Algebraic Conditions for Stability in Runge-Kutta Methods and Their Certification via Semidefinite Programming

In this work, we present approaches to rigorously certify $A$- and $A(\alpha)$-stability in Runge-Kutta methods through the solution of convex feasibility problems defined by linear matrix inequalities. We adopt two approaches. The first is based on sum-of-squares programming applied to the Runge-Kutta $E$-polynomial and is applicable to both $A$- and $A(\alpha)$-stability. In the second, we sharpen the algebraic conditions for $A$-stability of Cooper, Scherer, T{\"u}rke, and Wendler to incorporate the Runge-Kutta order conditions. We demonstrate how the theoretical improvement enables the practical use of these conditions for certification of $A$-stability within a computational framework. We then use both approaches to obtain rigorous certificates of stability for several diagonally implicit schemes devised in the literature.Comment: 30 pages, 1 figur

Analysis of two large functionally uncharacterized regions in the Methanopyrus kandleri AV19 genome

Background: For most sequenced prokaryotic genomes, about a third of the protein coding genes annotated are "orphan proteins", that is, they lack homology to known proteins. These hypothetical genes are typically short and randomly scattered throughout the genome. This trend is seen for most of the bacterial and archaeal genomes published to date.Results: In contrast we have found that a large fraction of the genes coding for such orphan proteins in the Methanopyrus kandleri AV19 genome occur within two large regions. These genes have no known homologs except from other M. kandleri genes. However, analysis of their lengths, codon usage, and Ribosomal Binding Site (RBS) sequences shows that they are most likely true protein coding genes and not random open reading frames.Conclusions: Although these regions can be considered as candidates for massive lateral gene transfer, our bioinformatics analysis suggests that this is not the case. We predict many of the organism specific proteins to be transmembrane and belong to protein families that are non-randomly distributed between the regions. Consistent with this, we suggest that the two regions are most likely unrelated, and that they may be integrated plasmids

Nanoproteomic analysis of ischemia-dependent changes in signaling protein phosphorylation in colorectal normal and cancer tissue

Additional file 1: Table S1. Clinical data for the 20 patients analyzed in the study. Presents patient clinical data including tumor stage and grade

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

Genome-wide multi-omics profiling of colorectal cancer identifies immune determinants strongly associated with relapse

The use and benefit of adjuvant chemotherapy to treat stage II colorectal cancer (CRC) patients is not well understood since the majority of these patients are cured by surgery alone. Identification of biological markers of relapse is a critical challenge to effectively target treatments to the ~20% of patients destined to relapse. We have integrated molecular profiling results of several “omics” data types to determine the most reliable prognostic biomarkers for relapse in CRC using data from 40 stage I and II CRC patients. We identified 31 multi-omics features that highly correlate with relapse. The data types were integrated using multi-step analytical approach with consecutive elimination of redundant molecular features. For each data type a systems biology analysis was performed to identify pathways biological processes and disease categories most affected in relapse. The biomarkers detected in tumors urine and blood of patients indicated a strong association with immune processes including aberrant regulation of T-cell and B-cell activation that could lead to overall differences in lymphocyte recruitment for tumor infiltration and markers indicating likelihood of future relapse. The immune response was the biologically most coherent signature that emerged from our analyses among several other biological processes and corroborates other studies showing a strong immune response in patients less likely to relapse

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

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