Chern class formulas for quiver varieties

In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on arbitrary composites of the maps. Our answer is a polynomial in Chern classes of the bundles involved, depending on the given rank conditions. It can be expressed as a linear combination of products of Schur polynomials in the differences of the bundles. The coefficients are interesting generalizations of Littlewood-Richardson numbers. These polynomials specialize to give new formulas for Schubert polynomials.Comment: 17 pages, 20 figures. The document is available as a .tar.gz file containing one LaTeX2e file and 20 (included) postscript files. Packages xypic and psfrag are used. Note that when viewed with xdvi, the text in figures looks bad, but it comes out right when printed. The paper is also available as one postscript file at http://www.math.uchicago.edu/~abuch/papers/quiver.ps.g

Seeing double with K2: Testing re-inflation with two remarkably similar planets around red giant branch stars

Despite more than 20 years since the discovery of the first gas giant planet with an anomalously large radius, the mechanism for planet inflation remains unknown. Here, we report the discovery of EPIC228754001.01, an inflated gas giant planet found with the NASA K2 Mission, and a revised mass for another inflated planet, K2-97b. These planets reside on ~9 day orbits around host stars which recently evolved into red giants. We constrain the irradiation history of these planets using models constrained by asteroseismology and Keck/HIRES spectroscopy and radial velocity measurements. We measure planet radii of 1.31 +\- 0.11 Rjup and and 1.30 +\- 0.07 Rjup, respectively. These radii are typical for planets receiving the current irradiation, but not the former, zero age main sequence irradiation of these planets. This suggests that the current sizes of these planets are directly correlated to their current irradiation. Our precise constraints of the masses and radii of the stars and planets in these systems allow us to constrain the planetary heating efficiency of both systems as 0.03% +0.03%/-0.02%. These results are consistent with a planet re-inflation scenario, but suggest the efficiency of planet re-inflation may be lower than previously theorized. Finally, we discuss the agreement within 10% of stellar masses and radii, and planet masses, radii, and orbital periods of both systems and speculate that this may be due to selection bias in searching for planets around evolved stars.Comment: 18 pages, 15 figures, accepted to AJ. Figures 11, 12, and 13 are the key figures of the pape

Asymmetric function theory

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.Comment: 36 pages, 8 figures, 1 table. Written for the proceedings of the Schubert calculus conference in Guangzhou, Nov. 201

Failure to detect mutations in U2AF1 due to changes in the GRCh38 reference sequence

The U2AF1 gene is a core part of mRNA splicing machinery and frequently contains somatic mutations that contribute to oncogenesis in myelodysplastic syndrome, acute myeloid leukemia, and other cancers. A change introduced in the GRCh38 version of the human reference build prevents detection of mutations in this gene, and others, by variant calling pipelines. This study describes the problem in detail and shows that a modified GRCh38 reference build with unchanged coordinates can be used to ameliorate the issue

Clonal architecture of secondary acute myeloid leukemia defined by single-cell sequencing

Next-generation sequencing has been used to infer the clonality of heterogeneous tumor samples. These analyses yield specific predictions-the population frequency of individual clones, their genetic composition, and their evolutionary relationships-which we set out to test by sequencing individual cells from three subjects diagnosed with secondary acute myeloid leukemia, each of whom had been previously characterized by whole genome sequencing of unfractionated tumor samples. Single-cell mutation profiling strongly supported the clonal architecture implied by the analysis of bulk material. In addition, it resolved the clonal assignment of single nucleotide variants that had been initially ambiguous and identified areas of previously unappreciated complexity. Accordingly, we find that many of the key assumptions underlying the analysis of tumor clonality by deep sequencing of unfractionated material are valid. Furthermore, we illustrate a single-cell sequencing strategy for interrogating the clonal relationships among known variants that is cost-effective, scalable, and adaptable to the analysis of both hematopoietic and solid tumors, or any heterogeneous population of cells

Momentum Distribution in the Decay B-->J/psi+X

We combine the NRQCD formalism for the inclusive color singlet and octet production of charmonium states with the parton and the ACCMM model, respectively, and calculate the momentum distribution in the decay B-->J/psi+X. Neglecting the kinematics of soft gluon radiation, we find that the motion of the b quark in the bound state can account, to a large extent, for the observed spectrum. The parton model gives a satisfactory presentation of the data, provided that the heavy quark momentum distribution is taken to be soft. To be explicit, we obtain epsilon_p=O(0.008-0.012) for the parameter of the Peterson et al. distribution function. The ACCMM model can account for the data more accurately. The preferred Fermi momentum p_F=O(0.57 GeV) is in good agreement with recent studies of the heavy quark's kinetic energy.Comment: revised version to be published in Phys. Rev. D; 27 pages, LaTeX, 7 eps figures, uses a4wide.sty, epsfig.sty and amssymb.st

A risk prediction model for the assessment and triage of women with hypertensive disorders of pregnancy in low-resourced settings: the miniPIERS (Pre-eclampsia Integrated Estimate of RiSk) multi-country prospective cohort study.

BACKGROUND: Pre-eclampsia/eclampsia are leading causes of maternal mortality and morbidity, particularly in low- and middle- income countries (LMICs). We developed the miniPIERS risk prediction model to provide a simple, evidence-based tool to identify pregnant women in LMICs at increased risk of death or major hypertensive-related complications. METHODS AND FINDINGS: From 1 July 2008 to 31 March 2012, in five LMICs, data were collected prospectively on 2,081 women with any hypertensive disorder of pregnancy admitted to a participating centre. Candidate predictors collected within 24 hours of admission were entered into a step-wise backward elimination logistic regression model to predict a composite adverse maternal outcome within 48 hours of admission. Model internal validation was accomplished by bootstrapping and external validation was completed using data from 1,300 women in the Pre-eclampsia Integrated Estimate of RiSk (fullPIERS) dataset. Predictive performance was assessed for calibration, discrimination, and stratification capacity. The final miniPIERS model included: parity (nulliparous versus multiparous); gestational age on admission; headache/visual disturbances; chest pain/dyspnoea; vaginal bleeding with abdominal pain; systolic blood pressure; and dipstick proteinuria. The miniPIERS model was well-calibrated and had an area under the receiver operating characteristic curve (AUC ROC) of 0.768 (95% CI 0.735-0.801) with an average optimism of 0.037. External validation AUC ROC was 0.713 (95% CI 0.658-0.768). A predicted probability ≥25% to define a positive test classified women with 85.5% accuracy. Limitations of this study include the composite outcome and the broad inclusion criteria of any hypertensive disorder of pregnancy. This broad approach was used to optimize model generalizability. CONCLUSIONS: The miniPIERS model shows reasonable ability to identify women at increased risk of adverse maternal outcomes associated with the hypertensive disorders of pregnancy. It could be used in LMICs to identify women who would benefit most from interventions such as magnesium sulphate, antihypertensives, or transportation to a higher level of care

High Resolution Models of Transcription Factor-DNA Affinities Improve In Vitro and In Vivo Binding Predictions

Accurately modeling the DNA sequence preferences of transcription factors (TFs), and using these models to predict in vivo genomic binding sites for TFs, are key pieces in deciphering the regulatory code. These efforts have been frustrated by the limited availability and accuracy of TF binding site motifs, usually represented as position-specific scoring matrices (PSSMs), which may match large numbers of sites and produce an unreliable list of target genes. Recently, protein binding microarray (PBM) experiments have emerged as a new source of high resolution data on in vitro TF binding specificities. PBM data has been analyzed either by estimating PSSMs or via rank statistics on probe intensities, so that individual sequence patterns are assigned enrichment scores (E-scores). This representation is informative but unwieldy because every TF is assigned a list of thousands of scored sequence patterns. Meanwhile, high-resolution in vivo TF occupancy data from ChIP-seq experiments is also increasingly available. We have developed a flexible discriminative framework for learning TF binding preferences from high resolution in vitro and in vivo data. We first trained support vector regression (SVR) models on PBM data to learn the mapping from probe sequences to binding intensities. We used a novel -mer based string kernel called the di-mismatch kernel to represent probe sequence similarities. The SVR models are more compact than E-scores, more expressive than PSSMs, and can be readily used to scan genomics regions to predict in vivo occupancy. Using a large data set of yeast and mouse TFs, we found that our SVR models can better predict probe intensity than the E-score method or PBM-derived PSSMs. Moreover, by using SVRs to score yeast, mouse, and human genomic regions, we were better able to predict genomic occupancy as measured by ChIP-chip and ChIP-seq experiments. Finally, we found that by training kernel-based models directly on ChIP-seq data, we greatly improved in vivo occupancy prediction, and by comparing a TF's in vitro and in vivo models, we could identify cofactors and disambiguate direct and indirect binding