The Zeta Function of a Hypergraph

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For $(d,r)$-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Sol\'e. Finally, we give an example to show how the generalized zeta function can be applied to graphs to distinguish non-isomorphic graphs with the same Ihara-Selberg zeta function.Comment: 24 pages, 6 figure

How Can Mathematics Students Learn to Play?

When we teach mathematics, we strive to teach students to think like mathematicians. In this paper we discuss one particular mathematical habit of mind that students do not naturally display. More specifically our study of voting patterns in data collected from classroom voting questions indicates that the undergraduate students who were in the classes using these questions did not understand the significance of counterexamples to statements, or lacked the ability to construct them, or both. Searching for counterexamples to disprove statements is a natural habit of mind for professional mathematicians. In this paper we give examples, and make some recommendations. We believe that if our students get used to routinely seeking out counterexamples, as they play with various mathematical ideas, they may also end up enjoying their mathematical experiences more

Promoting Active Studying: The Study Challenge

We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom

Non-equivalence of Wnt and R-spondin ligands during Lgr5+ intestinal stem-cell self-renewal

The canonical Wnt/β-catenin signaling pathway governs diverse developmental, homeostatic and pathologic processes. Palmitoylated Wnt ligands engage cell surface Frizzled (Fzd) receptors and Lrp5/6 co-receptors enabling β-catenin nuclear translocation and Tcf/Lef-dependent gene transactivation1–3. Mutations in Wnt downstream signaling components have revealed diverse functions presumptively attributed to Wnt ligands themselves, although direct attribution remains elusive, as complicated by redundancy between 19 mammalian Wnts and 10 Fzds1 and Wnt hydrophobicity2,3. For example, individual Wnt ligand mutations have not revealed homeostatic phenotypes in the intestinal epithelium4, an archetypal canonical Wnt pathway-dependent rapidly self-renewing tissue whose regeneration is fueled by proliferative crypt Lgr5+ intestinal stem cells (ISCs)5–9. R-spondin ligands (Rspo1–4) engage distinct Lgr4-6 and Rnf43/Znrf3 receptor classes10–13, markedly potentiate canonical Wnt/β-catenin signaling and induce intestinal organoid growth in vitro and Lgr5+ ISCs in vivo8,14–17. However, the interchangeability, functional cooperation and relative contributions of Wnt versus Rspo ligands to in vivo canonical Wnt signaling and ISC biology remain unknown. Here, we deconstructed functional roles of Wnt versus Rspo ligands in the intestinal crypt stem cell niche. We demonstrate that the default fate of Lgr5+ ISCs is lineage commitment, escape from which requires both Rspo and Wnt ligands. However, gain-of-function studies using Rspo versus a novel non-lipidated Wnt analog reveal qualitatively distinct, non-interchangeable roles for these ligands in ISCs. Wnts are insufficient to induce Lgr5+ ISC self-renewal, but rather confer a basal competency by maintaining Rspo receptor expression that enables Rspo to actively drive and specify the extent of stem cell expansion. This functionally non-equivalent yet cooperative interplay between Wnt and Rspo ligands establishes a molecular precedent for regulation of mammalian stem cells by distinct priming and self-renewal factors, with broad implications for precision control of tissue regeneration

Lancet

BACKGROUND: In 2015, the second cycle of the CONCORD programme established global surveillance of cancer survival as a metric of the effectiveness of health systems and to inform global policy on cancer control. CONCORD-3 updates the worldwide surveillance of cancer survival to 2014. METHODS: CONCORD-3 includes individual records for 37.5 million patients diagnosed with cancer during the 15-year period 2000-14. Data were provided by 322 population-based cancer registries in 71 countries and territories, 47 of which provided data with 100% population coverage. The study includes 18 cancers or groups of cancers: oesophagus, stomach, colon, rectum, liver, pancreas, lung, breast (women), cervix, ovary, prostate, and melanoma of the skin in adults, and brain tumours, leukaemias, and lymphomas in both adults and children. Standardised quality control procedures were applied; errors were rectified by the registry concerned. We estimated 5-year net survival. Estimates were age-standardised with the International Cancer Survival Standard weights. FINDINGS: For most cancers, 5-year net survival remains among the highest in the world in the USA and Canada, in Australia and New Zealand, and in Finland, Iceland, Norway, and Sweden. For many cancers, Denmark is closing the survival gap with the other Nordic countries. Survival trends are generally increasing, even for some of the more lethal cancers: in some countries, survival has increased by up to 5% for cancers of the liver, pancreas, and lung. For women diagnosed during 2010-14, 5-year survival for breast cancer is now 89.5% in Australia and 90.2% in the USA, but international differences remain very wide, with levels as low as 66.1% in India. For gastrointestinal cancers, the highest levels of 5-year survival are seen in southeast Asia: in South Korea for cancers of the stomach (68.9%), colon (71.8%), and rectum (71.1%); in Japan for oesophageal cancer (36.0%); and in Taiwan for liver cancer (27.9%). By contrast, in the same world region, survival is generally lower than elsewhere for melanoma of the skin (59.9% in South Korea, 52.1% in Taiwan, and 49.6% in China), and for both lymphoid malignancies (52.5%, 50.5%, and 38.3%) and myeloid malignancies (45.9%, 33.4%, and 24.8%). For children diagnosed during 2010-14, 5-year survival for acute lymphoblastic leukaemia ranged from 49.8% in Ecuador to 95.2% in Finland. 5-year survival from brain tumours in children is higher than for adults but the global range is very wide (from 28.9% in Brazil to nearly 80% in Sweden and Denmark). INTERPRETATION: The CONCORD programme enables timely comparisons of the overall effectiveness of health systems in providing care for 18 cancers that collectively represent 75% of all cancers diagnosed worldwide every year. It contributes to the evidence base for global policy on cancer control. Since 2017, the Organisation for Economic Co-operation and Development has used findings from the CONCORD programme as the official benchmark of cancer survival, among their indicators of the quality of health care in 48 countries worldwide. Governments must recognise population-based cancer registries as key policy tools that can be used to evaluate both the impact of cancer prevention strategies and the effectiveness of health systems for all patients diagnosed with cancer. FUNDING: American Cancer Society; Centers for Disease Control and Prevention; Swiss Re; Swiss Cancer Research foundation; Swiss Cancer League; Institut National du Cancer; La Ligue Contre le Cancer; Rossy Family Foundation; US National Cancer Institute; and the Susan G Komen Foundation

Taxonomy of the family Arenaviridae and the order Bunyavirales : update 2018

In 2018, the family Arenaviridae was expanded by inclusion of 1 new genus and 5 novel species. At the same time, the recently established order Bunyavirales was expanded by 3 species. This article presents the updated taxonomy of the family Arenaviridae and the order Bunyavirales as now accepted by the International Committee on Taxonomy of Viruses (ICTV) and summarizes additional taxonomic proposals that may affect the order in the near future.Peer reviewe

Genetic fine mapping and genomic annotation defines causal mechanisms at type 2 diabetes susceptibility loci.

We performed fine mapping of 39 established type 2 diabetes (T2D) loci in 27,206 cases and 57,574 controls of European ancestry. We identified 49 distinct association signals at these loci, including five mapping in or near KCNQ1. 'Credible sets' of the variants most likely to drive each distinct signal mapped predominantly to noncoding sequence, implying that association with T2D is mediated through gene regulation. Credible set variants were enriched for overlap with FOXA2 chromatin immunoprecipitation binding sites in human islet and liver cells, including at MTNR1B, where fine mapping implicated rs10830963 as driving T2D association. We confirmed that the T2D risk allele for this SNP increases FOXA2-bound enhancer activity in islet- and liver-derived cells. We observed allele-specific differences in NEUROD1 binding in islet-derived cells, consistent with evidence that the T2D risk allele increases islet MTNR1B expression. Our study demonstrates how integration of genetic and genomic information can define molecular mechanisms through which variants underlying association signals exert their effects on disease

Nurses' perceptions of aids and obstacles to the provision of optimal end of life care in ICU

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