A Generating Function for all Semi-Magic Squares and the Volume of the Birkhoff Polytope

We present a multivariate generating function for all n x n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semi-magic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of the polytope B_n of n x n doubly-stochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of B_n and any of its faces.Comment: 24 pages, 1 figure. To appear in Journal of Algebraic Combinatoric

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types

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

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

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

Quasi-periodic X-ray eruptions years after a nearby tidal disruption event

\ua9 The Author(s) 2024.Quasi-periodic eruptions (QPEs) are luminous bursts of soft X-rays from the nuclei of galaxies, repeating on timescales of hours to weeks1–5. The mechanism behind these rare systems is uncertain, but most theories involve accretion disks around supermassive black holes (SMBHs) undergoing instabilities6–8 or interacting with a stellar object in a close orbit9–11. It has been suggested that this disk could be created when the SMBH disrupts a passing star8,11, implying that many QPEs should be preceded by observable tidal disruption events (TDEs). Two known QPE sources show long-term decays in quiescent luminosity consistent with TDEs4,12 and two observed TDEs have exhibited X-ray flares consistent with individual eruptions13,14. TDEs and QPEs also occur preferentially in similar galaxies15. However, no confirmed repeating QPEs have been associated with a spectroscopically confirmed TDE or an optical TDE observed at peak brightness. Here we report the detection of nine X-ray QPEs with a mean recurrence time of approximately 48 h from AT2019qiz, a nearby and extensively studied optically selected TDE16. We detect and model the X-ray, ultraviolet (UV) and optical emission from the accretion disk and show that an orbiting body colliding with this disk provides a plausible explanation for the QPEs

Integrated genomic characterization of oesophageal carcinoma

Oesophageal cancers are prominent worldwide; however, there are few targeted therapies and survival rates for these cancers remain dismal. Here we performed a comprehensive molecular analysis of 164 carcinomas of the oesophagus derived from Western and Eastern populations. Beyond known histopathological and epidemiologic distinctions, molecular features differentiated oesophageal squamous cell carcinomas from oesophageal adenocarcinomas. Oesophageal squamous cell carcinomas resembled squamous carcinomas of other organs more than they did oesophageal adenocarcinomas. Our analyses identified three molecular subclasses of oesophageal squamous cell carcinomas, but none showed evidence for an aetiological role of human papillomavirus. Squamous cell carcinomas showed frequent genomic amplifications of CCND1 and SOX2 and/or TP63, whereas ERBB2, VEGFA and GATA4 and GATA6 were more commonly amplified in adenocarcinomas. Oesophageal adenocarcinomas strongly resembled the chromosomally unstable variant of gastric adenocarcinoma, suggesting that these cancers could be considered a single disease entity. However, some molecular features, including DNA hypermethylation, occurred disproportionally in oesophageal adenocarcinomas. These data provide a framework to facilitate more rational categorization of these tumours and a foundation for new therapies.ope

Integrated genomic analyses of ovarian carcinoma

A catalogue of molecular aberrations that cause ovarian cancer is critical for developing and deploying therapies that will improve patients’ lives. The Cancer Genome Atlas project has analysed messenger RNA expression, microRNA expression, promoter methylation and DNA copy number in 489 high-grade serous ovarian adenocarcinomas and the DNA sequences of exons from coding genes in 316 of these tumours. Here we report that high-grade serous ovarian cancer is characterized by TP53 mutations in almost all tumours (96%); low prevalence but statistically recurrent somatic mutations in nine further genes including NF1, BRCA1, BRCA2, RB1 and CDK12; 113 significant focal DNA copy number aberrations; and promoter methylation events involving 168 genes. Analyses delineated four ovarian cancer transcriptional subtypes, three microRNA subtypes, four promoter methylation subtypes and a transcriptional signature associated with survival duration, and shed new light on the impact that tumours with BRCA1/2 (BRCA1 or BRCA2) and CCNE1 aberrations have on survival. Pathway analyses suggested that homologous recombination is defective in about half of the tumours analysed, and that NOTCH and FOXM1 signalling are involved in serous ovarian cancer pathophysiology.National Institutes of Health (U.S.) (Grant U54HG003067)National Institutes of Health (U.S.) (Grant U54HG003273)National Institutes of Health (U.S.) (Grant U54HG003079)National Institutes of Health (U.S.) (Grant U24CA126543)National Institutes of Health (U.S.) (Grant U24CA126544)National Institutes of Health (U.S.) (Grant U24CA126546)National Institutes of Health (U.S.) (Grant U24CA126551)National Institutes of Health (U.S.) (Grant U24CA126554)National Institutes of Health (U.S.) (Grant U24CA126561)National Institutes of Health (U.S.) (Grant U24CA126563)National Institutes of Health (U.S.) (Grant U24CA143882)National Institutes of Health (U.S.) (Grant U24CA143731)National Institutes of Health (U.S.) (Grant U24CA143835)National Institutes of Health (U.S.) (Grant U24CA143845)National Institutes of Health (U.S.) (Grant U24CA143858)National Institutes of Health (U.S.) (Grant U24CA144025)National Institutes of Health (U.S.) (Grant U24CA143866)National Institutes of Health (U.S.) (Grant U24CA143867)National Institutes of Health (U.S.) (Grant U24CA143848)National Institutes of Health (U.S.) (Grant U24CA143843)National Institutes of Health (U.S.) (Grant R21CA135877

Integrative Genomic Analysis of Cholangiocarcinoma Identifies Distinct IDH -Mutant Molecular Profiles

Cholangiocarcinoma (CCA) is an aggressive malignancy of the bile ducts, with poor prognosis and limited treatment options. Here, we describe the integrated analysis of somatic mutations, RNA expression, copy number, and DNA methylation by The Cancer Genome Atlas of a set of predominantly intrahepatic CCA cases and propose a molecular classification scheme. We identified an IDH mutant-enriched subtype with distinct molecular features including low expression of chromatin modifiers, elevated expression of mitochondrial genes, and increased mitochondrial DNA copy number. Leveraging the multi-platform data, we observed that ARID1A exhibited DNA hypermethylation and decreased expression in the IDH mutant subtype. More broadly, we found that IDH mutations are associated with an expanded histological spectrum of liver tumors with molecular features that stratify with CCA. Our studies reveal insights into the molecular pathogenesis and heterogeneity of cholangiocarcinoma and provide classification information of potential therapeutic significance