The collocation method for mixed boundary value problems on domains with curved polygonal boundaries

We consider an indirect boundary integral equation formulation for the mixed Dirichlet Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and a cosine approximating space. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. A complete stability and solvability analysis of the transformed integral equations is given by use of a Mellin transform technique, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space

Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary

We consider a fully discrete qualocation method for Symm's integral equation. The method is that of Sloan and Burn [14], for which a complete analysis is available in the case of smooth curves. The convergence for smooth curves can be improved by a subtraction of singularity (Jeon and Kimn [10]). In this paper we extend these results for smooth boundaries to polygonal boundaries. The analysis uses a mesh grading transformation method for Symm's integral equation, as in Elschner and Graham [4] and Elschner and Stephan [7], to overcome the singular behavior of solutions at corners

High-dimensional deconstruction of pancreatic cancer identifies tumor microenvironmental and developmental stemness features that predict survival

Numerous cell states are known to comprise the pancreatic ductal adenocarcinoma (PDAC) tumor microenvironment (TME). However, the developmental stemness and co-occurrence of these cell states remain poorly defined. Here, we performed single-cell RNA sequencing (scRNA-seq) on a cohort of treatment-naive PDAC time-of-diagnosis endoscopic ultrasound-guided fine needle biopsy (EUS-FNB) samples (n = 25). We then combined these samples with surgical resection (n = 6) and publicly available samples to increase statistical power (n = 80). Following annotation into 25 distinct cell states, cells were scored for developmental stemness, and a customized version of the Ecotyper tool was used to identify communities of co-occurring cell states in bulk RNA-seq samples (n = 268). We discovered a tumor microenvironmental community comprised of aggressive basal-like malignant cells, tumor-promoting SPP1+ macrophages, and myofibroblastic cancer-associated fibroblasts associated with especially poor prognosis. We also found a developmental stemness continuum with implications for survival that is present in both malignant cells and cancer-associated fibroblasts (CAFs). We further demonstrated that high-dimensional analyses predictive of survival are feasible using standard-of-care, time-of-diagnosis EUS-FNB specimens. In summary, we identified tumor microenvironmental and developmental stemness characteristics from a high-dimensional gene expression analysis of PDAC using human tissue specimens, including time-of-diagnosis EUS-FNB samples. These reveal new connections between tumor microenvironmental composition, CAF and malignant cell stemness, and patient survival that could lead to better upfront risk stratification and more personalized upfront clinical decision-making

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