Quantum degrees of polarization

We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results. Still, we argue that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since, despite being rooted in the Stokes operators, each of these measures only captures certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness.Comment: 9 pages, 3 figures. v2: Minor corrections and improvement

Multicomplementary operators via finite Fourier transform

A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d-1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.Comment: 15 pages, no figure

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

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

The Role of Glypicans in Wnt Inhibitory Factor-1 Activity and the Structural Basis of Wif1's Effects on Wnt and Hedgehog Signaling

Proper assignment of cellular fates relies on correct interpretation of Wnt and Hedgehog (Hh) signals. Members of the Wnt Inhibitory Factor-1 (WIF1) family are secreted modulators of these extracellular signaling pathways. Vertebrate WIF1 binds Wnts and inhibits their signaling, but its Drosophila melanogaster ortholog Shifted (Shf) binds Hh and extends the range of Hh activity in the developing D. melanogaster wing. Shf activity is thought to depend on reinforcing interactions between Hh and glypican HSPGs. Using zebrafish embryos and the heterologous system provided by D. melanogaster wing, we report on the contribution of glypican HSPGs to the Wnt-inhibiting activity of zebrafish Wif1 and on the protein domains responsible for the differences in Wif1 and Shf specificity. We show that Wif1 strengthens interactions between Wnt and glypicans, modulating the biphasic action of glypicans towards Wnt inhibition; conversely, glypicans and the glypican-binding “EGF-like” domains of Wif1 are required for Wif1's full Wnt-inhibiting activity. Chimeric constructs between Wif1 and Shf were used to investigate their specificities for Wnt and Hh signaling. Full Wnt inhibition required the “WIF” domain of Wif1, and the HSPG-binding EGF-like domains of either Wif1 or Shf. Full promotion of Hh signaling requires both the EGF-like domains of Shf and the WIF domains of either Wif1 or Shf. That the Wif1 WIF domain can increase the Hh promoting activity of Shf's EGF domains suggests it is capable of interacting with Hh. In fact, full-length Wif1 affected distribution and signaling of Hh in D. melanogaster, albeit weakly, suggesting a possible role for Wif1 as a modulator of vertebrate Hh signaling

Measurements of the W production cross sections in association with jets with the ATLAS detector

This paper presents cross sections for the production of a W boson in association with jets, measured in proton–proton collisions at √s=7 TeV with the ATLAS experiment at the large hadron collider. With an integrated luminosity of 4.6 fb−1, this data set allows for an exploration of a large kinematic range, including jet production up to a transverse momentum of 1 TeV and multiplicities up to seven associated jets. The production cross sections for W bosons are measured in both the electron and muon decay channels. Differential cross sections for many observables are also presented including measurements of the jet observables such as the rapidities and the transverse momenta as well as measurements of event observables such as the scalar sums of the transverse momenta of the jets. The measurements are compared to numerous QCD predictions including next-to-leading-order perturbative calculations, resummation calculations and Monte Carlo generators