Two-sided stability and convergence of multistage and multistep methods for ordinary differential equations

AbstractA norm is introduced which allows the extension of bistability and biconvergence results of Stummel (“Topics in Numerical Analysis, II,” Academic Press, New York, 1975; “Approximation Methods in Analysis,” Aarhus Universiteit, 1973) (which apply to one-step methods) to the case of multistage and multistep methods

Finding the ℓ-core of a tree

AbstractAn ℓ-core of a tree T=(V,E) with |V|=n, is a path P with length at most ℓ that is central with respect to the property of minimizing the sum of the distances from the vertices in P to all the vertices of T not in P. The distance between two vertices is the length of the shortest path joining them. In this paper we present efficient algorithms for finding the ℓ-core of a tree. For unweighted trees we present an O(nℓ) time algorithm, while for weighted trees we give a procedure with time complexity of O(nlog2n). The algorithms use two different types of recursive principle in their operation

On the Origin of X-ray Emission From Millisecond Pulsars in 47 Tuc

The observed spectra and X-ray luminosities of millisecond pulsars in 47 Tuc can be interpreted in the context of theoretical models based on strong, small scale multipole fields on the neutron star surface. For multipole fields that are relatively strong as compared to the large scale dipole field, the emitted X-rays are thermal and likely result from polar cap heating associated with the return current from the polar gap. On the other hand, for weak multipole fields, the emission is nonthermal and results from synchrotron radiation of $e^{\pm}$ pairs created by curvature radiation. The X-ray luminosity, $L_x$, is related to the spin down power, $L_{sd}$, expressed in the form $L_x \propto L^{\beta}_{sd}$ with $\beta \sim 0.5$ and $\sim 1$ for strong and weak multipole fields respectively. If the polar cap size is of the order of the length scale of the multipole field, $s$ and $\beta \sim 0.5$, the polar cap temperature is $\sim 3 \times 10^6 K (\frac{L_{sd}}{10^{34}erg s^{-1}})^{1/8} (\frac{s}{3\times 10^4 cm})^{-1/2}$. A comparison of the X-ray properties of millisecond pulsars in globular clusters and in the Galactic field suggests that the emergence of relatively strong small scale multipole fields from the neutron star interior may be correlated with the age and evolutionary history of the underlying neutron star.Comment: 25 pages, 2 figures, accepted for publication in Ap

Chandra Phase-Resolved Spectroscopy of the Crab Pulsar

We present the first phase-resolved study of the X-ray spectral properties of the Crab Pulsar that covers all pulse phases. The superb angular resolution of the Chandra X-ray Observatory enables distinguishing the pulsar from the surrounding nebulosity, even at pulse minimum. Analysis of the pulse-averaged spectrum measures interstellar X-ray extinction due primarily to photoelectric absorption and secondarily to scattering by dust grains in the direction of the Crab Nebula. We confirm previous findings that the line-of-sight to the Crab is underabundant in oxygen, although more-so than recently measured. Using the abundances and cross sections from Wilms, Allen & McCray (2000) we find [O/H] = (3.33 +/-0.25) x 10**-4. Analysis of the spectrum as a function of pulse phase measures the low-energy X-ray spectral index even at pulse minimum -- albeit with large statistical uncertainty -- and we find marginal evidence for variations of the spectral index. The data are also used to set a new (3-sigma) upper limit to the temperature of the neutron star of log T(infinity) < 6.30.Comment: 20 Pages including 7 figures. Accepted for publication in the Astrophysical Journa

Pulsar Wind Nebulae and the X-Ray Emission of Non-Accreting Neutron Stars

The general properties of the non-thermal non-pulsed X-ray emission of rotation powered pulsars are investigated in the context of a pulsar wind nebula model. An examination of the observed X-ray emission from a sample of 23 pulsars from ASCA in the energy range between 2-10 keV reveals that the relation of X-ray luminosity, $L_x$, to the pulsar spin down power, $\dot{E}$, is steeper for the non-pulsed component than for the pulsed component. Specifically, $L_{x}^{npul} \propto \dot{E}^{1.4 \pm 0.1}$ for the non-pulsed component, whereas $L_{x}^{pul} \propto \dot{E}^{1.2 \pm 0.08}$ for the pulsed component. The former relation is consistent with emission from a pulsar wind nebula model in which $L_{x}^{npul} \propto \dot{E}^{p/2}$ where $p$ is the power law index of the electron energy distribution. The relation for the pulsed component, on the other hand, is consistent with a magnetospheric emission model.Comment: 27 pages, 5 figure

Search for CP Violation in the Decay Z -> b (b bar) g

About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between the two quarks and the gluon in three-jet events and by measuring the differential two-jet rate. No signal of CP violation is found. For the combinations of anomalous CP violating couplings, ${\hat{h}}_b = {\hat{h}}_{Ab}g_{Vb}-{\hat{h}}_{Vb}g_{Ab}$ and $h^{\ast}_b = \sqrt{\hat{h}_{Vb}^{2}+\hat{h}_{Ab}^{2}}$, limits of \hat{h}_b < 0.59$and$h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

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