Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and hazard rate e
stimator is proposed for randomly right censored data. Careful selection of the bandwidth in the proposed estimators yields estimates that are more efficient in terms of overall mean squared error performance, and in some cases achieves a nearly parametric convergence rate. Additionally, rapidly converging bandwidth estimates are presented for use in second-order kernels to supplement such kernel-based methods in hazard rate estimation. Simulations illustrate the improved accuracy of the proposed estimator against other nonparametric estimators of the density and hazard function. A real data application is also presented on survival data from 13,166 breast carcinoma patients.
It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector
field. Any spacetime admitting a covariantly constant null vector field ($CCNV$) belongs to the Kundt class of metrics, and more importantly admits a null Killing vector field. We investigate the existence of additional non-spacelike isometries in the class of higher-dimensional $CCNV$ Kundt metrics in order to produce potential solutions that preserve some supersymmetries.
A binary 1-error-correcting code can always be embedded in a 1-perfect code of some larger length
In February 1700, Isaac Newton needed a precise tropical year to design a new universal calendar that would supersede the Gregorian one. However, 17th-Century astronomers were uncertain of the long-term variation in the inclination of the Earths axis
and were suspicious of Ptolemys equinox observations. As a result, they produced a wide range of tropical years. Facing this problem, Newton attempted to compute the length of the year on his own, using the ancient equinox observations reported by a famous Greek astronomer Hipparchus of Rhodes, ten in number. Though Newton had a very thin sample of data, he obtained a tropical year only a few seconds longer than the correct length. The reason lies in Newtons application of a technique similar to modern regression analysis. Newton wrote down the first of the two so-called normal equations known from the ordinary least-squares (OLS) method. In that procedure, Newton seems to have been the first to employ the mean (average) value of the data set, while the other leading astronomers of the era (Tycho Brahe, Galileo, and Kepler) used the median. Fifty years after Newton, in 1750, Newtons method was rediscovered and enhanced by Tobias Mayer. Remarkably, the same regression method served with distinction in the late 1920s when the founding fathers of modern cosmology, Georges Lemaitre (1927), Edwin Hubble (1929), and Willem de Sitter (1930), employed it to derive the Hubble constant.
(abridged) Magnetic reconnection is the topological reconfiguration of the magnetic field in a plasma, accompanied by the violent release of energy and particle acceleration. Reconnection is as ubiquitous as plasmas themselves, with solar flares perh
aps the most popular example. Over the last few years, the theoretical understanding of magnetic reconnection in large-scale fluid systems has undergone a major paradigm shift. The steady-state model of reconnection described by the famous Sweet-Parker (SP) theory, which dominated the field for ~50 years, has been replaced with an essentially time-dependent, bursty picture of the reconnection layer, dominated by the continuous formation and ejection of multiple secondary islands (plasmoids). Whereas in the SP model reconnection was predicted to be slow, a major implication of this new paradigm is that reconnection in fluid systems is fast (i.e., independent of the Lundquist number), provided that the system is large enough. This conceptual shift hinges on the realization that SP-like current layers are violently unstable to the plasmoid instability - implying, therefore, that such current sheets are super-critically unstable and thus can never form in the first place. This suggests that the formation of a current sheet and the subsequent reconnection process cannot be decoupled, as is commonly assumed. This paper provides an introductory-level overview of the recent developments in reconnection theory and simulations that led to this essentially new framework. We briefly discuss the role played by the plasmoid instability in selected applications, and describe some of the outstanding challenges that remain at the frontier of this subject. Amongst these are the analytical and numerical extension of the plasmoid instability to (i) 3D and (ii) non-MHD regimes. New results are reported in both cases.
The MAJORANA Collaboration is constructing the MAJORANA DEMONSTRATOR, an ultra-low background, modular, HPGe detector array with a mass of 44-kg (29 kg 76Ge and 15 kg natGe) to search for neutrinoless double beta decay in Ge-76. The next generation o
f tonne-scale Ge-based neutrinoless double beta decay searches will probe the neutrino mass scale in the inverted-hierarchy region. The MAJORANA DEMONSTRATOR is envisioned to demonstrate a path forward to achieve a background rate at or below 1 count/tonne/year in the 4 keV region of interest around the Q-value of 2039 keV. The MAJORANA DEMONSTRATOR follows a modular implementation to be easily scalable to the next generation experiment. First, the prototype module was assembled; it has been continuously taking data from July 2014 to June 2015. Second, Module 1 with more than half of the total enriched detectors and some natural detectors has been assembled and it is being commissioned. Finally, the assembly of Module 2, which will complete MAJORANA DEMONSTRATOR, is already in progress.
We consider the case of light dark matter ($sim 10$ GeV). We discuss a simple $Z_2$ model of scalar self-interacting dark matter, as well as a related model of unstable long-lived dark matter which can explain the anomalous Kolar events observed decades ago.
Gamma-ray bursts (GRBs) are detectable out to very large distances and as such are potentially powerful cosmological probes. Historically, the angular distribution of GRBs provided important information about their origin and physical properties. As
a general population, GRBs are distributed isotropically across the sky. However, there are published reports that once binned by duration or redshift, GRBs display significant clustering. We have studied the redshift- and duration-dependent clustering of GRBs using proximity measures and kernel density estimation. Utilizing bursts detected by BATSE, Fermi/GBM and Swift/BAT, we found marginal evidence for clustering in very short duration GRBs lasting less than 100 ms. Our analysis provides little evidence for significant redshift-dependent clustering of GRBs.
We present a measurement of the azimuthal asymmetries of two charged pions in the inclusive process $e^+e^-rightarrow pipi X$ based on a data set of 62 $rm{pb}^{-1}$ at the center-of-mass energy $sqrt{s}=3.65$ GeV collected with the BESIII detector.
These asymmetries can be attributed to the Collins fragmentation function. We observe a nonzero asymmetry, which increases with increasing pion momentum. As our energy scale is close to that of the existing semi-inclusive deep inelastic scattering experimental data, the measured asymmetries are important inputs for the global analysis of extracting the quark transversity distribution inside the nucleon and are valuable to explore the energy evolution of the spin-dependent fragmentation function.
Based on a sample of etapr mesons produced in the radiative decay $J/psitogammaeta^{prime}$ in $1.31times 10^9$ $J/psi$ events collected with the BESIII detector, the decay $eta^{prime}toomega e^{+} e^{-}$ is observed for the first time, with a stati
stical significance of $8sigma$. The branching fraction is measured to be $mathcal{B}(eta^{prime}toomega e^{+} e^{-})=(1.97pm0.34(text{stat})pm0.17(text{syst}))times10^{-4}$, which is in agreement with theoretical predictions. The branching fraction of $eta^{prime}toomegagamma$ is also measured to be $(2.55pm0.03(text{stat})pm0.16(text{syst}))times10^{-2}$, which is the most precise measurement to date, and the relative branching fraction $frac{mathcal{B}(eta^{prime}to omega e^{+}e^{-})}{mathcal{B}(eta^{prime}to omega gamma)}$ is determined to be $(7.71pm1.34(text{stat})pm0.54(text{syst}))times10^{-3}$.
