The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Generalized McKay quivers of rank three

For each finite subgroup G of SL(n, C), we introduce the generalized Cartan matrix C_{G} in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi-definiteness as in the classical case of affine Cartan matrices (the case of SL(2,C)). The complete McKay quivers for SL(3,C) are explicitly described and classified based on representation theory

Longer telomere length in peripheral white blood cells is associated with risk of lung cancer and the rs2736100 (CLPTM1L-TERT) polymorphism in a prospective cohort study among women in China.

A recent genome-wide association study of lung cancer among never-smoking females in Asia demonstrated that the rs2736100 polymorphism in the TERT-CLPTM1L locus on chromosome 5p15.33 was strongly and significantly associated with risk of adenocarcinoma of the lung. The telomerase gene TERT is a reverse transcriptase that is critical for telomere replication and stabilization by controlling telomere length. We previously found that longer telomere length measured in peripheral white blood cell DNA was associated with increased risk of lung cancer in a prospective cohort study of smoking males in Finland. To follow up on this finding, we carried out a nested case-control study of 215 female lung cancer cases and 215 female controls, 94% of whom were never-smokers, in the prospective Shanghai Women's Health Study cohort. There was a dose-response relationship between tertiles of telomere length and risk of lung cancer (odds ratio (OR), 95% confidence interval [CI]: 1.0, 1.4 [0.8-2.5], and 2.2 [1.2-4.0], respectively; P trend = 0.003). Further, the association was unchanged by the length of time from blood collection to case diagnosis. In addition, the rs2736100 G allele, which we previously have shown to be associated with risk of lung cancer in this cohort, was significantly associated with longer telomere length in these same study subjects (P trend = 0.030). Our findings suggest that individuals with longer telomere length in peripheral white blood cells may have an increased risk of lung cancer, but require replication in additional prospective cohorts and populations

Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions

We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.Comment: 67 pages, 6 figure

Modelling the Influence of Foot-and-Mouth Disease Vaccine Antigen Stability and Dose on the Bovine Immune Response

Foot and mouth disease virus causes a livestock disease of significant global socio-economic importance. Advances in its control and eradication depend critically on improvements in vaccine efficacy, which can be best achieved by better understanding the complex within-host immunodynamic response to inoculation. We present a detailed and empirically parametrised dynamical mathematical model of the hypothesised immune response in cattle, and explore its behaviour with reference to a variety of experimental observations relating to foot and mouth immunology. The model system is able to qualitatively account for the observed responses during in-vivo experiments, and we use it to gain insight into the incompletely understood effect of single and repeat inoculations of differing dosage using vaccine formulations of different structural stability

A Halo-Based Galaxy Group Finder: Calibration and Application to the 2dFGRS

We use the halo occupation model to calibrate galaxy group finders in magnitude-limited redshift surveys. Since, according to the current scenario of structure formation, galaxy groups are associated with cold dark matter halos, we make use of the properties of the halo population in the design of our group finder. The method starts with an assumed mass-to-light ratio to assign a tentative mass to each group. This mass is used to estimate the size and velocity dispersion of the underlying halo that hosts the group, which in turn is used to determine group membership (in redshift space). This procedure is repeated until no further changes occur in group memberships. We find that the final groups selected this way are insensitive to the mass-to-light ratio assumed. We use mock catalogues, constructed using the conditional luminosity function (CLF), to test the performance of our group finder in terms of completeness of true members and contamination by interlopers. Our group finder is more successful than the conventional Friends-of-Friends group finder in assigning galaxies in common dark matter halos to a single group. We apply our group finder to the 2-degree Field Galaxy Redshift Survey and compare the resulting group properties with model predictions based on the CLF. For the $\Lambda$CDM `concordance' cosmology we find a clear discrepancy between the model and data in the sense that the model predicts too many rich groups. In order to match the observational results we have to either increase the mass-to-light ratios of rich clusters to a level significantly higher than current observational estimates, or to assume $\sigma_8 \simeq 0.7$, compared to the `concordance' value of 0.9.Comment: 18 pages, 13 figures. Accepted for publication in MNRA

Breakthrough SARS-CoV-2 infections among patients with cancer following two and three doses of COVID-19 mRNA vaccines: a retrospective observational study from the COVID-19 and Cancer Consortium

BACKGROUND: Breakthrough SARS-CoV-2 infections following vaccination against COVID-19 are of international concern. Patients with cancer have been observed to have worse outcomes associated with COVID-19 during the pandemic. We sought to evaluate the clinical characteristics and outcomes of patients with cancer who developed breakthrough SARS-CoV-2 infections after 2 or 3 doses of mRNA vaccines. METHODS: We evaluated the clinical characteristics of patients with cancer who developed breakthrough infections using data from the multi-institutional COVID-19 and Cancer Consortium (CCC19; NCT04354701). Analysis was restricted to patients with laboratory-confirmed SARS-CoV-2 diagnosed in 2021 or 2022, to allow for a contemporary unvaccinated control population; potential differences were evaluated using a multivariable logistic regression model after inverse probability of treatment weighting to adjust for potential baseline confounding variables. Adjusted odds ratios (aOR) and 95% confidence intervals (CI) are reported. The primary endpoint was 30-day mortality, with key secondary endpoints of hospitalization and ICU and/or mechanical ventilation (ICU/MV). FINDINGS: The analysis included 2486 patients, of which 564 and 385 had received 2 or 3 doses of an mRNA vaccine prior to infection, respectively. Hematologic malignancies and recent receipt of systemic anti-neoplastic therapy were more frequent among vaccinated patients. Vaccination was associated with improved outcomes: in the primary analysis, 2 doses (aOR: 0.62, 95% CI: 0.44-0.88) and 3 doses (aOR: 0.20, 95% CI: 0.11-0.36) were associated with decreased 30-day mortality. There were similar findings for the key secondary endpoints of ICU/MV (aOR: 0.60, 95% CI: 0.45-0.82 and 0.37, 95% CI: 0.24-0.58) and hospitalization (aOR: 0.60, 95% CI: 0.48-0.75 and 0.35, 95% CI: 0.26-0.46) for 2 and 3 doses, respectively. Importantly, Black patients had higher rates of hospitalization (aOR: 1.47, 95% CI: 1.12-1.92), and Hispanic patients presented with higher rates of ICU/MV (aOR: 1.61, 95% CI: 1.06-2.44). INTERPRETATION: Vaccination against COVID-19, especially with additional doses, is a fundamental strategy in the prevention of adverse outcomes including death, among patients with cancer. FUNDING: This study was partly supported by grants from the National Cancer Institute grant number P30 CA068485 to C-YH, YS, SM, JLW; T32-CA236621 and P30-CA046592 to C.R.F; CTSA 2UL1TR001425-05A1 to TMW-D; ACS/FHI Real-World Data Impact Award, P50 MD017341-01, R21 CA242044-01A1, Susan G. Komen Leadership Grant Hunt to MKA. REDCap is developed and supported by Vanderbilt Institute for Clinical and Translational Research grant support (UL1 TR000445 from NCATS/NIH)

Naked1 Antagonizes Wnt Signaling by Preventing Nuclear Accumulation of β-Catenin

Cyto-nuclear shuttling of β-catenin is at the epicenter of the canonical Wnt pathway and mutations in genes that result in excessive nuclear accumulation of β-catenin are the driving force behind the initiation of many cancers. Recently, Naked Cuticle homolog 1 (Nkd1) has been identified as a Wnt-induced intracellular negative regulator of canonical Wnt signaling. The current model suggests that Nkd1 acts between Disheveled (Dvl) and β-catenin. Here, we employ the zebrafish embryo to characterize the cellular and biochemical role of Nkd1 in vivo. We demonstrate that Nkd1 binds to β-catenin and prevents its nuclear accumulation. We also show that this interaction is conserved in mammalian cultured cells. Further, we demonstrate that Nkd1 function is dependent on its interaction with the cell membrane. Given the conserved nature of Nkd1, our results shed light on the negative feedback regulation of Wnt signaling through the Nkd1-mediated negative control of nuclear accumulation of β-catenin