Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established

Presence of 5-hydroxyguaiacyl units as native lignin constituents in plants as seen by Py-GC/MS

Instituto de Recursos Naturales y Agrobiología de Sevilla, CSIC, P.O. Box 1052, 41080-Seville, Spain 2Centro de Investigaciones Biológicas, CSIC, Ramiro de Maeztu 9, E-28040 Madrid, Spain E-mail address: [email protected] (J.C. del Río)The presence of 5-hydroxyguaiacyl moieties in the lignin from several plants has been assessed by Py-GC/MS. Different woody (eucalypt) and nonwoody (flax, hemp, kenaf, jute, sisal and abaca) angiosperms were selected for this study. The pyrolysis of whole fibers released lignin-derived products with p-hydroxyphenyl, guaiacyl and syringyl structures. Indeed, a series of compounds having a 5-hydroxyguaiacyl nuclei, including 3-methoxycatechol, 5-vinyl-3-methoxycatechol and 5-propenyl-3-methoxycatechol, were detected and identified in all samples, although in lower amounts than the normal guaiacyl and syringyl compounds. The analysis of the lignins isolated from the same plants also indicated the presence of 5-hydroxyguaiacyl moieties in the isolated lignins. These compounds are supposed to arise from the pyrolysis of 5-hydroxyguaiacyl moieties, which are supposed to be native constituents of lignin in plants forming benzodioxane substructures.This study has been supported by the Spanish Ministerio de Ciencia y Tecnología (MCyT) and FEDER funds (project AGL2005-01748) and the EU project BIORENEW (NMP2-CT-2006-026456). We thank CELESA S.A. (Tortosa, Spain) for providing the nonwoody plant samples, and ENCE for providing the eucalypt wood sample.Peer reviewe

Mathematical Musings of a Urologist

The derivatives with respect to the variable $r$ of $\pi r^2$ and $\frac{4}{3}\pi r^3$ are $2\pi r$ and $4\pi r^2$, respectively. This relates, through the derivative, the area enclosed in a circle to the length of that circle and, likewise, the volume of a sphere to the surface area of that sphere. The reasons why this works are basic to a first course in calculus. In this brief article, we expand on these ideas to shapes other than circles and spheres. Our approach is with the first year calculus student in mind

Engineering Analysis Studies for Preliminary Design of Lightweight Cryogenic Hydrogen Tanks in UAV Applications

A series of engineering analysis studies were conducted to investigate the potential application of nanoclay-enhanced graphite/epoxy composites and polymer cross-linked silica aerogels in cryogenic hydrogen storage tank designs. This assessment focused on the application of these materials in spherical tank designs for unmanned aeronautic vehicles with mission durations of 14 days. Two cryogenic hydrogen tank design concepts were considered: a vacuum-jacketed design and a sandwiched construction with an aerogel insulating core. Analyses included thermal and structural analyses of the tank designs as well as an analysis of hydrogen diffusion to specify the material permeability requirements. The analyses also provided material property targets for the continued development of cross-linked aerogels and nanoclay-enhanced graphite/epoxy composites for cryogenic storage tank applications. The results reveal that a sandwiched construction with an aerogel core is not a viable design solution for a 14-day mission. A vacuum-jacketed design approach was shown to be far superior to an aerogel. Aerogel insulation may be feasible for shorter duration missions. The results also reveal that the application of nanoclay-enhanced graphite/epoxy should be limited to the construction of outer tanks in a vacuum-jacketed design, since a graphite/epoxy inner tank does not provide a significant weight savings over aluminum and since the ability of nanoclay-enhanced graphite/epoxy to limit hydrogen permeation is still in question

Liquefying the Gulf Coast: A Cumulative Impact Assessment of LNG Buildout in Louisiana and Texas

This report represents a substantial endeavor aimed at providing a critical examination of the complex interplay between fossil fuel development, environmental justice, and climate justice in a region of the United States that has an enduring legacy of economic injustice and environmental racism. In recent years, the rapid expansion of liquefied natural gas (LNG) infrastructure along the Gulf Coast has raised significant concerns regarding the environmental and social consequences

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

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