On the number of representations providing noiseless subsystems

This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function $f_d(n)$ which is the fraction of all $d$-dimensional quantum systems which preserve $n$ bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.Comment: 17 pp, 4 figs, accepted for Physical Review

Fano Resonances in Electronic Transport through a Single Electron Transistor

We have observed asymmetric Fano resonances in the conductance of a single electron transistor resulting from interference between a resonant and a nonresonant path through the system. The resonant component shows all the features typical of quantum dots, but the origin of the non-resonant path is unclear. A unique feature of this experimental system, compared to others that show Fano line shapes, is that changing the voltages on various gates allows one to alter the interference between the two paths.Comment: 8 pages, 6 figures. Submitted to PR

Vicious walkers, friendly walkers and Young tableaux II: With a wall

We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of $n$-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absence of a wall and in the presence of a wall.Comment: 35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the statement of Theorem 4 and its proof were correcte

Design of a Microsphere-Based High-Throughput Gene Expression Assay to Determine Estrogenic Potential

Recently gene expression studies have been multiplied at an accelerated rate by the use of high-density microarrays. By assaying thousands of transcripts at a time, microarrays have led to the discovery of dozens of genes involved in particular biochemical processes, for example, the response of a tissue/organ to a given chemical with therapeutic or toxic properties. The next step in these studies is to focus on the response of a subset of relevant genes to verify or refine potential therapeutic or toxic properties. We have developed a sensitive, high-throughput gene expression assay for this purpose. In this assay, based on the Luminex xMAP system, carefully selected oligonucleotides were covalently linked to fluorescently coded microspheres that are hybridized to biotinylated cRNA followed by amplification of the signal, which results in a rapid, sensitive, multiplexed assay platform. Using this system, we have developed an RNA expression profiling assay specific for 17 estrogen-responsive transcripts and three controls. This assay can evaluate up to 100 distinct analytes simultaneously in a single sample, in a 96-well plate format. This system has improved sensitivity versus existing microsphere-based assays and has sensitivity and precision comparable with or better than microarray technology. We have achieved detection levels down to 1 amol, detecting rare messages in complex cRNA samples, using as little as 2.5 μg starting cRNA. This assay offers increased throughput with decreased costs compared with existing microarray technologies, with the trade-off being in the total number of transcripts that can be analyzed

Evolution of Symbiotic Bacteria in the Distal Human Intestine

The adult human intestine contains trillions of bacteria, representing hundreds of species and thousands of subspecies. Little is known about the selective pressures that have shaped and are shaping this community's component species, which are dominated by members of the Bacteroidetes and Firmicutes divisions. To examine how the intestinal environment affects microbial genome evolution, we have sequenced the genomes of two members of the normal distal human gut microbiota, Bacteroides vulgatus and Bacteroides distasonis, and by comparison with the few other sequenced gut and non-gut Bacteroidetes, analyzed their niche and habitat adaptations. The results show that lateral gene transfer, mobile elements, and gene amplification have played important roles in affecting the ability of gut-dwelling Bacteroidetes to vary their cell surface, sense their environment, and harvest nutrient resources present in the distal intestine. Our findings show that these processes have been a driving force in the adaptation of Bacteroidetes to the distal gut environment, and emphasize the importance of considering the evolution of humans from an additional perspective, namely the evolution of our microbiomes

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

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

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

The identification of QTL controlling ergot sclerotia size in hexaploid wheat implicates a role for the Rht dwarfing alleles

The fungal pathogen Claviceps purpurea infects ovaries of a broad range of temperate grasses and cereals, including hexaploid wheat, causing a disease commonly known as ergot. Sclerotia produced in place of seed carry a cocktail of harmful alkaloid compounds that result in a range of symptoms in humans and animals, causing ergotism. Following a field assessment of C. purpurea infection in winter wheat, two varieties ‘Robigus’ and ‘Solstice’ were selected which consistently produced the largest differential effect on ergot sclerotia weights. They were crossed to produce a doubled haploid mapping population, and a marker map, consisting of 714 genetic loci and a total length of 2895 cM was produced. Four ergot reducing QTL were identified using both sclerotia weight and size as phenotypic parameters; QCp.niab.2A and QCp.niab.4B being detected in the wheat variety ‘Robigus’, and QCp.niab.6A and QCp.niab.4D in the variety ‘Solstice’. The ergot resistance QTL QCp.niab.4B and QCp.niab.4D peaks mapped to the same markers as the known reduced height (Rht) loci on chromosomes 4B and 4D, Rht-B1 and Rht-D1, respectively. In both cases, the reduction in sclerotia weight and size was associated with the semi-dwarfing alleles, Rht-B1b from ‘Robigus’ and Rht-D1b from ‘Solstice’. Two-dimensional, two-QTL scans identified significant additive interactions between QTL QCp.niab.4B and QCp.niab.4D, and between QCp.niab.2A and QCp.niab.4B when looking at sclerotia size, but not between QCp.niab.2A and QCp.niab.4D. The two plant height QTL, QPh.niab.4B and QPh.niab.4D, which mapped to the same locations as QCp.niab.4B and QCp.niab.4D, also displayed significant genetic interactions