations with cardiovascular phenotypes and determine novel associations, notably with cholelithiasis risk. We perform sex-stratified GWAS meta-analysis of lipid levels and show that 3–5% of autosomal lipid-associated loci demonstrate sex-biased effects. Finally, we report 21 novel lipid loci identified on the X chromosome. Many of the sex-biased autosomal and X chromosome lipid loci show pleiotropic associations with sex hormones, emphasizing the role of hormone regulation in lipid metabolism. Conclusions: Taken together, our findings provide insights into the biological mechanisms through which associated variants lead to altered lipid levels and potentially cardiovascular disease risk.Peer reviewe

Implicating genes, pleiotropy, and sexual dimorphism at blood lipid loci through multi-ancestry meta-analysis

Abstract Background Genetic variants within nearly 1000 loci are known to contribute to modulation of blood lipid levels. However, the biological pathways underlying these associations are frequently unknown, limiting understanding of these findings and hindering downstream translational efforts such as drug target discovery. Results To expand our understanding of the underlying biological pathways and mechanisms controlling blood lipid levels, we leverage a large multi-ancestry meta-analysis (N = 1,654,960) of blood lipids to prioritize putative causal genes for 2286 lipid associations using six gene prediction approaches. Using phenome-wide association (PheWAS) scans, we identify relationships of genetically predicted lipid levels to other diseases and conditions. We confirm known pleiotropic associations with cardiovascular phenotypes and determine novel associations, notably with cholelithiasis risk. We perform sex-stratified GWAS meta-analysis of lipid levels and show that 3–5% of autosomal lipid-associated loci demonstrate sex-biased effects. Finally, we report 21 novel lipid loci identified on the X chromosome. Many of the sex-biased autosomal and X chromosome lipid loci show pleiotropic associations with sex hormones, emphasizing the role of hormone regulation in lipid metabolism. Conclusions Taken together, our findings provide insights into the biological mechanisms through which associated variants lead to altered lipid levels and potentially cardiovascular disease risk