Conservation law and Hamilton-Jacobi equations on a junction: the convex case

The goal of this paper is to study the link between the solution to an Hamilton-Jacobi (HJ) equation and the solution to a Scalar Conservation Law (SCL) on a special network. When the equations are posed on the real axis, it is well known that the space derivative of the solution to the Hamilton-Jacobi equation is the solution to the corresponding scalar conservation law. On networks, the situation is more complicated and we show that this result still holds true in the convex case on a 1:1 junction. The correspondence between solutions to HJ equations and SCL on a 1:1 junction is done showing the convergence of associated numerical schemes. A second direct proof using semi-algebraic functions is also given. Here a 1:1 junction is a simple network composed of two edges and one vertex. In the case of three edges or more, we show that the associated HJ germ is not a L 1-dissipative germ, while it is the case for only two edges. As an important byproduct of our numerical approach, we get a new result on the convergence of numerical schemes for scalar conservation laws on a junction. For a general desired flux condition which is discretized, we show that the numerical solution with the general flux condition converges to the solution of a SCL problem with an effective flux condition at the junction. Up to our knowledge, in previous works the effective condition was directly implemented in the numerical scheme. In general the effective flux condition differs from the desired one, and is its relaxation, which is very natural from the point of view of Hamilton-Jacobi equations. Here for SCL, this effective flux condition is encoded in a germ that we characterize at the junction

Simultaneous analysis of plasma and CSF by NMR and hierarchical models fusion

Because cerebrospinal fluid (CSF) is the biofluid which interacts most closely with the central nervous system, it holds promise as a reporter of neurological disease, for example multiple sclerosis (MScl). To characterize the metabolomics profile of neuroinflammatory aspects of this disease we studied an animal model of MScl—experimental autoimmune/allergic encephalomyelitis (EAE). Because CSF also exchanges metabolites with blood via the blood–brain barrier, malfunctions occurring in the CNS may be reflected in the biochemical composition of blood plasma. The combination of blood plasma and CSF provides more complete information about the disease. Both biofluids can be studied by use of NMR spectroscopy. It is then necessary to perform combined analysis of the two different datasets. Mid-level data fusion was therefore applied to blood plasma and CSF datasets. First, relevant information was extracted from each biofluid dataset by use of linear support vector machine recursive feature elimination. The selected variables from each dataset were concatenated for joint analysis by partial least squares discriminant analysis (PLS-DA). The combined metabolomics information from plasma and CSF enables more efficient and reliable discrimination of the onset of EAE. Second, we introduced hierarchical models fusion, in which previously developed PLS-DA models are hierarchically combined. We show that this approach enables neuroinflamed rats (even on the day of onset) to be distinguished from either healthy or peripherally inflamed rats. Moreover, progression of EAE can be investigated because the model separates the onset and peak of the disease

Polygenic risk score for atopic dermatitis in the Canadian population

Atopic dermatitis (AD) is characterized by a damaged skin barrier that allows allergens to penetrate the body, leading to sensitization and a higher risk of developing food allergies (relative risk [RR], 33.79), asthma (RR, 7.04), and/or rhinitis (RR, 11.75), all features of the atopic march.1 Recent evidence has shown that the atopic march can be modified in high-risk infants with early interventions directed at reestablishing and/or maintaining skin barrier function with intense use of simple emollients, and introducing food allergens early into the diet.2, 3, 4, 5 Although these constitute examples of low-intensity, high-impact interventions for health care systems, their successful and indiscriminate implementation in the whole population is neither feasible nor realistic. In this context, building a predictive tool to identify children at high risk of developing moderate to severe AD (MSAD) would allow targeted interventions with maximized impact. In this study, a polygenic risk score (PRS) with an area under the curve (AUC) of 88% and explaining 37% of MSAD variance was established for the Canadian population

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

Integrated Genomic Analysis of the Ubiquitin Pathway across Cancer Types

Protein ubiquitination is a dynamic and reversibleprocess of adding single ubiquitin molecules orvarious ubiquitin chains to target proteins. Here,using multidimensional omic data of 9,125 tumorsamples across 33 cancer types from The CancerGenome Atlas, we perform comprehensive molecu-lar characterization of 929 ubiquitin-related genesand 95 deubiquitinase genes. Among them, we sys-tematically identify top somatic driver candidates,including mutatedFBXW7with cancer-type-specificpatterns and amplifiedMDM2showing a mutuallyexclusive pattern withBRAFmutations. Ubiquitinpathway genes tend to be upregulated in cancermediated by diverse mechanisms. By integratingpan-cancer multiomic data, we identify a group oftumor samples that exhibit worse prognosis. Thesesamples are consistently associated with the upre-gulation of cell-cycle and DNA repair pathways, char-acterized by mutatedTP53,MYC/TERTamplifica-tion, andAPC/PTENdeletion. Our analysishighlights the importance of the ubiquitin pathwayin cancer development and lays a foundation fordeveloping relevant therapeutic strategies