Topological Quantum Error Correction with Optimal Encoding Rate

We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of arbitrary genus. We find a class of regular toric codes that are optimal. For physical implementations, we present planar topological codes.Comment: REVTEX4 file, 5 figure

A hierarchical Bayesian model to infer PL(Z) relations using Gaia parallaxes

Aims. We aim at creating a Bayesian model to infer the coefficients of PL or PLZ relations that propagates uncertainties in the observables in a rigorous and well founded way. Methods. We propose a directed acyclic graph to encode the conditional probabilities of the inference model that will allow us to infer probability distributions for the PL and PL(Z) relations. We evaluate the model with several semi-synthetic data sets and apply it to a sample of 200 fundamental mode and first overtone mode RR Lyrae stars for which Gaia DR1 parallaxes and literature Ks-band mean magnitudes are available. We define and test several hyperprior probabilities to verify their adequacy and check the sensitivity of the solution with respect to the prior choice. Results. The main conclusion of this work is the absolute necessity of incorporating the existing correlations between the observed variables (periods, metallicities and parallaxes) in the form of model priors in order to avoid systematically biased results, especially in the case of non-negligible uncertainties in the parallaxes. The tests with the semi-synthetic data based on the data set used in Gaia Collaboration et al. (2017) reveal the significant impact that the existing correlations between parallax, metallicity and periods have on the inferred parameters. The relation coefficients obtained here have been superseded by those presented in Muraveva et al. (2018a), that incorporates the findings of this work and the more recent Gaia DR2 measurements.Comment: 14 pages, 12 figures. Submitted to A&

Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates

We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-net condensate. Excitations appear in the form of quasiparticles and fluxes, as the boundaries of strings and membranes, respectively. The degeneracy of the ground state depends upon the homology of the 3-manifold. We generalize the system to $D\geq 4$, were different topological phases may occur. The whole construction is based on certain special complexes that we call colexes.Comment: Revtex4 file, color figures, minor correction

Controller time and delay costs - a trade-off analysis

Air traffic controller shortages remain a significant challenge in European ATM. Comparing different rules, we quantify the cost effectiveness of adding controller hours to Area Control Centre regulations to avert the delay cost impact on airlines. Typically, adding controller hours results in a net benefit. Distributions of delay duration and aircraft weight play an important role in determining the total cost of a regulation. Errors are likely to be incurred when analysing performance based on average delay values, particularly at the disaggregate level

Synthetic spectra of H Balmer and HeI absorption lines. I: Stellar library

We present a grid of synthetic profiles of stellar H Balmer and HeI lines at optical wavelengths with a sampling of 0.3 A. The grid spans a range of effective temperature 4000 K < Teff < 50000 K, and gravity 0.0 < log g < 5.0 at solar metallicity. For Teff > 25000 K, NLTE stellar atmosphere models are computed using the code TLUSTY (Hubeny 1988). For cooler stars, Kurucz (1993) LTE models are used to compute thesynthetic spectra. The grid includes the profiles of the high-order hydrogen Balmer series and HeI lines for effective temperatures and gravities that have not been previously synthesized. The behavior of H8 to H13 and HeI 3819 with effective temperature and gravity is very similar to that of the lower terms of the series (e.g. Hb) and the other HeI lines at longer wavelengths; therefore, they are suited for the determination of the atmospheric parameters of stars. These lines are potentially important to make predictions for these stellar absorption features in galaxies with active star formation. Evolutionary synthesis models of these lines for starburst and post-starburst galaxies are presented in a companion paper. The full set of the synthetic stellar spectra is available for retrieval at our website http://www.iaa.es/ae/e2.html and http://www.stsci.edu/science/starburst/ or on request from the authors at [email protected]: To be published in ApJS. 28 pages and 12 figure

An atlas of Calcium triplet spectra of active galaxies

We present a spectroscopic atlas of active galactic nuclei covering the region around the 8498, 8542, 8662 Calcium triplet (CaT) lines. The sample comprises 78 objects, divided into 43 Seyfert 2s, 26 Seyfert 1s, 3 Starburst and 6 normal galaxies. The spectra pertain to the inner ~300 pc in radius, and thus sample the central kinematics and stellar populations of active galaxies. The data are used to measure stellar velocity dispersions (sigma_star) both with cross-correlation and direct fitting methods. These measurements are found to be in good agreement with each-other and with those in previous studies for objects in common. The CaT equivalent width is also measured. We find average values and sample dispersions of W_CaT of 4.6+/-2.0, 7.0 and 7.7+/-1.0 angstrons for Seyfert 1s, Seyfert 2s and normal galaxies, respectively. We further present an atlas of [SIII]\lambda 9069 emission line profiles for a subset of 40 galaxies. These data are analyzed in a companion paper which addresses the connection between stellar and Narrow Line Region kinematics, the behaviour of the CaT equivalent width as a function of sigma_star, activity type and stellar population properties.Comment: 18 pages, 10 figures, accepted for publication in MNRA

The Nature of LINERs

We present $J$-band ($1.15-1.35 \mu$m) spectroscopy of a sample of nine galaxies showing some degree of LINER activity (classical LINERs, weak-[O {\sc i}] LINERs and transition objects), together with $H$-band spectroscopy for some of them. A careful subtraction of the stellar continuum allows us to obtain reliable [Fe {\sc ii}]$1.2567 \mu$m/Pa$\beta$ line ratios. We conclude that different types of LINERs (i.e., photoionized by a stellar continuum or by an AGN) cannot be easily distinguished based solely on the [Fe {\sc ii}]$1.2567 \mu$m/Pa$\beta$ line ratio. The emission line properties of many LINERs can be explained in terms of an aging starburst. The optical line ratios of these LINERs are reproduced by a model with a metal-rich H {\sc ii} region component photoionized with a single stellar temperature $T_* = 38,000$K, plus a supernova remnant (SNR) component. The [Fe {\sc ii}] line is predominantly excited by shocks produced by SNRs in starbursts and starburst-dominated LINERs, while Pa$\beta$ tracks H {\sc ii} regions ionized by massive young stars. The contribution from SNRs to the overall emission line spectrum is constrained by the [Fe {\sc ii}]$1.2567 \mu$m/Pa$\beta$ line ratio. Although our models for aging starbursts are constrained only by these infrared lines, they consistently explain the optical spectra of the galaxies also. The LINER-starburst connection is tested by predicting the time dependence of the ratio of the ionizing luminosity ($L_{\rm ion}$) to the supernova rate (SNr), $L_{\rm ion}$/(SNr). We predict the relative number of starbursts to starburst-dominated LINERs (aging starbursts) and show that it is in approximate agreement with survey findings for nearby galaxies.Comment: Accepted in ApJ (19 pages, 8 figures, uses emulateapj.sty

Building a Holistic ATM Model for Future KPI Trade-Offs

We present the model developed within the Vista project, studying the future evolution of trade-offs between Key Performance Indicators. The model has a very broad scope and aims to simulate the changes that business and regulatory forces have at a strategic, pre-tactical and tactical level. The relevant factors that will affect the air transportation system are presented, as well as the scenarios to be simulated. The overall architecture of the model is described and a more detailed presentation of the economic component of the model is given. Some preliminary results of this part of the model illustrate its main mechanisms and capabilities