We prove that various subgroups of the mapping class group $Mod(Sigma)$ of a surface $Sigma$ are at least exponentially distorted. Examples include the Torelli group (answering a question of Hamenstadt), the point-pushing and surface braid subgroups,
and the Lagrangian subgroup. Our techniques include a method to compute lower bounds on distortion via representation theory and an extension of Johnson theory to arbitrary subgroups of $H_1(Sigma;mathbb{Z})$.
We calculate the abelianizations of the level $L$ subgroup of the genus $g$ mapping class group and the level $L$ congruence subgroup of the $2g times 2g$ symplectic group for $L$ odd and $g geq 3$.
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gros
s-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
Some recent extensions to the GALPROP cosmic-ray propagation package are described. The enhancements include: an accurate solution option, improved convection formulation, alternative spatial boundary conditions, polarized synchrotron emission, new m
agnetic field models, updated gamma-ray production cross-sections, free-free radio emission and absorption, primary positrons, additional injection spectral breaks, deuterium production by pp fusion, hadronic energy losses, improved HEALPix skymap format, compatibility with latest HEALPix release, and various bug fixes. The Explanatory Supplement has been extensively updated, including details of these enhancements. A compatible plot package GALPLOT for GALPROP output is also provided, as well as other related software.
Precise gamma-ray emissivities from cosmic-ray interactions with interstellar gas have been recently derived using Fermi-LAT data, and used to constrain the local interstellar spectra of protons and leptons. We report on a continuing effort to exploi
t these emissivities combined with the latest hadronic gamma-ray production cross-sections and other constraints such as synchrotron emission for the leptonic component. The interstellar spectra provide important information for heliospheric modulation, and cosmic-ray origin and propagation.
We investigate the potential for the Deep Underground Neutrino Experiment (DUNE) to probe the existence and effects of a fourth neutrino mass-eigenstate. We study the mixing of the fourth mass-eigenstate with the three active neutrinos of the Standar
d Model, including the effects of new sources of CP-invariance violation, for a wide range of new mass-squared differences, from lower than 10^-5 eV^2 to higher than 1 eV^2. DUNE is sensitive to previously unexplored regions of the mixing angle - mass-squared difference parameter space. If there is a fourth neutrino, in some regions of the parameter space, DUNE is able to measure the new oscillation parameters (some very precisely) and clearly identify two independent sources of CP-invariance violation. Finally, we use the hypothesis that there are four neutrino mass-eigenstates in order to ascertain how well DUNE can test the limits of the three-massive-neutrinos paradigm. In this way, we briefly explore whether light sterile neutrinos can serve as proxies for other, in principle unknown, phenomena that might manifest themselves in long-baseline neutrino oscillation experiments.
The currently operating space missions, as well as those that will be launched in the near future, (will) deliver high-quality data for millions of stellar objects. Since the majority of stellar astrophysical applications still (at least partly) rely
on spectroscopic data, an efficient tool for the analysis of medium- to high-resolution spectroscopy is needed. We aim at developing an efficient software package for the analysis of medium- to high-resolution spectroscopy of single stars and those in binary systems. The major requirements are that the code has a high performance, represents the state-of-the-art analysis tool, and provides accurate determinations of atmospheric parameters and chemical compositions for different types of stars. We use the method of atmosphere models and spectrum synthesis, which is one of the most commonly used approaches for the analysis of stellar spectra. Our Grid Search in Stellar Parameters (GSSP) code makes use of the OpenMPI implementation, which makes it possible to run in parallel mode. The method is first tested on the simulated data and is then applied to the spectra of real stellar objects. The majority of test runs on the simulated data were successful in the sense that we could recover the initially assumed sets of atmospheric parameters. We experimentally find the limits in signal-to-noise ratios of the input spectra, below which the final set of parameters gets significantly affected by the noise. Application of the GSSP package to the spectra of three Kepler stars, KIC11285625, KIC6352430, and KIC4931738, was also largely successful. We found an overall agreement of the final sets of the fundamental parameters with the original studies. For KIC6352430, we found that dependence of the light dilution factor on wavelength cannot be ignored, as it has significant impact on the determination of the atmospheric parameters of this binary system.
This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlations of CMB data, using the hybrid approach employed previously: pixel-based at $ell<30$ and a Gaussian approximation to the distribution of spectra at h
igher $ell$. The main improvements are the use of more and better processed data and of Planck polarization data, and more detailed foreground and instrumental models, allowing further checks and enhanced immunity to systematics. Progress in foreground modelling enables a larger sky fraction. Improvements in processing and instrumental models further reduce uncertainties. For temperature, we perform an analysis of end-to-end instrumental simulations fed into the data processing pipeline; this does not reveal biases from residual instrumental systematics. The $Lambda$CDM cosmological model continues to offer a very good fit to Planck data. The slope of primordial scalar fluctuations, $n_s$, is confirmed smaller than unity at more than 5{sigma} from Planck alone. We further validate robustness against specific extensions to the baseline cosmology. E.g., the effective number of neutrino species remains compatible with the canonical value of 3.046. This first detailed analysis of Planck polarization concentrates on E modes. At low $ell$ we use temperature at all frequencies and a subset of polarization. The frequency range improves CMB-foreground separation. Within the baseline model this requires a reionization optical depth $tau=0.078pm0.019$, significantly lower than without high-frequency data for explicit dust monitoring. At high $ell$ we detect residual errors in E, typically O($mu$K$^2$); we recommend temperature alone as the high-$ell$ baseline. Nevertheless, Planck high-$ell$ polarization allows a separate determination of $Lambda$CDM parameters consistent with those from temperature alone.
Evolutionary structure searches predict three new phases of iodine polyhydrides stable under pressure. Insulating P1-H5I, consisting of zigzag chains of HI (delta+)and H2(delta-) molecules, is stable between 30-90 GPa. Cmcm-H2I and P6/mmm-H4I are fou
nd on the 100, 150 and 200 GPa convex hulls. These two phases are good metals, even at 1 atm, because they consist of monoatomic lattices of iodine. At 100 GPa the Tc of H2I and H4I are estimated to be 7.8 and 17.5 K, respectively. The increase in Tc relative to elemental iodine results from a larger omega-log from the light mass of hydrogen, and an enhanced lambda from modes containing H/I and H/H vibrations.
We use variable-pressure neutron and X-ray diffraction measurements to determine the uniaxial and bulk compressibilities of nickel(II) cyanide, Ni(CN)$_2$. Whereas other layered molecular framework materials are known to exhibit negative area compres
sibility, we find that Ni(CN)$_2$ does not. We attribute this difference to the existence of low-energy in-plane tilt modes that provide a pressure-activated mechanism for layer contraction. The experimental bulk modulus we measure is about four times lower than that reported elsewhere on the basis of density functional theory methods [{it Phys. Rev. B} {bf 83}, 024301 (2011)].
