Fair redistricting is hard

Gerrymandering is a long-standing issue within the U.S. political system, and it has received scrutiny recently by the U.S. Supreme Court. In this note, we prove that deciding whether there exists a fair redistricting among legal maps is NP-hard. To make this precise, we use simplified notions of "legal" and "fair" that account for desirable traits such as geographic compactness of districts and sufficient representation of voters. The proof of our result is inspired by the work of Mahanjan, Minbhorkar and Varadarajan that proves that planar k-means is NP-hard

Thermoelastic-damping noise from sapphire mirrors in a fundamental-noise-limited interferometer

We report the first high-precision interferometer using large sapphire mirrors, and we present the first direct, broadband measurements of the fundamental thermal noise in these mirrors. Our results agree well with the thermoelastic-damping noise predictions of Braginsky, et al. [Phys. Lett. A 264, 1(1999)] and Cerdonio, et al.[Phys. Rev. D 63, 082003 (2001)], which have been used to predict the astrophysical reach of advanced interferometric gravitational wave detectors.Comment: 4 pages, 2 figure

Revisiting the location and environment of the central engine in NGC1068

We revisit in this paper the location of the various components observed in the AGN of NGC1068. Discrepancies between previously published studies are explained, and a new measurement for the absolute location of the K-band emission peak is provided. It is found to be consistent with the position of the central engine as derived by Gallimore (1997), Capetti (1997) and Kishimoto (1999). A series of map overlays is then presented and discussed. Model predictions of dusty tori show that the nuclear unresolved NIR-MIR emission is compatible with a broad range of models: the nuclear SED alone does not strongly constrain the torus geometry, while placing reasonable constraints on its size and thickness. The extended MIR emission observed within the ionizing cone is shown to be well explained by the presence of optically thick dust clouds exposed to the central engine radiation and having a small covering factor. Conversely, a distribution of diffuse dust particles within the ionizing cone is discarded. A simple model for the H2 and CO emission observed perpendicularly to the axis of the ionizing cone is proposed. We show that a slight tilt between the molecular disc and the Compton thick central absorber naturally reproduces the observed distribution of H2 of CO emission.Comment: 17 pages, 11 figures, revised version for A&

Revision of the types of species of Alloxysta described by Cameron and Fergusson (Hymenoptera: Figitidae: Charipinae) and deposited in the Natural History Museum (London), including a key to the fauna of Great Britain

Type material of the species of Alloxysta described by Cameron and Fergusson and deposited in the Natural History Museum of London has been revised. Seven species are considered valid: Alloxysta abdera Fergusson, 1986, A. basimacula (Cameron, 1886), A. crassa (Cameron, 1889), A. mullensis (Cameron, 1883), A. piceomaculata (Cameron, 1883), A. pleuralis (Cameron, 1879) and A. semiaperta Fergusson, 1986. A. basimacula, A. crassa, A. maculicollis (Cameron, 1886), A. perplexa (Cameron, 1889) and A. piceomaculata are here removed from synonymy with A. macrophadna (Hartig, 1841). A. rufi ceps (Cameron, 1883) is removed from synonymy with A. victrix (Westwood, 1833). A. caledonica (Cameron, 1886) and A. perplexa are here synonymized with A. basimacula. A. maculicollis, A. ruficeps and A. ruficollis (Cameron, 1883) are here synonymized with A. castanea (Hartig, 1841). A. ancylocera (Cameron, 1886) was correctly synonymized with A. fuscicornis (Hartig, 1841), A. curvicornis (Cameron, 1883) was correctly synonymized with A. victrix and A. filicornis (Cameron, 1889) was correctly synonymized with A. macrophadna. Complete redescriptions and illustrations are given for valid species. A key for all the Alloxysta species found so far in Great Britain is given

Generation of Kerr non-Gaussian motional states of trapped ions

Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally existent in this kind of system. We present detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits the generation of complex non-Gaussian states with negative Wigner functions. Especially, superpositions of many coherent states are achieved at a fraction of the time necessary to produce the cat state.Comment: 6 pages, 5 figure